The Concept 'Horse' Paradox and Wittgensteinian Conceptual Investigations

THE CONCEPT “HORSE” PARADOX AND WITTGENSTEINIAN CONCEPTUAL INVESTIGATIONS

In Foundations of Arithmetic, Gottlob Frege contended that the difference between concepts and objects was absolute. He meant that no object could be a concept and no concept an object. Benno Kerry disagreed; he contended that a concept could be an object, and that therefore the difference between concepts and objects was only relative. In this book, Jolley aims to understand the debate between Frege and Kerry. But Jolley’s purpose is not to champion either side; rather, it is to utilize an understanding of the debate to shed light on the work of Ludwig Wittgenstein-and vice versa. Jolley not only sifts through the debate between Frege and Kerry, but also through subsequent versions of the debate in J. J. Valberg and Wilfrid Sellars. Jolley’s goal is to show that the central notion of Philosophical Investigations, that of a “conceptual investigation”, is a legacy of the Frege/Kerry debate and also a contribution to it. Jolley concludes that the difference between concepts and objects is as absolute in its way in Philosophical Investigations as it was in The Foundations of Arithmetic and that recognizing the absoluteness of the difference in Philosophical Investigations provides a beginning for a ‘resolute’ reading of Wittgenstein’s book.

In this fascinating and demanding study, Kelly Jolley uses the history of Frege’s notorious concept “horse” paradox to illuminate Wittgenstein’s conception of philosophy as a form of therapy. Jolley’s careful study of responses to the paradox sheds light on the nature of philosophical perplexity and the power and form of the Wittgensteinian response to such perplexity. Jolley also builds a persuasive case for the continuity both of Frege’s influence on Wittgenstein and of Wittgenstein’s concern with a therapeutic response to philosophical problems. This is a book which should command the attention not only of scholars of Frege and Wittgenstein, but also of anyone interested in the nature of conceptual analysis and investigation. Michael Kremer, University of Chicago USA

ASHGATE WITTGENSTEINIAN STUDIES Series editor: Mario von der Ruhr, University of Wales, Swansea, UK Ludwig Wittgenstein was one of the greatest philosophers of the twentieth century, his work leading to a variety of differing readings which in turn have had a diverse influence on contemporary philosophy. As well as exploring the more familiar Wittgensteinian themes in the philosophy of language, this series will be a centre of excellence for Wittgensteinian studies in mathematics, aesthetics, religion and philosophy of the mind. Wittgenstein’s philosophy has proved extremely fruitful in many contexts and this series will publish not only a variety of readings of Wittgenstein’s work, but also work on philosophers and philosophical topics inspired by Wittgensteinian perspectives.

The Concept “Horse” Paradox and Wittgensteinian Conceptual Investigations A Prolegomenon to Philosophical Investigations

KELLY DEAN JOLLEY Auburn University, USA

© Kelly Dean Jolley 2007 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise without the prior permission of the publisher. Kelly Dean Jolley has asserted his moral right under the Copyright, Designs and Patents Act, 1988, to be identified as the author of this work. Published by Ashgate Publishing Limited Gower House Croft Road Aldershot Hampshire GU11 3HR England

Ashgate Publishing Company Suite 420 101 Cherry Street Burlington, VT 05401-4405 USA

Ashgate website: http://www.ashgate.com British Library Cataloguing in Publication Data Jolley, Kelly Dean Concept “horse” paradox and Wittgensteinian conceptual investigations : a prolegomenon to philosophical investigations. - (Ashgate Wittgensteinian studies) 1. Wittgenstein, Ludwig, 1889-1951. Philosophical investigations 2. Frege, Gottlob, 1848-1925 3. Language and languages - Philosophy I. Title 192 Library of Congress Cataloging-in-Publication Data Jolley, Kelly Dean. The concept “horse” paradox and Wittgensteinian conceptual investigations : a prolegomenon to philosophical investigations / Kelly Dean Jolley. p. cm. -- (Ashgate Wittgensteinian studies) ISBN 978-0-7546-6045-3 (hardcover) 1. Wittgenstein, Ludwig, 1889-1951. Philosophische Untersuchungen. 2. Philosophy. 3. Semantics (Philosophy) 4. Object (Philosophy) 5. Kerry, Benno. 6. Frege, Gottlob, 1848-1925. Grundlagen der Arithmetik. I. Title. B3376.W563P53253 2007 192--dc22 2006034417 ISBN-13: 978 0 7546 6045 3

Printed and bound in Great Britain by TJ International Ltd, Padstow, Cornwall.

For my son and daughter, Eli and Sydney

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Contents

Acknowledgements

ix

Preface

xi

1 Bearings

1

2 Frege at Therapy

9

3 Logic’s Caretaker

23

4 Beating a Dead Concept “Horse”

49

5 Conceptual vs. Objectual Investigations

79

Bibliography

107

Index

111

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Acknowledgements I am deeply indebted to the work of Rush Rhees and Stanley Cavell. Theirs are the engrafted words I use to measure my understanding of Wittgenstein. I have learnt much generally from James Conant, from his writings and from conversations, and from the writings of Cora Diamond and of Michael Kremer. I owe more specific debts to Avrum Stroll, Ram Neta, Avner Baz, Rupert Read, Leonard Linsky, David Finkelstein, Alice Crary, Jay Elliot and Zed Adams. Much of the material in the book was presented to the University of Chicago Wittgenstein Seminar. I thank James Conant for inviting me, and I thank the attendees for their attention and comments. Chapter Two was written in part during a 1998 NEH Summer Seminar (at UCSD, directed by Stroll) on Wittgenstein and Moore. I am fortunate to work in Auburn’s philosophy department. Doing philosophy at Auburn often offers what J.L. Austin noted that doing philosophy too rarely offers— “the fun of discovery, the pleasures of cooperation, and the satisfaction of reaching agreement.” I thank my colleagues Michael Watkins, Eric Marcus, James Shelley, Roderick Long, Bill Davis and Jody Graham. All helped me. I am especially grateful to Michael and to Eric, who kindly and patiently endured many conversations about Frege and Wittgenstein, and who were ready always with helpful suggestions and comments. Of course, despite my quoting Austin, I do not mean to say that any of my colleagues agrees with what I say here. I mean only to describe our environment; I mean only to say that we do sometimes and on some things satisfyingly reach agreement. Another debt I owe is to the gifted students I have taught over the last several years. Teaching them and talking with them played a large role in my work. I thank especially Matthew Pugsley and Zachary Loveless, as well as Seth Hammock, David Dyas and Charles Johnson. I thank Micah Cobb and Stephen Shortt for their help in preparing the manuscript and the bibliography. I dedicate this book to my son and daughter, Eli and Sydney, even though they rightly dislike its title. And for them, these words (from Louis Zukofsky): Reject no one and Debase nothing. This is all-around Intellect.

The publishers have obtained permission from the copyright holders to reproduce all copyright material.

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Preface I never purposed to write a book on the Concept “Horse” Paradox. I wrote toward an understanding of the Paradox. Benno Kerry’s strangely resonant thrust, “The concept ‘horse’ is a concept easily attained”, and Gottlob Frege’s even more strangely resonant parry, “The concept ‘horse’ is not a concept”, kept fencing in my philosophical imagination. The two sentences never tired, but I did. Not until I reflected on Frege’s Context Principle (“Never to ask for the meaning of a word except in the context of a proposition”), did I began to see how to surmount the sentences, how to free myself from their fencing. Surmounting the sentences demanded thinking of the Paradox as dissoluble, as properly treated therapeutically. And even more, surmounting the sentences clarified what Wittgenstein meant by “therapy” in Philosophical Investigations. At that point, the Paradox and Philosophical Investigations locked together for me in an enlightening embrace: The Paradox lightened darkling dimensions of Philosophical Investigations and Philosophical Investigations did so for the Paradox. The Paradox typifies what Philosophical Investigations takes to be a philosophical problem. Philosophical Investigations demonstrates a method of philosophizing canny, crafty enough for the Paradox. Thinking of the Paradox and Philosophical Investigations together helped me see how the Tractatus works, and how its work is like and unlike the work of Philosophical Investigations. The Paradox reveals Philosophical Investigations as a variation upon and not a contradiction of the Tractatus. Philosophical Investigations is not a retractation of the Tractatus. The two books in fact are related in many of the ways that Johannes Climacus’ Philosophical Fragments is related to his Concluding Unscientific Postscript. Wittgenstein was from early until late thinking about the problems of philosophical logic. But he reconceived the problems, and philosophical logic itself, and with those changes came a change in his methods. To see the two books as warring with one another is confused, unless the war is a philosophical Civil War, the combatants brothers, the blood shed (if any) consanguine. Whatever fight there may be between the books, the fight is a family feud. –Perhaps the best example of two things that bear a family resemblance to one another (in the sense of Philosophical Investigations 67) is Wittgenstein’s books. Getting the full light of the Paradox on Philosophical Investigations forced me to think about contemporary responses to the Paradox, particularly the two deepest responses—J.J. Valberg’s and Wilfrid Sellars’s. Their responses fail instructively. Understanding their failures put me in a position to turn to Philosophical Investigations and to tell a story about that book that reveals it as the peculiar work of philosophy that it is.

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The chapters that follow often look like history of philosophy. But they are not history of philosophy, at least not straightforwardly. I am not trying to recapture Frege’s self-understanding of the Paradox, just as such, anywhere, even though I do talk that way. I also talk as if what I am after is Wittgenstein’s understanding of what Frege was doing, and of Wittgenstein’s self-understanding of his own doings in relation to Frege’s. But even that is not quite right: I am not claiming that Wittgenstein continually studied the Paradox or that he was thinking of it explicitly at every moment as he wrote Philosophical Investigations, etc. I talk as if I were claiming such things, but that is convenient shorthand. It keeps me from annoyingly personifying both the Paradox and Philosophical Investigations (as I do above), or from the longueurs of phrases like “If we understand the Paradox rightly, then we can best read Philosophical Investigations as …” What I am really after is the “objective tendency of the problematic” of Philosophical Investigations (another phrase I would rather avoid); and the Paradox limns the tendencies of the problematic. But it is simpler and more graceful to write as if what I am after is Frege’s intentions, his understanding of the Paradox in relation to Foundations of Arithmetic, or is Wittgenstein’s intentions, his understanding of the Paradox in relation to Philosophical Investigations. In sum, I am not offering this as scholarship, at least not straightforwardly. Parts of the book could be treated as scholarship, I suppose; more parts than I would like. But I believe that philosophy is not scholarship and, with Michael Oakeshott, I believe philosophy too often founders in scholarship. Anyone looking here for a comprehensive treatment of the literature of The Concept “Horse” Paradox or of the literature of Philosophical Investigations will be disappointed. I have learned from those literatures and I have sewn the pieces from which I have learned most into the fabric of the book. K.D.J. Auburn, Alabama 2006

“For is the kingdom of God become words or syllables? Why should we be in bondage to them if we may be free?” Holy Bible, Authorized Version: The Translators to the Reader

“My feeling is … that we have forgotten how mysterious these things are, and in general how different different things are from one another, as though we had forgotten how to value them.” The World Viewed, Stanley Cavell

“We are creatures of logic and not of silence.” “The Power of Words”, Brice Parain

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Chapter One

Bearings Before there can be any mention of understanding anything which he has communicated, one must first of all understand him from the point of view of his particular dialectic of communication, and understand everything from that point of view. For that particular dialectic of communication cannot be communicated in the traditional dialectical form. Soren Kierkegaard

A Glance Backward: Frege, Kerry and Hinting In a series of articles in the quarterly Vierteljahrsschrift für wissenschaftliche Philosophie, Benno Kerry refers to Gottlob Frege’s Foundations of Arithmetic and to other works of Frege’s. Frege is pleased by the references and shows his appreciation by writing “On Concept and Object,” in which he discusses the points that Kerry contests. Kerry contests Frege’s definition of “concept” and he contests Frege’s absolute distinction of concepts from objects. For Frege, Kerry contests the distinction partly as the result of a misunderstanding —specifically, a misunderstanding of what Frege says about concepts. Frege is unrestingly awake to the difficulties of understanding what he says about concepts. He notes early in his essay that his explanation of concepts “is not meant as a proper definition”. The reason for this is that concepts are logical simples. Frege rates logical simples to be stumbling-stones to (scientific) explaining and expositing. When a term is put into use as a name of a logical simple, the person to be instructed can only be led to understand the term by means of hints. To understand “On Concept and Object” as I think Wittgenstein understood it, we have to take seriously Frege’s hint about hinting. The essay is one long hint. Kerry’s misunderstanding is a misunderstanding of earlier hints about a logical simple, and so correcting the misunderstanding cannot be done simply by means of a definition. A definition that was not possible the first time is not rendered possible by a need for a second try. Misunderstood hints can only be corrected by further hinting. Frege’s talk of hints should be taken quite seriously. Frege knew that his talk of concepts had a peculiar status: it seems to be talk of an object—but an odd-ball sort of object; it seems to be talk that refers to an item—but an item that somehow defies reference. He calls his talk “hints” not because his talk is coy or gnomic. He calls his talk hints because there is a sense in which his talk can be understood and a sense in which it cannot. A hint, as we ordinarily think of one, is somewhat like that. When a person hints, the person hinted to has to “take” the hint in order to understand that at which the hinter is hinting. If the person hinted to fails to “take” the hint, the hinting talk is opaque: it means nothing to the person, it cannot be understood. But if the person hinted to “takes” the hint, then the hinting talk is transparent. It is important

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The Concept “Horse” Paradox and Wittgensteinian Conceptual Investigations

to understanding Frege’s hinting that we remember that the opacities of hinting, as well as its transparencies, come in varieties. The “taking” though is the most crucial feature of Frege’s hinting, since it reveals the specific variety of both the relevant opacity and the relevant transparency. If a person “takes” a hint, the person must be rightly receptive, the person must be appropriately poised. To be rightly receptive or appropriately poised is to be already engaged, even if only in a relatively unskilled way, in a particular task. The engagement in the task—and so in a fairly straightforward way, the task itself— comes to the aid of the hinting talk, and allows the person who “takes” the hint to see the talk as structured, as caught up in a matrix of significances, as opening or highlighting a way of doing or of going on with something. Here’s an example of what I have in mind. The actor, Clint Eastwood, was once asked what was the most important piece of advice any director had given him. He replied that once, during a scene, when his acting limped badly, the director shouted, “Don’t just do something; stand there!” For someone unengaged in the task of acting, whether actually or in imagination, these words are opaque—even paradoxical. Such an unengaged person cannot “take” the hint. And for such a person, finding out that the words worked, that they produced the right kind of change or result, it will seem that the words have done their work in secret or by magic. But for Eastwood, the words were not only meaningful, they were especially meaningful. The hint galvanized him and produced changes in his acting that he took to be momentous. When Frege talks about hinting, he often talks of the success of hinting as producing “a meeting of minds”. Gloss this as “mutual understanding”. This gloss is necessary because it helps to keep clear that Frege is not talking about the sort of meeting of minds enjoyed by two people who, say, know the same arithmetical truth, say, that 2 + 2 = 4. The sort of meeting of minds Frege is talking about is a sort much more difficult to capture, because the minds that meet in it do not meet in shared content. They meet instead in a shared aptitude for cognition of possible contents, or in a shared ability or skill, etc. The shared aptitude or skill need not be possessed by both to the same degree—and typically will not be, since this sort of meeting of minds is most common between teachers and students, masters and apprentices. Hinting is the didactic “discourse” of teaching that produces the meeting of minds. And learning here is not a matter of echoing the hints or of writing them down later on an exam, but of doing and being able to do, or being better able to do, certain kinds of things. I have dwelt on hinting for the following reason: dwelling on hinting makes clear the discordancy of Kerry’s response to Frege’s talk of concepts. Kerry fails to “take” Frege’s hints in Foundations, not only about concepts, but about hinting. Kerry takes Frege to be trying to produce a meeting of minds in content. Specifically, he takes Frege to be trying to produce agreement about his “definition” (Kerry’s revealing term) of concepts. He takes Frege to be advancing a definition and to be giving arguments designed to enforce its advancement. Kerry then responds in what he takes to be the right way: he contests the definition by providing a counterexample to it. That Kerry’s response is discordant should be clear enough. Frege is hinting, not defining. Frege is aiming for a different sort of meeting of minds with his reader, with

Bearings

3

Kerry, than Kerry thinks. Strictly speaking, Kerry’s response to Frege is irrelevant. But Frege does not ignore it as irrelevant, since its type of irrelevance to Frege’s talk about concepts makes it relevant to the problem of hinting. The difficulty for Frege is that he cannot stop hinting. The problem of hinting is a problem that requires hinting for its treatment. Kerry misunderstood the first hints; there is no guarantee he will understand the second, despite Frege’s obvious hope that Kerry will spice future attempts to understand with a pinch of salt and coat them with a dose of goodwill. Renford Bambrough tells a story that illustrates Frege’s fix: An American woman once said to me at the end of a lecture: “Will you please tell me what you have said? I find that I can’t pay any attention to the content when I am listening to that wonderful English accent.” Of course I had to refer her to somebody else, because if I had given her a summary I should inevitably have done it again in the same wonderful English accent.1

Kerry is like the American woman. Frege of course is like Bambrough, but Frege faces an even more difficult problem. No one can talk to Kerry in a way relevant to what Kerry needs without hinting; someone could talk to the American woman in an accent other than Bambrough’s. A Glance Forward My Handling of the Paradox The way I handle the Paradox needs to be explained. I do not attempt to solve the Paradox. In fact, I do not think that it can be solved; I do not think there is a Paradox to be solved. What I am answering is the question: why does it seem that there is a Paradox to be solved? I answer this question in what I think is the only way that it can be answered. I take seriously the claim that there is a Paradox to be solved, and I think some of the proposed solutions through. Specifically, I try to think about the Paradox in the way that I think Benno Kerry or a post-Kerry respondent thinks about it. I explore those ways of thinking from the inside, following them dedicatedly as far as they can coherently be followed. But in each case, the way of thinking becomes incoherent, breaks down. At breakdown, I begin diagnosis. I diagnose the way of thinking, traveling through it backwards from the breakdown back to the initial understanding of the Paradox. There, at the initial understanding of the Paradox, I reappraise the respondent’s understanding of the distinction between concepts and objects, and I propose another understanding of the distinction. My proposed understanding of the distinction avoids eventual breakdown because it is an understanding that keeps the Paradox from arising, and so from needing any solution.2 1 Bambrough, R., “How to Read Wittgenstein”, in Vesey, G. (ed.), Understanding Wittgenstein (Ithaca: Cornell University Press, 1974), p. 119. 2 I am idealizing: each of my discussions has its own ins-and-outs and so has a somewhat different structure.

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The Concept “Horse” Paradox and Wittgensteinian Conceptual Investigations

I stress that my understanding of the distinction is radically different from the understandings I explore; it is in no way homogenous with them. I do not see myself as competing in a contest of understandings with Kerry or the post-Kerry respondents. I have no horse, if I may be pardoned the phrase, in their Concept “Horse” Paradox Sweepstakes. My handling of the Paradox may seem unnecessarily troublesome and cluttered. After all, if I have an understanding of the distinction between concepts and objects that keeps the Paradox from arising, it might seem that I should provide the understanding and then foreclose on the Paradox straightaway. Doing so would avoid all the thinking-through of ways of thinking about the Paradox, and so render what I have to say trouble-free and uncluttered. I do not foreclose on the Paradox straightaway because there is no straight way with the Paradox. I take it that if I am to give a satisfying answer to the question of why it seems that there is a Paradox to be solved, I must first show that I can internalize the seeming—i.e., I must show that I understand the respondent from the inside, that I can enter histrionically into the Paradox. Second, I must cause the respondent genuinely to feel the need for another understanding of the distinction between concepts and objects—i.e., I must convict the respondent that his way of thinking about the Paradox breaks down, and does so on and in his own terms. Third, I must break—in part by accounting for it—the hold that the apparent fact of the Paradox has on the imagination of the respondent—i.e., I must convince him to see options where before he likely saw nothing at all. The short way to summarize all of this is to say that my way of handling the Paradox is a way of handling the respondent’s experience of the Paradox. Until I have justly represented and explored the experience, the experience will eclipse anything I might say straightaway about the Paradox. I handle the Paradox by transposing it from the objective to the subjective— using “objective” and “subjective” in Johannes Climacus’s sense.3 That is, I try to show that the character of concern should fall on the how and not on the what of the Paradox. As Climacus uses the terms, neither is epistemological. Rather, the terms mark out a difference in the character of concern: is it wholly directed upon an object, without even a glance at the subject’s relationship to the object (objective), or is it directed upon the subject’s relationship to the object (subjective)? When the character of concern is subjective, it is practical, bound to a task. In this case, it is bound to the task of thinking thoughts clearly, to the task of achieving clarity. Kerry and the post-Kerry respondents to the Paradox do not see that there is a how with which to be concerned. For them, the Paradox is objective, a Paradox of the what. Thinking this is natural enough, of course. Logic, the place of the Paradox, seems to be a place only of the what, of the objective. To allow that subjectivity enters into logic looks like a way of bargaining the rigor out of logic, of doing away with it. In logic, there is no how, no way. In Chapters Two through Four, I move from the objective to the subjective both inside each chapter and across the chapters. Chapter Four represents the most thorough subjectification of the Paradox. Chapter Five 3 In particular, note that Climacus’ sense of “objective” and “subjective” contrasts with Frege’s sense of the terms.

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shows how to begin to see the contrast between the subjective and objective in the method of Philosophical Investigations. The Structure of the Book Handling the Paradox as I do requires that the structure of my book be unusual. The book does not proceed in a straight line or without breaks. In Chapter Two and in Chapter Four, the most devotedly diagnostic chapters of the book, I am handling the Paradox, and a respondent or respondents, in the way I have sketched. Certain parts of the two chapters are therefore similar. The terminologies change as the respondents change, and so too my terms of criticism— but still each chapter is devoted to thinking through a way or ways of thinking about the Paradox. Each of the chapters also looks ahead, in its way, to Chapter Five, in which I characterize Wittgensteinian conceptual investigations: Chapter Two looks ahead by framing my exploration of Kerry’s response to the Paradox with passages from Philosophical Investigations; Chapter Four looks ahead by weaving into its texture terms and angles of criticism from Philosophical Investigations. Chapter Three is less diagnostic than the two chapters it stands between. But Chapter Three is not an interruption of the work of Chapters Two and Four; it is instead an interlude that allows me to deepen and sharpen many of the general issues that surround the Paradox. In Chapter Three I am interested in the Theory of Types and in its relation to what Hans Reichenbach called “formation rules”. My interest in these topics carries me into an extended investigation of Wittgenstein’s peculiar Tractarian criticism of the Theory (Wittgenstein claims to have made the Theory vanish) and of formation rules. Chapter Five is hardly a diagnostic chapter at all. Instead of diagnosis, I use the understanding of the distinction between concepts and objects won over the previous three chapters to characterize and clarify what Wittgenstein calls “conceptual investigations”. I differentiate conceptual investigations from what I call “objectual investigations”, and I explain how Wittgenstein develops a method of investigating that resolutely refuses to be a method of investigating objects. Much of the difficulty for readers of Philosophical Investigations is a difficulty tied to their failure to differentiate conceptual from objectual investigations. Readers of Philosophical Investigations confuse the investigation of concepts with the investigation of a type of object—as if conceptual investigation were a species of objectual investigation, as if concepts were a species of object. But this is to do to the method of investigation of Philosophical Investigations what Benno Kerry did to Frege’s distinction between concepts and objects: it is to treat the difference as other than absolute. The point of the fifth chapter then is to enforce the absoluteness of the distinction between conceptual and objectual investigations; or, put slightly differently, it is to obey, mutatis mutandis, Frege’s Third Principle (from Foundations of Arithmetic): “Never to lose sight of the distinction between concept and object.” One way of thinking about the entire book—a way of thinking about it that places it in relation to current work on Wittgenstein—is to think of it as a prolegomenon to a resolute reading of Philosophical Investigations (a resolute reading that grows out of a resolute handling of the Concept “Horse” Paradox). The term “resolute reading” has

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The Concept “Horse” Paradox and Wittgensteinian Conceptual Investigations

been important in recent work on the Tractatus and I think it will become important in future work on Philosophical Investigations.4 As is the case with the term when used of the Tractatus, when I use it of Philosophical Investigations I use it to name a family of readings of the book, not a unique reading of the book. A resolute reading of the Tractatus is a reading that (1) refuses to treat the “propositions” of the book as conveying ineffable thoughts, and that (2) rejects the idea that recognizing nonsense requires the application of a theory of sense and nonsense (a theory presented in the Tractatus). As I think of a resolute reading of Philosophical Investigations it is a reading that (1) refuses to treat grammatical remarks as debatable philosophical or empirical theses, and that (2) rejects the idea that rendering latent nonsense patent is a process that requires the application of a use-theory of meaning (a theory presented in Philosophical Investigations). While I do not claim to earn the right to the refusal, (1), or to the rejection, (2), I do claim to have made progress toward earning the right to both. Let me stress this: Chapter Five is the final cause of the earlier chapters. They exist because of it, and look forward to it. I am interested in the Paradox for the sake of Philosophical Investigations. I should add here that the chapters of the book fit together at once more tightly and more loosely than is common for book chapters. What I mean is that my concentration on the Paradox and on ways of responding to it makes the chapters fit very tightly together—they are, in the sense that repeated followings of a trail are repetitive, repetitive. But the followings of the trail happen, as I might put it, at different seasons, so the chapters are not dunningly repetitive. Each chapter however also represents a different stage in my thinking about the Paradox and about ways of responding to it, and so the chapters do not ascend to their conclusion in any smooth, gradient fashion, like a gently inclined, machine-built ramp. They ascend as the steps of a hand-built stairway do. This makes the chapters fit more loosely together than is common. Caveat Finally, before anything else, a warning: I’m writing this book under revocation. What I mean is that I am writing a book that I revoke, and that I intend to convince my reader to revoke. The specific weight of “revocation” I am invoking here is one that I will make clear as I unfold what I have to say. I am aware, I judge it fair to say that I am painfully aware, that this is no way to begin a book. Or maybe I should say that this is no way to begin most books: there are books and books and books, and their details make huge differences. My purpose in writing this book is to liberate myself from a certain paradox, The Concept “Horse” Paradox, and from a certain fixation, the question of Wittgenstein’s method in Philosophical Investigations. My hope in writing this book is to liberate others from certain paradoxes and certain fixations. I mention liberation as my

4 The term “resolute” is most closely associated with the work of James Conant and Cora Diamond.

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7

purpose because only if I am understood to have that purpose will it make much sense for anyone to read beyond these first few paragraphs. “After all,” someone might justifiably say, “if you revoke your book, and, even more, if you want me to revoke it, then it would be best for me not to read it at all. Yes?” Well, no. It would be best for a person not to read it if the person is already free of certain paradoxes or fixations. But I do not think most of us, if any, are already free. I doubt my troubles are solely mine—I am not that special, for better and for worse. I believe that as the structure of The Concept “Horse” Paradox is revealed in the coming chapters, most readers will find themselves implicated in the Paradox, and implicated in a way that ramiculates (to use J.L. Austin’s luxurious neologism) throughout the reader’s philosophical thinking. It is important to realize that writing a book under revocation is not the same as not writing one at all. Johannes Climacus says this in his Concluding Unscientific Postscript. To write under revocation is still to write—but to write from a particular point of view and with a particular purpose in mind. I will make clear the point of view in the next few chapters. I already have mentioned my purpose: liberation. To purpose liberation in philosophy requires, as I understand it, that what is written to that purpose be something the reader is able to unshoulder at the appropriate time. What is written should not permanently burden the reader, diminishing the reader’s liberty. A writer of a book misses what he aims to do, if he aims for the book to show the fly the way out of the fly-bottle, and if the showing yokes the fly uneasily to a textbook on fly-bottles. Such a burden is not light. I am likely, I know, to task my reader’s patience by talking of revocation at the beginning. Revocation is a gesture best performed as the curtain falls, not as it goes up. Even worse than the apparent bad timing, however, is the apparent hubris of revoking: it is well and good for Wittgenstein or Kierkegaard or even Socrates to revoke—they’ve earned the right to it, whether anyone can make anything of their revocations or not. But I have no special claim on anyone’s attention; in fact, I should be earning the right to be attended to at all. But that is what I am doing: the two tasks, revocation and earning the right to attention, do not come apart for me, since I want to be attended to but also want to be attended to rightly. As for hubris—I do not wish to be hubristic, but rather to be forthright, so far as my purpose allows. I am not comparing myself to Wittgenstein or Kierkegaard or Socrates, but appropriating a specific gesture of theirs. I appropriate the gesture because I want to appropriate their specific genre (of philosophical conversation or of writing). That genre I take to be one of retaining conviction under revocation, which means it is one that requires reconceiving conviction, its expression and the sorts of issues about which a person can be so convinced.

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Chapter Two

Frege at Therapy One thing I learned from Wittgenstein, in part from the Tractatus, but still more from personal contact, is that philosophical mistakes are often not refutable falsehoods but confusions; similarly the contrary insight cannot be conveyed in proper propositions with a truth-value. I offer as [an] instance of such insights Frege’s distinction between concept and object … Such insights cannot be demonstrated as theses, but only conveyed dialectically; the dialectic process largely consists in the art … of reducing to patent nonsense the buried nonsense that is found in attempts to reject these insights. We cannot refute nonsense by a straight-forward logical process; as Frege said, logic cannot deal with nonsense, but only characterise it as being nonsense. Peter Geach A simile that has been absorbed into the forms of our language produces a false appearance, and this disquiets us. “But this isn’t how it is!”—we say. “Yet this is how it has to be!” Philosophical Investigations 112

Introduction There is not a philosophical method, though there are indeed methods, like different therapies. Philosophical Investigations 1331

When struggling to understand—or just to cope with—Wittgenstein’s talk of therapy, it is easy to feel abandoned at a spot in his thinking as far from Frege as any. I propose to show that therapy begins in Frege. I first enter into the record two discussions of therapy by Rush Rhees—the two best discussions I know. I will not argue explicitly for these discussions as the best discussions of therapy. I will have to wait for another occasion to do that. However, that what Rhees says so compellingly illuminates what Frege does is itself an implicit argument in favor of Rhees’s discussion. I next examine Frege’s response to Benno Kerry in “Concept and Object”. I then show that the response lines up neatly with Rhees’s discussions. I do this by recasting Frege’s response in the terms provided by Rhees. I then consider the nature of the logical point Frege is making, and why therapy is internal to making the point. I end the chapter with a Coda that examines the Tractarian predecessornotion to therapy, elucidation. My tone will change somewhat in the Coda, since 1 All quotations from the Investigations will be from G.E.M. Anscombe’s translation (New York: The MacMillan Co., 1953); all quotation from Tractatus will be from C.K. Ogden’s translation (Mineola, New York: Dover Publications, 1999). All quotations from Frege’s Foundations of Artithmetic will be from J.L. Austin’s translation (Oxford: Basil Blackwell, 1980).

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The Concept “Horse” Paradox and Wittgensteinian Conceptual Investigations

there my aim will be to show how to fit elucidation into the structure of my earlier discussion. Before I begin, I judge that a word about the way I have constructed the sections of the chapter (preceding the Coda) is in order. Each section after the next begins, like this one, with remarks from Wittgenstein’s later writings. The remarks are not ornaments. In each section the remarks show Wittgenstein’s indebtedness to Frege’s thinking (and sometimes even to Frege’s specific wordings) and show how Wittgenstein both enlarges and limbers Frege’s thinking. Each section is written so that the remarks can show these things, at least upon reflection. Also, the sections build dialectically on one another, deepening and clarifying the structure of Frege’s response to Kerry. Finally, since my ultimate aim in this book is to provide a way of understanding Wittgenstein’s conceptual investigations, the sections and the remarks from Wittgenstein are meant to point forward to the later chapters, especially the last chapter. I intend for the remarks to remain in mind throughout the book, and for the final chapter to address them and Wittgenstein’s method. Finally, before I begin, I note that my examination of Frege’s response to Kerry gets it light from my desire to understand Wittgenstein’s talk of therapy. I do not claim that my examination of the response would harmonize with Frege’s selfunderstanding of the response (although I also do not claim that it would not).2 I want to highlight the lessons Wittgenstein learned from Frege—regardless of whether Frege self-consciously taught those lessons. Rhees on Therapy Here are Rhees’s discussions of therapy: Philosophy as therapy: as though the philosopher’s interest were in the personal disabilities of the perplexed: and as though he were not perplexed himself—as though philosophy were not discussion. Some remarks which Wittgenstein himself made are partly responsible for this. But he was suggesting an analogy with therapy; and he was doing this in order to bring out certain features in the method of philosophy: to show the difference between what you have to do here and what you would do in solving a problem in mathematics or in science. It was not a suggestion about what philosophy is interested in. If Wittgenstein spoke of “treatment’, it is the problem, or the question, that is treated—not the person raising it. It is not the personal malaise of the “patient” which makes the perplexity or question important. What has led me to this perplexity is not my personal stupidity. Rather it is a tendency in language which could lead anyone there, and keeps leading people there. This is why Wittgenstein or anyone doing philosophy can understand the difficulty and the discussion of it. In this respect it is no more personal than the problems of science are. If it were a silly question—then I suppose it would be personal. What makes the questions deep and important is just that they are not this. And for this reason you do learn something from the discussion: it is not as though you were simply being restored 2 In a different discussion, I would argue that Frege’s self-understanding is conflicted: he sometimes understands his response to Kerry (and his handling of related matters) as Wittgenstein does; he sometimes understands it in a way inconsistent with the way Wittgenstein does. This conflict manifests itself throughout Frege’s writings.

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to a normal state of mind. What makes you ask questions in philosophy is not a personal misfortune. And what can “cure” you is philosophy, is discussion, is understanding. If you do not understand, then you will not have benefited in any way. And this shows that the benefit cannot rightly be described as a “cure”. Wittgenstein speaks of “temptations” we feel in reflecting on language, and especially on logic. (Perhaps we keep wondering whether the grammar and the concepts we use allow us to grasp things as they really are, for instance.) But he is not saying something about human nature, or the special weaknesses of those who do philosophy. He sometimes spoke of analogies between philosophy and psychoanalysis, but these are analogies in method. The functional disorders which philosophy treats appear as delusions and dreams of our language ... And what he says about “tackling” philosophical difficulties might suggest, again and again, some analogy with treatment. To root out the difficulty we have to start thinking about these things in a new way; you have to call to mind something you have been doing all along—something which (for special reasons) it is hard to call to mind; you have to bring together practices which you know and take for granted, so that each of them appears in a different light; and this cannot be done all at once: we are concerned with problems whose answer you cannot reach just by thinking, but through practice …3

I will make use of these discussions below. Kerry’s Folly But the diviner would say: “Surely you know what [‘I feel in my hand that the water is three feet under the ground’] means. You know what “three feet under the ground” means, and you know what “I feel” means!” But I should answer him: I know what a word means in certain contexts. Thus I understand the phrase, “three feet under the ground”, say, in the connections “The measurement has shown that the water runs three feet under the ground.” The Blue Book

Kerry, commenting on Frege’s The Foundation of Arithmetic, objects to Frege’s distinction between concept and object. In Kerry’s words, Frege argues for “the view that the properties of being a concept and being an object are mutually exclusive.” Kerry says that such a view is no more plausible than is the claim that the relation of father to son “were one that could not be further reduced, that a man could not be at once a father and a son (though of course not, e.g., father of the man whose son he was).” Kerry reckons that he can rather simply show that Frege is mistaken. Kerry offers the following example: “The concept ‘horse’ is a concept easily attained.” Kerry claims that in this sentence a concept—namely, the concept “horse”—is playing the role of an object (just as a father might play the role of a son). Thus, the sentence shows that Frege’s view is mistaken. The opening paragraphs of Frege’s “Concept and Object” are crucial to understanding Frege’s response to Kerry. Frege accuses Kerry of confusing the psychological use of “concept” with its logical use. Anyone familiar with the introduction to The Foundations of Arithmetic will immediately recognize that Frege 3 Rhees, R. “A Symposium: Assessments of the Man and the Philosopher” in K.T. Fann (ed.), Ludwig Wittgenstein (New York: Delta Publishing, 1967), pp. 77–8.

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is accusing Kerry of failing to keep to one of Frege’s three fundamental principles: always to separate sharply the psychological from the logical, the subjective from the objective.4 Frege’s Foundations’ comment on this principle is that there in compliance with it, he has “used the word ‘idea’ always in a psychological sense, and [has] distinguished ideas from concepts and from objects.” In “Concept and Object”, Frege explains Kerry’s misunderstanding as follows: The word “concept” is used in various ways; its sense is sometimes psychological, sometimes logical, and sometimes perhaps a confused mixture of both. Since this license exists, it is natural to restrict it by requiring that when once a usage is adopted it shall be maintained. What I decided was to keep strictly to a logical use … Agreement about the mode of expression will easily be reached when once it is recognized that there is something that deserves a special term. It seems to me that Kerry’s misunderstanding results from his unintentionally confusing his own usage of the word “concept” with mine. This readily gives rise to contradictions, for which my usage is not to blame.5

Frege sees Kerry as confused about the use of “concept”. Confused, Kerry generates contradictions and then blames the contradictions on Frege’s usage of the word. Because he is confused about the use of “concept”, Kerry is confused by Frege’s distinction between concept and object. Frege claims that the distinction is absolute; Kerry denies it. Here Kerry transgresses against another fundamental principle of Frege’s: never to lose sight of the distinction between concept and object. (Kerry would of course say that he has not lost sight of the distinction but only that he is denying that the distinction is absolute; Frege would respond by saying that to deny that the distinction is absolute is to lose sight of the distinction. The reasons for Frege’s response will become clearer below.) The importance of recognizing that Kerry has failed to keep to these two principles is that it prompts the suspicion that Kerry has also failed to keep to the third of Frege’s principles, the so-called Context Principle: never to ask for the meaning of a word in isolation, but only in the context of a proposition.6 When we reach the heart of Frege’s response to Kerry, this suspicion is confirmed. To see that it is, reconsider Kerry’s counterexample to Frege’s claim that the concept/object distinction is absolute: (K) The concept “horse” is a concept easily attained. (K) is supposed to be a counterexample, since “the concept ‘horse”’ appears in it in the place of an object-expression. Given the way that Kerry misunderstands Frege, Kerry takes (K) to show that the concept-expression “the concept ‘horse”’ is playing the role of an object-expression; hence, Kerry takes (K) to show that the concept/object distinction is not absolute. That Kerry misunderstands Frege is easy to see after we remind ourselves how Frege understands the segmenting of statements like: 4 Frege, Foundations of Arithmetic, p. x. 5 Frege, G. “On Concept and Object” in Geach, P. and Black, M. (eds), Philosophical Writings of Gottlob Frege (Oxford: Basil Blackwell, 1977), p. 43. 6 Kerry’s failure at least to address these principles is made more serious by the fact that he wrote in response to the Foundations.

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(F) Silver is a horse.

For Frege, the sentence segments into an object-expression, “Silver”, and a concept-expression, “is a horse”. Frege thinks of object-expressions as saturated and of concept expressions as unsaturated. Frege represents the unsaturatedness of the concept-expression by writing it with a blank spot in it: “( ) is a horse”.7 The blank spot is a notational reminder of the difference in logical role between the concept-expression and the object-expression. When the object-expression saturates the unsaturated concept-expression, we get the statement (F). The problem Kerry faces is the problem of showing that an unsaturated concept-expression can substitute for a saturated object-expression: i.e., Kerry needs to be able to substitute, salva congruitate, an expression with a blank spot for one without. But this sort of substitution fails. Substituting an expression with a blank spot for one without it turns a statement into a mere farrago of words.8 Why does Kerry fail to see this? Because he transgresses the Context Principle. Kerry thinks about the words “the concept ‘horse”’ outside the context of a proposition and thinks that they must be a concept-expression. They must be—because the words seem to him to assign that role to themselves. With their logical role outside the context of a proposition assigned, Kerry finds a propositional context for the words, namely (K). Kerry segments (K) as Frege would, treating the words “the concept ‘horse”’ as an object-expression. Kerry then thinks he has counterexampled Frege since he (Kerry) thinks he has substituted words that play the role of a conceptexpression into the role of an object-expression: Kerry understands the words “the concept ‘horse”’ to play the role of a concept-expression outside the context of (K) and, while retaining that role, to also play the role of an object-expression in (K). If Kerry understands correctly, (K) would indeed be a counterexample. It should be clear now why Frege thinks Kerry misunderstands, and why (K) fails to worry Frege. What logical role the words “the concept horse”’ play is for Frege something that cannot be decided by considering the words divorced from context—only in contextual wedlock do words play a logical role, only in contextual 7 Keep in mind that speaking of “( ) is a horse” as a concept-expression only makes sense where we are abstracting from a particular statement(s), like (F); the same is true of speaking of “Silver” as an object-expression. 8 “… [O]bjects and concepts are fundamentally different and cannot stand in for one another. And the same goes for the corresponding words or signs. Proper names cannot really be used as predicates. Where they might seem to be, we find on looking more closely that the sense is such that they only form part of the predicate: concepts cannot stand in the same relations as objects. It would not be false, but impossible to think of them as doing so.” “Comments on Sinn and Bedeutung”, in Michael Beaney (ed.), The Frege Reader (Oxford: Blackwell Publishers Ltd., 1997), pp. 174–5. Joan Wiener’s Frege In Perspective (Ithaca: Cornell University Press, 1991) has influenced my understanding of Kerry’s problem here. I again warn the reader that with this description of the problem Kerry faces I mount a dialectical ladder that I will not kick away until just before the Coda. Only when I have progressed that far will it be clear what my description here means and fails to mean. (The same mounting and kicking-away will be repeated in the Coda, too.) As shall become clear, there is no coherent description of the problem Kerry faces; and that is ultimately the problem he faces.

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The Concept “Horse” Paradox and Wittgensteinian Conceptual Investigations

wedlock are words object-expressions or concept-expressions. And, in contextual wedlock, words absolutely will be one or the other, and not both. Kerry wants to be able both to decide the role of words outside the context of a proposition and then, holding that role constant, to put the words into a different role in the context of a proposition. This shows, I think, why Frege mentioned the possibility of a confused mixture of psychological and logical senses of “concept”. For Frege, the words “the concept ‘horse”’ in (K) are used as an object-expression— so, given what (K) says, the word “concept” has a psychological sense (say, it refers to an object in someone’s mind).9 Frege has no objection to the word having such a sense, so long as we do not confusedly mix this sense with his own sense of “concept”. But Kerry does confusedly mix them: he ignores the Context Principle in attempting to assign a role to the words outside the context of a proposition; but, he also heeds the Principle in attempting to assign a role to the words in the context of a proposition. Kerry thinks the words “the concept ‘horse”’ can have a Fregean, logical sense outside the context of (K) and then maintain that sense while having also a psychological sense inside the context of (K). Delusions of the Language A picture held us captive. And we could not get outside it, for it lay in our language and language seemed to repeat it to us inexorably. Philosophical Investigations 115

I want now to make use of Rhees’s discussions of therapy as they apply to Frege’s response to Kerry. The first thing to notice is that Kerry’s plight is the result of what Rhees calls a “delusion or dream” of the language. Kerry confronts the words “the concept ‘horse”’, and is deluded by the words themselves: he allows those words to suggest that they can assign themselves a logical role, that they can decide whether they are a concept-expression or an object-expression, outside the context of a proposition. Frege is himself alive to just such delusions of the language. In “Comments on Sinn and Bedeutung”, he writes: Such being the essence of a concept, there is now a great difficulty in the way of expressing ourselves correctly and making ourselves understood. If I want to speak of a concept, language, with an almost irresistible force, compels me to use an inappropriate expression which obscures—I might almost say falsifies—the thought. One would assume, on the basis of its analogy with other expressions, that if I say “the concept equilateral triangle” I am designating a concept, just as I am of course naming a planet if I say “the planet Neptune”. But this is not the case; for we do not have anything with … [an unsaturated] nature.10

The similarity of the compulsion Frege describes and the one to which Kerry succumbs is clear. Notice first that Frege blames language for the compulsion “… 9 It is important to remember that I am talking about the words in (K). The words, “the concept ‘horse”’, used as an object-expression in some other proposition, need not have a psychological sense. But Kerry intends them to have such a sense in (K). 10 Beaney, The Frege Reader, p. 174.

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language, with an almost irresistible force, compels me … .” It is in casting blame on language that Frege explains what I have taken Rhees to mean when talking of “delusions” of the language: “One would assume … that if I say ‘the concept “equilateral triangle”’ I am designating a concept.” Here we might imagine Kerry chiming in, “Yes! After all, the words are the words ‘the concept “horse”’! They must designate a concept!” “But”, as Frege would say, “this is not the case; for we do not have anything with … [an unsaturated] nature.” That is, the words cannot assign themselves the logical role of a concept-expression. Given the way such words are used, as in (K), the words have the role of an object-expression, despite the fact that the word “concept” is one of their fellow travelers. 11 The delusional power of the language lies in the analogies it suggests to its users. As Frege mentions, seeing in the words “the concept ‘equilateral triangle”’ an analogy to the words “the planet Neptune” is almost irresistible. Our familiarity with uses of the words “the planet Neptune” in such sentences as: (F’) The planet Neptune is distant from Earth

makes properly understanding the logical role of (shifting examples) “the concept ‘horse”’ difficult. We want to see the words as designating a concept, analogous to the way the words “the planet Neptune” designate a planet in (F’). But, since we think the words designate a concept, we think they must play the role of a conceptexpression. (However, insofar as the words designate a concept, they play the role of an object-expression—as do the words “the planet ‘Neptune”’ in (F’).) If we think of the words as assigning themselves a logical role, then as Kerry did and as Frege confesses being almost compelled to do, we succumb to a delusion of the language. Notice next that Frege is describing a delusion that is anything but personal: Kerry is preyed upon by it, but Frege almost is, too. The tendency in the language that preys upon Kerry could prey upon anyone. Kerry’s problem is not a personal shortcoming of his own; Kerry is not displaying a special weakness. The analogy that deludes him is there—in the language—awaiting anyone who is unwary. The Nature of Logical Investigations Our investigation is therefore a grammatical one. Such an investigation sheds light on our problem by clearing misunderstandings away. Misunderstandings concerning the use of words, caused, among other things, by certain analogies between the forms of expression in different regions of language. Some of them can be removed by substituting one form of expression for another; this may be called an “analysis” of our forms of expression, for the process is sometimes like one of taking a thing apart.

11 Someone might here object that there is no delusion in the language, but rather that Frege was deluded in his choice of terminology: he should never have used the term “concept”. But this objection—a version of which Frege responds to in the closing paragraphs of “Concept and Object”—fails to appreciate that any term Frege might have chosen would create the same sort of confusion, since an analog of (K) could be just as well be produced for it. As Frege might have said, “The difficulty can indeed be shifted, but not avoided.”

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The Concept “Horse” Paradox and Wittgensteinian Conceptual Investigations These are, of course, not empirical problems; they are solved, rather, by looking in to the workings of our language, and that in such a way as to make us recognize those workings: in despite of an urge to misunderstand them. The problems are solved, not by giving new information, but by arranging what we have always known. Philosophy is a battle against the bewitchment of our intelligence by means of language. Philosophical Investigations 90, 109

Kerry’s problem, the delusion of language to which he succumbs, is no more Kerry’s personal problem than a problem in science is; in this way, the delusion and a problem in science are alike. But the delusion is in other ways importantly unlike a problem in science. Kerry’s problem is a logical problem, not an empirical problem. Frege’s response to Kerry’s problem is a logical response—call the response a logical investigation. What Kerry misunderstands is the use of the words “the concept ‘horse”’. Frege responds by reminding Kerry how the words are used in (K) and how they fail to be used outside of (K). Such reminding will not solve an empirical problem: being reminded in this way of how words are used will not solve problems in, say, physics or chemistry.12 What Frege reminds Kerry of is something that Kerry has been doing all along. Kerry has been using words like the words “the concept ‘horse”’ as objectexpressions his whole life long. He has observed the absolute distinction between such expressions and concept-expressions. That he has is shown by the presumably largely correct inferences he has drawn over the course of his life, and so on. But Kerry finds it hard to call to mind what he has been doing for so long. Under the pressure of reflection, Kerry cannot bring himself to keep to the Context Principle, cannot bring himself to refuse to ask for the meaning of certain words in isolation from propositions. Confronted by the words “the concept ‘horse”’, Kerry thinks he discovers the logical role of the words by simply thinking about the words themselves. To prevent this, Frege (so to speak) discusses with Kerry. He urges Kerry to think about the words and their logical role in a different way: He asks Kerry to consider the logical role the words play in (K), and to realize that nothing gotten from reading the words in isolation from (K) (or some other proposition) can reveal their logical role. So, in order to help Kerry solve his problem, Frege needs to get Kerry to do something—to actually segment (K)—and not to just think about the words that appear in (K), and especially not to just think about them in isolation from (K). Learning to segment sentences, learning to keep to the Context Principle, is something that takes practice. The analogies in language that tempt us to transgress against the Principle crowd us from every side. The problems that prey upon us as a result of the analogies are not problems we solve by just thinking; we solve them by building up our resistance to being compelled by the analogies, by continually reminding ourselves that words cannot assign themselves a logical role. Put another way, we solve these problems by forcing ourselves not only continually 12 A question worth asking: Will reminders of how words are used solve problems in empirical linguistics? The briefest answer worth giving: No—use is not usage. What Frege is reminding Kerry of is not a bit of empirical linguistics; Frege is not reminding Kerry of the usage of certain German words. If Frege were doing so, he would be doing something much more like what Kerry takes him to be doing.

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to remember, but continually to keep to the Context Principle. Frege’s response works to make Kerry aware of how such problems are solved, to show Kerry how to free himself from “the concept ‘horse”’ fly-bottle. Freeing himself will require Kerry to understand how he became entrapped, as O.K. Bouswma makes clear: That fly that was let out of the fly-bottle understands how he got in there, since the condition of his being let out is that he should understand that. And now he can fly in and out as he likes. It is no longer a fly-bottle for him. He can now buzz in and out enjoying the structure of the bottle.13

Making us aware of how such problems arise and are solved, getting us to understand how we entrap ourselves and free ourselves from the fly-bottle, is the burden of Frege’s response. It is the burden of the therapist. As Frege writes in “Sources of Knowledge of Mathematics and the Mathematical Natural Sciences”: It is extremely difficult, perhaps impossible, to test every expression offered us by language to see whether it is logically innocuous. So a great part of the work of a philosopher consists—or at least ought to consist—in a struggle against language. But perhaps only a few people are aware of the need for this … The difficulties which … language entangles us in are incalculable 14

So therapy is internal to logical investigation. Therapy is internal to logical investigation because the scenes of logical investigation are the scenes of trespass against the Context Principle—the scenes of entanglement in language. Our entanglements in language do not result in falsehood but rather in nonsense. And therapy is responsive to nonsense: uniquely responsive to nonsense and responsive uniquely to nonsense. Therapy inoculates us against language. Summary The results of philosophy are the uncovering of one or another piece of plain nonsense and bumps that the understanding has got by running its head up against the limits of language. These bumps make us see the value of the discovery. Philosophical Investigations 119

It is all too easy to think that Frege’s response to Kerry is peculiarly unresponsive. It is all too easy to think that deciding for or against Frege or Kerry is a matter of deciding whether or not (K) is or can be meaningful. But that decision always comes one moment too late in the discussion. The decision needed is not whether (K) is or can be meaningful, but rather the decision whether Kerry can mean by (K) what he needs to mean by it, given his intention to counterexample Frege.15 To rush past that 13 Bouwsma, O.K., “The Blue Book”, in Philosophical Essays (Lincoln: University of Nebraska Press, 1965), p. 186. 14 Beaney, The Frege Reader, pp. 369–70. 15 Putting the point in terms borrowed from Stanley Cavell, Kerry’s problem is that not that (K) means something incoherent, but rather that Kerry means (K) incoherently—Kerry has been “prompted to insistent emptiness.” Cavell, S. The Claim of Reason (Oxford: Oxford University Press, 1979), p. 336.

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decision in order to decide whether (K) is or can be meaningful is to rush past the Context Principle, to rush past the need for and the possibility of therapy. It is to be guilty of Kerry’s Folly. Therapy can be found in Frege. Wittgenstein found it there. Coda: Tractarian Therapy The object of philosophy is the logical clarification of thoughts. Philosophy is not a theory but an activity. A philosophical work consists essentially of elucidations. The result of philosophy is not a number of “philosophical propositions”, but to make propositions clear. Philosophy should make clear and delimit sharply the thoughts which otherwise are, as it were, opaque and blurred. 4.112 What can be shown cannot be said. 4.1212 Now we understand our feeling that we are in possession of the right logical conception, if only all is right in our symbolism. 4.1213

It may seem that I am guilty of a peculiar philosophico-literay fallacy; call it “the fallacy of extruded middle”. After all, I’ve moved from Frege’s “Concept and Object” to Wittgenstein’s Philosophical Investigations and said nothing about Wittgenstein’s intervening work, particularly his work in the Tractatus. One reason for so far skipping the Tractatus is the fact that Frege’s influence on it is more widely recognized than is his influence on Philosophical Investigations. But, having made my case for Frege’s influence on Philosophical Investigations, I’ve reached a natural point from which to say a little about Frege’s influence on the Tractatus—particularly on the Tractatus’ counterpart to therapy, elucidation. The natural point I have reached is also, in many ways, a better point: Philosophical Investigations sheds at least as much light back on the Tractatus as the Tractatus does forward on Philosophical Investigations. (Wittgenstein was right to want the books bound together.16) To understand elucidation, we must understand two distinctions in the Tractatus. The distinction between sign and symbol, and the distinction between proper concepts and formal concepts. I will briefly explain these distinctions, then show how they enter into Frege’s argument with Kerry. Wittgenstein notes that in order to recognize the symbol in the sign, we must “consider the significant use” of the sign (3.326). In a passage from the “Notes Dictated to Moore”, Wittgenstein says that “… in ‘aRb’, ‘R’ is not a symbol, but that ‘R’ is between one name and another symbolizes.”17 What is crucial in this passage is the way that Wittgenstein uses logical syntactic employment (“logical syntactic employment” is Wittgenstein’s 3.327 gloss on 3.326’s “significant use”) 16 Wittgenstein says that his later way of thinking can be seen in the right light “only by contrast with and against the background of [his] old way of thinking” (PI, p. x). The reverse is also true, I think. 17 Wittgenstein, L., Notebooks 1914-1916 (New York: Harper and Row Publishers, 1969), p. 108.

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to discern the symbol in the sign “R”. The sign “R” on its own does not disclose a symbol, does not symbolize. Rather, “R” standing between two names symbolizes. This connects up intimately with Frege’s Context Principle. Wittgenstein is echoing the Context Principle, but in Tractarian terms: “Never ask what symbol is in a sign in isolation, but only in the context of the sign’s logical syntactic application.” (Thus is the Context Principle inceptive of the sign/symbol distinction.) The sign “R” symbolizes in “aRb”, but the sign “R” in isolation does not (yet) symbolize. In isolation from a proposition, a sign is divorced from the contextual wedlock, from the logical syntactic employment, in virtue of which it symbolizes.18 At 4.126 Wittgenstein explains why he introduces the expression “formal concept”: “I introduce this expression in order to make clear the confusion of formal concepts with proper concepts which runs through the whole of the old logic.” Wittgenstein goes on to say (4.127) that a propositional variable “signifies the formal concept, and its values signify the objects which fall under this concept.”19 For Wittgenstein, both Frege’s objects and concepts are formal concepts, i.e., each is a way of talking about the values of particular propositional variables.20 This has the result that neither objects nor concepts can be talked about: “That anything falls under a formal concept as an object belonging to it, cannot be expressed by a proposition. But it is shown in the symbol for the object itself” (4.126) In other words, whether something is an object or a concept is decided not by claims about it, but by recognizing the propositional variable of which it is the value.21 When Kerry treats (K) as a counterexample to Frege, Kerry confuses himself (putting this in the Tractarian terms I’ve been explaining) about both signs and symbols, and proper concepts and formal concepts. Kerry thinks that a sign can determine its own symbol—that is, he thinks that the words “the concept ‘horse’” provide themselves with the logical syntactical role of a concept. Kerry thinks that the words “the concept ‘horse”’, on their own and outside of contextual wedlock, determine their logical form, determine the propositional variable of which they are the value. (This shows how the two distinctions—sign/symbol and proper 18 That the Context Principle is inceptive of the sign/symbol distinction reveals something important about the Context Principle generally and about its role in the Tractatus specifically: the Context Principle—along with the other two principles––forms the methodological counterpart of the unity of the proposition. (Cf. 3.14–3.144.) I will come back to this point and develop it in later chapters. 19 Both my reader and the reader of the Tractatus must be cautious of Wittgenstein’s use of “object” in 4.126ff. This use is peculiar and potentially misleading. It may help the reader to compare this use of “object” with that in PI 373: “Grammar tells what kind of object anything is.” For more help, see Anscombe, G.E.M., An Introduction to Wittgenstein’s Tractatus (London: Hutchinson University Library, 1959), p. 122, n. 1. 20 Although I have not done so until now, I am adopting the typographical expedient of italicizing “object” and “concept” when using the terms for formal concepts. The expedient is meant to help with the potentially confusing talk of “object” in 4.126ff. See note 17. 21 Appreciating the philosophico-logical achievement of the Tractatus is a matter of seeing how Wittgenstein’s claim that “the object of philosophy is the logical clarification of thoughts”, etc., (4.112) fits together with two other claims: “The ‘logical constants’ do not represent” (4.0312) and “Every variable is the sign of a formal concept” (4.1271).

20

The Concept “Horse” Paradox and Wittgensteinian Conceptual Investigations

concept/formal concept—interrelate: to see the symbol in the sign is to recognize the propositional variable of which the sign is the value.) Kerry thinks that the words “the concept “horse”, outside the context of a proposition, assign themselves the value of a concept propositional variable. Again, Kerry is clear enough about the Context Principle to realize that the words “the concept ‘horse”’ are, inside the context of (K), the value of an object propositional variable. Kerry needs this to work so as to show that the distinction between concept and object is not absolute. And so Kerry manages confusedly to mix the logical and psychological, as was shown before. (As the value of an object propositional variable, the words “the concept ‘horse”’ have a psychological sense.)22 Frege’s response to Kerry is the model of and for Tractarian elucidation—the logical clarification of thoughts (4.112). Frege tries to get Kerry to understand that the symbol in the sign cannot be seen outside the context of significant use, outside of logical syntactic employment. He tries to get Kerry to recognize that nothing gotten from staring at “the concept ‘horse”’ in isolation from some logical syntactic employment can reveal of what propositional variable the words are the value. In essence, what Frege asks Kerry to see—and which Kerry does sort of see—is that “Every variable can be conceived as a propositional variable” (3.314). Kerry sort of sees that to fall under a formal concept is to be the value of a propositional variable, and that to be the value of a propositional variable is to play a particular logical syntactic role in a proposition. Getting Kerry clearly to see this is to get him to stop theorizing about the words of (K) and to do something—actually to segment (K). Kerry finds it hard to get completely clear about the logical form of (K) because he thinks of logical clarification—elucidation—as a theory and not as an activity: he thinks that elucidating culminates in a series of philosophical propositions that assign (formal) properties to propositions or parts of propositions (cf. 4.124 and 4.126). Instead, as Frege’s response shows, elucidating (K) is a matter of segmenting (K), of making (K) clear, of sharply delimiting the thought that (K) expresses. What Frege tries to show Kerry—and did show Wittgenstein—is that elucidating (K) is not a matter of having some number of thoughts about (K)’s logical form, but rather is a matter of thinking clearly when thinking (K). It is not a matter of thinking the form of some particular thought, but of thinking a thought with some particular form. Activity, not theory. How does Wittgenstein get from Frege’s response to Kerry to elucidation and then to therapy? Here’s a passage from Anscombe that can serve as both the beginning of the answer to that question and as a frame for some of the details I have supplied concerning the Tractatus: … Frege came to think that if something is a concept, we cannot correctly say that it is a concept—i.e., predicate the term “concept” of it—because an expression for a concept 22 It is in treating “the concept ‘horse’” as assigning itself the value of a concept propositional variable while being assigned the value of an object propositional variable that Kerry renders (K) opaque and blurred—and that he renders it opaque and blurred in this way sheds light on how and why it is that philosophical confusions arise (3.323–3.325) and why it is that “all the propositions of our colloquial language are actually, just as they are, logically completely in order” (5.5563).

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can significantly occur only in the place of a predicate, not as a subject of the predicate “concept”. This doctrine was what Wittgenstein expressed by saying: [“That anything falls under a formal concept as an object belonging to it, cannot be expressed by a proposition. But it is shown in the symbol for the object itself. (4.126)”]; e.g., if something falls under the “formal” concept concept or property, this is shown by the predicative character of the sign we use for that “something”; and again, a variable relating to properties will be one that we take as having one or more argument-places. In Wittgenstein … the notion of a “formal” concept, a concept that cannot be properly expressed by a predicate or general term, but only by the way we apply the corresponding sort of sign, is extended much more widely than this. Not only “concept”, “function”, “object”, but also “number”, “fact”, “complex”, are formal concepts.23

Anscombe describes nicely the way in which Wittgenstein in the Tractatus inherits and expands the possibilities of elucidation first displayed in Frege’s response to Kerry. By the time Wittgenstein writes Philosophical Investigations he will expand the possibilities yet again (quoting Michael Thompson): … It is one of the lessons taught by Wittgenstein, if I understand him, that we must recognize many intuitively more determinate distinctions of the sort Frege introduced [with his distinction between concept and object]. Wittgenstein of course calls the corresponding sort of distinction … a “grammatical difference”.24

Wittgenstein moves to elucidation and from there to therapy by reflecting on Frege’s response to Kerry, by enlarging and limbering that response. Anscombe claims that “… almost all that has been published about [the Tractatus] has been wildly irrelevant. If this has had any one cause, that cause has been the neglect of Frege and the new direction he gave to philosophy.”25 Anscombe would be right to claim this of Philosophical Investigations, too, particularly about therapy.

23 Anscombe, An Introduction to Wittgenstein’s Tractatus, pp. 122–3. 24 Thompson, M. “The Representation of Life” in Hursthouse, Lawrence and Quinn, (eds), Virtues and Reasons (Oxford: Oxford University Press, 1995), p. 249, n. 2. The initial italics are Thompson’s. 25 Anscombe, An Introduction to Wittgenstein’s Tractatus, p. 12.

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Chapter Three

Logic’s Caretaker What can be shown cannot be said. Now we understand our feeling that we are in possession of the right logical conception, if only all is right in our symbolism. Tractatus 4.1212–4.1213

Introduction After the general discussion of Tractarian therapy that ends the last chapter, I will discuss a specific application of that therapy, namely its application to the Russell’s Paradox and the Theory of Types. Wittgenstein ends Tractatus 3.333 by announcing summarily that he has made Russell’s Paradox vanish. Is this vanishment prestidigital? To answer this question, I am going to have to criss-cross the spare Tractarian landscape. But 3.333 will be my base camp, the spot from which I shall begin, and to which I shall return in criss-crossing the landscape. The purpose of my criss-crossing will be to come to a full understanding of the vanishment of Russell’s Paradox, to come into full possession of 3.333. In this chapter I explain Wittgenstein’s Tractarian claim to have made the Theory of Types vanish. I do so by showing how the claim hooks up with other central themes in the Tractatus, including the Context Principle, the distinction between sign and symbol, and the notion of an adequate symbolism. I finish by arguing that Wittgenstein has not logically transubstantiated the Theory of Types, turning it from expressible into inexpressible, from what can be said into what can only be shown, but that he has indeed made the Theory vanish. 3.333—a First Look The Theory of Types and 3.333 In January of 1913, Wittgenstein writes excitedly to Russell and comments that “the theory of types must be rendered superfluous by a proper theory of symbolism.” He explains his insight in the following way: … I have changed my views on “atomic” complexes: I now think that qualities, relations (like love) etc. all are copulae! That means I for instance analyse a subject-predicate proposition, say, “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 name must belong to one type … if I analyse the proposition Socrates is mortal into Socrates, mortal and (∃x y) εI (x, y), I want a theory of types to tell me that “mortality is Socrates” is nonsensical,

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The Concept “Horse” Paradox and Wittgensteinian Conceptual Investigations because if I treat “mortality” as a proper name (as I did) then there is nothing to prevent me from making the substitution the wrong way round. But if I analyse (as I do now) into Socrates and (∃x).x is mortal or generally into x and (∃x) ϕx 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 theories of types must be done away with by a theory of symbolism showing that what seem to be different kinds of things are symbolized by different symbols which cannot possibly be substituted in one another’s places. I hope I have made this fairly clear.1

What accounts for the change in Wittgenstein’s analysis of Socrates is mortal? Wittgenstein’s earlier letters to Russell contain the answer. Sometime in 1912, Wittgenstein writes to Russell that their problems “can be traced down to the atomic propositions.” Wittgenstein writes to Russell that this becomes clear “if you try to explain precisely in what way the Copula in such a proposition has meaning.” He ends the letter by noting that “I now think about ‘Socrates is human.’ (Good old Socrates!).” Then, later in 1912, in December, Wittgenstein writes to Russell and reports “… I had a long discussion with Frege about our theory of symbolism of which, I think, he roughly understood the general outline. He said he would think the matter over. The complex-problem is now clearer to me and I hope very much that I may solve it.” The next letter is the excited letter of January 1913. So, what accounts for the change in Wittgenstein’s analysis? My best guess is that it was his long discussion with Frege. But how could a discussion with Frege, even a long one, have brought about this change? To answer this, we need first to review Frege’s distinction between concepts and objects, and then to get clear about Wittgenstein’s new analysis. How would Frege have analyzed Socrates is mortal? He would have analyzed it into the object-expression “Socrates” and into the concept-expression “( ) is mortal.” The object-expression, “Socrates”, is saturated; the concept-expression, “( ) is mortal,” is unsaturated. The blank spot in it symbolizes the unsaturation of the concept-expression. As Frege understood his own analysis, “Socrates” and “( ) is human” are absolutely distinct. … [O]bjects and concepts are fundamentally different and cannot stand in for one another. And the same goes for the corresponding words or signs. Proper names cannot really be used as predicates. Where they might seem to be, we find on looking more closely that the sense is such that they only form part of the predicate: concepts cannot stand in the same relations as objects. It would not be false, but impossible to think of them as doing so.2

The absolute distinction between concepts and objects makes it impossible for one to take the place of the other. Attempting to substitute a concept-expression for an object-expression requires substituting an expression with a blank spot in it for one 1 Wittgenstein, Notebooks, 1914–1916, pp. 120–121. It is worth noting that the way of speaking in which Wittgenstein here indulges, namely speaking of “a theory of symbolism” will become a less and less often indulged in way of speaking. Noting this is important for properly understanding the dialectic of the Tractatus. 2 Beaney, The Frege Reader, pp. 174–5.

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without it. Substituting one for the other results, not in a new proposition, but rather in gabble. Wittgenstein’s new analysis of Socrates is mortal is an inheritance from Frege. For Frege, object-expressions and concept-expressions are different kinds of expressions, and the symbols for them different kinds of symbols.3 Wittgenstein’s symbolizing, despite its differences from Frege’s, shows that “Socrates” and “something is mortal” are different kinds of symbols. “Socrates” is symbolized by “x” and “something is mortal” by “(∃x) ϕx”. As it is for Frege’s, the way in which Wittgenstein’s symbols have to be combined is visible in the symbols themselves. “Socrates”, so to speak, fits into “something is mortal;” Socrates, so to speak, is the something that is mortal. The way in which the symbols are to be combined in Wittgenstein’s old analysis is not visible in the symbols themselves. The symbolization of the old analysis, (∃x y) εI (x, y) leaves invisible the way in which the symbols have to be combined. In particular, there seems to be no reason why “mortality” (“y”) could not be switched with “Socrates” (“x”) to yield Mortality is Socrates. In order to prevent this switch, the old analysis needs the help of a Theory of Types, since the Theory of Types is necessary if we are to tell that Mortality is Socrates is nonsense. The Theory of Types allows us to decree that Mortality is Socrates is ill-formed because in it is a proper name of one type, the type of “mortality”, is substituted into a place that can be occupied only by a proper name of a different type, the type of “Socrates”. The Theory of Types allows us to decree that Mortality is Socrates is nonsense because the theory tells us that anytime a substitution of the sort described occurs, the result is nonsense. As Russell put it: “In its technical form, [the theory] states merely that a word or a symbol may form a part of a significant proposition, and in this sense have meaning, without being always able to be substituted for another word or symbol in the same or some other proposition without producing nonsense.”4 That is, the theory consists of formation rules, as Hans Reichenbach explains: [The Theory of Types] rules out certain expressions as meaningless. According to this theory, it is not permissible to say that a class contains itself as a member; such a combination of words has no meaning. A class must be regarded as being of a higher type than its members; that it cannot be said to contain itself … In introducing the category meaningless for such expressions, Russell recognized that the solution must be sought, not 3 I am here and throughout deliberately and purposefully simplifying Wittgenstein’s acceptance of this point of Frege’s (in particular of his acceptance of the Context Principle). The extent to which Wittgenstein in 1913 accepts the point is unclear; the history of his acceptance is, to use Michael Kremer’s phrase, “complex and wavering.” It will not be until the time of the Tractatus that Wittgenstein’s acceptance becomes unwaveringand it never becomes uncomplicated. 4 Russell, B., Logic and Knowledge, ed. Robert Marsh (London: George Allen and Unwin, 1956), p. 334.

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The Concept “Horse” Paradox and Wittgensteinian Conceptual Investigations in a change of the truth rules, but in a revision of the formation rules of the language. In fact, the existence of the antinomies [like Russell’s Paradox] proves that the consistency of a language depends, to a great extent, on the formation rules.5

Mortality is Socrates breaks a formation rule, and so is impermissible, nonsense. A crucial feature of the Theory of Types now emerges: in order to decide whether or not an expression like Mortality is Socrates is well- or ill-formed, it is necessary to know the type of “mortality” and the type of “Socrates”. That is, it is necessary to know that “mortality” is of a higher type than is “Socrates”. And this is something it is necessary to know about “mortality” and about “Socrates” ahead of their evilstarred combination into Mortality is Socrates. But how does Wittgenstein’s new analysis show that the Theory of Types is superfluous? In the new analysis, “Socrates” can fit into “something is mortal.” There is no blank spot in “Socrates” for “something is mortal” to fit into. Wittgenstein’s symbolism renders impossible just the sort of type-transgressing substitution that Russell feared. As Wittgenstein put it, “it becomes impossible to substitute the wrong way round because the two symbols are now of a different kind themselves.” Wittgenstein’s new analysis makes the theory of types superfluous by eliminating any role for formation rules to play. I now am in position to take an initial look at 3.333: A function cannot be its own argument, because the functional sign already contains the prototype of its own argument and it cannot contain itself. If, for example, we suppose that the function F(fx) could be its own argument, then there would be a proposition “F(F(fx))” and in this the outer function F and the inner function F must have different meanings; for the inner has the form ϕ(fx), the outer the form ψ(ϕ(fx)). Common to both functions is only the letter “F”, which by itself signifies nothing.

Wittgenstein opens 3.333 by sharpening the point of his letter to Russell of January 1913. Notice: “… the functional sign already contains the prototype of its own argument and it cannot contain itself.” Wittgenstein’s idea here is, as in the letter, that the way the symbols combine is visible in the symbols themselves. The outer function has, so to speak, two blank spots; the inner only one. So there is no question of the outer and inner function being switched in a type-transgressing way. Nor is there any question of the sameness and difference of the two functions: the two functions are visibly different––our animal eyes (to use Frank Ebersole’s phrase) are revelators of the difference. Some Background Wittgenstein only talks of functions taking themselves as arguments because he has Russell, and Russell’s views, specifically in mind. In “The Theory of Logical Types”, Russell writes that: The paradoxes of symbolic logic concern various sorts of objects: propositions, classes, cardinal, and ordinal numbers, etc. By means of the theory … which reduces statements 5 Reichenbach, H., Elements of Symbolic Logic (New York: The Free Press, 1947), p. 222.

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that are verbally concerned with classes and relations to statements that are concerned with propositional functions, the paradoxes are reduced to such as concerned propositions and propositional functions.6

Given this claim of Russell’s, Wittgenstein needs only to talk of functions taking themselves as arguments, because that is the heart of the matter, what the matter can be reduced to.7 This becomes more evident when 3.333 is laid alongside a passage in which Russell provides an example of the Theory of Types at work. The above limitation of possible values for ϕz solves many paradoxes. Take for example the following. Let “f(ϕz)” mean “ϕz is not satisfied by itself as an argument,” i.e., “ϕ (ϕz) is false.” (If this were significant, it would be true in all ordinary cases. For example, it cannot be true that the function “x is a man” is a man; if therefore it is either true or false that it is a man, it must be false.) Let us now denote by f(ϕ) the function for which f(ϕz) is the value for the argument ϕz, and let us inquire whether f(fϕ) is true or false. If [it] is true, that means, by the definition of f, “it is false that f(fϕ) is false,” from which it follows that [it] is true. Thus whether we suppose f(fϕ) true, or whether we suppose it false, we are led into a contradiction. This contradiction disappears if “ϕ (ϕz)” is meaningless … The paradox of classes which are not members of themselves is also solved by the above considerations, if it is admitted that a class must always be defined by a propositional function. For then the class to be considered is the class of those classes which do not satisfy their defining functions. But as the class is derived from the function, it cannot, according to [the vicious-circle principle], be an argument to its defining function, and therefore it neither satisfies nor does not satisfy its defining function.8

Russell’s vicious-circle principle is an example of the sort of formation rule Wittgenstein is rejecting. For Wittgenstein, there is no reason to treat ϕ(ϕz) as meaningless, no rule to treat it as breaking. For Wittgenstein, ϕ(ϕz) is not an example of a function taking itself as its own argument: the inner function has only one blankspot; the outer, two. All the two functions have in common is “φ”, which by itself signifies nothing. Wittgenstein has no need of a vicious-circle principle. Logic must take care of itself Writing in his notebook, in 1914, Wittgenstein comments, as if reminding himself: “Logic must take care of itself.”9 He goes on to note further that this is an “extremely important and profound insight.” So logic is to take care of itself. What does this mean? Presumably, it means that logic can neither look to the left for help from psychology nor the right for help from metaphysics. It must be self-sufficient. Again, Wittgenstein in his notebook: 6 Slater, J.G. (ed.), The Collected Papers of Bertrand Russell, vol. 6 (London and New York: Routledge, 1992) pp.4–5. 7 I here follow Wittgenstein in accepting the reduction of classes to functions. I should also note (1) that I am confining my attention to the type of type trouble Wittgenstein addresses in 3.333 and am ignoring other paradoxes that have often been linked to the theory of types (how, or if, Wittgenstein addresses these other paradoxes I leave open for now;) and, (2) that I am treating Wittgenstein as responding to the Simple theory of types (how, or if, Wittgenstein addresses the Ramified theory I leave open for now, too). 8 Slater, The Collected Papers of Bertrand Russell, p. 7. 9 Wittgenstein, Notebooks, 1914–1916, p. 2.

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The Concept “Horse” Paradox and Wittgensteinian Conceptual Investigations Once more: logic must take care of itself. A possible sign must also be capable of signifying. Everything that is possible at all, is also legitimate. Let us remember the explanation why “Socrates is Plato” is nonsense. That is, because we have not made an arbitrary specification, NOT because a sign is, shall we say, illegitimate in itself.

Wittgenstein continues: It must in a certain sense be impossible for us to go wrong in logic. That is already partly expressed by saying: Logic must take care of itself.10

If logic must take care of itself then it must be impossible for us to go wrong in logic. But how can it be impossible for us to go wrong in logic? We cannot go wrong in logic because anything that is possible in logic is also legitimate, permitted. There is no possible but impermissible logical maneuver. Wittgenstein continues in his notebook by contrasting his way of thinking about permissibility and possibility in logic with his understanding of Frege’s. Frege says: every well-formed sentence must make sense; and I say: Every possible sentence is well-formed, and if it does not make sense that can only come of our not having given any meaning to certain of its parts. (Even when we believe we have done so.)

(As Wittgenstein understands Frege, Frege is disintegrated––he both reveals that there is no need for a Theory of Types and (nonetheless) works as if there were a need for it. Wittgenstein in the Tractatus tries to integrate Frege––to bring him to appreciate the full consequences of revealing that there is no need for a Theory of Types.11 Earlier I stressed Wittgenstein’s inheritance of one point from Frege; here I stress a rejected point; later I will return to the inherited point.) As Wittgenstein understands Frege’s position here, some sentences are well-formed and some illformed. Thus, even for Frege, there are some sentences that are illegitimate in themselves. Wittgenstein, however, thinks that all possible sentences are wellformed; and he thinks this for Fregean reasons. There is no possible sentence that is not well-formed: no sentences are illegitimate in themselves. Frege’s position makes it possible to do something impermissible in logic: sentences can be constructed that may not be constructed, that are not permissible. So, on Frege’s view as Wittgenstein understands it, it is possible to make a mistake in logic. Now, whatever complications this position creates for Frege as Wittgenstein understands him, and whatever might be said to show that this position is an isolated aberration in Frege’s thinking, this position is very much Russell’s; remember Reichenbach’s comment that, according 10 Wittgenstein, Notebooks, 1914-1916, p. 2. 11 As I suggested above, Wittgenstein’s response to Frege’s philosophizing is complicated—nearly as complicated as Wittgenstein’s philosophizing itself. For more on that response (and on Frege’s disintegration), see especially James Conant’s “Elucidation and Nonsense in Frege and the Early Wittgenstein”, in Crary and Read (eds), The New Wittgenstein (London and New York: Routledge, 2000), pp. 174–217 and Cora Diamond’s “Inheriting from Frege: The Work of Reception as Wittgenstein Did It,” forthcoming. See also Anthony Palmer’s Concept and Object (London: Routledge, 1988), pp. 29–41.

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to the Theory of Types, certain combinations of expressions, sentences, are not permissible. The Theory of Types is the prophylactic against the logically possible but logically impermissible. Think about Wittgenstein’s Tractatus example, Socrates is identical, to illustrate this point. Russell would concede that this is a sentence; but he would contend that since “identical” is not an adjective, the sentence is not well-formed. So, Socrates is identical is an impermissible sentence. Another way of putting the point is to say that Socrates is identical transgresses a formation rule. Anyone who employs the sign is making a mistake. Wittgenstein rejects formation rules. For him, every possible sentence is permissible; every possible sentence is well-formed. Whereas for Russell, the genus of sentences divides into two species, the well-formed and the ill-formed, for Wittgenstein there are sentences—which are formed, if you will—and non-sentences, signs that resemble sentences but that lack a form altogether, that are unformed. For Wittgenstein, the trouble that plagues Socrates is identical is not that it is ill-formed. No, Socrates is identical is troubled because we have not given a meaning to part of it: we have failed to provide a meaning for “identical” as an adjective. Socrates is identical does not try to say something that cannot be said, it does not try to speak something out but gulp on it (as it does for Russell); it simply does not—as yet—say anything. If we provided a meaning for “identical” as an adjective, then the sentence would say that Socrates has whatever property it is that “identical” stands for. Contrast Russell, again: Russell would say of the sentence that “identical” does have a meaning—the meaning it has in, say, Mark Twain is identical to Samuel Clemens. Given that of “identical”, Socrates is identical is ill-formed. The Elements of Logical Space, Part One: Signs and Symbols Reflecting on this difference clarifies exactly where we should locate the substantive disagreement between Frege and Russell, on one hand, and Wittgenstein, on the other. Russell thinks of the elements of logical space as subsentential—as words with particular meanings. “Identical” with its particular meaning is an element of logical space. Its meaning fits it to play some sentential roles and misfits it to play others. Sentences are formed by combining various elements of logical space. If the combination is permissible, then the sentence is well-formed; if not, not. In either case, it is possible to inspect the elements combined and to specify the contribution each makes to the sentences. In ill-formed sentences, the contributions made by the elements clash with one another—they will not, so to speak, lie down together. So, as Russell thinks of the elements, the person combining the elements is called upon to be logic’s caretaker. It is possible for the elements of logical space to be combined in impermissible ways. (Think of the person, alternatively, as logic’s matchmaker, presiding over couplings logically happy and logically unhappy.) Wittgenstein does not think of the elements of logical space as Russell does. For Wittgenstein, the elements of logical space are first and foremost sentential, not subsentential. Each of the sentential elements of logical space is well-formed. But to further clarify this, I need to return to 3.333.

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Wittgenstein comments that the two functions ϕ(fx) and ψ(ϕ(fx)) have in common “only the letter ‘F’, which by itself signifies nothing.” Here, Wittgenstein is relying on his distinction, drawn earlier in the 3’s, between sign and symbol. The sign is the part of the symbol perceptible by the senses. Two different symbols can therefore have the sign (the written sign or the sound sign) in common—they then signify in different ways. It can never indicate the common characteristic of two objects that we symbolize them with the same sign but by different methods of symbolizing … In the language of everyday life it very often happens that the same word signifies in two different ways—and therefore belongs to two different symbols—or that two words, which signify in different ways are apparently applied in the same way in the proposition. Thus the word “is” appears as the copula, as the sign of equality, and as the expression of existence; “to exist” as an intransitive verb like “to go”; “identical” as an adjective; we speak of something but also of the fact of something happening. (In the proposition “Green is green”—where the first word is a proper name and the last an adjective—these words have not merely different meanings but they are different symbols). Thus there easily arise the most fundamental confusions (of which the whole of philosophy is full). In order to avoid these errors, we must employ a symbolism which excludes them, by not applying the same sign in different symbols and by not applying signs in the same way which signify in different ways. A symbolism, that is to say, which obeys the rules of logical grammar—of logical syntax. (The logical symbolism of Frege and Russell is such a language, which however, does still not exclude all errors.) In order to recognize the symbol in the sign we must consider the significant use. The sign determines a logical form only together with its logical syntactic application. 3.32–3.327

In 3.333, “F(F(fx))” appears to be a case of a function acting as its own argument. However, if we consider the logical syntactic application of the sign, we see—as noted above—that although the functions share a sign, “F”, they do not share a symbol. The outer “F”, considered in its significant use, has two blank spots; the inner “F” only one. Hence, the two signs are different symbols. Given this, there is no danger of Russell’s Paradox arising. Whatever the signs may lead us (mistakenly) to believe, there will be no sentence in which a function acts as its own argument. I here interpolate a few more remarks on the sign/symbol distinction, on formation rules and on compositionality. I do so mainly to make clear how what I have done and will do stand in relationship to compositionality. It might seem that rejecting formation rules is, in effect, rejecting compositionality. What I want to show is that that seems clear only when the compositionality story we have in mind is simple (I’ll characterize simplicity below). But simple compositionality stories face dialectical difficulties—difficulties I will sketch. When a compositionality story is suitably complicated, it is not clear that rejecting formation rules is rejecting compositionality.

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The formation rules, as Reichenbach (and Russell) understands them, apply to expressions. Now, what does Reichenbach mean by “expressions”? Specifically, does he mean signs or does he mean symbols? I think that Reichenbach wants to mean something like signs; at any rate he does not want to mean symbols. I’ll come back to this. Formation rules are meant to characterize subsentential expressions, and to do so independent of any role that expressions play in a sentence. That is, the rules specify, ahead of any formation in which the expression might function, the contribution of that expression to the formation. In a way that is purely “formal” (in one sense of that contested term: i.e., in a way that is independent of sentential role), the rules specify how to construct sentential expressions from finite sets of subsentential expressions. So the rules tell us how to put expressions together. Reichenbach’s formation rules are, thus, crucially part of simple compositionality stories. On such stories, it is supposed to be clear that our understanding novel sentences requires piggybacking our understanding of novel sentences on our understanding of the novel sentences’ subsentential expressions. The formation rules in their positive role will tell us how, so to speak, to put the novel sentences together and thus how to understand them. But of course not every novel formation of expressions is going to be one that can be understood. Since that is so, simple compositionality stories include a negative role for formation rules: without them used in the negative role, there’s too much potential novelty for any (one’s) understanding. The rules then are appealed to in order to reject particular combinations as ill-formed. The formation rules for composing sentences out of subsentential expressions are going, then, to have both a positive and a negative role: among formations, they separate the wellfrom the ill-formed. The trouble for simple stories is that they also require that our understanding of the subsentential expressions be an understanding in isolation from sentential roles. But such an understanding looks too insubstantial to do what it is meant to do—to explain our understanding of novel sentences composed of those expressions. For example, consider the expression “rake”, and the sentences: The rake is too rusty to be of any use. Please rake the yard. Tom is a rake.

What understanding of “rake”, what understanding achievable in isolation from sentential roles, is going to explain our understanding of these three sentences? Even if we think that we can discern some understanding so achievable, how could it do any more than, so to speak, contribute something to the sentence that will nonetheless fail to fix the sentences’ meanings? What there is to understanding “rake” in isolation from its sentential role, if anything, looks like something that has to be common to its sentential role as a noun, a verb and an adjective, and yet also something that falls short of being what there is to understanding it as a noun, a verb, etc. But then what-there-is-to-understanding-“rake” is not going to explain my understanding of any one of the sentences, since understanding any one of them requires more than an understanding achievable in isolation from sentential role. Even worse, how could

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rules that govern formation do what they need to do when what they govern is this insubstantial? It is hard to see how a rule governing something this insubstantial could determine that a sentence is well- or ill-formed. And so it is hard to see how a simple compositionality story can explain what it serenely assumes it can explain. I take this to suggest that simple compositionality stories cannot do what they assume they can. For such stories to do what they assume they can, they will have to complicate themselves, they will have to incorporate contextuality; i.e., they will have to tell compositional stories in which subsentential expressions are understood in relation to sentential roles. A defender of a simple compositionality story might try to complicate his story, but in a way that is meant not to incorporate contextuality. He might argue that there are, so to speak, three “rakes” in my three sentences; he might argue that “rake” is homonymous. He would say that each “rake” will appear on different lists of subsentential expressions. Appearing in different lists, the rules of composing sentences in which the expressions appear will also be different. But the question at this point is this: what is the significance of being listed in one list as opposed to another? It looks like it will have to be this: being listed on one list is to be noun“rake”, on another verb-“rake”, and etc. In other words, the lists themselves will end up standing in relation to sentential roles, and through the lists themselves, those expressions listed. Contextuality ends up as part of the story after all. Viewed from the vantage point of the Tractatus, the dialectic looks like this. Simple compositionality stories want to be stories about composing with signs. But no such story will succeed in its aim of explaining how we understand novel sentences or how we distinguish the well- from the ill-formed. Still, to complicate the story by making it a story about composing with symbols is to give the game away. So—the simple compositionality story tries to become, not complicated, but less simple, by finding something to compose with that is both more than a sign and less than a symbol. The story about homonyms is an attempt at a less simple compositionality story. But, again using the language of Tractatus, it turns out that for a subsentential expression to appear on one list as opposed to another is for relationships to sentences to be after all intruded into the story. The expressions on the list, although they look, when considered in isolation, like signs, are, when considered as listed, symbols—propositional variables (3.313). The tellers of simple compositionality stories look to be stuck in an unlucky variant of the position of Buridan’s Ass—hungry, but immobile between two meals equally inedible. Signs won’t do, nor symbols neither. Now, I admit that this is, at best, a sketch of the dialectical difficulties facing simple compositionality stories. But I wanted briefly to indicate two things: (1) that simple compositionality stories, stories that dispense entirely with contextuality, are not clearly successful stories; and (2) that rejecting formation rules need not require jettisoning anything but the beclouded simple compositionality stories, since the correct story, whatever it, in its details, may be, will presumably be one that will intertwine compositionality and contextuality. Later, I supply an example of the workings required by the correct story––at least by the lights of the Tractatus.

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Misunderstanding the Distinction between Signs and Symbols Ishiguro A good way to bring out Wittgenstein’s distinction between sign and symbol is to show how easy it is to misunderstand it. Hide Ishiguro attempts to explicate 3.333 as follows: How are we to read “ϕ(ϕ)”? Is (ϕ) a name? If it were, “ϕ(ϕ)” would be a concatenation of two names and in English that is not a sentence … Could the “ϕ” on the left side then be a predicate? For Wittgenstein suggests that when the sign “ϕ” appears to the left side of a name, the fact of its doing so expresses that the thing named has a certain property. But the “ϕ” on the right hand side ceases to be a sign for a propositional function. Thus, “ϕ(ϕ)” is not more well-formed than “Is blue is blue.”12

The problem with Ishiguro’s explication is that it dithers between signs and symbols. On the one hand, when she asks, “How are we to read ‘ϕ(ϕ)’?”, she seems to be talking about signs and asking after the significant use. That is, she seems to be trying to see the symbols in the signs. But, when she does so, when she sees the name-symbol in the signs, she does not make it clear which of the two signs she is looking through (so to speak). She needs to make this clear; otherwise in trying to see the symbol in the signs she ignores the logical syntactic application. After all, if we are considering the sign, “ϕ(ϕ)”, somewhat like “F(F(fx))”, presents us with two signs that must be different symbols, since the inner one lacks a blank spot and the outer one has one. The crucial point here is that, for Wittgenstein, if there are symbols to see in the signs, then “ϕ(ϕ)” is a sentence and “ϕ” a feature of a possible sentence. So, if there is a symbol to be seen, what is seen is something well-formed or something that is a feature of something well-formed. So, it could not turn out that “ϕ(ϕ)”, if there is a symbol to be seen in it, is ill-formed. On the other hand, when Ishiguro ignores the differences between the first and the second “ϕ”, when she concludes that if the left hand “ϕ” is a function, then the right hand side ceases to be a sign for a propositional function, she seems to take it that she is looking at symbols, not at signs. (She seems to take it that the symbols in the signs have already been seen, and been seen to be “ϕ(ϕ)”.) She then concludes that, having seen the symbol in the sign, the symbol can be seen to be ill-formed. Dummett A related but more complicated misunderstanding occurs in Michael Dummett’s work on Frege’s philosophy of language. Dummett is talking of Frege (not Wittgenstein), but the point of Frege’s that Dummett is discussing is the point that Wittgenstein inherits from Frege and leans on in 3.333. (The emphasis in the quotation is mine.)

12 Ishiguro, H. “Wittgenstein and the Theory of Types” in Block, I. (ed.), Perspectives on the Philosophy of Wittgenstein (Cambridge, Mass.: MIT Press, 1981), p. 54. I use Ishiguro as my example because she understands so much of the Tractatus so well. If she can (and does) go wrong here, anyone can. I should also note that, despite my criticism of this passage, I am indebted to Ishiguro’s paper.

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The Concept “Horse” Paradox and Wittgensteinian Conceptual Investigations It is fundamental principle of Frege’s theory, and one which he reiterates repeatedly, that a symbol for an incomplete expression can never occur without its argument-place, or argument-places, with the sole exception of a bound variable in that of its occurrences in which it occurs next to the quantifier or other operator that binds it … The result of adherence to this principle is that, in Frege’s symbolic language, it is not merely forbidden, but actually impossible, to violate distinctions of type. If, for example, we attempt to insert a first-level predicate “F(ζ)” in the argument-place of another first-level predicate “G(ζ)”, we do not get a sentence at all, for “F(ζ)” still contains a gap, represented by the “ζ” which remains to be filled. If, on the other hand, we attempt to insert a proper name “α” in the argument-place of a second-level predicate “Mx ϕ(x)”, we are unable to do this, because “α” contains no gap into which we can insert the bound variable “x”. Thus, so far as Frege’s own symbolic language is concerned, his doctrine of levels does not so much prescribe the meaninglessness of certain expressions as draw attention to their non-existence. It earns the right, however, to be called a theory of significance by the light which it throws, indirectly, upon natural language. Natural language constantly violates the principle that an expression which is by its sense incomplete cannot occur without its argument-place. Most adjectives, for example, are either first-level predicates or first-level relational expressions with their argument-places suppressed … Frege would say that we can only gain an explicit understanding of the tacit workings of natural language—the way in which the sense of this context is related to the use of an adjective in it’s primary position, after the copula—by observing how such uses of the adjective do duty for what is achieved in the symbolic language by means of bound variables. But, precisely because natural language violates the principle that each expression incomplete in its sense must carry with it its argument-place(s), it does become possible within natural language to form meaningless but grammatically correct sentences which violate the distinctions of type and in the symbolic language could not be constructed at all.13

Unlike Ishiguro, Dummett understands that for anyone who adheres to Frege’s principle, as Wittgenstein does, there will be no ill-formed expressions in an adequate symbolic language. (“… [I]n the symbolic language [they] could not be constructed at all.”) So, for example, if “ϕ(ϕ)” is an expression in an adequate symbolic language, then it is well-formed. (If it is not an expression in an adequate symbolic language, then it is simply a sign in which we perhaps could see symbols (in a context of significant use).) However, Dummett fails to see that what he says of natural language denatures Frege’s principle (at least as Wittgenstein is concerned to inherit it.) If a sentence in a natural language is meaningless, the explanation cannot be that the sentence type-transgresses. It is no more possible to type-transgress in a natural language than in a symbolic language (whether adequate or not). Any natural language sign in which a symbol can be seen is meaningful. A meaningless natural language sign is one in which no symbol can be seen. But this means that it is also one that will not type-transgress: it is not ill-formed but rather unformed. If, in a natural language, a word appears that is—given its context of significant use—incomplete in its sense, then that word carries a blank spot with it. True, the blank spot is invisible—and it is this that makes the symbolic language the tool for perspicuity that it is—but it 13 Dummett, M., Frege: Philosophy of Language (Cambridge, Mass.: Harvard University Press, 1973), pp. 50–51.

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is nonetheless there (i.e., there in the context of significant use). To deny that is to allow the sign completely to eclipse the symbol, to refuse to see the symbol in the sign. The difference between the symbolic language and the natural language is that the symbolic language is used to show the symbols seen in the signs of a natural language. When there are no symbols to be seen in the signs, then the signs of natural language are meaningless—but not because something has happened in them that cannot happen in the symbolic language, but rather because nothing has happened in them at all. And that is why there is no representing them in the symbolic language. The problem is not that the symbols in its signs type-transgress, the problem is that there are no symbols in its signs. Meaningless, because type-transgressing, sentences no more exist in natural language than in symbolic language. Dummett must both be able to see and not to be able to see symbols in the signs of natural language. Notice that he says that it is “possible to form meaningless but grammatically correct sentences which violate the distinctions of type and in the symbolic language could not be constructed at all.” But how can Dummett know of these sentences that they violate distinctions of type—type-transgress—if the sentences cannot be represented in the symbolic language at all? To represent a sentence in the symbolic language is to see the symbols in its signs. Dummett here does what Wittgenstein objects to Russell doing: Dummett thinks that it is possible to see the symbol in the sign of something subsentential while denying that is it possible to see any symbol in the sentential sign. But, for Wittgenstein, to see symbols in the subsentential signs is to see the symbol in the sentential sign, and vice versa. Ordinary Language is in Perfect Logical Order We are now in a position to understand something in the Tractatus that is often misunderstood: the status of ordinary language. Anscombe points out that: It is a mistake to suppose that the dictum “Ordinary language is all right” is the expression only of Wittgenstein’s later views … [T]he sentences of ordinary language no more fail to express a sense than our Roman numeral fails to express a number. The one expresses a sense, the other a number, perfectly. And so the ideal order that characterizes language is there in every sentence of ordinary language. But: “Everyday language is a part of the human organism and is just as complicated. It is humanly impossible to gather the logic of ordinary language from it directly” (4.002). This, then, is why, according to Wittgenstein, we study logic and construct logical symbolisms: in order to understand the “logic of language” …14

Anscombe is right, perfectly. And what she is right about is one of the things Dummett is wrong about. Dummett thinks of symbolic language as better than natural or ordinary language, and better in the following way: in it, certain mistakes cannot occur that can occur in ordinary language, namely type-transgressions. But, for Wittgenstein, type-transgressions cannot occur in any language, whether symbolic or natural. The way in which the symbolic language is better than the ordinary one is that we can gather the logic of language from the symbolic language directly: 14 Anscombe, An Introduction to Wittgenstein’s Tractatus, p. 92.

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gathering it from the ordinary language is harder because the ordinary language is less perspicuous—for example, blank spots in its expressions are not visible as they are in the symbolic language. The Elements of Logical Space, Part Two: The Context Principle and the Unity of the Proposition This brings me back to the question of how Wittgenstein sees the elements of logical space. Answering this question required that I further explore the sign/symbol distinction—and so it now also requires that I address two closely related topics, Wittgenstein’s use of the Context Principle and his recognition of the unity of the proposition. The Context Principle is inceptive of the sign/symbol distinction. Again, the Context Principle, as Frege states it, is: “Never to ask for the meaning of a word in isolation, but only in the context of a proposition.” Wittgenstein’s version of this in the Tractatus is: “An expression has meaning only in a proposition. Every variable can be conceived as a propositional variable.” (3.314) Wittgenstein uses the Context Principle to draw the sign/symbol distinction: it is only possible to see the symbol in the sign in the context of a proposition. That is why Wittgenstein says at 3.327 that “the sign determines a logical form only together with its logical syntactic application.” Conceiving of every variable as a propositional variable is conceiving of every symbol as a logical form. Wittgenstein points this out by saying that “An expression presupposes the forms of all propositions in which it can occur. It is the common characteristic mark of a class of propositions. It is therefore represented by the general form of the propositions which it characterizes.” (3.311–3.312) A proposition is something that contains symbols, not merely signs. For two propositions to have something in common is for each proposition to contain a symbol the other contains, and not merely for each to contain a sign the other contains. It is best to think of the Context Principle as I think Wittgenstein and Frege think of it: as the methodological counterpart of the recognition of the unity of the proposition.15 Gilbert Ryle brings this out well, talking of “Frege’s difficult but crucial point”: … [that] the unitary something that is said in a sentence or the unitary sense that it expresses is not an assemblage of detachable sense atoms … [and] it was … Wittgenstein who, developing arguments of Frege, showed that the sense of a sentence is not, what had hitherto been tacitly assumed, a whole of which the meanings of the words in it are independently thinkable parts, but, on the contrary, that the meanings of the parts of a sentence are abstractible differences and similarities between the unitary sense of that 15 The full methodological counterpart of the recognition of the unity of the proposition is Frege’s Three Principles, taken together. The Context Principle enjoys, rightly, a kind of pride of place among the Three, but I believe the Three should ultimately be understood together, and in this way: to deny any one is to deny each of the other two. To deny any one is thus also to fail to recognize the unity of the proposition. For more on this, see Anthony Palmer, Something to Talk About (Inaugural Lecture, University of Southampton, 1978). I develop this in more detail in Chapter 5.

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sentence and unitary senses of sentences which have something but not everything in common with that given sentence …16

Fully to recognize the unitary sense of a proposition is to recognize the hopelessness of asking for the meaning of a word in isolation from the context of a proposition. The Context Principle is a methodological warning against that hopeless enterprise. We ought always to keep before our eyes a complete proposition—because only in it have the words really a meaning. If I look at a word in isolation, failing to keep a complete proposition before my eyes, then all I can see is a sign. The sign in isolation lacks any life; it is completely opaque. Because it is completely opaque, I cannot see any symbol in it. And that it is opaque is what drives me to the realm of the psychological or metaphysical in an attempt to secure a meaning for it. It is worth noting that whatever I find in those realms, if anything, will end up being double-counted: I will treat what I find in the realms both as what allows me to see the symbol in the sign and as the symbol in the sign: that is, I will treat the psychological/metaphysical item as supplying the sign with a logical syntactic application and as the symbol in the sign in that logical syntactic application. An Adequate Symbolism When Wittgenstein says that logic must take care of itself—and calls this an extremely profound and important insight—he is registering the view of logic that the full recognition of the unity of the proposition requires. The unity of the proposition allows for the creation of an adequate symbolism. What Wittgenstein sees is that it is the sign in the crucible of logical syntactic application that reveals the symbol. If propositions were not unities, there would be no revelation of symbols, no crucible of logical syntactic application. If propositions were not unities, they could not have (make) sense—at least not the sense that propositions (make) have. But, given that propositions are unities, there is no need to look to somewhere else, particularly to metaphysics, in order to decide whether or not a symbolism is adequate. This point is crucial and many have missed it, including Max Black. Wittgenstein’s conception of the philosophy of language (the search for its essence) required a stand on ontological issues: anybody who hopes to delineate a Begriffsschrift that adequately manifests the grain of reality must have at least some schematic view concerning the true structure of thought and its true, if hidden, connexion with reality; for how is one to distinguish the “accidental” from the “essential” features of language except in terms of prior notions about what “reality” is like?17

Black thinks that we must have some view of what reality is like before we can ask if a symbolism is adequate—presumably, adequate to describe that reality. But this mistakes adequacy, as it interested Wittgenstein. 16 Ryle, G. “Letters and Syllables in Plato”, Collected Papers, vol. 1 (London: Hutchinson, 1971), p. 58. 17 Black, M., A Companion to Wittgenstein’s Tractatus (Cambridge: Cambridge University Press, 1964), p.7.

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To explain this, I need to distinguish between symbolism(s) and the logic of our language. Wittgenstein sometimes calls the latter “logical syntax” or “logical grammar”— as per 3.325. One way of determining whether a symbolism is adequate is to determine whether or not it allows signs to be combined in such a way that nothing is said by them, although that nothing is said by them cannot be seen in them. That is, there is nothing in the way the signs are constructed that shows that they cannot be combined in a particular way. In such an inadequate symbolism, there is a failure on the part of the symbolism to be adequate to the logic of our language, to, you might say, logical syntax. The failure is revealed by the need, on the part of the symbolism, to be supplemented by rules for the combination of its signs: the failure is revealed by the need to say what is not being shown. (What is not being shown, and is being said, is that such signs may not be combined.) An adequate symbolism does not fail to show its own logical syntax. An adequate symbolism needs no formation rules to prevent possible but impermissible combinations of its signs. In an adequate symbolism, permissible and possible combinations of signs coincide. Another way of determining whether a symbolism is adequate is to determine whether or not the symbolism allows signs to be combined ambiguously. Whenever signs are combined ambiguously, the symbolism fails to show what cannot be said. An ambiguous symbolism is inadequate to the sense of the propositions whose sense it is to show, which is another way of saying that the notation is inadequate to the logic of our language, to logical syntax. Consider again 3.325: In order to avoid [the fundamental confusions of which the whole of philosophy is full], we must employ a symbolism which excludes them, by not applying the same sign in different symbols and by not applying signs in the same way which signify in different ways. A symbolism, that is to say, which obeys the rules of logical grammar—of logical syntax.

Putting this in the terms I am using, Wittgenstein is saying the following: To avoid the fundamental confusions of which philosophy is full, we must employ a symbolism which excludes them, by not using the same sign in different logical syntactic applications and by not superficially applying signs in the same way which do not have the same logical syntactic applications. A symbolism, that is to say, which obeys the rules of logical syntax—a symbolism which displays the logic of our language.

An adequate symbolism is adequate to the sense of the proposition being symbolized. That is, an adequate symbolism shows all that the proposition cannot say. A symbolism that shows all that a proposition cannot say shows exactly what the inferential powers of the proposition are; it makes the proposition’s sense visibly clear. Adequacy here is not a measure of the relationship between the symbolism and reality. Rather, adequacy is a measure of the relationship between the symbolism and the proposition’s sense: an adequate symbolism articulates the proposition. Putting things this way risks misunderstanding, however. Putting things this way makes it sound as if there is, after all, something external to an adequate symbolism to which it is adequate: namely, a proposition’s sense. But, if what an adequate

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symbolism does is to show all that the proposition cannot say, and so if what it does is make the sense visibly clear, then it is wrong to think of the proposition’s sense as external to an adequate symbolism. After all, an adequate symbolism just shows the sense, so it is best to think of the symbolism as internal to that sense. Of course, that we can so think of it reveals that the “adequate” in “adequate symbolism” is not the measure of a relationship between the symbolism and anything external to the symbolism. Rather, the relationship being measured is best understood as the relationship between the symbolism and the logic of our language, between the symbolism and logical syntax. An Example Wittgenstein provides a good example of an inadequate symbolism at 4.0411: If we tried, for example, to express what is expressed by “(x).fx” by putting an index before fx, like: “Gen.fx”, it would not do, we should not know what was generalized. If we tried to show it by an index g, like: “f(xg)” it would not do—we should not know the scope of the generalization. If we were to try it by introducing a mark in the argument places, like “(G, G).F(G,G)”,

it would not do—we could not determine the identity of the variables, etc. Wittgenstein’s point is that the first way of symbolizing generality would be ambiguous between “(x)fx” and “(f)fx”: we would not know what was being generalized. If we try to remedy this by using an index—a subscript—we would still be troubled since we would not be able to distinguish between generalized disjuncts and a generalized disjunction. If we try another remedy, this time introducing the generality symbol into the argument place, we would not be able to identify the variables; in particular, we would be unable to decide whether “(G,G)ϕ(G,G) v ψ(G, G)” should be read as “(x, y) ϕ(x, y) v ~ϕ(x, y)” or as “(x, y) ϕ(x, y) v ~ϕ(y, x)”.18 In his Notebooks, in a parallel passage, Wittgenstein notes that the proposed symbolizations all “lack the power to portray the requisite sense.”19 Again, what we see is that the symbolization is adequate, if it is, to the sense of the propositions. Logic needs no help; it takes care of itself. Understanding what an adequate notation is helps us to see that. Black’s notion that logic must appeal to metaphysics is wrong-headed. There is no need to have a view, not even a schematic one, about the true nature of the connection between thought and reality in order to judge whether a symbolism is adequate or not. There is nothing external to an adequate symbolism that it adequates or fails to adequate itself to. The ways in which a symbolism can fail to be adequate show that an appeal to ontology is superfluous:

18 I am leaning on Anscombe’s commentary on the passage. See An Introduction to Wittgenstein’s Tractatus, pp. 139–141. For a more detailed consideration of the passage (as well as for a useful discussion of contextualism and holism in the Tractatus) see Michael Kremer’s “The Multiplicity of General Propositions,” Nous 26: 4, 1992, pp. 409–26 (as well as his paper mentioned above). 19 Wittgenstein, Notebooks, 1914–1916, p.18.

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The Concept “Horse” Paradox and Wittgensteinian Conceptual Investigations What can be shown cannot be said. Now we understand our feeling that we are in possession of the right logical conception, if only all is right in our symbolism. (4.1212–4.1213)

I need now to make explicit something I have so far left implicit. I have turned Wittgenstein’s “Logic must take care of itself” in two different ways. I have turned it against the idea that there are possible but impermissible sentences, possible but impermissible combinations of subsentential units. And I have turned it against the idea that logic must appeal to either psychology or to metaphysics. I take these two ways of turning “Logic must take care of itself” to be internally related. If someone thinks that there are possible but impermissible sentences, then appealing to either psychology or to metaphysics to rule them impermissible is going to be almost irresistible. If someone thinks that logic cannot take care of itself, that it needs psychology or metaphysics as its caretaker, then psychologizing or metaphysicalizing logic is going to be almost irresistible: we will think of logic as reflecting how thinkers think or as reflecting what there, ultimately, is. To so think of logic will create, first, a need for formation rules (it will be possible for logic to step beyond what is psychologically or metaphysically permissible) and, second, the requirement that the formation rules embody psychological laws or metaphysical first principles. Any authority logic has will be lent to it by psychology or by metaphysics. Think of Max Black. Wittgenstein’s Tractarian conception of logic shows the way to depsychologize logic without metaphysics (without invoking, say, a Third Realm, a realm of thoughts) and it shows the way to demetaphysicalize logic without psychology (without invoking, say, an Intentional Realm, a realm of sui generis psychological acts and objects). Wittgenstein, we might say, shows us how to be logicists about logic. The Elements of Logical Space, Part Three: Making Sense So how does Wittgenstein see the elements of logical space? He does not see them as subsentential. As Russell thought of the elements, the elements are subsentential. For Wittgenstein, the elements of logical space are, first and foremost, sentences— and sentences are unities. Wittgenstein arrives at the parts of sentences by segmenting sentences. He does not arrive at propositions by combining subsentential parts. As I have noted, Wittgenstein keeps to the unity of the proposition.20 To bring out the difference between Russell and Wittgenstein more starkly, let me indulge in the following two versions of a Just So Story: How a Person Makes Sense of a Sentence. For Russell, a person makes sense of a sentence by recognizing, and securing in thought, the independently thinkable subsentential elements of logical space, by noticing how the elements are combined, and by following rules for using the individual elements and their combination. If the person can do all this, then the 20 By treating propositions as primary, as the first and foremost elements of logical space, Wittgenstein completely avoids the problem of the unity of the proposition, a problem Russell struggles with repeatedly and unsuccessfully.

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person will have made sense of the sentence. So, to take an example, a person who makes sense of the sentence “Jesus wept” recognizes, and secures in thought, the subsentential proper name, “Jesus”, and he will do the same with the subsentential concept-expression, “wept”. He will then notice that the elements have been combined in such a way that the proper name comes before the concept-expression. He will then follow the rules for using the individual elements that tell him that the proper name “Jesus” properly names Jesus and that the concept-expression “wept” stands for wept. Finally, he will follow the rules for using the combination that tell him that those elements in that combination are used to express the thought that Jesus wept. All of these things can be initiated unconditionally, initiated on any sentence encountered. It will also be possible, on Russell’s version of the story, for a person to recognize the elements, secure them in thought, notice how they are combined and then to realize that those elements ought not to be combined in that way. So combined, there is no thought that they can be used to express—even though the elements of the non-thought have been recognized and secured in thought. The person can do this because what the person can do can be done unconditionally, to any sentence encountered. For Russell, making sense of a sentence is a process that can culminate, not just in the person knowing what thought the sentence expresses, but also in knowing that there is no thought the sentence could express. Such a process allows fixing the meaning of expressions to be done independently of making sense of the whole sentence. Oddly, this possibility means that the process of making sense can reveal that sense cannot be made. This possibility means that, on Russell’s version of the story, logic will not take care of itself: we can, or others can, make mistakes in logic. We do so, or they do, by combining elements that ought not to be so combined. On Russell’s version of the story, we can give a sign the wrong sense—just what Wittgenstein denies that we can do at 5.4732. So how, for Wittgenstein, does a person make sense of a sentence?21 Well, the person does it by seeing the symbols in the signs. And how does a person do that? The person does it by making the sentence make sense. If the person can do this, the person can segment a sentence into elements-in-logical-syntactic-application and the person can fix the meanings of names, concept-expressions and relationexpressions. Now, it is crucial to note that, on Wittgenstein’s version of the story, none of the things the person can do are things the person can do unconditionally to sentences—as are the things the person can do on Russell’s version. Instead, the things the person can do are things that he can only do conditionally to sentences. Let us use “Jesus wept” again. A person may take the sentence to segment into a proper name and a concept-expression—but the person may do so only if the thought he takes to be expressed by the sentence is that the person “Jesus” properly names, whoever it might be, falls under whatever concept the concept-expression stands 21 Wittgenstein is not claiming that words in a proposition no more have a meaning than do the letters in a word. To claim that would be to lose sight of the difference between a proposition and a word. I can understand a proposition I have never encountered before, but not a word—this is essential to what a proposition is. Cf. 4.027.

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for. If the person knows that the name “Jesus” properly names Jesus, then he may take the sentence to be the name “Jesus,” properly naming Jesus, standing left of the concept-expression—but only if the thought he takes to be expressed by the sentence is that Jesus falls under whatever concept “( ) wept” stands for. Now, if the person knows what concept the concept-expression stands for, then the person can take the sentence to be the name “Jesus”, properly naming Jesus, standing to the left of the concept-expression for the concept, ( )wept—but only if he takes the whole sentence to express the thought that Jesus wept. So the sentence “Jesus wept” just is that proper name standing to the left of that concept-expression—it is that particular combination of those particular elements—only if the sentence expresses the thought that Jesus wept. This shows that fixing the meaning of expressions in a particular sentence is not something that can be done independently of making sense of the whole sentence.22 A proposition combines expressions, but it only combines expressions that can be combined in that way. It is not an accident that the expressions may be combined (in that way). It is not the case that uncombined expressions come first and that it then turns out, somehow, that they combine (or not). For Wittgenstein, what is given are expressions combined in a certain way. Given propositions, we are given possible combinations of expressions; given expressions, we are given the possible segmentation of propositions. If segmentation is the segmentation of expressions, then expressions are not only the contents of propositions, they are also the segments of propositions: as Wittgenstein puts this point in the Tractatus, more or less, expressions are both “form and content” (2.025) For Wittgenstein, we can recognize the meaning of a word in a proposition. We cannot recognize the meaning of a word outside the proposition. For Russell, we can recognize the meaning of a word outside the proposition. In fact, for Russell, the meanings of words are so readily recognizable that it is possible to track samenessof-meaning from a verb in one proposition to the verbal noun in another proposition. Here’s Russell, from The Principles of Mathematics: “The question is: What logical difference is expressed by the difference of grammatical form? And it is plain that the difference must be one in external relations.”23 And it is plain that this accounts for Russell’s inability properly to understand Frege’s concept/object distinction, since that distinction itself can only be drawn in a proposition. Put another way, the difference between concept and object is not one in external relations. On Wittgenstein’s way of thinking about the elements of logical space, mistakes in logic are impossible. No sentence will be an improper combination of expressions, since, if a group of words is a sentence, then it will be the combination of expressions that may be combined that way. “Any possible proposition is well-formed.”

22 This section is largely a pasticcio of a section (pp. 109–111) of Cora Diamond’s “What Nonsense Might Be” in her Realism and the Realistic Spirit (Cambridge, Mass.: MIT Press, 1991). 23 Russell, B. The Principles of Mathematics (New York: W.W. Norton and Company, Inc., 1938), p. 48.

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On this way of thinking about the elements of logical space, there is no need for a Theory of Types. There is simply no problem for the theory to solve or to prevent. There are no possible but impermissible combinations of expressions to quarantine. So is the vanishment of Russell’s Paradox prestidigital? No. No prestidigitation is necessary to make the non-existent vanish. Wittgenstein’s Negative Alternative? It is impossible to avoid mentioning a thing by mentioning that we won’t mention it. One might as well, in talking to a man with a long nose, say: “When I speak of noses, I except such as are inordinately long”, which would not be a very successful effort to avoid a painful topic. Bertrand Russell

But I think I hear an odd objection: “Ok wait. Wittgenstein hasn’t really made the paradox vanish. He hasn’t really rejected the theory of types. What he’s done—as you’ve made clear—is move the type-bump in the logical rug around. He’s not rejected the Theory of Types, all he’s done is move the theory from the realm of the sayable to the realm of the unsayable—that is, to the realm of the showable.” Properly responding to this objection requires thinking through what Wittgenstein means by “show” in the Tractatus. Traditionally, Wittgenstein has been understood in the following way: there are things that can be said, and they are said by intelligible sentences; and there are things that cannot be said, and they are shown by (a particular species of) unintelligible, nonsensical sentences. This diagram roughly captures the traditional view:24

What can be said

What cannot be said

…

Intelligible sentences

Unintelligible sentences that show these things

Plain unintelligible sentences

The objector, then, is saying something like this. “Look, the Theory of Types is there alright, in the Tractatus, but it’s stealthily, silently, show-ily there. Russell’s formation rules are all things that are shown by (a particular species) of nonsensical sentences.” The idea is that talk of types is unintelligible but nonetheless that it shows us things that are unsayably so: Russell’s formation rules are misfiring attempts to codify what we see to be unsayably so. To use D.S. Schwayder’s term, showing is Wittgenstein’s negative alternative to the Theory of Types.25, 26

24 I owe the essentials of this diagram to Cora Diamond. See her paper “Ethics, Imagination and the Method of Wittgenstein’s Tractatus” in Crary and Read (eds), The New Wittgenstein (London and New York: Routledge, 2000), p. 150. 25 Schwayder, D., “Gegenstande and Other Matters”, Inquiry 7: 4, 1964, p. 398. 26 Understanding showing in this way is and has been popular. Irving Copi, in his The

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To see why this is a mistake, let’s approach the saying/showing distinction from an angle that is slightly different. Wittgenstein draws the distinction between showing and saying within an intelligible proposition. “The proposition shows its sense. The proposition shows how things stand, if it is true. And it says, that they do so stand.” (4.022) Now, why does Wittgenstein draw this distinction, and draw it this way, and draw it here? He does so because he recognizes that it is essential to propositions that we can understand propositions we have never encountered before (4.027). This is one crucial difference between propositions and words. There is no meaning of the sentence that I must learn in order to understand a new sentence as there is a meaning of a word that I must learn in order to understand a new word. Wittgenstein makes this point in the 1914 notes: “It is obvious that, e.g., with a subject-predicate proposition, if it has any sense at all, you see the form, so soon as you understand the proposition, in spite of not knowing whether it is true or false.” So, the distinction between what a proposition shows and what it says is a way of registering something essential to propositions. An intelligible proposition says all that it has to say. It is not that the proposition’s contentful cup runneth over—that it has so much to say that some of it ends up having to be shown, spilling over into ineffability. Now, this sense of “show”, the sense that contrasts with “say” and which is drawn only within an intelligible proposition, I call the aseptic sense of “show”. Aseptic showing is inextricably bound up with an adequate symbolism. When a proposition shows its sense, when I understand it, I see its form: I see the symbols in its signs. It’s true that what I see can only be shown, not said. But that only seems strange if what can only be shown is taken to be, somehow, propositional. That is, if what we can only be shown is taken to be something that registers some feature of reality, something that registers that certain entities have certain properties or lack certain properties. Thinking of showing as the negative alternative to the theory of types makes thinking of what is shown as, somehow, propositional, well nigh compulsory. After all, if the misfiring talk of types is absorbed into an adequate symbolism, then, since the talk is propositional (even if unintelligible), what the symbolism shows must be propositional. Talk of types is an attempt to register features of reality, to record that some entities have certain properties or lack others. Anything that replaces such a theory must, somehow, record the same. But what is shown is not, somehow, propositional. It is best to think of what is shown not as something of which we can, ineffably, have knowledge-that. What is shown is best thought of as something of which we can have knowledge-how. That I see what is shown is not a matter of my closed-mouthedly possessing a piece of knowledge-that. That I see what is shown is a matter of my knowing-how to do something with a proposition, namely how to make it make sense, how to see symbols in its signs. I know how to understand it, and do. Now, I think of knowledgehow as ineffable, but unmystically so. Michael Kremer, who thinks of this matter much as I do, writes that: Theory of Logical Types (London; Routledge and Keegan Paul, 1971), p. 75, comments that the doctrine of showing “illustrate[s] the way a logical doctrine can be realized by a language without having to be stated explicitly.” And this, he continues, “ is at the heart of Wittgenstein’s response [to the Theory of Types] … We need not state these provisions at all: it suffices to build them into the very structure of language.”

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We should not read talk of “showing”, and correlatively of “perceiving”, “seeing”, “recognizing”, that which is shown, on the model of a relation between a subject and some ineffable, fact-like entity … This form of the idea of showing is exactly what the Tractatus wants to teach us to abandon. Rather, we should read talk of “showing”, and correlatively of “seeing”, on the model of the demonstration of a technique, and the uptake required to understand the demonstration. In essence, my suggestion is that one who “sees” that which is shown, is simply one who “knows how to go on.”27

The Tractatus aims to bring us back into full, workshop possession of this knowledgehow, to allow us to rest easy in it. It aims to bring us back into agreement with ourselves—by allowing us to bring our symbolism back into agreement with the sense of our propositions, by allowing us to overcome our misunderstandings of the logic of our language. Think here of the plight Wittgenstein describes in Philosophical Investigations: When … we disapprove of the expressions of ordinary language (which are after all performing their office), we have got a picture in our heads which conflicts with the picture of our ordinary way of speaking. Whereas we are tempted to say that our way of speaking does not describe the facts as they really are … As if the form of expression were saying something false even when the proposition faute de mieux asserted something true. 402

This plight resembles the plight the Tractatus aims to help us escape. We get a picture into our heads which conflicts with ordinary language: it is not so much, in the Tractatus, that we are tempted to say that our way of speaking does not describe the facts as they really are; rather, we are tempted to say that our way of speaking requires certain “facts” to be in place in order for our way of speaking to describe the facts. We then think of these “facts” as what is shown by the misfiring talk of types. These “facts” are metaphysical, and they undergird the making of sense, the describing of the facts. We start to think that the forms of propositions, that what is shown by our misfiring talk of types, must assert something “true”––in order for the proposition faute de mieux to make sense, to describe (rightly or wrongly) any fact, at all. Thinking this way is thinking of showing as a negative alternative to the theory of types. What we are shown are the “facts”, what is “true”; what we are shown makes describing the facts, saying what is true, possible. The misfiring talk of types shows us the “facts”. But the most crucial thing to keep in mind when resisting the claim that showing is the negative alternative to the theory of types is that, for Wittgenstein, unintelligible “sentences” show nothing (in the aseptic sense). Remember that Wittgenstein thinks of an unintelligible “proposition” as such that no symbols can be seen in its signs—an unintelligible “proposition” is gabble, a mere farrago of words, mere signs. Since such is not really a proposition, there is no asking for the meanings of the words in the farrago of words. In the farrago, the words mean nothing.28 A farrago of words cannot be understood; it does not show its 27 Kremer, M. “Mathematics and Meaning in the Tractratus”, Philosophical Investigations 25: 3 2002, p. 297. 28 That is, the person who produces the farrago means nothing by the words. We can, of course, look up the meanings of the words in the dictionary, but we’ll have no reason for preferring any of the words’ meanings to any other.

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sense since it has no sense. When I encounter a farrago of words, nonsense, I cannot see the symbols in the signs and then see that they do not belong together: no, I see no symbols at all; nothing shows. So showing has no role to play in the activity of ruling certain combinations of words ill-formed, the very activity in which the Theory of Types is called upon to play a role. There is no place for such activity as Wittgenstein sees things, no place for a Theory of Types. Wittgenstein does not say: Nonsense shows its sense and shows what must be the case, if it is nonsense; but, nonsense cannot say that things so stand.

So showing is not an alternative, not even a negative one, to the Theory of Types. Wittgenstein does away with the Theory of Types. Showing does not take the place vacated by the Theory of Types, it rather makes clear that there was no need for the Theory of Types to have been in place: there was never a place for a Theory of Types. As Wittgenstein says in his 1914 Notes “… [A] theory of types is impossible.”29 Only where there are possible but impermissible combinations of expressions is a Theory of Types possible. A Final Thought One final thought: Philosophical Investigations 50, one of the most infamous passages in the later work, is a good example of Wittgenstein recycling the kind of point he makes in 3.333. In Philosophical Investigations 50, Wittgenstein claims that there is one thing of which we can say neither that it is or is not a meter long—the standard meter stick in Paris. I think we can represent Wittgenstein’s reasoning here best against the backdrop of 3.333: To say of the standard meter stick that it is a meter long or not a meter long is to try incoherently to treat a function as if it could take itself as an object. Here’s what I have in mind. One of the deep contrasts between the Tractatus and Philosophical Investigations is that in the later work Wittgenstein recognizes both (1) that anything that has to exist in order for a proposition to make sense is “an instrument of the language” and (2) that all sorts of odds and ends, bits of the world, like sticks, could thus end up as instruments of the language. The sense we can make is, we might say, contingent on what we are and, even more surprisingly, on what we find lying about: it is contingent on very general facts of nature (Philosophical Investigations II xii). As I understand Wittgenstein, if we take something up and use it as a standard, it becomes an instrument of the language, of logic; and so, the standard meter stick is, qua standard, an instrument of the language, of logic. Now let’s take the Philosophical Investigations notion and transpose it, to the degree that we can without confusing distortion, into the tonality of the Tractatus. We might say that the logical role of the standard meter stick, the way it is used as a standard, is as a function-fixative. That is, the standard meter stick is used in such a way as to fix the meaning of something with a blank spot, something unsaturated. In that role, we can think of the standard 29 Wittgenstein, Notebooks, 1914–1916, p. 108.

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meter stick as inheriting the blank spot, the unsaturatedness of the function whose meaning it fixes; the standard meter stick is itself, again, an instrument of logic. True, if we stare transfixedly at the “stick” itself, outside the context of significant use, we see no blank spot: but that is just to stare, so to speak, at the sign, not the symbol. When we consider the standard meter stick, when we consider it in its context of significant use, it is revealed as fixing the meaning of a function, and so as inheriting—as an instrument of logic—the symbolic features of a function. Any attempt metrically to measure the standard meter stick, to measure, so to speak, the symbol, requires using the “stick” in two different ways at once—both as a function-fixative and as an argument. But in two such different uses, all that is common is the sign, the “stick”: but that by itself signifies nothing. When I put the “stick” itself into the blank spot of “( ) is a meter,” the “stick” is no longer being used as the standard meter stick; for it is now just a “stick”, something to be measured, not a measure. The outer and inner “sticks” have different meanings, since they have different forms. When we confuse the two “sticks”, we are being taken in by signs, and are not seeing the symbols in them. When we see the point of Philosophical Investigations 50 in the light of 3.333, we realize that Kripke, in his famous reply to the passage in his Naming and Necessity, fails to see the sort of point that Wittgenstein is making. I’m not arguing that Wittgenstein’s remarks about the standard meter stick are right, although I am deeply sympathetic to them; I’m arguing that they are best interpreted against the backdrop of 3.333.

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Chapter Four

Beating a Dead Concept “Horse” The matter cannot, I think, be explained in the sense of being given a foundation; it comes out in all our discourse, and a good understanding of it can be conveyed only dialectically, by removing errors and confusions, and for the rest talking around the matter in the hope that people will catch on. Peter Geach

Introduction I want to begin this chapter by regrouping. Kerry criticized Frege’s distinction between concepts and objects. Frege held that the distinction was absolute— concepts cannot play the role of objects; objects cannot play the role of concepts. Kerry tried to show that Frege was mistaken by putting a concept into the role of an object. Frege elucidated the distinction between concepts and objects by calling concepts unsaturated and objects saturated. He symbolized the distinction by writing concept-expressions with blank spots and object-expressions without them. So Frege segmented the proposition “Silver is a horse” into (symbolically) “( ) is a horse” (as the concept-expression) and “Silver” (as the object-expression). In the proposition, the saturated “Silver” saturates the unsaturated “( ) is a horse.” Kerry thought that he could show Frege’s mistake by means of the proposition “The concept ‘horse’ is a concept easily attained.” As Kerry understood himself, he had, by means of that proposition, put a concept—“the concept ‘horse’’’—into the object-expression position, the blank spot, in “( ) is a concept easily acquired.” Thus Kerry took himself to have counterexampled Frege; Kerry took himself to have shown that concepts can play the role of objects; Kerry took himself to have shown the distinction relative, instead of absolute. I think that Kerry was confused about what he took himself to have done. I do not think that Kerry was wrong, exactly; I think he was confused. There is no coherent description of what Kerry took himself to be doing; he was doing nothing at all— although it certainly seemed to him that he was doing something of great logical moment. Like the befuddled weaver in Wittgenstein’s Philosophical Investigations, Kerry was sitting at an empty loom, he was going through the motions of weaving, and he was thinking that he was weaving. But he was not weaving. I want to assess two particular post-Kerry respondents to Frege—two postKerry respondents to the Concept “Horse” Paradox (since I will be talking about the Paradox continually, I will abbreviate to: “CHP”). The particular respondents I want to assess are J.J. Valberg and Wilfrid Sellars. I’ll also have something more to say of Kerry before I finish; but he will not be one of my foci. I divide this chapter into two parts, Part One, titled “Valbergian Impropriety” and Part Two, titled “Nagging Sellars”. In Part One, Section One, I concentrate on

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Valberg’s response to the CHP and present it briefly. As the section title, I have used Frege’s paradoxical remark “The concept ‘horse’ is not a concept.” After showing how Valberg proposes to respond to the CHP, I turn to his response to a related paradox in a paper of G.E.M. Anscombe’s. In her paper, Anscombe is led to a paradoxical remark of her own, namely “The direct object is not a direct object.” That remark is the section title of Section Two. In it, I not only describe Valberg’s response to Anscombe’s paradox—call it the Direct Object Paradox (“DOP”), I also look closely at her understanding of the curious perplexity that led her into paradoxy. Finally, by using some notions both from Frege and from Wittgenstein, I show that Anscombe’s understanding of the curious perplexity she faces, and her response to it, is philosophically more satisfying than Valberg’s response to it, or his similar response to the CHP. In Part Two, Section One—“Sellars Contra Geach”—I enter a discussion between P.T. Geach and Sellars in medias res. Sellars responds to Geach in a way that sets up his (Sellars’s) response to Frege. Sellars’s response to Geach takes him (Sellars) across territory covered by Valberg, but in a different direction. In Section Two–– “Sellarsian Incompleteness”—I grade Sellars’s response to Frege, and show how and why it fails. Finally, I assess post-Kerry responses to the CHP more generally, and I reckon the features that such responses tend to have. I return in that section to Kerry. Also, I explain why I rate the CHP no real paradox. The final Section is titled “A Final Look at the CHP?” Let me say a little more about my verdict on the CHP. The CHP teaches a hard lesson, of that there’s little doubt. But the CHP teaches a different hard lesson—a radically different hard lesson—than the one it is commonly understood as teaching. It is commonly understood to teach a hard lesson about the metaphysical foundations of logic, or of language, or (perhaps best) of the logic of our language. But I understand the CHP to teach a hard lesson about its own nature as a paradox, and about our nature as creatures of paradoxy. The CHP engages with an ineradicable tendency of ours: a tendency to understand all genuine distinctions as, somehow and (in some acceptation of “ultimate”) ultimately, distinguishing between objects of which we can (must) take cognitive—perceptual or conceptual—grasp. But the tendency goes further. It also understands all genuine distinctions to be such that, again, somehow and ultimately, what is distinguished must be distinguished in terms that make their relations to one another articulable. For so long as this tendency holds sway in our thinking, the CHP will seem a genuine paradox: it will seem to teach a lesson about the metaphysical foundations of the logic of our language by seeming to teach a lesson forbidden to it by its own rules of pedagogy. But I think the CHP teaches us a lesson in self-control, and so a lesson in selfknowledge. I’m tempted to say, borrowing notions from Kant, that the hard lesson the CHP teaches is a lesson in discipline—say, in the discipline of pure reason.1 That discipline is hard because, first, discipline is hard; it goes against a tendency. It is hard, second, because reason itself seems to be properly the discipliner, not the disciplined. And it is hard, third, because, given the first and second hardnesses, we 1 Kant, I. Critique of Pure Reason, trans. Kemp Smith, N. (London: MacMillan, 1961), A709/B737–A710/B738.

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hardly know what to make of things said to us solely to prevent errors of reason or train reason to constraint. Kant called things said solely for these purposes “negative instruction”; and he thought that negative instruction could be distinguished from positive instruction by a consideration of the mere content of the instruction given. I’ll argue, instead, that negative instruction—which I will call alternately throughout the chapter “expressions of grammatical understanding”, “hints”, “elucidations” or “ladderlanguage”—is to be distinguished from positive instruction by a difference in the way certain language is used. The respondents to the CHP that I am going to discuss, Valberg, Sellars and, along the way, Kerry, all want to find positive instruction in the CHP, they want to find in it expansions of our knowledge—even if paradoxical expansions. I use Kant here because I want to filiate what I am about to do with what he has done, but also because I think his notions are particularly useful for first forming the points I want to make. I will leave the notions behind now, but I want them to linger in mind during what I am about to do, since their lingering should help what I do appear in its proper aspect. This chapter builds on Chapter Two and Chapter Three. I employ several different vocabularies in which responses to the CHP can be rehearsed, some of which are introduced in those earlier chapters, some not. I employ Frege’s, early Wittgenstein’s, late Wittgenstein’s, Valberg’s, Anscombe’s, Sellars’s and my own terminology. I mostly make do first with Valberg’s and Anscombe’s, and second with Sellars’s, but I do sometimes use Frege’s or Wittgenstein’s or mine. I hope the vocabulary shifts won’t be confusing. I take it that describing the rebarbative vocabularies that have grown up thorny around the CHP is of value; it helps to acclimate thinking to the strangeness of the CHP. The shifts in vocabulary also help to preview points made in the final section of the chapter. Valbergian Impropriety The Concept “Horse” is not a Concept J.J. Valberg’s fascinating paper, “Improper Singular Terms”2, begins and ends with Frege’s CHP. Valberg’s primary aim in the paper is to widen a narrow-mindedness that is expressed in a standard objection to Frege’s handling of the CHP: [Frege’s paradox] touches not just his object-concept distinction but the very notion that objects (individuals, entities) can be distinguished from something else. We are to suppose individuals on the one hand and something different, something absolutely different, namely concepts, on the other. That there should be an identity between a concept and an individual is out of the question … So how can one assert that there are things from

2 Valberg, J.J., “Improper Singular Terms”, Proceedings of the Aristotelian Society vol. LXXI, 1970–71, pp. 121–45.

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The Concept “Horse” Paradox and Wittgensteinian Conceptual Investigations which individuals must be distinguished? We have just this truism to take account of, that everything which is is an individual, and beyond this nothing much can be said.3

Although I know that it will not yet be clear, I want to post Valberg’s way of handling the CHP here, for reference’s sake. Valberg offers a way of understanding Kerry’s “The concept ‘horse’ is a concept easily attained”, a way of rewriting it that reveals its logical form: “The concept: horse is easily attained.” Valberg believes that this new sentence allows us to solve Frege’s paradox and so frees us from the catacombs of the CHP. So how are we to understand Valberg’s sentence? Valberg is trying to secure a way to talk about concepts. He wants to find a way to talk about something other than objects, individuals. He finds a way to do so—or thinks he does—by imitating certain moves of Anscombe’s in her “The Intentionality of Sensation”4. I’ll come back to Valberg’s imitation of Anscombe; for now, though, I will concentrate on the way that Valberg arrays his argument. Valberg begins by distinguishing between singular and general terms. Singular terms are terms that definitely designate something (whether real or non-existent). General terms are terms that describe something (whether truly or falsely). We typically think of singular terms as the subjects of sentences; we typically think of general terms as the predicates of sentences. The problem of talking about individuals doesn’t arise, for Valberg, where singular terms are concerned. When we use a singular term we are designating an individual, typically the subject of our sentence. But what about when we use a general term, when we describe the subject of our sentence, when we predicate? Are we talking about individuals then? Valberg distinguishes two types of predicates; he dubs them “predicate1” and “predicate2”. The first is what the subject of a sentence is said to have by that sentence. Take the sentence: (1) Socrates is bald.5

If we ask of (1) what it says Socrates to have, the answer will be—baldness. So, the predicate1 of (1) is baldness. Valberg accordingly treats predicates1 as abstract individuals. This allows Valberg to treat the predicate1 of (1) as no problem: When we use a general term to predicate1, we are after all designating an individual—an abstract one. On this way of understanding predication, predication does not require that there be things absolutely distinct from individuals, concepts, which play an important role in our sentences. No, on this way of understanding predication, concepts turn out just to be individuals. But this way is not the way of understanding predication that Valberg wants to explore, in important part because it concedes to the narrow-mindedness he objected to when characterizing the CHP. Anyway, Valberg puts this way of understanding predication to one side and proceeds at length to explore the second way. 3 Valberg, “Improper Singular Terms”, p. 121. 4 Anscombe, G.E.M., “The Intentionality of Sensation”, Metaphysics and the Philosophy of Mind, Collected Papers, vol. II, (Oxford: Basil Blackwell, 1981), pp. 1–21. 5 The numbering of propositions in this section is mine, not Valberg’s.

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The second type of predicate is what the subject of a sentence is said to be by that sentence. If we ask of (1) what it says Socrates to be, the answer will be—bald. So, the predicate2 of (1) is bald. But we’ve run into a problem here that we avoided on the first, narrow-minded way of understanding predication. The problem becomes clear if we concentrate on the sentence: (2) The predicate2 of (1) is bald.

But the predicate2 of (1) is not—bald. As Valberg puts it, the predicate2 of (1) “is not to be compared with the head of a man.” The problem becomes even clearer if we compare the predicate1 of (1) with its predicate2. (1), on a first reading, says of Socrates that he has baldness; but on a second reading, (1) does not say of Socrates that he is baldness. Valberg: What is the predicate2 of (1)?, i.e., What is Socrates said by (1) to be? How should we answer? We must answer, it seems, just by using the expression “bald”. What Socrates is said by (1) to be is, simply: bald. But in thus answering we do not designate any individual. For what would that individual be? It would not be the expression “bald” itself. We use, not mention, this expression in answering; Socrates is not said by (1) to be an expression. Nor is it the attribute [the predicate1] of being bald. That would require our using something like “baldness” or “being bald”, which, as remarked, would be entirely out of place. I find it natural to say there is no individual thereby designated, no individual which is what Socrates is said by (1) to be, i.e., no individual which is the predicate2 of (1). Yet there is a sense in which this predicate is something. And if asked, What?, we answer again by using “bald”; for by thus answering we say what Socrates is said by (1) to be.6

Valberg notes that (2)—which manifests the problem he is discussing—is “distinctly odd”. He claims that (2) is subject to what he calls a “change of aspect”: “looked at one way it makes sense; but from another angle it turns into nonsense.”7 Valberg hard-focuses on the use of “bald” in (2). When “bald” is used one way, (2) seems silly—to recur to Valberg’s comment, predicate2 cannot be compared to a man’s head. But when it is used another way, (2) seems fine, seems true, in fact. Valberg tries to describe this use, or at least to shed light on it, by likening the use of “bald” in answer to a question like, “What is the predicate2 of (1)?”, to answering a question like, “Who killed Cock Robin?”, not by using an expression which designates the culprit, but instead by “just bringing him forth.” Valberg admits that you can’t take the predicate2 of a sentence “by the scruff of the neck”, of course.8 But then he checks himself: “Or perhaps we should say that to do so you must proceed in the manner described—by just using certain expressions. That is the only way to approach them.” He continues by noting that: The absolutely trivial fact is that we get to the predicate2 of a sentence only through some bit of language, and only through one expression can we reach the meaning of another. We can say that the meaning or predicate2 is presented by an expression, and that, in a 6 7 8

Valberg, “Improper Singular Terms”, pp. 128–9. Valberg, “Improper Singular Terms”, p. 129. Valberg, “Improper Singular Terms”, p. 131.

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The Concept “Horse” Paradox and Wittgensteinian Conceptual Investigations sentence to this effect, such an expression is a presenting term. Finally, we may speak of the “is” preceding this expression as that of presentation, distinguishing it both from the “is” of predication and identity.9

After noting this “absolutely trivial fact”, and after introducing presenting terms, Valberg points out that when we read a sentence like (2) in the way he is trying to describe, when we use “bald” as a presenting term––and “is”, it turns out, as the “is” of presentation—we naturally pause before the presenting term, “bald”. To mark this pause, Valberg introduces a punctuation mark, the colon. The colon indicates that the term following it neither is (properly) singular nor is general. In order to differentiate this use of the colon from others, Valberg italicizes the presenting term that follows the colon. So (2), when it makes sense, is to be re-written as: (2’) The predicate2 of (1) is: bald.

Valberg thinks that (2’) reveals the logical form of (2), when “bald” in (2) is used in the way that makes sense. Presenting terms are then to be added to the stock of terms, singular and general. Singular terms divide into those which definitely designate an individual and those which definitely designate what is non-individual. Valberg calls the first a “proper singular term” and the second an “improper singular term.” The the-phrase in (2) is an improper singular term. It differs from other the-phrases not by failing definitely to designate but rather in what is definitely designated. Valberg draws his conclusion: Contrary to an ancient opinion, we can say what is not. We can also speak of what is not an individual. Everything, whether or not an individual, is a possible subject of discourse, though not every subject of discourse is an individual.10

Valberg then applies his conclusion to the CHP. As I noted, he rewrites Kerry’s sentence as: The concept: horse is easily attained.

What should we make of this sentence? Well, let’s look at it as Frege would have looked at it. Recall that, for Frege, we come by the parts of a thought by an analysis of a thought; we do not come by a thought by combining independently meaningful parts. Now, Frege would analyze the sentence into an object-expression, “the concept: horse”, and a concept-expression “( ) is easily attained.” The objectexpression would refer to a concept in the psychological sense. Given that reference, the sentence is not only meaningful, it is true. But of course, given that reference, the sentence does not say what Valberg claims it says. Valberg wants the sentence to segment as Frege thinks it does—except that he wants the singular term, the objectexpression, to definitely designate something non-individual. Frege would have 9 Valberg, “Improper Singular Terms”, p. 131. 10 Valberg, “Improper Singular Terms”, p. 135.

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understood such an expression to definitely designate an object, an individual. Keep this contrast in mind. The Direct Object is not a Direct Object Let’s go back to the sort of sentence Valberg called on initially to introduce improper singular terms. Consider (2’) again. (2’) The predicate2 of (1) is: bald.

Valberg claims that his inspiration for presenting terms is a passage from Anscombe’s “The Intentionality of Sensation”. In that passage, Anscombe is talking about the peculiarity of grammatical knowledge, of grammatical comments. What Anscombe appreciates, and what Valberg intends to appreciate, too, is that we cannot ply the use/mention distinction so as to make clear what grammatical knowledge consists of or so as to make clear the character of grammatical comments. Anscombe thinks that an expression of grammatical knowledge, a grammatical comment, involves a “special use” of a word or phrase. For example, when we ask “What does the sentence [‘John sent Mary a book’] say John sent?” we answer by using the phrase “a book”. But when we do so we are not naming a piece of language. That is, we are not mentioning the phrase “a book” when we answer the question—if we were, our answer would be clearly false. Anscombe’s answer to the question of what the sentence says that John gave Mary is captured in a Valbergian sentence: (A)

What the sentence says John gave Mary is: a book.

Here the final phrase is a presenting phrase. And Valberg explicitly thinks of his presenting terms as an Anscombian bequest. But he also thinks he has found a way to improve upon his inheritance. To make this clear, I need to explain what Anscombe is doing in more detail. Anscombe wants to make clear how we should think about the intentionality of sensations. Her work on that specific problem, luckily and unluckily, is not important for my immediate purpose. What is important is the way in which Anscombe preps to work on that problem. She does it by thinking about intentional objects generally. She notes that it is extremely tempting to treat as intentional objects bits of language; but it is also extremely tempting to treat as intentional objects what bits of language stand for. Anscombe notes that grammarians do talk of bits of language as the intentional, the “direct” or “indirect”, objects. She then writes that: However, the matter is not so easily settled. Of course I do not want to oppose the practice of grammarians. But it is clear that the concept of a direct object—and hence the identification of the sentence-part now called the direct object—is learned somewhat as follows: the teacher takes a sentence, say “John sent Mary a book” and says: “What did John send Mary?” Getting the answer “A book” he says: “That is the direct object.” Now the question does not really suppose, and the pupil, if he goes along with the teacher, does not take it, that any particular people, of whom the sentence is true, are in question, and so we may say that when the teaching is successful the question is understood as equivalent to

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“What does the sentence ‘John gave Mary a book’ say John sent Mary?” The grammatical concept of a direct object is acquired by one who can answer such questions.11

Anscombe’s worry is about a question that presses hard at this point: namely, the question of what is communicated by the phrase that is given as the correct answer. Is that phrase used or mentioned? Anscombe reformulates this question as “Is the direct object a bit of language or rather what the bit of language stands for?” Anscombe rates this question more than a mere question of terminology; she instead rates it a “substantive-seeming question of curious perplexity.”12 Anscombe details the toils of the curious perplexity. On one hand, it seems that it can’t be a book that is the direct object. For there is no answer to the dialecticallynext question: “Which book?” Since the sentence is not being considered as true (I should note that the sentence is also not being considered as false—rather, it is just being considered), there’s no answer to the question—unless it is “No book”. But that cannot be right as an answer, since the verb in the sentence has a direct object. So the phrase that is given in correct answer must be mentioned when it is so given. On the other hand, it seems that it can’t be a bit of language that is the direct object. The reason for this is that the answer to the question “What does the sentence say that John sent Mary?” cannot be “the bit of language ‘a book’”. After all, although John sent Mary something that presumably had words in it—he didn’t send her words. So the phrase that is given in correct answer must be used when it is so given. But at this point, where things certainly seem curiously perplexing enough, things get more curiously perplexing. Saying that what John is said to have sent is a bit of language is wrong. But if it is, then so too is saying that what John is said to have sent is a direct object. John did not send Mary a direct object. Anscombe concludes all this, and concludes from it, that “What this shows is that there is a way of taking ‘The direct object is not a direct object’ which makes it true.” She says that we can isolate that way of taking “The direct object is not a direct object” by likening it to “The direct object is not a girl.”13 It is at this juncture that Valberg intervenes and makes his suggestion. … Then we may write, “The direct object of S [ S = ‘John sent Mary a book’] is: a book” in which the the-phrase is an improper singular term and the words “a book” a presenting term. Miss Anscombe’s point that “there is a way of taking ‘the direct object is not a direct object’ which makes it true” could now be explained simply by noting the falsehood of, “The direct object of S is: a direct object”; for it is the words “a book” and not “a direct object” which present what S says John sent Mary.14

What would Anscombe make of this intervention? The most important thing to attend to is that Valberg’s intervention, his way of handling the DOP, is a way of finding something of the right sort for Anscombe to be talking about. His way of 11 12 13 14

Anscombe, “Intentionality”, p. 6. Anscombe, “Intentionality”, p. 6. Anscombe, “Intentionality”, p. 7. Valberg, “Improper Singular Terms”, p. 133, n. 3.

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handling the DOP requires the introduction of a presenting term; and, presenting terms are not, as we have seen, mentioned terms. Presenting terms present nonindividual somethings. By means of them, we talk about what is non-individual. But Anscombe denies that using words in the way that Valberg wants to capture as a presentational use is a way of using words to talk about what they, on that use, stand for. Consider a bit more that Anscombe has to say. She says that what we need to understand this use of words is an ear for a certain kind of use. And, she says, having this ear is indispensable. To show this, she once more enters the toils of the argument over the use of the phrase. The argument began with stating reasons why a direct object can’t be something that the direct-object phrase stands for. Yet one can, one correctly does, say “a book” in answer to the question “What does the sentence say John sent Mary?” which asks the same thing as “What is the direct object in that sentence?” Nevertheless the way the phrase “a book” is being used is such that one can’t sensibly ask “Which book?” We must conclude of “objects” (direct, indirect and likewise intentional) that the object is neither the phrase nor what the phrase stands for. What then is it? The question is based on a mistake, namely that an explanatory answer running say “An intentional (direct, indirect) object is such-and-such” is possible and requisite. But this need not be so. Indeed the only reasonable candidates to be answers are the ones we have failed. But what is the actual use of the term? Given a sentence in which a verb takes an object, one procedure for replying to the question: “What is the object in this sentence?” is to recite the object phrase. If putting the object phrase in quotes implies that the object … is a piece of language, that is wrong; if its not being in quotes implies that something referred to by the object phrase is the object, that is wrong too. To avoid the latter suggestion one might insist on putting in quotes; to avoid the former one might want to leave them out. One is inclined to invent a special sort of quotes; but the question is how the phrase within the new quotes would function—and if we understand that, we don’t need a new sign. So ends the argument.15

At this point it should be obvious that we have reached a pretty explicit clash between Anscombe and Valberg. Valberg is going to accuse Anscombe of the sort of narrowmindedness that he criticized in responses to the CHP. Anscombe is going to accuse Valberg of trying to find a way to avoid the necessity of the ear, of trying to find something to talk about in a case where that is precisely what isn’t needed. Valberg wants to find a way to expand our ordinary—constative—use of language, we might say (and so to expand it in a way that forgoes, or at least does not employ specially, the ear); and, when we use the expanded constative language, we straightforwardly talk about the extraordinary, the non-individual. Before we explore this clash further, though, I want to note one more piece of Anscombe’s view, because I think it sheds light on the clash. … [T]he question “What does the sentence [‘John sent Mary a book’] say John gave?” is fundamental for understanding either “direct object” or “direct-object phrase” as I am

15 Anscombe, “Intentionality”, p. 8.

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The Concept “Horse” Paradox and Wittgensteinian Conceptual Investigations using those expressions; and hence for understanding “direct object” when it is used for a phrase. And though the question is answered (like many questions) by uttering a phrase— in this case “a book”—the phrase has a special use in answer to that question “What does the sentence say John gave?” It can name neither a piece of language, nor anything that the piece of language names or otherwise relates to, nor indeed anything else. The interest of the question and answer is the rather special interest of getting grammatical understanding. Grammatical understanding, and grammatical concepts, even the most familiar ones like sentence, verb, noun, are not so straightforward and down-to-earth a matter of plain physical realities as I believe people sometimes suppose. The concept of a noun, for example, is far less of a physical concept than that of a coin; for someone might be trained to recognize coins with fair success though he knew nothing of money, but no one could be trained to recognize nouns without a great familiarity with language; and yet the concept of a noun is not one which he will automatically have through that familiarity, as he will that of a coin if he operates with coined money. Indeed the explanations of grammatical terms are only hints at what is really grasped from examples. Thus no one should think that by merely adopting the usage of modern grammarians, for whom the direct object is a word or words, he has avoided handling difficult concepts and remained in a plain man’s world of plain things.16

The ear that Anscombe thinks indispensable is an ear for the expression of grammatical understanding—for hearing grammatical comments correctly. And Anscombe thinks that grammatical understanding is a special sort of understanding: ultimately, she thinks that grammatical comments on grammatical terms are only “hints” at things we really understand by means of examples. Grammatical understanding is not correctly represented, we miss what is special about it, if we represent it is as if it were just another case of plainly handling the plain things that populate the plain man’s world. The ear for the expression of grammatical understanding is one that we have in virtue of our familiarity with grammar. Here Anscombe makes use of Frege’s term, “hints”. Frege thought that saying that “The concept ‘horse’ is not a concept” was a way of giving his reader a hint, a way of inviting his reader to meet him, as he famously put it, “halfway”.17 Moreover, Anscombe’s notion that ultimately what we understand when we understand grammar is bound up with examples is Fregean, too. For Frege it was crucial to rely on what he called “a general feeling for the German language.” Frege hoped his reader would grasp his hints fully, and then manifest that understanding in the manipulation of the Begriffsschrift. So there was for Frege a check, so to speak, on whether or not his reader had taken the hint, had gathered what was necessary from the examples. Following Anscombe, we can think of both the CHP and the DOP as paradoxes that turn on the expression of grammatical understanding. (Anscombe does mention explicitly that she thinks of the CHP this way.) “The concept ‘horse’ is not a concept” and “The direct object is not a direct object” are both attempts to express grammatical understanding. Kerry responds to Frege by treating Frege’s expression of grammatical understanding as if it is an attempt to express something that remains firmly in the plain man’s world of plain things—and so Kerry treats Frege’s expression as obviously wrong; the concept “horse” is, if it is that, certainly 16 Anscombe, “Intentionality”, p. 8–9. 17 Frege, G., “On Concept and Object”, p. 45.

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a concept; and no plain man would think otherwise. So, Kerry concludes that Frege is confused: concepts and objects are not absolutely distinct. Concepts are objects. Anscombe’s view resembles Frege’s. Valberg’s, in its way, resembles Kerry’s. Unlike Kerry perhaps believed, Valberg doesn’t believe that everything that is is an individual; Valberg does not suffer from the narrow-mindedness he sees in many of the responses to Frege. But Valberg does suffer from a narrow-mindedness—the narrow-mindedness of thinking that anything of intellectual significance must be something that can be said straightforwardly, talked about. As Valberg understands himself, he is prepared to grant to Frege that there is a distinction between concepts and objects. He is even, in his way, prepared to grant Frege that the distinction between them is “absolute”. For Valberg, after all, concepts can be secured cognitively only by presenting terms, by improper singular terms. Objects can be secured cognitively only by proper singular terms. Those things referred to by proper singular terms are individual; those things referred to by improper singular terms are non-individual. So there’s a great distance, we might say, between concept and object—a distance great enough surely to please Frege. But is it? To answer, think about Anscombe again. Anscombe ties grammatical comments to examples. Why? Anscombe does not think that expressing grammatical understanding can be like expressing other sorts of understanding. Grammatical understanding is tied to examples because, unmoored from examples, the understanding takes on a false appearance. To see what I mean, let me sketch the narrow-mindedness of Kerry and the narrow-mindedness of Valberg in a way that more clearly reveals each as suffering from that fault, although in different ways. Each of the two suffers from the notions (a) that thoughts can be itemized and (b) that possessing grammatical understanding is a matter of being able cognitively to secure the items that together make up thoughts.18 Kerry thinks that there is no reason, if a concept is one of the items that make up a thought, why that concept cannot become the object of a thought. The same, too, is true of Valberg. Each thinks of the item that is a concept differently— Valberg will chafe at the term “item” since he denies that a concept is an individual. But, as I think Valberg would have to admit, so long as we do not treat “item” as implying an individual, he does think of concepts as items in thoughts. For Valberg, presenting terms allow us to cognitively secure an item from a thought and then to think about that item, to bring our thoughts to bear on it. Mutatis mutandis ditto Kerry, but simpler. For each, grammatical familiarity ultimately is to be construed as familiarity with items in thoughts. One way of understanding Frege—and Anscombe, too, mutatis mutandis ditto—is as rejecting the notion that thoughts can be itemized and the notion that we can have further thoughts about those items. For Frege, to say that the distinction between concepts and objects is absolute is to say that it is a distinction that lacks a genus.19 By that I mean that, for Frege, concepts and objects are not species of any 18 I am leaning here on terminology borrowed from Anthony Palmer’s Concept and Object, p. xv. 19 Although the terminology here is mine, I hope that the terminology will recall to mind Soren Kierkegaard’s relative vs. absolute oppositions, particularly the latter—which

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shared genus. To grasp that sort of distinction, for Frege, is to grasp a distinction wholly unlike, say, the distinctions among sorts of apples; even more, it is to grasp a distinction wholly unlike the distinction between apples and oranges. There is no way to compare concepts with objects. Wittgenstein will put the matter this way in The Blue Book: “There are no subtle distinctions between logical forms as there are between the tastes of different kinds of apples.”20 Now I know this may sound mysterious. But keep in mind, as I mentioned, that the distinction between concepts and objects is one that can be grasped—and its grasp can be manifested. Grasping this distinction is manifested in manipulating the Begriffsschrift. When I symbolize properly, in a way that captures the actual inferential potential of a thought, the symbolization will reflect the distinction between concepts and objects. The crucial thing to understand here is the relationship between thoughts and the Begriffsschrift. Symbolizing a thought in the Begriffsschrift is not having a thought (a second one) about the thought (the first one)––it is instead thinking the first thought clearly. That may seem like jugglery; but it is not. For Frege, the Begriffsschrift is internal to thought. It does not stand, over and above—or anyway, separated from—thought. To think a thought is to grasp Begriffsschrift: it is not to grasp something to which the Begriffsschrift can then be applied. The Begriffsschrift is not a tool for thinking about thoughts; it is a tool for thinking thoughts clearly. When the Begriffsschrift is utilized, it makes a thought perspicuous—not by talking about the thought or about the items that make it up, that is, by allowing us to think about the thought. It makes a thought perspicuous by allowing us to see the symbols in its signs. The Begriffsschrift is superior to a natural language—to English, say— only in perspicuity, only in its ability to show the distinctions more clearly that must already be grasped if the English is understood. The Begriffsschrift explicitates thoughts; it does not somehow replace them, add to them or allow us to talk about them or the items in them. Here’s W.D. Hart, talking about Wittgenstein’s view of Begriffsschrift in the Tractatus: According to Tractatus 5.5563, however, all propositions of ordinary language are in perfect logical order just as they stand. To clarify a proposition of ordinary language is not to replace it by a proposition that means something different than the original; it is rather to replace the original by a proposition which means exactly the same thing as the original but which expresses the sense of the original exactly, rigorously, and precisely … [W]hen we follow Wittgenstein, we start with two things, an ordinary proposition[al sign] and its sense, and we clarify the former by substituting a new propositional sign that expresses the latter precisely and accurately by making its logical form apparent.21

Anscombe’s talk of grammatical understanding and of the odd status of expressions of it is, as I have noted, Fregean. Notice that for Anscombe, the role of “The concept are, according to Kierkegaard—oppositions without mediation. 20 Wittgenstein, L., The Blue and Brown Books (London: Basil Blackwell, 1958), p. 19. 21 Hart, W.D., “The Whole Sense of the Tractatus”, Journal of Philosophy 69,: 9, 1971, p. 281.

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‘horse’ is not a concept” and the role of “The direct object is not a direct object” is—using another of Frege’s terms—elucidatory. Their role is to counter confusions of a particular sort—call them logical distinction confusions. Their role is to clarify, and by so doing, to eliminate logical distinction confusions. When someone fails to understand this sort of clarification, or fails to see what sort of help it is meant to be, then we must start again with examples (and hope for the best). At any rate, we must try to engage the grammatical understanding of the person who is confused or who fails to understand the clarification. We counter logical distinction confusions with elucidations. As Anscombe notes of her own procedure: “But these examples, where we talk about direct objects, are harmless and profitable because certain sorts of suggestions about direct objects are patent nonsense.”22 Once elucidations have elucidated, done their bit in eliminating logical distinction confusions, they, so to speak, go dark. And they should go dark, because were they to remain lit, they would encourage misunderstanding. Elucidations, as odd as it sounds to say this, get their light from the confusions they engage. When the confusions go, the elucidations go dark.23 And that brings me back to Valberg. Valberg takes himself to be doing more than elucidating when he says what he says by means of presenting terms. He is actually talking about items—the non-individual—by means of those terms. But from Anscombe’s point of view, that is to take a step too far, to stray from the grammatical high road. Valberg does not take himself to be hinting. One way of seeing why Anscombe would be dissatisfied with what Valberg does is to think about her comment about the indispensability of the ear in the expression of grammatical understanding. Valberg has more or less done what Anscombe anticipates someone might be tempted to do. He has invented, in effect, special quotes. The special quotes are supposed to allow ordinary talk to be about the extraordinary. But as Anscombe notes, the question is about how the phrase in the quotes is to be used: once we understand that, we don’t need Valberg’s special quotes. And once we understand that the phrase is used to express grammatical understanding, and, given the special interest, the peculiar status, of that understanding, we will not take ourselves to be making the acquaintance of an item our previous narrow-mindedness kept us from making the acquaintance of. (As if we previously refused to mix with items of that sort.) No, we’ll see that we’re just helping ourselves or others to the clearer thinking of a thought. If Valberg understood himself, understood his presenting terms, as doing nothing more than aiding the expression of grammatical understanding, I’d have little to quarrel with him about. But he’d also have little to say that goes beyond Anscombe. Valberg however wants to extend our cognitive reach, to add items to the inventory of items we can think about. And it’s there that I part company with him, and there that I think Anscombe would, too. Valberg wants to give more than hints. He doesn’t of course take himself quite to be handling plain things in the world of the plain man. But he does take himself to be handling somethings, items: the non-plain, the

22 Anscombe, “Intentionality”, p. 9. 23 I am alluding here to PI 109.

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non-individual somethings designated by presenting terms. And he takes himself to handle them by means of extended constative language. Conclusion of Valbergian Impropriety The way of thinking about grammatical understanding that Anscombe offers may seem—often does seem—hopeless. It can seem that expressions of grammatical understanding, elucidations, must either talk about something—as Kerry and Valberg in their different ways would have it, or they talk about nothing—as it may seem that Anscombe would have it. (Elucidating will seem at best unstable between saying something and saying nothing; at worst, clearly to tilt in the latter direction.) If elucidations talk about nothing, there’s no way in which they can engage any confusion, no way in which they can perform any intellectually significant task. Anyone who wants from elucidations what Anscombe wants from them seems selfmated (to borrow Geach’s term). The charge of self-mate is, I think, driven by our desire to dignify our logical distinction confusions. We want to think of ourselves, when we are so confused, as considering an alternative (set of) logical distinction(s). We are prepared, of course, to find that the alternative is mistaken, false. And if so, well, then we are, as we said we might be, mistaken. We are mistaken in the way that someone who believes what is false is mistaken. Anyone who undertakes to engage with our confusion, we think, must then be considering an alternative (set of) logical distinctions, alternative to what we are considering. We see our confusion as of a quite superficial kind. But I think that logical distinction confusions are not mistakes of false belief; they are confusions in a deeper sense, muddles. When we are so confused, we are not considering anything in particular, despite our desire to say that we are. To engage with logical distinction confusions then is to muddle wrestle, to try to find a way to help someone whose plight of mind is much different than the plight of mind of the believer of the false. It’s not that the television’s picture is clear but the television is on the wrong channel. It’s that the television’s picture is scrambled. Meeting such plights of mind requires something different than a change of channel; we have to fiddle with the controls. At a similar juncture, explaining what Wittgenstein is doing in philosophy, explaining Wittgenstein’s salvific effort on behalf of those in such plights of mind, O.K. Bouwsma asks himself—“Brain-washing?”. He answers—“Yes, something more like that.”24

24 Bouwsma, O.K., “Introduction”, Hustwit, R. and Craft, J.L., (eds), Towards a New Sensibility (Lincoln: University of Nebraska Press, 1982), p. xviii.

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Nagging Sellars Introduction Sellars’s far-ranging paper, “Grammar and Existence: A Preface to Ontology”25, contains, among many other things, a response to the CHP. The response is an integral part of a very long and very complicated argument against Platonism—an argument designed by Sellars to release his readers from “Platonistic anxieties”. Sellars does not attempt to calm the anxieties by refuting Platonism—the paper is a Preface to Ontology, remember. Instead, he tries to show that there are as yet unbarred paths around Platonism. The response to the CHP is part of a dialectical map drawn by Sellars as he tries to find paths for pursuing ontology outside the mazeways of Plato’s Still-bristling Beard. I undertake to extract Sellars’s response from his paper and then to criticize it. Extracting it is not easy. It is not easy because the response winds around and attaches itself to other arguments in the paper; and that makes extracting the argument sensitive work. There is really no way of cleanly extracting the response: it emerges from the paper trailing viscid bits of argument and exposition. Moreover, extracting it is not easy because Sellars himself does not endorse the response, and for reasons that indirectly relate to my reasons for criticizing it. I am, however, going to ignore Sellars’s lukewarmness to the response as well as his reasons for that lukewarmness. I will treat the response as if it were whole-heartedly endorsed by Sellars. I do so because I want to explore my own reasons for criticizing the section, independently of Sellars. I do so because it will make my focus clearer and because it will allow me to make of Sellars’s response what I want dialectically to make of it, not what Sellars wants dialectically to make of it. I believe that my criticism of Sellars’s response to Frege’s response to Kerry—that is, of Sellars’s response to the CHP—is such that it can, with suitable modifications, be shown to cut against the sum of Sellars’s attempts to calm Platonistic anxieties. That is not because I take the CHP—understood as I understand it—to in any way vindicate Platonism; I do not. It also does not in any way vindicate Nominalism.26 Understood as I understand it, the CHP instead vindicates a Ramsey’s Maximresponse to the debate between the Platonists and Nominalists; but I will not investigate that vindication.27 Sellars purpose in his paper is to examine “a current dogma.” The dogma is that to sanction the move from sentences like

25 Sellars, W., “Grammar and Existence: A Preface to Ontology”, Science, Perception and Reality (London: Routledge and Kegan Paul, 1963), pp. 247–81. 26 Frege’s handling of the CHP, particularly Frege’s way of thinking about concepts, has been taken as (an attempt to do) just this. See, for instance, Bergman, G. “Frege’s Hidden Nominalism”, Philosophical Review LXVII, October 1958, pp. 437–59. 27 Consider, as a first step in the direction of such a vindication, Wittgenstein’s remark in PI 383: “Nominalists make the mistake of interpreting all words as names, and so of not really describing their use, but only, so to speak, giving a paper draft on such a description”. So, too, realists. – Of course, it is a long way from this footnote to the vindication of my claim.

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64 (1)

S is white

to (2) (Ef) S is f

(and similar moves) is “to sanction the move from empirical statements to statements asserting the existence of entities of a higher order than perceptible individuals.” Sellars initially assumes that the entities of a higher order are “straightforward abstract entities such as Triangularity, Mankind”, etc. Following this, he turns his attention to an idea of Geach’s—an idea that is a bestowal from Frege. That idea is that sanctioning the moves from empirical statements to the other is to sanction a commitment to “non-individual entities, entities which have no names, but are, somehow, stood for by parts of speech other than names.”28 I will begin by looking at Sellars’s consideration of Geach’s work on matters related to the CHP. Note that I just have been and will be using Sellars’s numbers for propositions, and that I will not be considering all the propositions he numbered—so the numbers used will not proceed quite naturally. Note also that I’m joining Sellars’s consideration mid-stream. I hope that the similarities between Sellars and Valberg will help to make this mid-stream entry a little less disorienting than it might be. My conclusion to this part of the chapter will be that Sellars’s response to Frege’s response to Kerry is confused. The larger conclusion I want to draw from both parts is that that there is no CHP—at least as it is typically understood. Thinking that there is a CHP shows, among other things, a failure fully to appreciate the radical character of Frege’s thinking. (A failure of which Frege himself was sometimes guilty.) Sellars contra Geach Geach argues that (1) “S is white” entails the general statement (26) There is something which S is (i.e., white)

and Geach sees, too, that (27) There is something that S has (i.e., whiteness)

is not to be confused with it. As Sellars understands Geach, Geach’s “There is something which S is” corresponds to Sellars’s earlier (25) “S is something.” And Geach’s insisting that the something which S is is white, and not whiteness, corresponds to Sellars’s distinguishing of “S is something” from “S has (exemplifies) something.” I rehearse all this quickly, since it is the same distinction that matters so much to Valberg— namely, the distinction between predication1 and predication2. Sellars, like Geach and like Valberg, thinks the distinction is crucial. Sellars turns to another example: 28 Sellars, “Grammar and Existence”, pp. 247–8.

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(25) Jack and Jill are both tall.

Geach takes this to entail (26) There is something which Jack and Jill both are.

And Geach also argues that this is not to be confused with (261) There is something which Jack and Jill have in common.

To attach the rider “i.e., tallness” to (26) would be a mistake. The “proper rider” is “i.e., tall”. Thus, Geach’s (26) is the counterpart of Sellars’s (2) “(Ef) S is f”; and, from Sellars’s point of view, Geach has “correctly seen that [(2)] does not involve a commitment to the use of such abstract singular terms as ‘whiteness’ or ‘tallness’.” Still, Sellars thinks that Geach has built his insight into a larger mistake. Geach wants to read (262) There is something (i.e., tall ) which both Jack and Jill are

as committing us, not to an abstract or universal entity, but rather to a property—tall. Two accounts of properties are to be found in Geach, as Sellars reads him: one a cautious account that turns on a grammatical mistake, the other a less cautious, Fregean account that is subtle and difficult to expose. I will follow through the details of Sellars’s response to Geach’s first account, since they will matter to Sellars’s response to Frege and my criticism of it. I will not follow through all the details of Sellars’s response to Geach’s second account. I will follow through some details, up to the mid-point (more or less) of the response. There, Sellars provides his response to Frege; there, I shift my focus from Sellars’s response to Geach to Sellars’s response to Frege. The response to Geach I leave at loose-ends. The cautious account Sellars exposes in this way. (262) “has the prima facia appearance of an existence statement” and Sellars thinks Geach is deceived by it. As Sellars notes, even “if the entities Geach introduces are what things are rather than what they exemplify, they are abstract entities nonetheless … and Geach’s denial that these entities are individually referred to by such singular terms as ‘tallness’ is open…to the reply that he has avoided the abstract individual tallness only at the expense of treating the adjective tall as a peculiar kind of singular term …”29 Here the possibility of Valberg’s position shows itself to Sellars. Sellars sees the possibility of the position, sees the possibility of improper singular terms, but he won’t actualize, as it were, the possible position; even more, he takes actualizing the possibility to be a bad idea—a philosophical expense one would like to avoid. Sellars has no interest in non-individual referring terms. (Recall how Sellars assesses the Fregean move Geach makes: it is to commit, not to items that have names (even if improper ones), but to items that are, somehow, stood for by parts of speech other than names.) 29 Sellars, “Grammar and Existence”, p. 259.

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According to Sellars, the grammatical mistake Geach is deceived by is this: he treats (26) as if it began with “There is a something …” instead of, as it does, with “There is something … .” If it began the way Geach is deceived into seeing it begin, then it would make sense to cast about for a common noun—like property—to specify what sort of something there is which Jack and Jill both are. But that would yield (263) There is a property which Jack and Jill both are

and that, according to Sellars, is nonsense. One way of avoiding Geach’s mistake is to see that generalizing (29) Tom is a man

to (30) Tom is something

can be expressed as (301) There is something that Tom is.

But also we must see, simultaneously, that (301) does not distinguish generalizing (29) from generalizing (31) Tom is tall

What we need further to see is that there is a rhetorical device in the offing that allows us to distinguish between the generalizations of (29) and of (31). Sellars calls the device “question-echoing counterparts.”30 The question-echoing counterpart of (29) is (291) A man is quid Tom is: Tom is who is a man

and of (31), (311) Tall is quale Tom is: Tom is who is tall

The point of these counterparts is to highlight the diversity of roles in English of the question-word “what”. The interrogative “quale” indicates that the answer is to be in terms of an adjective; “quid” indicates that it to be in terms of a common noun. We can then truncate the two counterparts as (341) There is somequale which Tom is (i.e. tall) (351) There is somequid which Tom is (i.e. a man)

This allows us to rework the nonsensical (263) as the sensical 30 Sellars, “Grammar and Existence”, p. 260.

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4

(26 ) There is somequale which Jack and Jill both are (i.e. tall)

What Sellars stresses here is that, although in (265) Tall is what (quale) Jack and Jill both are

tall stands in as the grammatical subject, the “role” it plays (the shudder-quotes are Sellars’s) is unique—“and is, indeed, rhetorical in character. It would surely be a howler to suppose that because it is functioning in this context as a grammatical subject, it is in any more profound sense functioning as a subject. Its role is rhetorically derivative from its adjectival role in the original, non-question-echoing statement.”31 In this way, Sellars thinks he can avoid Geach’s mistake—the mistake Geach makes in his first account—of making the wrong thing of the claim that there is something which Jack and Jill both are. Sellars thinks that he has found a way of forming sentences such that something other than a singular term is the grammatical subject of the sentence. A singular term is only superficially grammatically the subject of the sentence; depth-grammatically, the subject is an adjective. I’ll return to this innovation of Sellars’s a bit later. Sellars now turns to Geach’s second, Fregean account. Sellars sets the account up by recounting a bit of Frege’s “On Concept and Object”. It will be remembered that Frege distinguishes between concepts and objects and is faced by the problem: “How can one say of anything that it is a concept?” For the term “concept” being, presumably, a common noun, we should be able to make statements of the form (36) ____ is a concept Frege, however, rules out such statements on the ground that [whatever fills the blank] will be an object rather than a concept.32

Now Sellars thinks that something can fill the blank—something like man or triangular. Sellars confesses, though, that these fill-ins “feel” wrong: context (36) requires a singular term rather than an adjective or a common noun to fill it in. As we have seen, Sellars thinks that his investigation of Geach’s first account shows that we can form sentences in which something other than a singular term is the grammatical subject. For example: (40) Triangular is what (quale) the table is

Or (41) Men is what (quid) Tom and Dick are

But the trouble with these is, again, feel: nothing in these contexts permits the introduction of a common noun—neither the common noun “concept”, nor 31 Sellars, “Grammar and Existence”, p. 261 (emphasis in the original). 32 Sellars, “Grammar and Existence”, pp. 261–2.

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“property”. Sellars responds to this feel-trouble by asking whether it shows that Frege was misguided in distinguishing between objects and concepts. This question moves Sellars into the heart of his response to Frege. Sellars says that Frege did have something important in mind which he builds into his notion of a concept, and which does not require the use of adjectives, common nouns or verbs as the grammatical subjects of sentences. For the significant core of Frege’s doctrine is compatible with the idea that the common noun context [(36)] requires something like a singular term for its subject, and hence with the rejection of a simple concept-object dichotomy. The clue to the correct formulation of the core theme is found in his characterization of concepts as “unsaturated”. For, in effect, this means that we may be able to get somewhere with “unsaturated” singular terms—if we can find such—as the subject of statements of the form [(36)]. For among singular terms available to us … are singular terms of the form “that-p”, and we know what an unsaturated singular term of this form would look like. In short, we hit upon, for example (393) That x is triangular is a concept. On this analysis, concepts would be “unsaturated” propositions. And if, as Frege seems to do, we use the term “object” in such a manner that anything referred to by a singular term is an object, we would have to say that concepts differ from objects not by being non-objects, but by being “unsaturated” or “incomplete” objects.33

Before I criticize this line of thinking, I again point out the loose-ends: how does Sellars here manage a response to Geach’s second, Fregean account? As I’ve said, I am not going to answer this question. A full answer to it would take nothing less than a full recap of several more difficult sections of Sellarsian argument. I leave those sections to the discriminating courage of my reader. Sellarsian Incompleteness Leaving alone Sellars’s response to Geach’s second, Fregean account, what goes wrong in Sellars’s response to Frege? Why can’t Sellars bargain some of the absoluteness of the concept/object distinction away? Why can’t he treat the concept/ object distinction as a distinction among kinds of objects, saturated ones and unsaturated ones? It is certainly true that Frege’s own language can tug reflection in this direction. By calling objects saturated and concepts unsaturated, Frege seems to suggest that they are two species of one genus—much as fried and unfried eggs are both eggs. If this seeming suggestion is correct, then Frege’s own terminology deconstructs his absolute distinction between concepts and objects. But Frege does not mean to do that. The distinction between saturated and unsaturated is, again, a distinction without a genus. There’s no genus, x, that is either specifically saturated or specifically unsaturated. To understand this, we need to think more carefully about the nature of the distinction between object-expressions and concept-expression—as I think 33 Sellars, “Grammar and Existence”, p. 264.

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Wittgenstein thought about it. The distinction is knotted together with the Context Principle, i.e., the distinction can be drawn only in the context of a proposition. Outside of propositional context, there are neither object-expressions nor conceptexpressions. To call something an “object-expression” or a “concept-expression” is to elucidate its logical role in a proposition. No sign is, as such and outside of a proposition, an object-expression or a concept-expression. No sign can assign itself a logical role. And this, by the way, includes Frege’s parentheses, considered simply as signs, and not as essentially tied to an example proposition. It is worth pausing here explicitly to combat a possible misunderstanding. The distinction between the saturated and the unsaturated is not a distinction between items that do assign themselves a logical role outside of a proposition—the saturated— and those which do not—the unsaturated. Some have thought that the saturated is saturated on its own, outside of a proposition. (I take it that Frege’s terminology is itself partially to blame for that, since “saturated” can, especially as Frege uses it, suggest something that, so to speak, sits solidly and independently on its own bottom.) But to call something saturated or unsaturated is to say something of its role in a proposition. The words “the object ‘Bob’” can no more assign themselves the role of an object-expression than can the words “the concept ‘horse’” assign themselves the role of a concept-expression. The point is intimate with Anscombe’s point that: Grammatical understanding and grammatical concepts, even the most familiar ones like sentence, verb, noun, are not so straightforward and down-to-earth a matter of plain physical realities as I believe people sometimes suppose. The concept of a noun, for example, is far less of a physical concept than that of a coin …34

Anscombe’s point is that grammatical distinctions—noun, verb, etc.—are of the same sort as the distinction between concept-expressions and object-expressions. Words cannot assign themselves the role of noun or of verb. To be a noun or to be a verb is to play a certain role in a proposition. (It is easy to overlook this, to think that some feature of a word (say, an ending it has or might have) or some feature of an expression (say, its containing the word “the”) is that feature of the word or expression by which the word or expression assigns itself the role of verb or noun.) Sellars’s trouble is that he looks at the expression That x is a triangle and sees something gappy, something conceptual. The variable, x, represents the gappiness, the conceptuality. Sellars then thinks that the gappiness remains, is still present, when the expression is moved to fill the blank spot in (36) ____“is a concept.”

One reason Sellars thinks this is presumably that the “x”, which he takes to represent the gappiness, remains in the expression. Let’s now slow down and review the motion of Sellars’s thinking and see if (393) will do what Sellars wants, and solve the Fregean problem.

34 Anscombe, “Intentionality”, p. 8.

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Sellars comes by the expression “that x is triangular” in this way. He considers the unsaturated proposition “x is triangular”. That, given what Frege has said, is indeed gappy. But, as it stands and given what Frege has said, it says nothing, stands for nothing. Sellars wants it to stand for something, something gappy. He recalls that his previous discussion revealed in passing that we can create singular terms of the form “that-p”. And so, since we can, Sellars creates (393), and he understands it as segmenting into the singular term, the object-expression, “that x is triangular” and concept-expression, “___ is a concept.” (393) is, for Sellars, a rewriting of (391) Triangularity is a concept

and it makes explicit an implicit gappiness in the latter. The trouble here is that, if “that x is triangular” is a singular term, then it has no gaps, despite the look of the expression, despite its “x”. Sellars, though, wants somehow to take the unsaturated proposition, “x is triangular”, with its gappiness, and, while retaining that gappiness, transform the unsaturated proposition into a singular term, an object-expression, in (393). But even now I’m letting Sellars’s thinking move too fast. Let’s review again. Sellars looks at “x is triangular” and sees an unsaturated proposition. Now, in one way that’s OK; in another, it’s not. When “x is triangular” is understood as an abstraction, not an extraction, from a proposition, say, from “The pyramid is triangular”, then “x is triangular” can be seen as a concept-expression: in such a case, we are not treating the sign “x is triangular” as if, on its own, it is a concept-expression. On its own it is no sort of expression at all, neither a concept, nor an object-expression. On its own, it is neither saturated nor unsaturated. Early in his paper, Sellars takes the time to point out that, when we are reflecting on logic, we often do so by making use of “informal readings” of statements, readings that make certain logical relations intuitive. And Sellars cautions himself and his readers that such “informal readings” are, as he puts it, “contrived readings.” He says of a contrived reading that it “generates puzzles as soon as its auxiliary role is overlooked, and it is made the focal point of philosophical reflection …”35 Sellars, I think, is guilty of doing what he cautioned himself and his readers not to do. For Frege—at least as Wittgenstein reads him—a concept-expression, properly so-called, is a contrivance, something with a purely auxiliary role. It is something made use of as an aid in thinking clearly some proposition or other. It is not itself such as to be made the focal point of philosophical reflection; doing so generates puzzlement and confusion. Another way of seeing my point is to consider a distinction of J.J. Valberg’s, one that I did not mention in Part One of the chapter.36 Valberg distinguishes semantically dependent descriptions from semantically independent descriptions. A semantically dependent description is a description of an expression in light of the semantic role it plays in a given proposition. A semantically independent description of an expression is a description in isolation from any given proposition. Sellars wants to describe “x 35 Sellars, “Grammar and Existence”, p. 250. 36 Valberg, “Improper Singular Terms”, p. 122.

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is triangular” as gappy—and to have that description be a semantically independent description. But it can’t be—“gappy” is a semantically dependent description. Sellars attempts to save Frege from himself by bargaining away the absoluteness of Frege’s distinction between concepts and objects. But the absoluteness of the distinction is presupposed in grasping the distinction. Sellars must both see that and then manage not to see it. And that’s just what he does. He sees gappiness for what it is when he chooses a concept-expression; he sees that what he has chosen is what he has chosen it to be only semantically dependently. Then, he begins, as it were, to think that the gappiness of the expression is something that he has guaranteed by tricking the expression out with the sign, “x”. And that means he thinks the expression is a concept-expression in virtue of some feature of its own—considered as a sign. The expression then is transmuted into a semantically independent concept-expression. Once it transmutes, it then can be moved about, and, specifically, inserted into the blank-spot, the gap, of some other concept-expression. But anything that fills the gap in a concept-expression is an object-expression. Sellars sort of sees that, but he wants to be able to see the expression as semantically independently remaining a concept-expression while it is simultaneously a semantically dependent objectexpression: and only such a confusion could possibly be confusedly thought to stand for an unsaturated object. That’s the way Sellars crumbles, cookie-wise. Keep in mind that I am not ultimately accusing Sellars of having thought The False in responding to Frege. Sellars has, at the crucial juncture of his response, not managed any thought at all, he has produced nothing that will stably withstand the demand for judgment: he wants logically to segment (393) in incompatible ways. A Final Look at the CHP? I want to conclude by taking a larger view than I have so far. Specifically, I want to conclude by superintending the sort of responses to the CHP that Valberg and Sellars give, and that Kerry gives. I think that doing so helps us to see that there is no CHP—at least not as traditionally understood. Consider Kerry. Kerry tries what is perhaps most direct in responding to Frege: he treats words as assigning logical roles to themselves. But in doing so he doublecounts. He takes the words, “the concept ‘horse’” to name what Frege calls a concept, and so, to be, in virtue of what they name, a concept-expression. But, if they name something, then they are an object-expression. So, Kerry first counts the words an object-expression and then counts them a concept-expression. He loses count, however, and thinks he’s only counted the words once. One important feature of Kerry’s response is its irresolute ex concessis structure. Kerry takes himself to concede to Frege the distinction between concepts and objects. We can imagine him saying, “Yes, Gottlob, right. There’s just such a distinction. But it is not an absolute distinction, since a substitution you rule out I show to be ruled in.” Kerry intends to accept the distinction between saturated and unsaturated; but he does not see the radical character of the distinction, he does not see how big a distinction the distinction is. He intends to accept the distinction, but he intends, too,

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to show that the distinction is not absolute. But he can’t accomplish both at once. Either he doesn’t really concede the distinction to Frege; or he doesn’t really take himself to have successfully substituted. I think the incoherence in his intentions is hidden from Kerry by nothing more, and nothing less, than a trick of sequaciousness. That is, he begins by taking himself to concede the distinction, and then he tries to formulate a counterexample to the claim that the distinction is absolute, and then he finds a counterexample—but at this point he is no longer conceding the distinction. From Frege’s point of view, the problem is that, somewhere in the sequence, what Frege calls a concept has either transmuted into a concept in the psychological sense or has been scrambled together with a concept in a psychological sense. Another way of thinking about the incoherence in Kerry’s intentions is this: He begins by hearing Frege’s distinction as what I take it to be—an expression of grammatical understanding. He uses, we might say, just the sort of ear to hear Frege that Anscombe would say he should. But then, when he begins to reflect on the distinction, he becomes hard of hearing. He no longer quite hears an expression of grammatical understanding, he loses his ear for the difference in use. He instead hears something else, something that does not require great familiarity with language: he hears Frege as introducing him (Kerry) to two new, unfamiliar items: objects and concepts. I want to pause here to reinforce an important point. The irresolute ex concessis structure of Kerry’s response results from his first hearing and then not hearing Frege as expressing grammatical understanding. When Kerry hears Frege as expressing such, Kerry hears nothing with which to argue. He’s all concession. But then he begins to reflect on what Frege says, on the words themselves, and he no longer hears the words Frege said as Frege said them. To use Anscombe’s language, Kerry forgets that what Frege said was a hint, what Frege would’ve called an elucidation. To use Sellars’s language, Kerry forgets that what Frege said was contrived, that it played an auxiliary role. Instead, he makes what Frege said the focal point of philosophical reflection, makes it a claim about a plain man’s world of plain things—or, better, a claim about an unplain man’s world of unplain things, but one modeled on claims about the plain man’s world and things. By forgetting how Frege said the words he said, Kerry forgets also their requisite link to familiarity with language, and he forgets that the words are tied to examples. In short, he forgets that Frege appealed to “a general feeling for the … language.” Kerry cannot keep the peculiar ring of what Frege said in his ear. Failing to keep it, he returns to Frege’s words, and treats them as gazingstock; he shifts, we might say, from his ear to his eye. Treating what Frege said as gazingstock, Kerry cannot help but to treat it as constative. He then begins to investigate, to test, what was said constatively, to see if it is so. This irresolute ex concessis structure repeats, with variations, in Valberg’s response and in Sellars’s. I showed the structure briefly in both. In Valberg, it shows in his intending to accept a distinction between singular and general terms, and then in his intention to divvy up singular terms into the proper and the improper. It also shows in his forgetting of the need for an ear, and his attempting to substitute for it a way of talking ordinarily about extraordinary items.

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So what should we say about the CHP? Well, I’ve said quite a bit already in answer to that, and I will say a bit more; but, before I do, I want to assemble some typical features of post-Kerry responses to the CHP. I’ve already started doing this, in talking about the irresolute ex concessis structure of the responses. Think of my assembling as an attempt to provide a catalog of the typical features of a post-Kerry response to the CHP. I do not pretend to provide a complete catalog. Count the irresolute ex concessis structure the first feature. Now, others: Second feature: responses to the CHP tend quickly to become typographical extravaganza: italics, boldface, mention-quotes, shudder-quotes, semi-colons, colons—all these are sucked into in the dialectical vortex. Third: responses to the CHP tend quickly to become terminological extravaganzas: presenting terms, improper singular terms, contrived readings, auxiliary roles, questionechoing counterparts—all these, too, are sucked into the dialectical vortex. Reflecting on these extravaganzas reveals a frustration (I’ll count this the fourth feature)—a frustration we can characterize from the general point of view of the respondents, of Kerry, Valberg and Sellars (and, sometimes, Frege himself) as a running up against the limits of language. Each is quite sure that he has something to say, but that his saying it is prevented because of a lack of competence on the part of the language. Each respondent becomes an extravaganzist because there is something he wants to do and needs language’s help in doing, but the language can’t seem to do it. The language is no helpmeet. So each attempts to augment the language, with typography, with terminology, with … whatever. Each takes himself to have secured something for talking or thinking about, but something that the language can’t seem to secure for itself. And each thinks he can limber up the language by a little innovation. Fifth: each respondent takes himself to have secured an insight into talking and thinking that is fit for an “I know that …”-context. The typographical and terminological innovations are designed to make what each has to say fit for an “I know that ...”-context. Each supplies himself with a thought to think, indeed knowingly to think. Some respondents, though none of the ones I am discussing, take themselves to be debarred from actually putting the insight into the context— they treat some feature of their circumstances or some feature of the insight itself— to prevent saying “I know that [the insight].” But the prevention is no cure—each still thinks that the insight is fit for the context, even if the fit can’t be articulately exploited. Sixth: each respondent comes to see Frege’s distinction as bit of previously unfamiliar information. That is, as I have already discussed in Kerry, each comes to see what Frege said as something that can be understood properly while standing in no relation to familiarity with the language. Another way of putting this is to say that each comes to think of Frege’s distinction as independent of, external to, our ways of talking or thinking. So seen, what Frege said is something that is not an elucidation, or a hint, or a grammatical comment––or even a reminder: it’s news. Seventh: and this is I think crucially related to both the ex concessis structure and the typographical extravaganzas, each respondent comes to see the need for bits of instruction or helpful descriptions that are not, as such, to be used as bits of constative language are. The bits are reckoned to be auxiliary or contrived or

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hints or whatnot. (Sellars calls them “ladder-language” and I’ll use that as my general term for all these bits.) But, then, after seeing the need for such reckoning, and satisfying it, the respondent decides that the bits of ladder-language are what they are in relation to bits that are used constatively, especially the bits that are needed to say what needs saying—the insight, the news. The insight or news, said in language used constatively, is what the ladder-language leads us up to. But notice that here the respondent often becomes bemused. I can bring out the bemusement best by asking some questions. If we can in constative language say what needs to be said, why is there a need for ladder-language? Moreover, how is it that ladderlanguage can stand in the right sort of relation to constative language such that it can lead up to it? Ladder-language might elucidate constative language (in the way I’ve been exploring and illustrating)—that’s one way it might lead up to it. But the constative language it elucidates does not follow from it, conclusion-like. And the constative language it elucidates is not language that succeeds in talking about items constatively that the ladder-language talks about, ladder-like. If the constative language follows from it, conclusion-like, how can ladder-language really fail to be constative language or, put the other way round, how can it really be ladderlanguage? If the constative language that it leads up to can talk constatively about what ladder-language elucidates, ladder-like, how can the ladder-language really be necessary? The respondents both want and don’t want ladder-language, just as, and to the degree that, they want and then don’t want the absolute distinction. Since what I said about hinting/grammatical commenting/elucidating was said briefly, and since I’ve just used the term “ladder-language” with so little welcoming ceremony, I should say a bit more here about both, to ensure proper understanding. I’ve been trying to illustrate what I have in mind along the way, but the illustrations may not be as much help as I want them to be. So: “hint”, “elucidation”, “grammatical comment” or, in cumulo, “ladder-language”, as I am using the terms, are most clearly explained by relating them to the Begriffsschrift. Ladder-language elucidates what it elucidates by putting the person who understands the elucidator in a position properly to manipulate the Begriffsschrift. That understanding can be manifested by manipulating the Begriffsschrift. Ladder-language, as I understand it, is what is needed in order to enable a person to understand the distinction between what propositions that make sense say and what they show. Ladder-language does not enable a person to understand a distinction between what proposition-like items that make nonsense say and what they show. Such items neither say nor show. I am eager here to borrow from Michael Kremer. He writes: … I would suggest that uses of “showing” in the Tractatus may be two-sided. On the one hand, talk of showing can tempt us into the nonsensical illusion that we grasp a realm of super-facts beyond the reach of language. On the other hand, talk of showing can, innocently enough, direct us to the practical abilities and masteries that are part of our on-going talking, thinking and living.37

37 Kremer, M., “To What Extent is Solipsism a Truth?”, Stocker, B. (ed.), Post-Analytic Tractatus (Burlington, VT: Ashgate: 2004), p. 63

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The point I am eager to borrow is Kremer’s point that there is a kind of understanding that can be gleaned from the person who is innocently showing—an understanding appropriately thought of as a sort of knowledge-how. It is ineffable—but much as practical abilities and masteries generally are. The ineffability is a homely ineffability. A warning: the distinction between knowing-that and knowing-how I am employing here has to be treated as a distinction without a genus. I don’t think that in so treating it I am resisting the traditional way of understanding the distinction—in fact, I think the traditional debate is in important part a debate over how to treat the distinction. I am treating the distinction as some of the participants in the traditional debate over knowing-that and knowing-how have treated or intended to treat it. (That is, for some participants in the debate, to resist reducing the second to the first is often a way of registering (and often of confusedly registering) that the distinction lacks a genus.) But where, among know-hows, does what I am talking about here fit? Is it a skill, a kind of taste, a moral know-how (of the sort embodied in virtue)? I think it shares features with each of these, although it is not clearly best understood as any one of them. I can only gesture at this know-how. Like moral know-how, there is an always already-ness that characterizes it. Unlike a skill, there was no time at which we lacked this know-how, knew that we lacked it, and then set about learning it. Although this know-how is inculcated, and not imparted, we were never (exactly) its self-aware trainees. Like a taste, an appreciation, when the know-how is properly inculcated, we are not just able to do something competently, we come to care about what is inculcated, to take certain things seriously. But it is crucial to note the character of this caring, this seriousness: it is part of proper inculcation. Improper inculcation may still produce competence, or something very much like it. It is here that the know-how reveals a limited similarity to a skill. The know-how can be most clearly manifested in manipulating the Begriffsschrift—and that is a particular skill. And the know-how can, through a lack of practice, or through a lack of care or of seriousness, do something like rust. Such rusting may be thought of either as solely a change in my “equipment”, that is, solely in my mastery of Begriffsschrift (where the problem is, say, just a lack of practice or recent exposure); or, it may be thought of as a change in me—a coming no longer to care for or take seriously something I previously did. Still, unlike moral knowledge, there is a particular skill that can manifest this sort of know-how. When the rusting is a change in me and not merely in my “equipment”, the loss of knowhow is best thought of as moving from something like good taste to something like no taste.38 We might call this know-how “conceptual appreciation”; but I’ll just mention this title and not employ it. One last warning here. Perhaps the most alluring temptation that faces the person who is employing ladder-language is the temptation to think that there is 38 I am indebted here to Ryle’s “On Forgetting the Difference Between Right and Wrong”, Collected Papers , vol. 2, (Bristol: Thoemmes Press, 1990), pp. 381–91; and to remarks of Hans-George Gadamer’s from Truth and Method (New York: Seabury Press, 1975), esp. pp. 390ff.

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some feature of a form of words that qualifies it to be part of ladder-language or not to be part of ladder-language. Yielding to the temptation commonly results in sleuthing through the diction of a person wrestling with the CHP and finding words or phrases therein that are either “proper” or “improper”. But a crucial lesson of the CHP, as I understand it, is that there is no feature of a form of words that qualifies it to be or not be part of ladder-language. What is decisive is the way the form of words is being used. Perhaps certain forms of words when used as ladder-language are, for some people or perhaps even for many people, psychologically less likely or more likely to cause trouble, to advance or to retard understanding. But that is the only differentiation here to make. No particular diction—considered on its own—is going to mark out the person using ladder-language from the person who is not. No particular form of words has an atmosphere of ladder-languageness (or of constativeness) that travels with it through (logical) space. Conclusion At this juncture someone might object that the respondents whose responses I’ve been typifying end up looking quite a lot like Frege (as Wittgenstein read him) and Anscombe and Wittgenstein (early and late)—a lot like the philosophers I think we should follow here. I comment on this as Cavell does on a similar fact: The work of these philosophers forms a sustained and radical criticism of such respondents—so of course it is “like” them. It is “like” them in the way that any criticism is “like” what it criticizes. But ultimately, the work of these philosophers and of the respondents is radically unlike: to use an example of Anscombe’s, as radically unlike as soap and washing.39 Why is that? Why this radical unlikeness? Well, I’ve done my best throughout the chapter to provide answers to that question. There is a gulf fixed between the work of these philosophers and the respondents, a gulf that closely resembles the gulf between constative language and ladder-language because it is that gulf. The gulf is another of these distinctions without a genus. The philosophers I think we should follow do not take themselves to be trying to bargain the absoluteness of the distinction between concepts and objects away—although I admit they occasionally slip from the strait and narrow onto the broad way. But, no, they are trying to make clear that we can come to see the CHP as no paradox at all only by letting the distinction between concepts and objects be the distinction it is. It is not a distinction with a genus. It is not a distinction of which we need to be informed; we need rather to be reminded of it. It is not a distinction which we recognize and then, having recognized it, impose on thoughts that were thinkable before the imposition. Again, it is know-how, not know-that. The distinction is of philosophical importance not because it can be given as an answer, in some bit of constative language, to a deep philosophical question. The distinction is of philosophical importance because it is implicated as deeply

39 Anscombe, G.E.M., “Will and Emotion”, From Parmenides to Wittgenstein , Collected Papers vol. 1, (Minneapolis: University of Minnesota Press, 1981), p. 104.

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in thoughts as any distinction could be. No matter how far into thinking nature we retreat, when we turn to think we find such distinctions retreating and turning with us. They are a part of what we are. They are elements in that tawny grammar, that mother-wit, that know-how, that we are initiated into when we are initiated into what Cavell calls “human speech and activity, sanity and community.”40 They are what we do. They are what thinkers do. There are distinctions and distinctions—and so of course the details make a difference. One of the things that reflecting on the CHP’s respondents reveals is how very hard it is to keep straight distinctions among distinctions. After we have distinguished quantitative distinctions from qualitative distinctions, we think we’ve finished distinguishing distinctions. But there are more distinctions to make yet. Is the distinction between soap and washing quantitative or qualitative? It seems to me to be neither. But it’s still a distinction, for all that. Consider, in closing, Augustine’s famous question, “What is time?”, and his famous recoiling upon his own question. There was, therefore, not time before you [God] made anything, since time itself is something you made. No time could be eternal along with you, since you are always there; and if time were always, it would not be time. Then what is time? Who can give that a brief or easy answer? Who can even form a conception of it to be put into words? Yet what do we mention more often or familiarly in our conversation than time? We must therefore know what we are talking about when we refer to it, or when we hear someone else doing so. But what, exactly, is that? I know what it is if no one asks; but if anyone does, then I cannot explain it.41

Augustine asks a question. And asked, he cannot answer. Part of the reason he cannot answer is that he longs for a certain kind of answer: a brief and easy one. But he has no brief and easy answer. Worse still, he doesn’t even have a conceptual draft on such an answer; he cannot even form a conception of time that he can (begin to) articulate. Augustine takes his confession of inarticulateness to be genuine confession: he’s searched himself before God and found no conception of time that he can (begin to) articulate. But Augustine cannot quite rest easy in his confession—after all, he must confess further that he is guilty of all sorts of temporal words and deeds. He has talked and been talked to of events that took little time, a long time or no time at all. He has judged things temporary and permanent. He has observed the hours; he has worshipped or mourned or fasted on days; he has battled the demon of the noontide. In the evening, in the morning, and at noonday he prayed, and that instantly. He has wished time away and hoped for time back. He has arrived early, promptly and late. He is a practical horologist. Even more, he has confessed and is confessing by biographizing, by looking into his own history: “… [You] made me (but not my memory) begin in time … In time I began to smile …”, etc. So the first confession’s genuineness sits uncomfortably beside what must further be confessed. The tension 40 Cavell, S., “The Availability of Wittgenstein’s Later Philosophy”, Must We Mean What We Say?, (New York: Charles Scribners and Son, 1968), p 52. 41 Augustine, Saint Augustine’s Memory, trans. Wills, G. (New York: Viking Press, 2002), pp. 205–6.

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is captured in his words: “I know what it is if no one asks; but if anyone does, then I cannot explain it.” Augustine’s difficulty is that the “anyone” who might ask includes himself. When he asks of himself, he can give no answer. When he isn’t asking, he talks and does in ways that seem to him to require that he has an answer within him: we might say that when he isn’t asking, he seems to live an answer to the question. And so, I think, he does. But he longs for a certain kind of answer, one that although he cannot provide it, determines the space, as it were, into which an answer could fit. It determines the space that his knowledge should occupy. That space is wrongly shaped for a life, for a lived answer to the question. What he does is the answer to his question, but he cannot see how to see it as the answer. And isn’t something of the same the problem for the respondents to the CHP?

Chapter Five

Conceptual vs. Objectual Investigations Philosophical investigations: conceptual investigations. The essential thing about metaphysics: it obliterates the distinction between factual and conceptual investigations. Zettel 418 Wittgenstein wanted the two books [the Tractatus and Philosophical Investigations] read together. This has not helped people to see the Investigations as a book on the philosophy of logic; it has led many … to read the Tractatus as a theory of knowledge. (The Latin title is generally truncated, and no one remembers what Wittgenstein called it.) Rush Rhees

Introduction Let me re-share the faith that is within me: We cannot fully understand Wittgenstein’s philosophy, including the so-called later philosophy, without understanding how he appropriates the work of Frege. Tracing out the way Wittgenstein appropriates Frege’s work in his Philosophical Investigations is difficult. By the time of that book, Wittgenstein’s thinking about Frege has been constant for decades, deepening for decades. What he appropriates from Frege by that time, in that book, is so completely assimilated into his own thinking that it is hard to separate it out. It certainly doesn’t peel off, or float on the surface; it’s tempting to say that Frege is in Philosophical Investigations as the leaven is in the leavened loaf. Making the trouble worse is the fact that Wittgenstein’s appropriation of Frege’s work is most significant, but also most completely assimilated, in Wittgenstein’s conception of philosophy and of method. What I am going to do in this chapter is to show some of Frege’s influence on Wittgenstein’s conception of philosophy, and so provide some aid for rightly understanding his method. I begin by talking about some terminological problems that make what I am doing tricky. I then exposit and consider three ways of understanding Wittgenstein’s method each of which contrasts with mine. As I criticize each of the three ways, important elements of my way of understanding Wittgenstein’s method emerge. After expositing the three misreadings, I finish presenting my way of understanding his method. Along the way, I discuss, among other things, Frege’s three principles, the nature of the concept/object distinction, judgments and language-games, and Wittgenstein’s three successor principles to Frege’s.

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Method and Problems Wittgenstein’s method has been much discussed. But many of the discussions have been vitiated by a crucial misconception: many discussions take it for granted that Wittgenstein’s method is something that can be described in isolation from his work on philosophical problems. The basic idea seems to be that Wittgenstein’s method is independent of his understanding of philosophical problems, or that it is independent enough for the method to be intelligibly discussed while putting off discussion of the nature of philosophical problems. Certain remarks that Wittgenstein himself makes have played a role in this misconception: “What matters is that a method has been found”; and so on. Such remarks have suggested that Wittgenstein discovered a method of philosophizing and that he then brought the method to bear on philosophical problems. When he did so, the method revealed that the problems were of such-and-such a nature, and that some, many, were not really problems at all, at least not the sort of problems they had been taken to be. On this misconception, Wittgenstein’s major discovery is his method, and it can be celebrated and imitated on its own. But this gets things backwards. It is better, truer to picture Wittgenstein as puzzled centrally by philosophical problems, by what they are. He begins, slowly, to understand what they are. His understanding is early shaped by the debate between Frege and Kerry; and it is late shaped by it, too. Wittgenstein sees revealed in their debate features of the nature of problems of philosophy that were hard to see before the debate. As he later develops, Wittgenstein sees more and more deeply into the nature of philosophical problems, and he simultaneously sees more and more deeply into the debate between Frege and Kerry. His method is entirely driven by his developing understanding of the nature of philosophical problems. In what follows, I provide a skeleton key to Philosophical Investigations. Call it a Concept “Horse”-shaped skeleton key. I am not going to argue for my skeleton key. I am not going to assemble other readers of Philosophical Investigations before me, and then argue against them serially and by name. (My focus is on generic misreadings of Wittgenstein, not on the speciations of the misreadings in the work of particular readers. My goal is to wrangle not with straw men, but rather with abstract men, as it were, against general tendencies rather than specific tendencies.) The bulk of my argument for my skeleton key, such as it is, has been presented in the foregoing chapters. My task now is re-describing the key and showing how to use it to open Philosophical Investigations. So what follows is largely narrative and digressive rather than argumentative. Again, what I want is to show how to open Philosophical Investigations: I am not providing a detailed reading of the book, nor I am writing commentary on it. As I will discuss, I do not think commentary is a real possibility for the book. I do not think explanation is a real possibility. But this certainly does not mean that I do not think that Philosophical Investigations is comprehensible, and it certainly does not mean that I do not think it has lessons to teach—lessons that we can learn and assess the learning of by others. My aim in this chapter is to ply the foregoing investigations of the Concept “Horse” Paradox as objects of comparison to Philosophical Investigations. (“Objects of comparison”: my Wittgensteinian inflection of “skeleton key”.) When these are used as objects

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of comparison, the book, so to speak, organizes itself, and a passway through it becomes available. There are stones in the passway, yes; and the passway is narrow, but it seems to me the only passable passway through the book. A Peculiar Method Wittgenstein’s philosophical method is peculiar. Wittgenstein himself distinguished two uses of “peculiar” (and of “particular”)—the transitive and the intransitive.1 The transitive use is the most familiar. On the transitive use, the term can be further specified or explained. For example, if I whisper to you that the house we are visiting has a peculiar smell, and then specify its peculiarity—it smells like a locker room with potpourri scattered about—then I’ve used the term transitively. I have trans-ed, as it were, to the specification. On the intransitive use, the term cannot be further specified or explained. The term is used to note something, to make it noticeable, to highlight it, to emphasize it. (Much as, when using a highlighter, I am not writing comments in the text, but emphasizing a certain part of the text.) For example, I might wrinkle my nose when smelling a perfume, and comment that the perfume has the most peculiar odor. When I use “peculiar” in this intransitive way, I am emphasizing the odor; I am drawing attention to it as what it is. When I have used the term in this way, there is no trans-ing to a specification. Richard Wollheim employs this distinction memorably in Art and Its Objects. I can make my employment of the distinction clearer by looking briefly at his. Wollheim notes that we might say that … Philosophers of art who make reference to the aesthetic attitude are systematically ambiguous as to whether they intend a particular attitude in the transitive or intransitive sense. On the whole, it would look as though, despite the many theories which try to give a positive characterization of the aesthetic attitude, the attitude can be conceived of as a particular attitude only in the intransitive sense: for every characterization of it in terms of some further description or set of descriptions seems to generate counterexamples.2

1 He does so in The Blue and Brown Books, p. 158ff. 2 Wollheim, Richard. Art and Its Objects (Cambridge: Cambridge University Press, 1980), Section 41ff. Wollheim’s continuing comments are worth quoting, too. But there is room here for misunderstanding. For it might be thought that this is the same as saying that really there is no such thing as the aesthetic attitude; or, more mildly, that there is nothing distinctive of the aesthetic attitude. But to interpret the argument this way—which is as common among those who accept as those who reject it—is to miss its point. The point is not that there is nothing distinctive of the aesthetic attitude, but rather that there need not be any comprehensive way of referring to what is distinctive of it other than as the aesthetic attitude. In other words, we should regard Wittgenstein’s argument as against what he takes to be a pervasive error in our thinking: that of identifying one phenomenon with another phenomenon more specific than it, or that of seeing everything as a diminished version of itself. I think that a parallel missing of the point occurs commonly among both fans and enemies of Philosophical Investigations. Wittgenstein’s argument against a pervasive error in our thinking turns out to be an argument against a pervasive error in our thinking about Wittgenstein.

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I think that many commentators on Philosophical Investigations have made an error like the error of the philosophers of art Wollheim criticizes. The commentators sign off on the form of words “Wittgenstein’s method is peculiar”, but they do so thinking that the word “peculiar” is used transitively. That is, they think that they can further specify or explain the peculiarity of Wittgenstein’s method. Thinking that, they are then baffled whenever their specifications or explanations are wholly lame or limp badly, when they fail to accommodate the text or when they generate counterexamples or worries that seem as though they ought to be irrelevant to what Wittgenstein is doing. Unfortunately, the lameness or limping does not make them re-evaluate their use of “peculiar”; it instead leads them to think that there is an ineffability-trouble connected to Wittgenstein’s method in Philosophical Investigations. They construe the ineffability-trouble with the method on analogy with their understanding of the ineffability-trouble with the content of the Tractatus. Since, in Philosophical Investigations, the ineffability-trouble is with the method, not the content, they tend to think that the ineffability-trouble is trickier to track in Philosophical Investigations than in the Tractatus. These commentators end up treating Wittgenstein as having a methodological insight in Philosophical Investigations—a methodological insight that is both a thought and, in some way, inexpressible. To the extent that they try to say helpful things about the ineffable methodological insight, they make Delphic pronouncements about it or they make bizarre, anti-philosophical claims about it. I need to slow up here and explain. Let me take the Delphic pronouncements first. One way of responding to the peculiarity of Wittgenstein’s method is to treat it as something that “shows”. As you would expect, this use of “shows” is meant to mirror its use in the Tractatus. The commentatorial idea is that Wittgenstein’s methodological insight is, as it were, spoken in the form of his investigations: and what is spoken in the form is stated, is a statement of the insight. Thinking this leads commentators into all sorts of “showy” gymnastics, as they contort through the contours of a complicated investigation as if doing so were spelling out the statement Wittgenstein is making. I’ll have more to say about these Delphic pronouncements as this chapter ends. Now for the anti-philosophical claims. Stymied by the intransitive peculiarity of Wittgenstein’s method, some commentators conclude that they are stymied because they are treating Wittgenstein’s methodological insight as itself a philosophical insight. As such, they are stymied in their attempts to state it because they are treating the statement as of the wrong sort: Wittgenstein’s insight is an insight about philosophy, but it has no standing as, indeed can have no standing as, a philosophical insight. It is an epiphilosophical insight (to borrow Arthur Schopenhauer’s term), where “epiphilosophical” means after philosophy. (I choose Schopenhauer’s term

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in part because many who think about Wittgenstein’s method this way are End of Philosophy philosophers.3) And so Wittgenstein’s method is transformed from a method of philosophy into a method on philosophy—philosophy is attacked from without by the means of Wittgenstein’s epiphilosophical method. The method is not itself philosophical, although it is designed for an attack on philosophy. In what follows, I am throughout concerned with the intransitive peculiarity of Wittgenstein’s method. My intention is not to try, somehow, to convert it into a transitive peculiarity and then to trans to a specification of it. My intention is also to avoid treating his method as captured in an ineffable thought, or as being captured in a non-philosophical, epiphilosophical thought. I want to emphasize, highlight, the method by drawing attention to it as what it is. As I said, I do this by means of comparisons of the method with my investigations of the Concept “Horse” Paradox. The comparisons, in other words, are not roundabout specifications of the method. Instead, they are meant to allow us better to see the method as what it is. Terminological Difficulties Anyone who wants to read Philosophical Investigations as I do, who sees in it a shaping concern with Frege’s distinction between objects and concepts, will find the terminology of the book a stumbling-block. Both the term “concept” and “object” appear in a variety of uses in Philosophical Investigations, and only occasionally do the uses line up neatly with the Fregean logical use of the terms. The variety of uses means that any attempt at a concordance treatment of the book creates illusions. Each occurrence of each of the terms has to be taken up and handled individually. What Wittgenstein most commonly does with the terms is something that resembles what Frege, in informal moments, does, too. Frege points out that he did not come by judgments by combining concepts, but that he rather came by concepts by considering the articulation of judgments. So, on this informal use of “concept”, the term is not being employed in what Frege would count as the psychological or as the logical use of the term, but it is not a confused mixture of the two, either. It is rather a generic term for any logical articulation of whatever is logically articulated. Wittgenstein’s use of the term in Philosophical Investigations is most often of this sort: Wittgenstein uses “concept” most often as a term for any logical articulation of a language-game. Failure to recognize this is among the causes of misreadings of the book, and it certainly plays a role in the misreadings I will consider below. There is a related use of “object” in Philosophical Investigations. For example, in 373, Wittgenstein comments darkly “Grammar tells what kind of object anything is.” This use of “object” is itself informal. Wittgenstein does not mean to be invoking Frege’s logical sense of the term, at least not exactly. Rather, he is using the term in a way that is closely allied with the informal use of “concept”. 3 Schopenhauer coins this term in the final essay of vol. 2 of The World as Will and Representation (New York: Dover Publications Inc., 1958), Chapter 50, pp. 640–646. I underline here that as I use the term “metaphilosophy” it is philosophy of philosophy, and so philosophy; I do not use it univocally with “epiphilosophy”. Remembering this will matter later.

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I can make this clearer by noting the way in which Wittgenstein employs a bit of symbolism in Tractatus. There, Wittgenstein employs the symbol, “ξ”, as an informal symbol that is not tied to any particular logical category. Now, although the symbol is not tied to any particular logical category, it is tied to logical categories: that is, anything symbolized as “ξ” will belong to some logical category or other—but it has not yet (perhaps because doing so in a particular dialectical context would be tendentious) been tied to any one. So, too, Wittgenstein’s use of “object” in 370. Grammar tells us what logical category anything belongs to. This way of using “object” then mirrors the informal use of “concept”—it is a way of talking about a logical articulation without prejudging the precise logical articulation being (or to be) talked about. When Wittgenstein is talking about conceptual investigations, he is using the term “conceptual” in this informal way. But, as I hope Frege’s similar use of the term helps to make clear, this informal use, while not Frege’s logical use, is closely related to that use. That is, this informal use of the term carries with it the priority of language-games, or of logically articulated unities. Frege’s informal use carries with it the priority of judgment. The informal use of the term is not univocal with its use for the unsaturated, but it is inextricably tied to the notions of the saturated and the unsaturated. As I proceed, I will be careful, at least by manipulating context, to make clear how I am using “concept” (and “object”). Reading Wittgenstein Wrong (MR1) I want to talk about a way of reading Wittgenstein that is wrong-headed, thoroughly wrong-headed, but—for reasons that Kerry and the post-Kerry respondents to the Concept “Horse” Paradox make clear—very hard to avoid: misreading Wittgenstein as if the investigation of concepts were the investigation of objects. The sort of object that concepts are taken to be is something that varies across the individual members of this species of misreaders. Typically, concepts are taken to be peculiar objects, smoky, gaseous or ethereal, objects only to be found by a gambade into a spooky realm. I am not interested in sleuthing out all the different sorts of objects concepts have been taken to be. The mistake of this misreading is not in choosing a sort of object for concepts to be; it is in treating concepts as objects. Misreading Wittgenstein in this way typically results in the reader thinking of conceptual investigations on a strained analogy with objectual investigation–– usually, empirical or factual investigation. Linguistics, Empirical or Introspective A common form of this misreading—call it Misreading 1 (MR1)—is as follows: Wittgenstein’s conceptual investigations are investigations of the use of words— where use is taken as something objectual. This objectual view of the use of words takes one of two common forms: on the first, finding out what the use of a word is turns out to be an empirical or factual matter—a matter of, say, taking polls or tracking the linguistic habits of some relevant community; on the second, finding out

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what the use of a word is turns out to be an empirical or factual matter, too—but a matter of introspectively taking stock of ourselves and of our linguistic dispositions. Call the first of these Empirical Linguistics; call the second Intuitive Linguistics. Empirical Linguistics is, as a reading of Wittgenstein, hopeless. This has not kept some readers from pinning their hopes to it, however. Wittgenstein’s talk of the use of words is not Empirical Linguistics—good or bad. Wittgenstein ran no polls. He consulted no lexicographers. And to criticize Wittgenstein for not doing such things is an ignoratio. Perhaps the clearest sign of this is the way in which he consults himself when he is trying to understand the sense or nonsense of some form of words, and the way he pushes his reader to consult herself. Wittgenstein’s investigations are first-person investigations. Noting this can, unfortunately, take us in the direction of Introspective Linguistics. Introspective Linguistics contains a muted insight; it is not wholly mistaken. But, still, it is a misreading. That it is can be brought out with little fanfare. All that really needs to be done is to remember Frege’s First and Third principles. Introspective Linguistics loses sight of the distinction between concepts and objects, and so, when it searches for the use of words, it does not sharply separate the psychological from the logical. What are introspected in Introspective Linguistics’ search for uses are concepts in the psychological sense, vortices in the stream of consciousness. The muted insight that is at work in this common form is best understood differently, as an appeal either to grammar (in Wittgenstein’s proprietary sense) or to phenomenology. When we unfold the grammar of a word, or when we describe a language-game, we are getting at what Wittgenstein means by “the use of words.” What we will countenance as relevant when we do this is important. For example, empirical or factual evidence—even introspective evidence that is culled from the passing internal show—will be irrelevant to the task at hand. What is said at such moments is directly vulnerable only to other bits of grammar or description—to new examples that highlight unforeseen folds of the grammar or unanticipated dimensions of the language-game. What is said at such moments is indirectly vulnerable to the facts— but to facts of “a very general nature.” The use of a word is not a function of any internal state of the user—whether the state is understood to be occurrent or dispositional. In particular we need to avoid thinking that an internal state of a user of words—one that shows up in introspection—is evidence for the use of a word. Evidence is irrelevant. The truth that Wittgenstein is relying on when he makes his first-person claims or pushes his reader to make her own is not a truth about his own or his reader’s internal states; it is instead the truth that “a natural language is what native speakers of that language speak.”4 As a speaker of a language, I do not have evidence for what to say when, for what should be said when. I do not have evidence for whether what I say makes sense or does not. But that does not mean that I do not have authority as a speaker of 4 Cavell, S., “Must We Mean What We Say?” in Must We Mean What We Say?, p 5. This section is not only indebted to Cavell’s essay, but is meant to apostrophize it. I cannot enter fully into the complications of this discussion, but Cavell’s essay is the place to go if anyone wants to go on from my partial entry into the complications.

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the language. It is rather that my authority is not one that involves evidence. When I judge this or that form of words to be sense or nonsense, I express my authority as expressive (in the language). Call this, if you want, self-knowledge—but such self-knowledge is shaped wholly differently than is knowledge about others. I am not reporting knowledge about my own internal states as I might knowledge about someone else’s. (If internal states were in question, and given that there is no reason to impugn Kerry’s sincerity when he reports his having succeeded in using a concept-expression as an object-expression, Frege, and we, should capitulate to Kerry. But Frege did not; and we should not.) What I am relying on at such moments is my “feel” for the language. My having such a “feel” for the language is not what I am relying on as evidence for what I say having, it is not what confers authority on what I say; my “feel” is my authority. Recall Frege’s falling back on the feeling for German discussed in the last chapter. Turning Topsy-turvy As I said, when we treat conceptual investigations as a type of objectual investigation, we are violating Frege’s principles. When we treat conceptual investigations as a type of objectual investigation, it is difficult to avoid scrying the psychological realm to find what we take ourselves to need. And so we sometimes turn Philosophical Investigations itself into a psychological investigation. Stanley Cavell has best seen this problem: We know of the efforts of such philosophers as Frege and Husserl to undo the “psychologizing” of logic (like Kant’s undoing Hume’s psychologizing of knowledge): now, the shortest way I might describe such a book as Philosophical Investigations is to say that it attempts to undo the psychologizing of psychology, to show the necessity controlling our application of psychological and behavioral categories; even, one could say, to show the necessities in human actions and passions themselves. And at the same time it seems to turn all of philosophy into psychology—matters of what we call things, how we treat them, what their role is in our lives.5

Cavell here I think makes clear first that Philosophical Investigations is not only not doing psychologism, but that it is undoing psychologism. But he makes clear, second, that Wittgenstein’s way of undoing psychologism can have the strange effect of making it seem as though he is, after all, doing psychologism. That is, Wittgenstein’s way of undoing the psychologism of psychology can seem purchased at the cost of turning philosophy itself into psychology. The situation reminds me of the passage on idealism in Frege’s “Thoughts” which begins, “It’s strange how in reflection opposites turn topsy-turvy …” Reflecting on psychologism in Philosophical Investigations can seem to turn it topsy-turvy—from the anti-psychologizing of psychology to the psychologizing of philosophy. But to think the book does turn topsy-turvy is to have gotten turned around.

5 Cavell, S., “Aesthetic Problems of Modern Philosophy” in Must We Mean What We Say?, p. 91.

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When Philosophical Investigations seems to have undone the psychologizing of psychology at the expense of psychologizing philosophy itself, then it is often true that Philosophical Investigations is being treated as an objectual investigation. To use Frege’s categories in a loose, but (I trust) suggestive way, it will seem as though items from the Second Realm, the outer realm, or the First Realm, the inner realm, have somehow acquired legislative power over all philosophical disputes. To think this is to mistake the character of Wittgenstein’s interest in what we call things, in our treatment of them or in their place in our lives. For Wittgenstein, these are not First or Second Realm items; they are mutatis mutandis Third Realm matters. Or, better, Wittgenstein’s character of interest in these matters is an interest in them as such as to have standing in or as such as to stand in relationship to the Third Realm. A lot of the work Wittgenstein does in Philosophical Investigations is work done to overcome the strangeness of thinking of these matters in relation to the Third Realm; and, correlatively, it is work done to overcome the strangeness of thinking of the Third Realm as where we always already are. Wittgenstein, like Heidegger, requires of us a leap—but a leap onto the firm soil of our lives, to where we already are and have been. Let me unpack this a bit. The best way to do so is to look at Philosophical Investigations 108. We are talking about the spatial and temporal phenomenon of language, not about some non-spatial, non-temporal phantasm. [Note in margin: Only it is possible to be interested in a phenomenon in a variety of ways.] But we talk about it as we do about the pieces of chess when we are stating the rules of the game, not describing their physical properties.

One way of thinking about what Wittgenstein is doing is to think of him as attacking the Third Realm, disavowing any need for it. While there is something right about that (Wittgenstein would surely have thought of Frege’s Thoughts as phantasms), it seems to me to miss the center of gravity in the remark. It is better to think of Wittgenstein as wooing the Third Realm, as moving it closer to us. He is exorcising the phantasms of the Third Realm, so as to make room for what really belongs there— the stuff of our lives. But we cannot see how the stuff of our lives could belong there when the Third Realm seems eerily distant and crowded full with phantasms. Also, we cannot see how the stuff of our lives could belong there when the stuff of our lives is, well, this stuff: bumpy, bulging, nattering stuff. Wittgenstein is, however, trying to get us to change the character of our interest (or, more complicatedly, our uninterest) in the stuff of our lives. He is trying to get us to see ourselves as Kings and Queens, or perhaps even as Pawns, and to see the stuff of our lives accordingly. To get us to see things this way is to depsychologize psychology, it is to get us to see the necessities controlling our lives and the applications in our lives of those necessities (of callings, treatings, roles, and etc.). When we see this, we see that there is not as much threatening about the apparent psychologizing of philosophy as we might have thought. First, because the psychology is a depsychologized psychology; and, second, because philosophy is not turned into psychology (even depsychologized psychology), but rather is rendered sensitive to psychological items such that, were they to remain psychologized,

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it would be properly insensitive to. What we call things, for example, may seem beneath philosophical notice—at least until we notice the necessities that calling involves, necessities involved in our calling (as opposed to performing another action), the necessities in something’s being such as to be called (not everything will answer (to) a call), and in our acknowledging another as having called something that can be called, etc. Knowing how to speak and to be spoken to (even in simple ways) requires knowing how to take in stride numerous necessities. When we take an interest in the stuff of our lives in a way that brings these necessities to light, we have made the stuff of our lives Third Realmish. Kant, recall, takes Transcendental Idealism to be required by Empirical Realism. Kant’s point as I understand it is that we can only recover our common sense view of things, our common sense view of experience as openness to the world, if we recognize that experience itself involves certain (categorial) necessities. To think of experience as if it does not involve those (categorial) necessities is to think of experience as happenstantial awakeness—a thin sentience—instead of as a disciplined understanding—a thick sapience. And it is only the Transcendental Idealist who can think of experience as a disciplined understanding. Kant may or may not be right about the power of Transcendental Idealism; but he is right that genuine openness to the world is what experience as a disciplined understanding gives us. Happenstantial awareness gives us, not openness to the world, but “openness” to the fluctuations of consciousness. A similar structure is present, I think, in the relationship between Wittgenstein’s depsychologized psychology and his “psychologized” philosophy. To think of our psychological lives as involving necessities requires that we philosophize in a way that is properly responsive to those necessities. In other words, if we recognize that our psychological lives have a grammar, then we must philosophize, if we are to philosophize realistically, in a way that is responsible to that grammar. As a result, our philosophizing will have to submit to that grammar, our speculations will have to yield to the role that things have in our lives, to how we treat things, to what we call them. Reading Wittgenstein Wrong (MR2) This second misreading (MR2) is not so much an independent misreading as it is a subtler version of the first misreading. The person who misreads Wittgenstein this way is a person who apparently respects the unsaturatedness of concepts, and so apparently respects the difference between conceptual and objectual investigation. But the person does so by treating concepts as unsaturated objects. Items in Frege’s First and Second Realms, MR2 holds, are saturated objects, and, as such, objects that sit on their own bottoms. But concepts are unsaturated objects—they do not sit on their own bottoms; they are, as it were, ontologically precarious, wobbly, at least when considered as potential denizens of either of the first two Realms. Since they are ontologically precarious in the first two Realms, they need to be placed in a realm of their own, one that can house the unsaturated, a Third Realm—a realm in

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which they can, because of the peculiar environment, sit unwobbling on their own bottoms. MR2’s way of thinking about concepts is mistaken in part because of the way in which it misunderstands the relationship between the saturated and unsaturated, on one hand, and the judgment, on the other. It is also mistaken in its treatment of unsaturatedness. Frege prioritizes judgments. His distinction between concepts and objects, between the saturated and the unsaturated, cannot be understood apart from that prioritizing. Judgments are alpha and omega. The terms, “saturated” and “unsaturated,” are best understood as phenomenologically descriptive. (Many, most even, of Frege’s arguments are phenomenological—but his phenomenological register is so different from, say, Husserl’s, that even very sensitive readers of Frege often miss this fact: Dummett.6) Here’s what I mean: Start with a judgment, a particular sort of unit or unity, an articulated unity. Now: Think about what it means for it to be articulated. Its articulations cannot be recognized as such if, when they are recognized, they do not bear unmistakable signs of their being articulations of something that is a unit, a unity. Frege’s distinction is meant to bear such signs. The saturated and the unsaturated articulations of a judgment are still ways of looking, as it were from an angle, at the judgment itself. They are abstractions from the judgment, not extractions from it—as Ryle famously puts it. (There are no extractables in a judgment.) The saturated and the unsaturated are not, phenomenologically first and foremost, made for each other, but made from judgments. They can be distinguished only within a judgment. Unfortunately, Frege’s terms themselves, or more precisely the term “saturate”, suggests that this is not so, since it suggests that what is saturated can— when appropriately situated—sit on its own bottom, independent of a judgment. This is indeed how MR2 treats the saturated. But that is a mistake, and Frege (at least sometimes) acknowledges that it is The self-subsistence which I am claiming for number is not to be taken to mean that a number word signifies something when removed from the context of a proposition, but only to preclude the use of such words as predicates or attributes, which appreciably alters their meaning.7

That is, a saturated term is such only within a judgment. Taken apart from a judgment, no term is as such saturated or unsaturated. A saturated term no more assigns itself that status, independently, than an unsaturated term does. Neither articulation of a judgment is anything outside of the judgment. A judgment is not arrived at via first cognitively securing independently heterogeneous items and second fastening one to the other––by means of a contingent and convenient fittingness. Rather, the articulations of a judgment are arrived at via abstracting dependently heterogeneous items within it—and their fittingness is neither contingent nor convenient, but inherited from each’s logical station and its duties. 6 For more on Frege-as-phenomenologist, see Tragesser, R., Phenomenology and Logic (Ithaca: Cornell University Press, 1977), pp. 41–50. 7 Frege, Foundations of Arithmetic, p. 72.

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For Wittgenstein, the language-game has priority; and it has it in roughly the way that judgment has priority for Frege. 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. 654

For Wittgenstein, when he uses “concept” informally, a concept is an articulation of a language-game. And language-games articulate into more than objects and concepts (in the logical sense); they articulate into those often, but also often into judgments, and perhaps into still other articulations. (For Wittgenstein in Philosophical Investigations, there is no way of fixing, ahead of confronting a particular languagegame, what articulations are involved in it. This is a deep change from the Tractatus. There, Wittgenstein remarked that “there are no surprises in logic”; in Philosophical Investigations, he repeatedly reminds himself and his interlocutors that logic is often surprising. A relevant example here is provided by the builders described at the opening of the book: their language-game articulates into units expressed by “block”, “slab”, “pillar” and “beam”, but these articulations are neither concepts (unsaturated), nor objects (saturated), nor judgments.8 They just are the articulations they are, whatever they are. Call them what you will.9) That judgments are articulations of language-games makes a characteristic motion in Wittgenstein’s thinking easier to understand. We need to know or imagine the language-game in which a judgment occurs if we are to understand the judgment. We should say that judgments, in a way that is akin to concepts (in the logical sense) and like objects, are unsaturated. They are completed, saturated, by the language-game itself. This point needs careful development. Readers of Wittgenstein often have seen that language-games are necessary in order rightly to articulate judgments. I agree that that is so. We might say, using Tractatus’ terms, that it is the language-game that allows us to see the symbols in signs. But the language-game, as it were, does more than that. It not only allows us to see the symbols in the signs of a judgment, it also reveals the judgment’s inextricability from the language-game. It does this by revealing the judgment’s own particular unsaturatedness. A judgment is, thus, an abstraction from the language-game. It is available to thought, to consideration and evaluation, to the extent that it is only when kept in internal relationship with the language-game that is its home. For Wittgenstein, mind meets world in language-games––not in anything subjudgmental or even in something judgmental. For Frege, following Kant, mind meets world in the judgmental, in judgments. That is, mind meets world in something truth-valuable. For Wittgenstein, since mind meets world in language-games, mind does not meet world, at least not initially, in something truth-valuable. This is a deep difference between Kant and Frege, and Wittgenstein, a deep difference in the midst of deeper similarity.

8 Goldfarb, W. “I want you to bring me a slab”, Synthese 56, 1983, pp. 265–82. 9 Rhees, R. “Questions on Logical Inference” in Vesey, G. (ed.), Understanding Wittgenstein (Ithaca: Cornell University Press, 1974), pp. 30–48, especially p. 38.

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For Kant and for Frege, even if not in exactly the same way for each, mind meets world in judgment. And this meeting is one that must be immediate: the only possible mediator would be still another judgment—and that is regressive, viciously so. Kant writes: If understanding in general is to be viewed as the faculty of rules, judgment will be the faculty of subsuming under rules … But if it is sought to show in general how we subsume under rules, that is, how we distinguish whether something does or does not come under them, then that could only be by means of another rule. This, in turn, for the very reason that it is a rule, again demands guidance from judgment.10

Wittgenstein, I think, concurs with Kant. But, for him, language-games play a similar structural role to that played by judgments for Kant. For Kant, we must be able to make judgments without, in so doing, being guided by a judgment. For Wittgenstein, we must be able to play language-games without, in so doing, being guided by a language-game. We can play a language-game, we can learn to play one, without its being the case that we are playing another language-game, or doing what only playing another language-game would allow us to do. Playing language-games, then, is ultimately something that we simply do, that we just do—it is a feature of our natural history. There is no philosophical explanation of our ability to play languagegames, no more than there is a philosophical explanation of birds’ ability to fly or beavers’ ability to build dams. It is sometimes said that animals do not talk because they lack the mental capacity. And this means: “they do not think, and that is why they do not talk.” But—they simply do not talk. Or to put it better: they do not use language—if we except the most primitive forms of language. Commanding, questioning, recounting, chatting, are as much a part of our natural history as walking, eating, drinking, playing. 25 What we are supplying are really remarks on the natural history of human beings; we are not contributing curiosities, however, but observations which no one has doubted, but which have escaped remark only because they are always before our eyes. 415

A Caution We should be cautious here, however, since the way I’ve put things can be easily misunderstood. Language-games do not stand apart, as it were over and above or even alongside the world. To think this is to miss the multidimensionality of languagegames. It is, in particular, to miss the way in which language-games are commingled with the world, are world-involving. At the end of Chapter Three, I pointed out that, for Wittgenstein, items in the world can be and are themselves instruments of the language, of language-games. And, earlier in this chapter, I gestured at the way in which Wittgenstein seeks to bring out the Third Realmish character of the stuff of our lives. The world, the things in it, facts of our nature, etc., are all caught up in language-games. We might put this point by saying that language-games, and so the logic of our language, is vulnerable to contingency. Were things to change, were certain things in the world to change (especially very general features of it, like, say, 10 Kant, I. Critique of Pure Reason, (A133/B172).

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the relative stabilities of the weights of things—lumps of cheese—that do not change randomly) certain language-games would cease, might never have developed, will continue but in variation, etc. Wittgenstein’s Third Realm is vulnerable in certain ways to both time and change. This vulnerability is what makes his Third Realm a Realm of surprises—unlike Frege’s. (About Frege’s Third Realm there is an alwaysthe-same-always-goddamn-sameness.) The fact that one language-game is played does not allow us simply to project the dimensionality of the rest of logical space, does not allow us simply to project what other language-games are played, or how they are played. (The Tractatus works dialectically through its version of the notion that such projection is open to us.) One crucial function of many of Wittgenstein’s imagined language-games and of many of his fictitious natural histories is to bring this home to us. Wittgenstein says that “Essence is expressed by grammar” (371) (italics in original)—but we must acknowledge just how craftily said this is. Wittgenstein did not say that essence is created by grammar. He did not say that essence is explained by grammar. The essences that grammar expresses are not human artifacts, any more than human beings are themselves, just as such, human artifacts, or any more than language is itself a human artifact. What Wittgenstein reminds us of, when he reminds us that commanding, questioning, etc. are parts of the natural history of human beings, is that the essences that grammar expresses are themselves vulnerable to time and to change. But their vulnerability is not a vulnerability to a mere change of mind on our part, as if we could on a weekend decide to undo the essences of the working week. And their vulnerability to time is not a vulnerability to mere disuse or to our forgetfulness, as if an essence could rust or molder, or fust from inattention. Nonetheless, since the grammar that expresses essence has its being in languagegames, and since language-games can change, essences can change. I am highlighting that our interests, although they can change, do not change randomly; and, I am highlighting that for the essence of a thing to be an expression of our interest in it does not make it the case that our interest creates that essence. Our interest rather creates the stage, as we might put it, upon which the essence appears—whether to strut or fret, or to just exist composedly. I will wait until later in the chapter to further clarify the nature of the interest that interests Wittgenstein. I will not further pursue the details of the differences between Kant and Frege, and Wittgenstein on judgment, since my primary task was to criticize MR2. But the differences between Kant and Frege, and Wittgenstein, are important to a full understanding of the problems with MR2. As I hope is clear, MR2, although it attempts properly to value and properly to handle the saturated and the unsaturated, fails to do so. It fails by failing to respect the priority of the language-game. MR2 treats not only objects and concepts, in Frege’s logical sense, but also all other articulations of language-games as independently heterogeneous items—items made for unities, but not from unities.

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Kerry’s Folly and Metaphilosophy These two misreadings each make mistakes that are species of Kerry’s mistake. MR1 is the crudest form of Kerry’s mistake—perhaps, in its context, even a cruder mistake than Kerry’s. MR1 simply casts aside the absolute distinction between concepts and objects, and sees the distinction as non-absolute, indeed as one of merely “external relations” (to use Russell’s Principles’ phrase). MR2 is subtler, and much closer to Kerry’s mistake. MR2 sort of sees the absolute difference between concept and object, but then it doesn’t see it, and then doesn’t even sort of see it. One common camp follower of Kerry’s Folly misreadings is a misreading of much of the metaphilosophy of Philosophical Investigations. The remarks in the middle of the book (in its dialectical middle, not in its paginal middle), the remarks devoted to philosophy, tend to be segregated by the misreading from the rest of the book. This segregating of Wittgenstein’s methodological remarks involves invoking, explicitly or implicitly, a distinction between methodological, metaphilosophical remarks and philosophical remarks. How the invocation goes, as well as when it is made, as well as the degree to which it is made explicit or remains implicit, changes across commentators. Here’s the patter: The philosophical remarks may require strenuous effort to understand (if they can be understood); but the methodological remarks can be understood facially (if they can be understood). The two Kerry’s Folly misreadings support a deep-seated picture of the relationship between methodological remarks and the remarks that manifest the method. The picture is one on which the methodological remarks are meant to introduce the remarks that manifest the method. Methodstating remarks must be such that they can be understood without understanding the method-manifesting remarks, otherwise the method-stating remarks are misfits. They fail in their introductory task. Compare: The instructions given for taking a test and the test questions answered according to the instructions. Once it is seen, one of the most striking of the continuities between the Tractatus and Philosophical Investigations is the placement of the (bulk of the) methodological remarks. In both books, the methodological remarks are sandwiched in the dialectical middle—in the 4’s in the Tractatus; and from around §§89-133 in the Philosophical Investigations. Why are the method-stating remarks sandwiched by method-manifesting remarks? Because, sandwiched in this way, the remarks resist the application of the deep-seated picture. Sandwiched in this way, the suggestion is that the method-stating remarks stand in an internal relation with the methodmanifesting remarks. That is, the method-stating remarks are to be understood only in relation to the method-manifesting remarks, and vice-versa; understanding one group requires understanding the other. Wittgenstein doesn’t get around to telling his reader about philosophizing his way until the reader has been exposed to some of that way of philosophizing. How does this work; why does it work? A full answer to this would require little short of a detailed reading of the first 81 or so remarks of the Philosophical Investigations. Since that is more than I can provide, let me (poorly but, I hope, still helpfully) substitute the following: as I earlier suggested, the question that goes deepest in the Philosophical Investigations

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is the question, “What is a philosophical problem?” Wittgenstein wants, above all, to reveal the character of philosophical puzzlement. As we have seen, languagegames are a crucial revelator of that character. Wittgenstein begins the book with a simple picture of language, Augustine’s. He then introduces, as part of the treatment of the picture, the notion of a language-game. He first uses a language-game to show what a language would look like for which Augustine’s picture is correct. He then shows how language-games can be deployed to rid us of certain philosophical temptations—in particular, the temptations bound together in the philosophical conception of meaning. By doing this, he begins to show how language-games can be used to make clear(er) what a philosophical problem is. One thing crucial to note is that Wittgenstein is doing with language-games something more than we might at first notice he is doing. That is, we almost certainly will notice that language-games can allow us to free ourselves from the idea that there is a necessary form of language; we almost certainly will notice, too, that language-games can show us that certain questions can be properly shrugged at, treated as undemanding. But what we may miss is that language-games are also being used by Wittgenstein to help us understand why we find the idea of a necessary form of language so necessary, and to understand why, even when we can properly shrug at them, we find certain demanding questions so demanding. Language-games, in other words, enter crucially in Wittgenstein’s revelation of what philosophical problems are, of what the character of philosophical puzzlement is. So, from the first remark on, Wittgenstein is teaching us things we need to understand if we are to understand the methodological remarks in the middle of the book; and from the middle remarks back, we are meant to see that the nature of philosophical problems and of philosophical puzzlement has been revealing itself. And of course it continues to reveal itself from the middle remarks forward. Wittgenstein’s methodological remarks are not descriptions of what past philosophy has been, nor are they descriptions of what all future philosophy should be. His remarks are descriptive—in the sense of that term internal to his philosophical work—of what his philosophy is. The reason why a misreading of the metaphilosophical remarks is a camp follower of the Kerry’s Folly misreadings is that it, like the Kerry’s Folly misreadings, wants to secure something to philosophize about that is independent of Wittgenstein’s way of philosophizing about it. Even if, at the level of the philosophical remarks, the metaphilosophy misreader is willing to grant that it is hard to appreciate what Wittgenstein is up to except by being up to it with him, the misreading will contend that we can at least grasp his descriptions of what he is up to without being up to it with him. Kerry wanted to do logic with Frege; but Kerry did not want to have to beg pinches of salt or entreat his readers to meet him halfway. He thought he could do logic with Frege while parting company with him about how to prepare himself and others for doing logic with Frege or for commenting on what he and the others were doing in doing logic. Kerry wanted a subject matter for meta-logic that could be grasped independent of a grasp of logic. The metaphilosophy misreader wants to do philosophy with Wittgenstein while parting company with Wittgenstein about how to prepare himself and others for doing philosophy with Wittgenstein, or for commenting on what he and the others are doing in doing philosophy. The

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metaphilosophy misreader wants a subject matter for Wittgenstein’s metaphilosophy that can be grasped independently of a grasp of Wittgenstein’s philosophy. A Just-So Story: Fregensteinian Conceptual Investigations I will now describe a third misreading of Wittgenstein. I’ll describe it by telling a short just-so story about a philosopher who I’ll dub “Fregenstein”. This story is meant to serve as the final rung on the ladder that I have mounted in order to see Wittgenstein’s conceptual investigations aright. In good Wittgensteinian fashion, I will, after climbing the ladder, kick it away, kick Fregenstein away. I should say that I think Fregenstein is a cousin to Wittgenstein. The Fregensteinian reading I am going to briefly describe is not a version of Kerry’s Folly, as were MR1 and MR2; it is instead an unripened version of Wittgenstein’s own method in Philosophical Investigations. I do not intend for Fregenstein’s philosophical investigations to stand up to concentrated scrutiny, but rather for my description of them to allow us to clamber to a new place to stand as we scrutinize Wittgenstein. To picture Fregenstein, picture Wittgenstein as if, in Philosophical Investigations, he were employing Frege’s Three Principles as Frege stated them and using terms like “object” and “concept” straightforwardly in Frege’s logical sense. With this picture of Fregenstein in mind, we might say that in Philosophical Investigations Fregenstein is sharply distinguishing the investigation of an object from the investigation of a concept. These two types of investigations are going to be radically unlike; one is the investigation of the saturated, the other of the unsaturated. To investigate the unsaturated, we cannot proceed as we might otherwise proceed. Concepts are not available, independent of judgments, to be investigated. Since we do not encounter concepts except in judgments, conceptual investigation will have to proceed by means of investigating judgments. Let me expand on this Fregensteinian point. Frege’s recognition of the unity of the proposition required that he think of the “parts” of thoughts as being such that not all of them could be, so to speak, within the reach of definition. In particular, the unsaturated “parts” of thoughts could not be within the reach of definition. As is made clear in Frege’s debate with Kerry, as well as in other places in Frege’s writing, concepts cannot be defined. If I attempt to make a concept a definiendum, I fail sharply to separate object and concept—even more, my attempt is defeated: the definiendum in a definition sentence is an object. One way of putting this is that the spot in a definition sentence that the definiendum fills is one that takes an objectexpression. So, if I want to investigate a concept, I will have to do so by considering judgments in which the concept functions. There, in the only place it can be studied, is the concept to be studied. Fregenstein privileges agreement in judgments because only if we agree in judgments can we share concepts to be investigated. Given this constraint, Fregenstein can be seen in his insistence on agreement in judgment to be rightly resisting a tendency that Frege, too, deplored: the tendency to use “the definite article to stamp as an object what is a function and hence a non-object.” Fregenstein, again like Frege, will treat this tendency as one that despoils “the logical source of knowledge.”

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Another related and crucial thing to bear in mind while we consider Fregenstein is that the term “conceptual” in his term, “conceptual investigation”, must not be construed psychologistically—that is, in the way that Kerry construed it in his abortive attempt to counterexample Frege’s claim that objects and concepts are absolutely distinct. That concepts are not to be construed pyschologistically makes clear why Fregenstein turns his face resolutely against certain conceptions of the role of the inner in his conceptual investigations. For reasons that Frege more or less makes clear, nothing inner—think of Frege’s treatment of the inner realm and of its denizen ideas in “Thoughts”—could determine the shape or outcome of a conceptual investigation. As Fregenstein might write, “It shews a fundamental misunderstanding, if I am inclined to study the headache I have now in order to get clear about the philosophical problem of sensation” (314). Consider, as an example, since my “quote” of Fregenstein brings it to mind, the philosophical problem of pain. When we philosophers take an interest in pain, ours is not an interest in whether a particular person is in pain or not. Like anyone else, even we philosophers would take the person’s sincere word on whether he is in pain as deciding whether he is or not. The philosophers’ problem is not a problem about whether to doubt sincere first-person avowals or denials of pain. The philosophers’ problem is a problem, as we often find ourselves saying, about the concept of “pain”. Even so, we are not, from Fregenstein’s point of view, quite ready to take ourselves or what we say fully seriously. That is, we philosophers tend to think we can solve the problem of the concept of “pain” by rehearsing things we take ourselves to know about pain, where the logic of what we rehearse requires that we treat pain as an object, not as a concept. We treat pain as something we can make the subject of various judgments, and as something that we can therefore say true (and false) things about. What we know something about, where that takes the form of putting the focal item in the subject spot of a judgment, is not relevant to the problem posed by the concept of pain. The need for reminders, for agreements in more than definitions, for the concern with, not phenomena, but the possibilities of phenomena, for the interest in the proper handling of methods of representation, for description as opposed to theory, for perspicuous representation as opposed to topical description—all these needs stand together in the investigation of the unsaturated. Reminders of what we should say when are needed to give us a sample of judgments in which the concept we are investigating is at home. We need agreement in judgments because it is only by agreeing in judgments that we manifest shared concepts. We are concerned not with phenomena, but with their possibilities, because our concern is logic, not psychology. We care about methods of representation because we are not interested in what is represented—an empirical interest, an interest in the Second, the outer, realm, or an interest in the First realm via the second—but rather in methods of representation—a conceptual interest, an interest in the Third realm. As I said, I think there is quite a bit that is true in the story. I’m not going explicitly to sort the true from the false, the ripe from the unripe—I hope that will become clear as I briefly present what I take to be the right story.

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The Three Principles Frege keeps to three principles in his thinking, and those three principles—or, more accurately—their successors, are principles Wittgenstein keeps to as well. In fact, a very useful way of thinking about Wittgenstein’s philosophizing, from its beginning, is to think of Wittgenstein as striving to keep to Frege’s principles. I say “striving” here to highlight the complicated way in which Wittgenstein appropriates Frege’s three principles. As Wittgenstein moves from Notebooks to Philosophical Investigations, his philosophizing is a prolonged attempt fully to appropriate the three principles. For Wittgenstein, keeping to Frege’s principles is never a simple matter of first having understood once-for-all what each requires, and then second keeping to it. Rather, Wittgenstein’s understanding of Frege’s principles remained constantly responsive to the difficulties of keeping them and to the results of keeping them. In other words, the principles are for Wittgenstein living principles (in something like F.R. Leavis’s sense of the term). The principles are caught up in the field of force of the problems whose treatment is guided by them. And so what it is to keep to the principles is not fixed ahead of the problems, but is rather fixed in the treatment of the problems. The point here is to see the difference between the three principles and, say, the Ten Commandments. Frege’s three principles, recall, are: Always to separate sharply the psychological from the logical, the subjective from the objective; Never to ask for the meaning of a word in isolation, but only in the context of a proposition; Never to lose sight of the distinction between concept and object.

When Frege introduces the principles, he also discusses their interrelationship: In compliance with the first principle, I have used the word “idea” always in the psychological sense, and have distinguished ideas from concepts and from objects. If the second principle is not observed, one is almost forced to take as the meanings of words mental pictures or acts of the individual mind, and so to offend against the first principle as well. As to the third point, it is a mere illusion to suppose that a concept can be made an object without altering it.11

Frege comments here on each of his three principles, in order. He notes that failing to keep to the second principle, the Context Principle, results in failing to keep to the first principle. James Conant, in his work, has shown how failing to keep to the second principle results in failing to keep to the third.12 One way of understanding the first chapter of this book is as showing how failing to keep to the third results in failing to keep to the first. I agree with Conant’s claim that the three principles are related in such a way that a failure to keep to any one of them results in a failure to

11 Frege, Foundations of Arithmetic, p. x. 12 Conant, J., “Elucidation and Nonsense in Frege and the Early Wittgenstein”, pp. 174–217.

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keep to each of the other two—I think this is true for Frege, but I’m certain it is for Wittgenstein. Frege’s three principles are the methodological counterparts of the recognition of the unity of the judgment. Frege prioritizes judgment, not only in Begriffsschrift, but also in his method. An advantage Frege enjoys because of his prioritizing judgment is that he has no need to give an account of how universals inhere in particulars, how a concept attaches to an object, or how the parts of a judgment adhere to each other. For Frege, parts of judgment lead no independent life outside of the context of a judgment. Frege has no problem of the unity of judgment to face—unlike, say, Russell. As I understand them, Frege’s three principles are the methodological imperatives required by his recognition of the unity of judgment. So understood, the principles are not to be thought of as justified by some segment of Frege’s thinking, but rather the principles reflect the recognition that provides shape and direction to all the segments of his thinking. To see the legacy of Frege’s three principles in Philosophical Investigations, it is best to think of the successors of them that are at work there: Always to separate sharply the psychological from the logical, the private from the public. Never to ask for the meaning of a word or proposition in isolation, but only in the context of a language-game. Never to lose sight of the distinction between concepts (and conceptual investigations) and objects (and empirical investigations).

Like Frege’s three principles, these principles are the methodological counterparts of the recognition of a unity—but of the unity of the language-game, not of the judgment. Like Frege’s, Wittgenstein’s principles are interlocking—to deny any one is to deny each of the other two. For example, to deny the second is to deny the first: if we ask for the meaning of a word outside the context of a language-game, then we will be almost forced to cast about looking for meanings in the psychological realm, a realm we will picture as private—a realm like Frege’s inner realm. We will also, in looking for that, there, lose sight of the distinction between concepts and objects. We will be looking for something that we understand as an object, as expressed in an object-expression. And, since we understand what we are looking for as an object, we will look for it as we look for objects—we will conduct an objectual investigation. We will look for the object empirically, or at least we will look for the object in a way that duplicates the structure of empirical investigations. One thing that should be said here—a small, cautionary thing—is that the distinction between the public and private is not a political distinction. The distinction, as the first principle in its wording intimates, is a distinction that is linked to the distinction between the logical and the psychological. Linking the logical and the public, as I think Wittgenstein does, has numerous important ramifications: one general one I have already mentioned (i.e., coming to see the stuff of our lives as Third Realmish); one particular one is revealed in the so-called Private Language Argument. What Wittgenstein is doing there is showing just how deep into (the stuff of) our lives the logical, the public, goes. Even where we might think we have found our way to something purely private that must count philosophically, we find instead

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that either there, too, are found necessities, logic, or we find nothing that we can regard as a something at all. We may, at that point, sound a yawp barbarously over the rooftops of the academy, but either our yawping will have a point, and so be subject to necessities, or it won’t, and so will be merely yawping at the last. Wittgenstein’s attempt to see the stuff of our lives as Third Realmish is not something that begins only later in his philosophizing. The famous opening lines of the Tractatus are also devoted in part, and in their specific way, to accomplishing that task: “The world is everything that is the case. The world is the totality of facts, not of things … The facts in logical space are the world. The world divides into facts” (1–1.2; emphasis mine). As Wittgenstein reconceives the task later, the crucial task is to see language-games as not only “dividing” the world, but as involving the world, and so as vulnerable in important ways to changes in it (as I have suggested above). Vulnerability like this on the part of language-games makes it far harder to see how to distinguish the essential from the inessential in the logic of our language than doing so seemed to be in the Tractatus. (It becomes so hard, in fact, that it is not always clear that the distinction between essential and accidental has a secure purchase on language-games, or, if it does, where it does.) At the very least, the vulnerability requires that the understanding of a language-game requires an understanding of its details; there is no “gist” of a language-game to be understood in isolation from its details. A language-game is a concrete whole, and it is, so to speak, a self-moved activity. Any putative understanding of a language-game that leaves it indebted to something outside itself is flawed. In the Tractatus, to the degree that languagegames are even discerned in it, they were not understood as concrete wholes, or as self-moved activities. They were indebted to logical space, and their gist could be understood in isolation from their details—in fact, their details were considered a distraction. The Right Story: Wittgensteinian Conceptual Investigations Let me shift back into my story: By thinking of judgments as requiring the context of a language-game, Wittgenstein is formulating various questions against a backdrop of broadly Kantian considerations. To make this clear, I want to look at the string of remarks, §§240-242. To understand this string of remarks, we need to understand two different kinds of considerations, Cartesian ones and Kantian ones. When Wittgenstein says what he says about the peacefulness of mathematics, his interlocutor takes him to be invoking human agreement as a way of settling the question of whether something is true, or if not true, false. But Wittgenstein rejects this way of understanding his invocation. He invokes human agreement in mathematics, but not as a way of addressing, at least not immediately, what I am calling Cartesian considerations—considerations about whether certain mathematical judgments are true (or, if not true, false). Wittgenstein invokes agreement, not to settle what is true (or if not true, false) but rather to help his interlocutor to see how agreement in mathematics is possible. That is, the notion of agreement that Wittgenstein invokes is not that of agreement of opinions—where two people agree that some proposition is true—but rather an agreement in judgments—where two

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people agree in the language they use, in language-game, in form of life. This is a notion of agreement that does not contrast, as agreement in opinion does, with disagreement. The considerations here are Kantian—considerations about whether mathematical judgments are so much as true-or-false. A Kantian notion of agreement is required in order to make sense of disagreement. Wittgenstein is answering here the question, “How is dis/agreement of opinions possible?”—and he is answering it by invoking agreement in judgments. To invoke this, to invoke language-games, is not to give an account of what it is for something to be true, (or if not true, false); rather, it is to give an account of what it is for something to have, to use a Kantian phrase, objective purport. Disagreement is not the contrast here, but rather lacks objective purport. Grammatical objects are parasitic on language-games; grammatical objects are parasitic on our agreements in judgments. We agree in judgment insofar as we play the same language-games. Language-games are articulated unities, articulated unities of words and deeds: Philosophical Investigations 7: “I also shall call the whole, consisting of the language and the actions into which it is woven, a languagegame.” It’s this fact about language-games that explain Wittgenstein’s comments about mathematicians in the 240’s. All this sheds light on why the language-game is “proto-phenomenon”, the “primary thing”, on why forms of life are “given”. There is no accounting for agreement in judgments that does not presuppose agreement in judgments, no accounting for language-games that does not presuppose language-games. Forms of life are given because they are as far as philosophy can go, so to speak; they are what philosophy must employ but not explain. This “limit” on what philosophy can do reflects Frege’s starting, as he does, with judgments, and his arriving at concepts by considering the articulation of judgments. Frege has no explanation to offer for the unity of judgment: it is the protophenomenon, the primary thing, what is given. Wittgenstein has no explanation to offer for the “unity” of the language–game; it is the proto-phenomenon, the primary thing, what is given. We can, if it helps, see Wittgenstein’s use of the term “form of life” as his way of finding a term to range across, in a related tricky sense to that of “object”, language-games. But, so used, the term does not enter into any explanation of the “unity” of a language-game. Reminding us of this is the burden of most of Wittgenstein’s remarks about family resemblance. To better understand what I’ve said, it will help to take a brief look back at the Tractatus. There, Wittgenstein treats Frege’s object/concept distinction as a distinction between formal concepts. Formal concepts contrast with material concepts. Much of the same burden borne by formal concepts in Tractatus is borne by grammar in Philosophical Investigations. In Philosophical Investigations, grammatical investigation is the investigation of concepts, of methods of representation, of the possibilities of phenomena. Consider the following difficult but useful passage from Cavell; consider in particular the way he complicates the word “concept”:

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In a Wittgensteinian context, “call” is related to grammatical criteria and generic objects. The criteria do not relate a name to an object, but, we might say, various concepts to the concept of that object.13

We can align Cavell’s remark with Tractatus’ distinction between material concepts and formal concepts. According to Cavell (as I read him), J.L. Austin is interested in the application of material concepts (is this a goldfinch?), whereas Wittgenstein is interested primarily in the application of formal concepts. (The two uses of “application” are not univocal.) That is, Wittgenstein is interested primarily in Kantian and not in Cartesian considerations. Cavell’s reach for the phrase “relating various concepts to the concept of that object” is his attempt to register, rightly, the difference between establishing that something falls under a material concept, is an object of such and such a sort (a goldfinch), and establishing that there is an object of a certain kind to attach a forthcoming name, or piece of information, to. I want to pause to look more closely at the Tractatus’ distinction between formal and material concepts (below, material concepts are called “proper concepts”), and about the peculiarity of formal concepts. In the sense in which we speak of formal properties we can now speak also of formal concepts. (I introduce this expression in order to make clear the confusion of formal concepts with proper concepts which runs through the whole of the old logic.) That anything falls under a formal concept as an object belonging to it, cannot be expressed by a proposition. But it is shown in the symbol for the object itself. (The name shows that it signifies an object, the numerical sign that it signifies a number, etc.) Formal concepts cannot, like proper concepts, be presented by a function. For their characteristics, the formal properties, are not expressed by means of functions. The expression of a formal property is a feature of certain symbols. The sign that signifies the characteristics of a formal concept is, therefore, a characteristic feature of all symbols, whose meanings fall under the concept. The expression of the formal concept is therefore a propositional variable in which only this characteristic feature is constant. 4.126

Notice that here Wittgenstein distinguishes two sorts of “fallings under”—that enjoyed by something that falls under a material concept, say of a’s being F, and that enjoyed by something that is a value of a particular sort of variable. Corresponding to these two ways of “falling under”, there are two different sorts of “application” to consider, and so speaking of the application of a proper concept is different from speaking of the application of a formal concept. Wittgenstein goes on to say that: The propositional variable signifies the formal concept, and its values signify the objects which fall under this concept. 4.127

He also says that: A formal concept is already given with an object, which falls under it … 4.12721 13 Cavell, S. The Claim of Reason, p. 73.

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The notion of a propositional variable is obviously central here. Wittgenstein explains it in the 3’s, in the remarks following sharply on the heels of the Tractatus’ Context Principle in 3.3: “Only the proposition has a sense; only in the context of a proposition has a name meaning.” Wittgenstein says that what characterizes the sense of a proposition is a symbol. A symbol “presupposes the forms of all the propositions in which it can occur.” Since this is so, the symbol is presented by a variable, whose values are the propositions that contain the symbol. (The symbol is constant, everything else variable.) Wittgenstein dubs this variable “the propositional variable.” If we place Cavell’s remarks about relating the concept of the object to various other concepts against these Tractatus remarks, we can see that the rehearsal of criteria, in the form that most interests Cavell, is very like that of presenting an expression by means of a propositional variable. Notice, too, that assigning a value to a propositional variable is a matter of giving the propositions whose common characteristic the variable is. So, even in Tractatus, the notion of agreement in judgments is lurking, and playing a key role. Cavell continues that criteria are necessary for the possibility of acquiring any information about objects: “you cannot be told the name of that object because there is as yet no object of that kind for you to attach a name to: the possibility of finding out what it is officially called is not yet open to you.” The idea is that, in Tractatus’ terms, you do not yet understand what formal concept the value is a value of. Without that, you can do nothing with it. Cavell now mobilizes Philosophical Investigations 371: “Essence is expressed by grammar”. Grammar tells us what kind of object anything is because grammar shows formal concepts, so to speak, or, perhaps better, because grammar reveals the formal concept that a particular value is the value of. In the economy of Philosophical Investigations, formal concepts are best understood as expressions of our interest. We cannot be interested in something, but interested in it in a characterless way. Our interest is always an interest with a certain character. A formal concept expresses a charactered interest of ours. To make this clear, I need to discuss Wittgenstein’s use of “interest” in Philosophical Investigations 570: “Concepts lead us to make investigations; are the expression of our interest, and direct our interest.” As I understand it, Wittgenstein is using “interest” as (what Kenneth Burke might call) a “deflected name” of what Kant named “spontaneity”. Concepts are expressions of our spontaneity. This is true of both formal and material concepts, but is, so to speak, even more true of formal than of material concepts. Formal concepts are more spontaneous than material concepts. The difference is reflected in the role of criteria in each case. As I have said, following Cavell, providing criteria for formal concepts is a matter of presenting an expression by means of a propositional variable, a matter of relating the concept of the object to other concepts. Providing criteria for material concepts is a matter of providing what Kant calls “marks” of the concept—e.g., the marks of being a goldfinch. Failing to recognize this crucial difference among concepts—which is not well marked terminologically in Philosophical Investigations—has led to a corrupted understanding of Wittgenstein’s remarks on family resemblance. Those (in)famous

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remarks are almost universally (Rhees is one noteworthy exception) understood as about material concepts. But they are instead remarks about formal concepts. Wittgenstein is not talking about concepts like (to use Rhees’s example) “lemon” but rather about “game”, “language” or “number”. In an anticipatory passage in The Blue Book, Wittgenstein writes: We talk of kinds of numbers, kinds of propositions, kinds of proof; and also of kinds of apples, kinds of paper, etc. In one sense what defines the kinds are properties, like sweetness or hardness, etc. In the other the different kinds are different grammatical structures.14

Wittgenstein here is marking the sort of distinction I am bringing out. Family resemblances are needed for thinking rightly about grammatical structures, formal concepts, not for thinking rightly about apples or paper. When I classify something as a game, my doing so is not a function straightforwardly of the marks or properties of what I have classified; it is rather a similarity in the grammatical structure of what I have classified to the grammatical structures of other things I have classified. (Note that the ambiguity of “kind” is reflected here in “classified”.) In other words, I recognize in this the same “face” I recognized in that, and that, and so on. But the similarity in “face” is not a straightforward similarity in “features”. Perhaps the most crucial thing to see here is that treating different grammatical structures as of the same kind is a matter of resolution, not one of compulsion. Defending such a resolution will throw me back on criteria (in the relevant sense) and will require of me that I relate what I take to be the concept of each to other concepts. Being able so to relate them does not seal any logical deal, however. But it may be that my relating is persuasive, more persuasive than anyone else’s, and so it may become the de facto accepted relating.15 We might say that the degree to which grammatical structures, formal concepts, are spontaneous is reflected in the role of resolution (and lack of compulsion) here. At any rate, what I hope I’ve made clear is that taking the remarks on family resemblance to be Wittgenstein’s entry into the Nominalist/Realist controversy is to too simply take them. At the very least, Wittgenstein has changed the layout of the controversy. Concepts, I have said, are expressions of our spontaneity. Formal concepts more so; material concepts less so. (Even though material concepts are less spontaneous,

14 Wittgenstein, The Blue and Brown Books, p. 19. 15 I talk of persuasion, but I do not have in mind persuasion merely rhetorical, but rather persuasion that involves logic. The reason why I talk of persuasion is that it seems to me that the defense of a relating of grammatical structures is conducted in arguments that are neither deductive nor inductive, but rather analogical. I take analogical argument to be sui generis, comparable both to deductive argument and to inductive argument, but not rightly classified as either. Like a deductive argument, an analogical argument has a conclusion that rests on nothing more than its premises (no other information is needed); like an inductive argument, the conclusion of an analogical argument can be denied even while its premises are affirmed (and without contradiction). I should note that my classification of analogical argument is itself a classification of a grammatical structure, of a kind of proof.

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they still fall, so to speak, on the side of spontaneity, of our interests. Wittgenstein is no abstractionist.) Concepts are expressions of our charactered interests: formal concepts are more wholly the expression of our charactered interest; material concepts are what becomes of our charactered interests as they wrangle with our world. In fact, with material concepts, the world so much seems to win the wrangling that we have a hard time seeing that they are still expressions of our charactered interests. But they are. That is one reason why if very general facts of nature were to change, “the formation of concepts different from the usual ones will become intelligible” to us (Philosophical Investigations II, xii). That is, we can see how things might go for us conceptually (as the result of wholesale natural changes), because we, our charactered interests, would have a role to play in the formation of the new concepts with which we would wrangle with our changed world. If our material concepts involved our charactered interest to no degree at all, it is hard to see how the formation of new concepts could become intelligible to us. Our material concepts, in such a situation, would be, to use Kant’s term, heteronomous: they would be imposed on us from the outside. But if they were heteronomous, it is hard to see how they could be transparent to us, as they are; if they were autonomous, it is hard to see how they could be involved in our knowledge of the world, how they could be modes of presentation of that world. Conclusion Wittgenstein once said that philosophy would be best if written as a poetic composition. And in a crucial remark in Philosophical Investigations, he divides “understanding a sentence” in two: We speak of understanding a sentence is the sense in which it can be replaced by another which says the same; but also in the sense in which it cannot be replaced by any other. (Any more than one musical theme can be replaced by another.) In the one case the thought in the sentence is something common to different sentences; in the other, something that is expressed only by these words in these positions. (Understanding a poem.) 531

Wittgenstein aimed at something very like a poetic composition in the case of both the Tractatus and Philosophical Investigations. Compositionally, Philosophical Investigations has more in common with Ezra Pound’s Cantos than it does with most works of philosophy. Given that, we should in one way find unmysterious Philosophical Investigations’ resistance to paraphrase, to commentary, to explanation. The fate that befalls Philosophical Investigations too often is the fate that befalls the Cantos: source-hunting, too-solemn rereadings proffered as clarifications, dismissals of what is (in one sense) inexplicable as if it were incomprehensible, grossly irrelevant commentary. What Wittgenstein did was to write a book that engages (in full awareness) its reader’s intellectual appetitive attitudes (wishing and willing and suchlike)—and not just its reader’s intellectual cognitive attitudes (believing and knowing and suchlike). Philosophical Investigations is not written to change what we believe; it is written to change what we will. (This is true in its way of the Cantos,

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too.) Reading Philosophical Investigations well requires more of us—not less—than reading other works of philosophy well requires. To read it well, we have to become submissive to these-words-in-these-positions, and we have to be willing to measure our understanding by our ability to understand these-words-in-these-positions, and by our ability to make clear to ourselves why it is these-words and these-positions, and not others. We have to reject or moderate our ingrained philosophical tendency to measure our understanding by our ability to paraphrase, to rewrite the thought from one sentence to another as if that were the check on understanding the sentence. But even more, we have to realize the degree to which and the ways in which our wills are complicated in the problems of philosophy and in our philosophizing. Finding our way free of a philosophical problem is more than coming to believe something we previously did not believe or were unaware of believing. Finding our way free also involves changing what we will, it involves actions like hearkening, yielding, repenting, and resisting temptations. To be imprisoned by a philosophical problem is, in important part, to be double-minded: the instability of the problem or of its solutions is, partly, our own instability. Kerry is the example. And so I am recirculated to the intransitive peculiarity of Wittgenstein’s method. A poem of the sort Wittgenstein has parenthetically in mind in Philosophical Investigations 531 is one that does a peculiar poetic work—and “peculiar” is intransitive. There will be no specification of the poetic work done that can be transed to. Rather, such talk highlights the work done. Talk of the peculiar philosophical work done by Philosophical Investigations is like that, too. It is one thing to be subjected to that work; quite another to make clear what such subjection is like, or how like it is to elation. My reader, if waiting now, at last, patiently and patiently, to be told what Wittgenstein’s method is, hoping for a dip into the transitive—expecting that with me there will be the part where I say I can’t say it and the part where I take it back—will be disappointed. I have tried to take my reader to Wittgenstein’s peculiar method via objects of comparison; and that is all I can do. The rest is for the reader. And the reader should remember that it is Philosophical Investigations and the Concept “Horse” Paradox, after all, and not this book, that I ask the reader to try to understand.

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Index Anscombe, G. 9, 19, 20–21, 35, 39, 50–76 Augustine, 77–78, 94

Language-game 79–100 Logic xiii, 4, 9, 25–28, 35–42, 50, 86, 89–99 Logical articulations 83–84

Black, M. 37–40 Cavell, S. ix, xiii, 17–18, 76–77, 85–86, 100–102 Conant, J. ix, 6, 28, 97 Concepts As expressions of interest 102–104 Formal 8–21, 100–104 Material 100–104 Use in Philosophical Investigations 83–84 Conceptual investigations vii, 5, 79–105 Context Principle xi, 12–19. 23, 25, 36–37, 97, 102 Copi, I. 43 Diamond, C. ix, 6, 28, 42–34 Dummet, M. 33–35, 89 Epiphilosophy 82–83 Gadamer, H. 75 Geach, P. 9, 12, 49–50, 62, 64–68 Grammar 11, 19, 58, 63, 76–102 Grammatical understanding 51–72 Grammatical comments 55–58 Logical grammar 30, 38 Hart, W. 60

Meaning xi, 6, 16, 28–29, 36–37, 41–47, 53, 97–98 Metaphilosophy 83, 93–95 Natural language 33–35 Oakeshott, M. xiii Objectual investigations viii, 5, 79–105 Palmer, A. 28, 36, 59 Psychologism 27, 40, 86–87, 96 Rhees, R. ix, 9–11, 14–15, 79, 90, 103 Russell, B. 23–31, 35, 40–43, 93, 98 Ryle, G. 36–37, 75, 89 Schwayder, D. 43 Sellars, W. i, xi, 49–51, 63–73 Sign/symbol distinction 19–20, 30–47, 70–71 Dithering between sign/symbol 33–34 Symbolism Adequate and inadequate 37–40, 44–45 Third Realm Fregean 40 Wittgensteinian 87–99 Transitive and intransitive uses of terms 81–83, 105

Ishiguro, H. 33–34 Kant, I. 50–51, 86, 88, 90–92, 99–104 Kerry, B. i, iv, xi, 1–5, 9, 10–21, 49–52, 54, 58–59, 62–64, 71–73, 80, 84, 86, 93–96 Post-Kerry respondent to Paradox 3–4, 49–50, 72–73, 84 Kremer, M. ix, 25, 39, 44–45, 74

Unity Of language-game 98 Of proposition, Judgment 19, 36–37, 40 Valberg, J. i, xi, 49–57, 59–62, 64–65, 70–73 Wollheim, R. 81–82