Russell vs. Meinong: The Legacy of 'On Denoting'

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Russell Vs. Meinong : the Legacy of "On Denoting" Routledge Studies in Twentieth Century Philosophy (Online) ; 29 Griffin, Nicholas.; Jacquette, Dale. Taylor & Francis Routledge 0415963648 9780415963640 9780203888025 English Russell, Bertrand,--1872-1970.--On denoting-Congresses, Meinong, A.--1853-1920--(Alexius),-Congresses. 2009 B1649.R94R88 2009eb 121/.68 Russell, Bertrand,--1872-1970.--On denoting-Congresses, Meinong, A.--1853-1920--(Alexius),-Congresses.

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Page i Russell vs. Meinong

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Page ii Routledge Studies in Twentieth-Century Philosophy 1. The Story of Analytic Philosophy Plot and Heroes Edited by Anat Biletzki and Anat Matar 2. Donald Davidson Truth, Meaning and Knowledge Edited by Urszula M. Zeglén 3. Philosophy and Ordinary Language The Bent and Genius of Our Tongue Oswald Hanfling 4. The Subject in Question Sartre’s Critique of Husserl in The Transcendence of the Ego Stephen Priest 5. Aesthetic Order A Philosophy of Order, Beauty and Art Ruth Lorland 6. Naturalism A Critical Analysis Edited by William Lane Craig and J P Moreland 7. Grammar in Early Twentieth-Century Philosophy Richard Gaskin 8. Rules, Magic and Instrumental Reason A Critical Interpretation of Peter Winch’s Philosophy of the Social Sciences Berel Dov Lerner 9. Gaston Bachelard Critic of Science and the Imagination Cristina Chimisso 10. Hilary Putnam Pragmatism and Realism Edited by James Conant and Urszula Zeglen 11. Karl Jaspers Politics and Metaphysics Chris Thornhill 12. From Kant to Davidson The Idea of the Transcendental in Twentieth-Century Philosophy Edited by Jeff Malpas 13. Collingwood and the Metaphysics of Experience A Reinterpretation Giuseppina D’Oro 14. The Logic of Liberal Rights A Study in the Formal Analysis of Legal Discourse Eric Heinze 15. Real Metaphysics Edited by Hallvard Lillehammer and Gonzalo Rodriguez-Pereyra 16. Philosophy After Postmodernism Civilized Values and the Scope of Knowledge Paul Crowther 17. Phenomenology and Imagination in Husserl and Heidegger Brian Elliott 18. Laws in Nature Stephen Mumford

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Page iii 19. Trust and Toleration Richard H. Dees 20. The Metaphysics of Perception Wilfrid Sellars, Critical Realism and the Nature of Experience Paul Coates 21. Wittgenstein, Austrian Economics, and the Logic of Action Praxeological Investigations Roderick T. Long 22. Ineffability and Philosophy André Kukla 23. Cognitive Metaphor and Continental Philosophy Clive Cazeaux 24. Wittgenstein and Levinas Ethical and Religious Thought Bob Plant 25. The Philosophy of Time Time before Times Roger McClure 26. The Russellian Origins of Analytic Philosophy Bertrand Russell and the Unity of the Proposition Graham Stevens 27. Analytic Philosophy Without Naturalism Edited by A. Corradini, S. Galvan and E.J. Lowe 28. Modernism and the Language of Philosophy Anat Matar 29. Russell vs. Meinong The Legacy of “On Denoting” Edited by Nicholas Griffin and Dale Jacquette

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Page v Russell vs. Meinong The Legacy of “On Denoting” Edited by Nicholas Griffin and Dale Jacquette New York London

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Page vi First published 2009 by Routledge 270 Madison Ave, New York, NY 10016 Simultaneously published in the UK by Routledge 2 Park Square, Milton Park, Abingdon, Oxon OX14 4RN Routledge is an imprint of the Taylor & Francis Group, an informa business This edition published in the Taylor & Francis e-Library, 2008. To purchase your own copy of this or any of Taylor & Francis or Routledge’s collection of thousands of eBooks please go to www.eBookstore.tandf.co.uk. © 2009 Taylor & Francis All rights reserved. No part of this book may be reprinted or reproduced or utilised in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Library of Congress Cataloging in Publication Data Russell vs. Meinong : the legacy of "on denoting" / edited by Nicholas Griffin and Dale Jacquette. p. cm.—(Routledge studies in twentieth-century philosophy) Includes bibliographical references and index. ISBN-13:978-0-415-96364-0 (hbk) ISBN-10:0-415-96364-8 (hbk) ISBN-13:978-0-203-88802-5 (ebk) ISBN-10:0-203-88802-2 (ebk) 1. Russell, Bertrand, 1872–1970. On denoting—Congresses. 2. Meinong, A. (Alexius), 1853–1920—Congresses. I. Griffin, Nicholas. II. Jacquette, Dale. III. Title: Russell versus Meinong. B1649.R94R88 2009 121'.68—dc22 2008020354 ISBN 0-203-88802-2 Master e-book ISBN ISBN10: 0-415-96364-8 (hbk) ISBN10: 0-203-88802-2 (ebk) ISBN13: 978-0-415-96364-0 (hbk) ISBN13: 978-0-203-88802-5 (ebk)

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Page vii Dedicated to the memories of our teachers and mentors, Roderick M. Chisholm and Richard (Routley) Sylvan

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Page ix Contents    Preface  Acknowledgements    Introduction: Russell and Meinong in Retrospect DALE JACQUETTE AND NICHOLAS GRIFFIN 1 Logic and Denotation ALASDAIR URQUHART 2 Antirealism and the Theory of Descriptions GRAHAM STEVENS 3 Russell vs. Frege on Definite Descriptions as Singular Terms FRANCIS JEFFRY PELLETIER AND BERNARD LINSKY 4 A Cantorian Argument Against Frege’s and Early Russell’s Theories of Descriptions KEVIN C. KLEMENT 5 ‘On Denoting’: Appearance and Reality GIDEON MAKIN 6 Explaining G. F. Stout’s Reaction to Russell’s ‘On Denoting’ OMAR W. NASIM 7 Russell on ‘the’ in the Plural DAVID BOSTOCK 8 Psychological Content and Indeterminacy with Respect to Being: Two Notes on the Russell-Meinong Debate JOHANN CHRISTIAN MAREK

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Page x 9  Meditations on Meinong’s Golden Mountain DALE JACQUETTE 10  Rethinking Item Theory NICHOLAS GRIFFIN 11  Contra Meinong PETER LOPTSON 12  Who is Afraid of Imaginary Objects? GABRIELE CONTESSA 13  Russell’s Definite Descriptions de re GREGORY C. LANDINI 14  Quantifying in and Anti-Essentialism MICHAEL NELSON 15  Points, Complexes, Complex Points, and a Yacht NATHAN SALMON     Contributors   Index

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Page xi Preface The essays collected in this volume were selected from a total of forty-one contributions written for presentation at an international conference on ‘Russell vs. Meinong: 100 Years After “On Denoting”’, held 14–18 May 2005, at McMaster University, Hamilton, Ontario, Canada. The meeting was attended by more than one hundred philosophers, logicians, and historians of philosophy from fourteen countries, and featured critical, expository, and original philosophical investigations primarily inspired by the late nineteenth- and early twentieth-century writings of Bertrand Russell and Alexius Meinong. The idea to organize the convention, in the manner in which such events sometimes replicate, came about when the editors attended a previous conference on ‘Mistakes of Reason: A Conference in Honour of John Woods’, at the University of Lethbridge, Alberta, Canada, 19–21 April 2002. Woods’s work on the logic of fiction, among many other topics, was the occasion for a number of papers on nonexistent objects, and in particular on Alexius Meinong’s object theory logic and semantics. During a day-long walk in the Lethbridge environs after the programme had ended but before we returned to our respective universities, Griffin and Jacquette lamented the lack of informed, accurate discussions of Meinong’s philosophy. We bemoaned the fact, as Meinong scholars are often compelled to do, that Russell’s criticisms of Meinong after 1905 had soured the analytic philosophical community on the real merits of Meinong’s thought, and predisposed many writers thereafter to dismiss Meinong’s unique and in many ways commonsensical approach to mind and meaning, in the period when Russell’s logical methods set the agenda for the most exciting original developments in philosophical analysis. We commiserated accordingly on the fact that Meinong studies have never received a fair, impartial hearing in mainstream analytic philosophy since Meinong’s writings were mostly untranslated, and Russell’s objections had led so many critics to discount Meinong’s Gegenstandstheorie , usually without bothering to read or think about it for themselves. The trouble is only compounded by the further fact that many thinkers sympathetic to Meinong’s object theory, usually in some revisionary but still recognizably Meinongian application, regard Russell’s

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Page xii most influential opposition as based on false attributions to Meinong of theses the latter never accepted. Meinong’s exact views are subtly different than the rightly objectionable positions Russell sometimes ascribes to him, despite Russell’s acute understanding and appreciation for Meinong’s empiricist methodology. Thus, we walked and talked about the sad state of Meinong scholarship among analytic philosophers. Approximately one week later, Jacquette proposed to Griffin that the upcoming date of 2005 might be an appropriate opportunity to organize a symposium on Russell and Meinong, in celebration of the 100th anniversary of the 1905 publication of Russell’s landmark essay, ‘On Denoting’, in which Russell’s criticisms of Meinong first became widely known. Griffin, Director of the Bertrand Russell Research Centre at McMaster, generously offered to host the conference, attracting specialists on Russell and Meinong, and, in some instances, on the intersection of philosophical interests of and historical interaction between Russell and Meinong, and such historically and spiritually related figures as Gottlob Frege. The rest, as they say, if not quite history, was generally considered to have been successful in bringing together Russell and Meinong scholars airing many of the issues that continue to divide Russellian extensionalism from Meinongian intensionalism in contemporary philosophical logic and semantics. The papers included in this volume represent some of the most interesting recent work, especially on the historical and philosophical collision between Russell and Meinong that came into sharp focus in Russell’s justly celebrated 1905 essay. The point of the collection is not to archive what transpired at the conference, for, on the contrary, the conference itself was a means to an end in bringing the issues discussed in these essays to a wider philosophical audience. We commend these essays to all readers interested in open ongoing consideration of the extraordinary philosophical options represented by these two seminal but frequently misunderstood twentieth-century thinkers. That a healthy dispute about Russell and Meinong will surely continue is indicated by the fact that the editors themselves have by no means resolved their differences, but continue to disagree fundamentally about the correct interpretation of, and logical and philosophical significance of key passages in Russell, Meinong, and, for that matter, Frege. Nicholas Griffin Canada Research Chair in Philosophy and Director, Bertrand Russell Research Centre McMaster University Hamilton, Ontario, Canada Dale Jacquette Lehrstuhl ordentlicher Professur für Philosophie, Schwerpunkt theoretische Philosophie Universität Bern, Switzerland

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Page xiii Acknowledgements The editors first and foremost would like to thank the authors for their excellent contributions. For assistance in funding the 2005 conference on ‘Russell vs. Meinong: 100 Years After “On Denoting”’, we are grateful especially to the Provost’s Office, Dean’s Office, and Philosophy Department of McMaster University, the Academic Vice President’s Office of Wilfrid Laurier University, the Mind Association for a Conference Grant, the Social Sciences and Humanities Research Council of Canada (SSHRC), and the Austrian Cultural Forum and Attaché, Toronto. Special thanks are due also to Kenneth Blackwell, editor of Russell: The Journal of Bertrand Russell Studies . Many individuals helped in organizing and facilitating the conference, including Sarah Halsted, Gülberk Koç, Carl Spadoni, Amanda White and the staff of the Bertrand Russell Research Centre: Andrew Bone, Arlene Duncan, Michael Stevenson, and Sheila Turcon. Arlene Duncan additionally offered invaluable service in copy-editing and preparing the typescript of the volume, while Gülberk Koç and Duncan Maclean put aside other pressing matters at short notice to work on the index. We are indebted, finally, to Pamela Swett of the McMaster Department of History for advice and encouragement at an early stage of the conference planning.

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Page 1 Introduction Russell and Meinong in Retrospect Dale Jacquette and Nicholas Griffin La théorie c’est bon, mais ça n’empêche pas d’exister. —Jean-Martin Charcot There is widespread agreement among philosophers, logicians and historians of these subjects, who often agree on little else, that Bertrand Russell’s remarkable essay, ‘On Denoting’, published in the journal Mind in 1905, is one of the most important philosophical studies of the twentieth century. The theory of definite descriptions that Russell propounded in the paper launched a new phase in the development of analytic philosophy and provided a new pattern for philosophical analysis. Russell’s theory of definite descriptions had a major impact, not only on logic and the philosophy of language, but also on metaphysics, epistemology, and logical and philosophical methodology. It was with good reason, therefore, that Frank P. Ramsey referred to the theory as ‘that paradigm of philosophy, Russell’s theory of descriptions’. For almost fifty years, the theory looked like as uncontroversial an example of progress in philosophy as anyone was ever likely to find. At the same time, alternative theories seemed to have been definitively consigned to the rubbish-bin of history. One of the most important, well-developed and suitably ignored alternatives preceding Russell’s analysis appeared in Alexius Meinong’s object theory ( Gegenstandstheorie ). Russell was well-aware of Meinong’s work, against which he raises interesting objections in clearing the way for the presentation of his own ultimately very different approach. As a result of Russell’s criticisms, especially in ‘On Denoting’ and later writings on philosophical logic, Meinong’s theory seemed for a long time to be enmeshed in insuperable difficulties. Thus, assuming he was writing a final obituary for Meinong’s lifework, Gilbert Ryle, in ‘Intentionality-Theory and the Nature of Thinking’ ( Jenseits von Sein und Nichtsein , edited by Rudolf Haller, 1972), wrote: ‘Let us frankly concede from the start that Gegenstandstheorie itself is dead, buried and not going to be resurrected. Nobody is going to argue again that, for example, “there are objects concerning which it is the case that there are no such objects”. Nobody is going to argue again that the possibility of ethical and aesthetic judgments being true requires that values be objects of a special sort.’

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Page 2 Moreover, compared to the subtlety and sophistication of Russell’s analysis of definite descriptions, Meinong’s object theory can sometimes appear naïve and simple-minded; although many of its adherents would prefer to describe the theory as natural and commonsensical. The unchallenged dominance of Russell’s analysis of definite descriptions did not last indefinitely. From 1950 onwards, problems began to be discovered in Russell’s proposal; in particular, critics, beginning with P. F. Strawson in his important essay, ‘On Referring’, expressed deep-seated concerns about whether Russell’s analysis treated natural language uses of definite descriptions properly, and whether and how well it could be combined with such newly emerging logical theories as quantified modal logic. Somewhat later, philosophers began to develop theories of objects, loosely based on Meinong’s, which avoided the objections that Russell had raised against Meinong’s theory. The prospects for a rehabilitation of Meinong’s theory in light of its most unsympathetic critics, who for some time paid only scant attention to Meinong’s actual position, quickly led to new interest in understanding Meinong’s views in accurate detail, to the careful reading and study of Meinong’s voluminous writings, and to the re-emergence of Meinong himself as an important philosopher. Moreover, some of the new Meinongian theories of objects were found to be subject to fresh difficulties, not created by Russell, which turned out to be less tractable than was initially hoped. Meanwhile, the availability of Russell’s Nachlaß in the Bertrand Russell Archives at McMaster University, and in particular the publication of many unpublished logic manuscripts in The Collected Papers of Bertrand Russell, cast Russell’s theory in a radically new light. All of these trends converge today, a century after ‘On Denoting’ was published, to create an exegetical and philosophical situation of some complexity. On the one hand, there is a mass of new historical scholarship, about both Russell and Meinong, which has not circulated very far beyond specialist scholars in the two camps. Russellians have remained ignorant of much of the recent work of Meinong scholars, and vice versa. On the other hand, there are continuing problems and controversies concerning contemporary Russellian and Meinongian theories that new generations of logicians and philosophers need to consider as historical-philosophical background to their own ongoing research into the problems of logic, mathematics and the meaning of thought and language. To appreciate the philosophical issues arising in Russell’s 1905 analysis of definite descriptions, covering a range of topics including but by no means limited to a critique of Meinong’s object theory, we must say something about the background and intellectual biographies of Russell and Meinong. Russell (1872–1970) is by common consent one of the most important philosophers of the twentieth century. Among his many writings on logic, philosophy and social criticism, ‘On Denoting’ is the compact work by which he is most often introduced to new students of philosophy. The essay

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Page 3 is nevertheless a paradox in itself; some parts are the very model of lucidity, while other parts remain obscure and the subject of interpretative disputes to the present day. The essay was almost rejected by Mind, and was not much read or discussed until at least a decade after its publication, when it gained enormous prominence among logically and mathematically minded philosophers. Russell began his academic career when he entered Trinity College, Cambridge University, in 1890. There, he distinguished himself in advanced studies of philosophy and mathematics and became a Fellow of the college in 1895. Hailing from an aristocratic British family, raised largely by his grandmother, from whom he learned German, Italian and French along with his native English, Bertrand Arthur William Russell frequently found his noble family background in conflict with his acute democratic social consciousness and his desire to devote his life to philosophy and mathematics. Russell’s sense of moral and social obligation is dramatized in particular by his opposition to Great Britain’s involvement in World War I, as a result of which he was sentenced to prison. It was during this imprisonment, over ten years after the publication of ‘On Denoting’, that Russell wrote a popular philosophy book, Introduction to Mathematical Philosophy , in which many of the themes of ‘On Denoting’, including even more severe and questionable criticisms of Meinong, are explored. Russell, writing his dissertation on the philosophy of mathematics, and in particular geometry, entered the ranks of university philosophers as a kind of neo-Hegelian in what was then the prevailing postKantian atmosphere of Cambridge, inspired, among others, by F. H. Bradley. Russell visited the Mathematical Congress in Paris in 1900, where he became fascinated with the work of the Italian mathematician Giuseppe Peano. Peano had developed a mathematical notation for logical concepts in order to represent the basic axioms of arithmetic, which Russell studied and later adapted and expanded upon with great enthusiasm. Peano’s logic figures prominently in Russell’s early logicist efforts to reduce all of mathematics to basic principles of formal symbolic logic, following unwittingly in the footsteps of Gottlob Frege, whose analysis of the concept of number Russell independently discovered. In 1903, Russell published his first important book, The Principles of Mathematics. Later, with his collaborator A. N. Whitehead, he developed and extended the mathematical logic of Peano and Frege, culminating in 1910 to 1913 in the monumental three-volume work, the Principia Mathematica . The project of Principia Mathematica is more technically elaborated but similar in spirit to that of Frege. Russell was especially influenced by the two volumes of Frege’s 1893 and 1903 Grundgesetze der Arithmetik ( Basic Laws of Arithmetic ). In 1910, Russell was appointed lecturer at Trinity College. When World War I broke out, he participated actively in the No Conscription Fellowship and was fined £100 as the author of a leaflet criticizing a twoyear

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Page 4 prison sentence that had been imposed on a conscientious objector who had refused military service. In the mood of misguided patriotism that prevailed at the time, Trinity College then further retaliated in 1916 by depriving Russell of his lectureship. Russell was offered a position at Harvard University in the United States, but was unable to obtain a passport to leave England in order to accept the appointment. As previously mentioned, in 1918, Russell was sentenced to six months imprisonment for an article he had written in the London Tribunal . Russell’s 1905 essay ‘On Denoting’ epitomizes the early ambitions of analytic philosophy in the twentieth century. That paradigm of philosophy, as Ramsey described Russell’s theory of definite descriptions in the 1930s, continues to inform philosophical analysis in studies far afield of logic and semantics. Russell demonstrates a way of penetrating the surface grammar of a specific set of expressions with important philosophical implications and systematically unpacking their component meanings. Like a beam of white light entering an optical prism and emerging in a spectrum of colours at the other end, Russell breaks definite descriptions down into distinct ontic, uniqueness and predication constituents. To say that ‘The present King of France is bald’, according to Russell, is to say: (1) (falsely) that there exists an entity that has the property of being a present King of France; (2) that there exists at most one entity that has the property of being a present King of France; and (3) that the existent entity in question has the further property of being bald. Meinong need have no quarrel with conditions (2) and (3) in Russell’s analysis of definite descriptions; the disagreement between the two thinkers centres squarely on the existence condition in requirement (1). Russell’s theory of definite descriptions marks an important turning point in his philosophical development, as he breaks from his prior qualified admiration for Meinong’s Gegenstandstheorie . Russell also departs sharply from Frege in ‘On Denoting’, rejecting in particular Frege’s concept of senses, which he had previously acknowledged in the special case of definite descriptions. To riff on the spirit of Charcot’s epigram above, a favourite quotation of Sigmund Freud’s—abstract theory is valuable, but that doesn’t stop something from existing. Meinong might add that even the most beautiful and powerful analysis of thought or language also does not necessarily exclude the nonexistent. Alexius Meinong (1853–1920), the polemical foil for Russell’s criticisms of object theory in ‘On Denoting’, was born in the Austro-Hungarian Empire garrison town of Lemberg (Lvov), Poland. Meinong’s ancestors were German, but his grandfather had immigrated to Austria. At the time of his birth, Meinong’s father was serving the Austrian emperor Franz Josef as a senior military officer stationed in Lemberg. Like Russell, Meinong was a member of the European aristocracy, being related to the royal House of Handschuchsheim, and legally held title as Ritter von (Knight of) Handschuchsheim. Again, however, much like Russell in keeping with his

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Page 5 republican convictions, Meinong never used this patrician form of address. In 1862, he began six years of private tutoring in Vienna, followed by another two years at the Vienna Academic Gymnasium. Meinong enroled in the University of Vienna in 1870, where his first major subjects were German philology and history. Later, suppressing his own interests to study music and temporarily resisting parental pressure to enter the diploma programme in law, Meinong concentrated exclusively on history, completing his dissertation in 1874 on Arnold von Brescia, the medieval religious and social reformer. Meinong reports that during this time his interest in philosophy was overshadowed by historical studies. His philosophical appetite was whetted and reawakened only when, in preparation for the philosophical component of a mandatory examination on topics related to his dissertation research (the Nebenrigorosum ), he undertook a self-directed study of Kant’s Critique of Pure Reason and Critique of Practical Reason . To broaden his historical background, and possibly to appease his parents, Meinong entered the University of Vienna law school in the autumn of 1874. There, he devoted his time to Carl Menger’s lectures on economics, which influenced his later work on value theory. It was just before the 1874 to 1875 winter term that Meinong decided to turn his attention to philosophy. Franz Brentano, charismatic lecturer in philosophy at the height of his powers at just this time, had recently joined the philosophical faculty of the University of Vienna, and he and Meinong had met in connection with Meinong’s Nebenrigorosum . Significantly, Meinong denies that Brentano directly influenced his decision to study philosophy, but acknowledges that as a result of their encounter he was persuaded that his progress in philosophy would improve under Brentano’s direction. Brentano recommended that Meinong undertake his first systematic investigations in philosophy on David Hume’s empiricist metaphysics. Meinong accordingly completed his Habilitationsschrift on Hume’s nominalism in 1877, resulting in Meinong’s first philosophical publication, the Hume-Studien I, appearing in 1878 in the Sitzungsberichte der Wiener Akademie der Wissenschaften , and followed by a sequel on Hume’s theory of relations, the HumeStudien II, in 1882. During this four-year interval, while studying with Brentano and working out his interpretation of Hume, Meinong held the position of Privatdozent in philosophy at the University of Vienna. In this capacity, he tutored some of Brentano’s most talented students, including Christian von Ehrenfels, the founder of Gestalt psychology, and Alois Höfler, with whom Meinong later collaborated on his first explorations of the logical and conceptual foundations of object theory, the Logik of 1890. In 1882, Meinong was appointed Professor Extraordinarius at the University of Graz, receiving promotion to Ordinarius in 1889, where he remained until his death. At Graz, Meinong established the first laboratory for experimental psychology in Austria, which flourished under his directorship. Throughout his long tenure at Graz, Meinong was engaged in difficult philosophical problems and simultaneously occupied with psychological

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Page 6 investigations, especially those Brentano designated as belonging to empirical descriptive psychology. Here, for the philosophically most active forty-three years of his life, Meinong wrote his major philosophical treatises and edited collections of essays on object theory, philosophical psychology, metaphysics, semantics and philosophy of language, theory of evidence, possibility and probability, value theory and the analysis of emotion, imagination and abstraction. His philosophical studies, as Russell in his 1904 to 1906 Mind reviews of Meinong’s works remarks, were distinguished by an uncompromising empiricism that Brentano had helped foster. The empirical outlook in philosophical studies stood in stark opposition to the prevalent post-Kantianism that, again in parallel with the academic situation at Russell’s Cambridge University, ruled the Austrian philosophical community at the time. The Graz school of phenomenological psychology and philosophical semantics that centred on Meinong and his students made important advances in all major areas of philosophy and psychological science. The most notable feature of Meinong’s work, the underlying foundation even of his work in experimental psychology, was the doctrine of the distinctive intentionality of thought, which he inherited from his teacher, Brentano. Brentano in his 1874 treatise, Psychologie vom empirischen Standpunkt , had argued that psychological properties are different from purely physical properties by virtue of the intentionality, ‘aboutness’, or object-directedness of the psychological, a feature not shared by purely physical phenomena. If every thought is ‘about’ something or intends an object, then, as Meinong quickly understood, adopting the medieval Scholastic distinction that Brentano had absorbed from his in-depth studies especially of Thomas Aquinas, some thoughts are about existent (physical, spatiotemporal) objects, some thoughts are about subsistent (abstract, platonic) objects and some thoughts, most remarkably, intend or are about objects that are altogether beingless, that neither exist nor subsist. Such objects, from Meinong’s perspective, a view that Brentano himself never accepted, are nevertheless essential to understanding the thoughts by which the objects are intended. Whereas Brentano had distinguished three basic categories of thoughts, presentation ( Vorstellung), judgement ( Urteil ) and emotion ( Gefühl, Gemütstätigkeiten ), Meinong in his 1901 (second edition 1910) work, Über Annahmen, eponymously introduced a fourth category of assumptions. He argued that the mind has unlimited freedom of assumption to entertain intended objects correlated with any combination of constitutive properties, including objects that do not exist, and even those that metaphysically speaking cannot possibly exist. Thus, the notorious Meinongian objects of the golden mountain and round square enter into intentionalist philosophy of mind and intensionalist logic and semantics. We can make whatever assumptions we like, nothing prevents us from doing so, by combining properties of any sort together experimentally in thought, to consider their consequences, and even if only to conclude that no such objects exist or could possibly exist.

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Page 7 Meinong never says that the most adventurous of these thoughts intend existent objects. Although many of our thoughts are obviously about things that exist, Meinong does not try to say, what would in any case be clearly absurd, that the golden mountain and round square exist or have being, even ‘in’ our thoughts. Rather, he holds that despite their beinglessness, such intended objects must belong to a semantic order of mind-independent objects, which it is the responsibility of a complete object theory to consider. It is, of course, the nonexistence of certain intended Meinongian objects that seems at first to have intrigued Russell, but which he later decided must be denounced as incoherent and banished from the foundations of logic and the philosophy of mind and language. The existence conditions for definitely described objects in Russell’s three-part analysis of definite descriptions has sparked the greatest controversy in the years since Russell published ‘On Denoting’. By denying the possibility of referring to and truly predicating ordinary properties of nonexistent objects, Russell complicates the theory of referential meaning for false statements, works of fiction, mistaken scientific theories and hypotheses, and expressions of the products of fantasy and imagination. Where Meinong unifies the semantics of all such commonplace feats of reference and predication in an ontically neutral fashion, treating them as no different than discourse about intended objects that happen to exist, Russell, from a contrary but also legitimate philosophical perspective, sharply divides the meaning of thought and language according to whether or not their ostensible objects actually exist. Where common sense might ordinarily want to insist that, in thinking, for example, about the conflicts among distinct gods in the opening passages of Homer’s Iliad, that we can say true things about the gods even though they do not exist, Russell will insist that all such predications are simply false. We may naïvely believe, as Meinong holds, that we are directed in thought towards beingless objects when we say, for example, that ‘The god of the sea is different from the goddess of love’. We may suppose that we are thinking about different, distinct, albeit nonexistent objects that nevertheless each have individuating properties (one living in the depths of the ocean, carrying a trident, the other having been born from the foam created when Chronus castrated his father Uranus and cast his testicles into the sea, and so on), but Russell’s analysis of definite descriptions effects to point out the impossibility of treating such attributions as literally true. Instead, we must analyse these statements, and when we do so, looking past and through their superficial surface grammar, adopting the best theory of the meaning and truth conditions of such sentences when confronted with a variety of logical and semantic puzzles, we will come to see that we cannot in fact say anything true about non-existent entities. Nor does Russell’s position substitute unjustified logical sophistication for the deliverances of philosophically uncorrupted common sense, but rather it highlights another facet of common sense, calling upon intuitions according to which things that do not exist cannot have

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Page 8 properties, and hence cannot be the subjects of true property attributions in thought and linguistic predication. The dispute between Russell and Meinong, accordingly, is not merely a straightforward conflict of common sense with convoluted logical complexity, but rather a dynamic quarrel of different opposing commonsense insights and intuitions. This fact accounts for the enduring interest in the classic opposition between Russell and Meinong, as played out among other ways in Russell’s criticisms of Meinong in ‘On Denoting’. What we find is not merely Russell taking issue with a theory that he finds mistaken, but a more perennial dispute between referential extensionalism and referential intentionalism and intensionalism, between the ‘robust sense of reality’ in a phrase Russell famously if controversially coined and the free flights of imagination and fantasy that characterize much of our thinking and demand just as sound an understanding and logical analysis. Russell’s prestige deservedly exerted a powerful influence on generations of philosophers. Their apprenticeship typically featured a close study of ‘On Denoting’ to embrace the rallying cry of Russell’s robust sense of realism by limiting reference to existent objects only. It became a part of this tradition also to ridicule Meinongianism, often without bothering to read Meinong’s writings, as Russell had with at least an initial dose of sympathy. The intentionalist tradition that continued the line of thought begun by Brentano through Meinong and others was nevertheless not extinguished with the publication of Russell’s invaluable essay or subsequent criticisms in such works as Introduction to Mathematical Philosophy . Many scholars since 1905 have doubted whether Russell properly understood the logic and semantics of definite description, despite his name’s being so closely associated with the topic. More particularly, it has come increasingly to be questioned whether Russell accurately evaluates the prospects of Meinong’s admission of beingless intended objects to a semantic domain alongside existent physical spatiotemporal and abstract entities. Russell rejects Meinong’s semantic doctrine as logically incoherent in those applications in which we try to speak of an existent round square as being existent, round and square. By overlooking certain of Meinong’s key distinctions, Russell disputes Meinong’s central contribution to an intentionalist theory of mind and meaning, by which it is otherwise possible to refer and truly predicate constitutive properties of nonexistent as well as existent objects. These are among the principal topics explored by the papers collected in this volume. The authors not only focus on the logic of Russell’s theory of definite descriptions and its conflict with a Meinongian theory of nonexistent objects, but shed light also on many aspects of Russell’s analysis that do not directly concern his battle against nonexistent objects. A fruitful and ongoing conversation about these vital topics of philosophical psychology, logical theory and semantics, in their complex historicalphilosophical context, is vigorously advanced by the contributions presented here. The

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Page 9 papers take up themes that Russell first sounded in his groundbreaking, endlessly rewarding essay, marking essential differences of perspective that fundamentally determine logical, semantic, and metaphysical theory-building in many parts of philosophy. The present collection of papers tackles the Russell vs. Meinong debate in both historical and philosophical categories. It provides an overview of the latest exegetical scholarship on the two philosophers as well as detailed accounts of some of the problems facing the current incarnations of their theories. Several of the essays naturally reflect special interests in Russell’s complex adversarial relation to Meinong’s object theory. Papers by Alasdair Urquhart, Graham Stevens, Kevin Klement, Gideon Makin, Omar W. Nasim, and David Bostock deal primarily with historical issues. They portray a very different account of Russell’s theory and its context than has prevailed over most of the intervening century since ‘On Denoting’ was published. Francis Jeffry Pelletier and Bernard Linsky, on the other hand, consider the only other theory of descriptions, apart from Meinong’s at which Russell also took aim in ‘On Denoting’, namely, Frege’s. Johann Christian Marek and Dale Jacquette address the actual Russell vs. Meinong debate. Finally, papers by Nicholas Griffin, Peter Loptson, Gabriele Contessa, Gregory C. Landini, Michael Nelson, and Nathan Salmon deal with current problems in the two theories. The editors send forth this parcel of new research on Russell’s analysis of definite descriptions and the theory of meaning in ‘On Denoting’, the recurrent tension between extension and intension, existence and the projections of imagination, and thus of Russell vs. Meinong, with the hope and expectation, not that the essays collected here will finally resolve these disputes, but that they reflect some of the best current thinking on these longstanding problems, and that they will provoke further discussion and cultivate renewed interest in the underlying philosophical issues that originally motivated as they importantly divided the groundbreaking philosophical work of Russell and Meinong.

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Page 10 1 Logic and Denotation Alasdair Urquhart THE SIGNIFICANCE OF RUSSELL’S THEORY Why is Bertrand Russell’s theory of descriptions important? Russell’s short and hastily written (Urquhart 1995) paper of 1905 (Russell 1905a; 1994: Paper 16), has elicited an enormous quantity of commentary. However, there is no universal agreement as to why this particular paper is so important, or what its exact significance is, either logically or philosophically. The theory was originally conceived as a contribution to logic, but today, professional logicians who do not work in areas closely related to philosophy have at best a nodding acquaintance with the theory, and in general, Russell’s theory is considered a marginal topic. Discussion of the theory of descriptions is almost entirely confined to professional philosophers, and even in this community of researchers, there does not seem to be complete agreement as to why the theory matters. A common view of the theory is that it is a basic contribution to the analysis of the meaning of propositions in ordinary language. This view is already clear in Ramsey’s paper of 1929, entitled ‘Philosophy’. Ramsey says, ‘Sometimes philosophy should clarify and distinguish notions previously vague and confused, and clearly this is meant to fix our future meaning only’, adding to this remark the striking footnote: ‘But in so far as our past meaning was not utterly confused, philosophy will naturally give that, too. E.g. that paradigm of philosophy, Russell’s theory of descriptions’ (Ramsey 1931:263). This view of the significance of the theory is, I believe, the dominant one today, and the problem of the meaning of descriptions in ordinary language dominates current discussions of Russell’s theory. Another popular view is that it is a great contributor to ontological economy. This is the most important feature of the theory for Quine. In his famous essay ‘On What There is’ (1963:5) he writes: ‘Russell, in his theory of so-called singular descriptions, showed clearly how we might meaningfully use seeming names without supposing that there be the entities allegedly named’, and sees the theory as the first step in trimming the ontological luxuriance of Plato’s tangled beard.

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Page 11 Neither of these views of Russell’s theory is inaccurate, in that Russell himself often emphasized both aspects in promoting it. However, I wish to discuss the theory from a viewpoint that is a little different from either of those given above. I would like to look at it as a contribution to the foundations of logic. When he conceived the basic ideas, Russell was engaged in a large-scale project in the foundations of mathematics and logic, and the theory originally appeared to him as a solution to various problems that had plagued him for some time. To understand what those problems were, however, we need to understand the logical background from which the theory emerged. Russell himself gives the theory a central place in the evolution of his logical work. Writing to Philip Jourdain on 15 March 1906, he presents the theory as a crucial breakthrough: In April 1904 I began working at the Contradiction again, and continued at it, with few intermissions, till January 1905. I was throughout much occupied by the question of Denoting, which I thought was probably relevant, as it proved to be…. I tried to do without ι as an indefinable, but failed; my success later, in the article ‘On Denoting’, was the source of all my subsequent progress. (Grattan-Guinness 1977:79) As his letter makes clear, Russell’s central concern was the solution of the paradoxes and the construction of satisfactory foundations for logic. The analysis of meaning, and ontological/metaphysical questions, though prominent in some of his later writings, take second place at this time to the central problem of the paradoxes. Russell even seemed to have thought occasionally that a solution to the problems of denoting would in itself lead to a solution to the paradoxes. On 14 April 1904, writing to Alys from Cambridge, where he had gone to work with Whitehead, Russell said: ‘Alfred and I had a happy hour yesterday, when we thought the present King of France had solved the Contradiction; but it turned out finally that the royal intellect was not quite up to that standard’ (Russell 1994: xxxiii). Late in life, Russell still presented the theory as a contribution to logic, rather than philosophy, as this quote from My Philosophical Development makes plain: The theory of descriptions, mentioned above, was first set forth in my article ‘On Denoting’ in Mind, 1905. This doctrine struck the editor as so preposterous that he begged me to reconsider it and not to demand its publication as it stood. I, however, was persuaded of its soundness and refused to give way. It was afterwards generally accepted, and came to be thought my most important contribution to logic. (Russell 1985:63)

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Page 12 RUSSELL’S LOGICAL UNIVERSE OF 1903 Russell’s first extended manuscripts on the theory of denoting, subsequent to the frequently quoted passages written in 1902 and published in The Principles of Mathematics, were written in 1903. These papers contain frequent references to Russell’s contemporary logical research and clearly form part of the same project. The transition from philosophical discussions of denoting concepts to the analysis of axioms for logic is seamless. Consequently, to understand the problems that Russell was trying to solve, we have to attempt a rough sketch of the logical universe as he conceived it around 1903 to 1905.1 The logical manuscripts of this period (most of which remained unpublished until 1994) exhibit one of Russell’s intellectual traits that his commentators find most disconcerting, the Protean and chameleonlike character of his thinking. Ideas are proposed and then discarded within the space of only a few pages, and it is difficult to single out consistent threads in his thought. What is worse, most of the logical theories of this period turned out to be inconsistent, posing almost insurmountable problems of interpretation. The best we can do is to single out certain themes that remain constant throughout these years, while many other ideas went through bewildering changes. The manuscripts of this period show the overwhelming influence of Gottlob Frege. Even though he had revealed the worm of inconsistency gnawing at the roots of Frege’s system, Russell remained convinced that Frege’s basic strategy for tackling the problem of the paradoxes was sound. Frege reacted to Russell’s revelation of the paradox by adding a hastily written appendix to the second volume of his Grundgesetze der Arithmetik . The ad hoc patch recommended in this appendix shows that Frege believed that his fundamental strategy for deriving mathematics from logic was correct, but that it required some minor and local modifications to avoid contradictions. In other words, the contradictions could be avoided by some fairly simple and perhaps obvious adjustments to the unrestricted comprehension axiom. In a note added in proof to Appendix A of The Principles of Mathematics, Russell wrote of Frege’s own hasty patch to the system of his Grundgesetze: ‘As it seems very likely that this is the true solution, the reader is strongly recommended to examine Frege’s argument on this point’ (Russell 1937:522). Indeed, all of Russell’s attempts to solve the Contradiction from 1903 to 1905 can be seen as variants on Frege’s own abortive attempt. That is to say, the aim is to avoid the paradoxes by placing direct restrictions on the comprehension principle, within the overall framework of an untyped theory of functions. Why are descriptions important as part of this project? The reason is not far to seek. A large number of important mathematical concepts, and particularly notions involving mathematical functions, can be formulated as descriptions. This fact is clearly visible in the surviving fragments of the logical diary that Russell kept in 1904, given the title ‘Fundamental Notions’ in volume 4 of the Collected Papers (Russell 1994:111–259). Page

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Page 13 after page of this paper are concerned with denoting functions and denoting complexes. For example, we find on one page a ‘List of Principal Denoting Functions’ (Russell 1994:201), and on a slightly later page a list of ‘Denoting Functions’ (Russell 1994:206). This logical diary, taken together with the papers more specifically devoted to the theory of denoting, show that it is completely artificial to separate the logical from the philosophical aspects of the theory of denoting at this time in Russell’s career. The search for an adequate set of primitive propositions for logic and the foundations of mathematics, and the search for an adequate theory of denoting, are inextricably linked. Russell’s idea was that the solution to the paradoxes should not be an ad hoc patch, but rather should result from a clear view of the logical universe, as it emerged from philosophical reflection on basic concepts. This idea stands out clearly in a letter Whitehead wrote to Russell on 30 April 1904. In response to some remarks of his collaborator in a letter that is now lost, Whitehead says: I am in complete agreement with you as to the necessity of your immediate line of work. I have been bombarding you with formal developments from Pps [primitive propositions] embodying a certain stage for the following reasons. For the technical development we want reasonably general Pps which give us all we want and exclude the contradiction. I agree that such Pps (except by a miracle) will only turn up in a philosophical analysis of the subject—and that the better the analysis, the better the Pps. (Russell 1994: xxxix) Complexes Throughout the period from 1903 to 1905, the notion of ‘complex’ is central in Russell’s thinking. The opening paragraph of the 1904 paper ‘On Functions’ (Russell 1994:96–110) gives a clear statement of the idea: A complex is a unity formed by certain constituents combined in a certain manner. The notion of a constituent of a complex is indefinable. A proposition is a complex; so is everything else which is in any way capable of being analyzed. The complexity that Russell is describing here is logical complexity, so we need to know the primitive elements from which his logical universe was built at this time. The manuscripts of 1903 provide a sketch of a remarkably parsimonious set of primitives. In the brief set of working notes ‘Dependent Variables and Denotation’, Russell lists his ‘Indefinable complexes’ as: (1) Implication: p q, (2) Substitution: , (3) Universal quantification: ( y)• , (4) Functional application: φ| x, (5) Functional abstraction: ( p), together with an ‘indefinable function’, the description operator, ι (Russell 1994:298).

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Page 14 In addition to purely logical postulates governing implication, substitution and universal quantification, Russell requires postulates governing functional application and abstraction. In an early set of notes on functions from 1903 (Russell 1994:53) he states two primitive propositions:   The context makes it plain that the expression Y is a shorthand notation for the complex . The resulting logical system bears a strong resemblance to modern theories of the lambda calculus (Barendregt 1984), perhaps not a surprising fact given that Russell’s system and the lambda calculus have a common ancestor in the work of Frege. There is a further similarity between this system and theories of lambda calculus with unrestricted functional abstraction and classical logic; Russell’s theory is inconsistent, since we can deduce a form of Russell’s paradox in it. Setting R = ~(x| x), we have R| R = { ~(x| x)}|R = ~(R| R), so that R| R is a proposition equal to its own negation, and this leads immediately to a contradiction, if we use the axioms of classical propositional logic. Russell, of course, must have realized the contradictory nature of his primitive propositions very quickly. Some other rough notes from a little later in 1903 give a list of fourteen ‘inadmissible functions’ (Russell 1994:72); in addition to the function R above, these include the identity function ( x) and the negation function (-x). Russell’s strategy for avoiding the paradoxes from about 1903 to 1905 was to attempt a kind of balancing act. On the one hand, he wanted to avoid contradictions by ruling out ‘inadmissable functions’, while on the other hand, he needed enough logical strength to allow the deduction of standard mathematical axioms, and in particular the axioms of arithmetic and the theory of real numbers. Of course, this strategy in the end proved a failure, but at least initially, Russell did not have a clear conception of the far-reaching nature of the logical paradoxes. In the early manuscripts of 1903, on postulates for functions, the aim is to single out ‘functional complexes’, that is to say, those complexes X that define functions ( X ) by using the functional abstraction operator. A typical example of a primitive proposition based on this idea is   an attempt from another of the rough notes on functions (Russell 1994:70). In words, the primitive proposition says: ‘If X is a functional complex, then it satisfies the principle (of λ-conversion) stated without restriction above.’ Since our main concern in this chapter is with the theory of denoting and not with Russell’s abortive foundational efforts, we shall not describe further the twists and turns of his heroic labours aimed at separating out the logical sheep from the logical goats. Rather, we now concentrate on the finer details of the ontology that he presupposes at this time.

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Page 15 Russellian Propositions During the period from 1903 to 1905, Russell adhered consistently to the view that individuals are themselves constituents of true propositions about them. There are many passages from this period in which Russell explicitly espouses this view. A particularly clear example is to be found in the 1903 paper ‘On Meaning and Denotation’: When we make a statement about Arthur Balfour, he himself forms part of the object before our minds, i.e. of the proposition stated. If we say, for instance, ‘Arthur Balfour advocates retaliation’, that expresses a thought which has for its object a complex containing as a constituent the man himself; no one who does not know what is the designation of the name ‘Arthur Balfour’ can understand what we mean : the object of our thought cannot, by our statement, be communicated to him. (Russell 1994:315– 16) This passage also contains Russell’s standard epistemological argument for the view. However, we are not concerned here with Russell’s theory of knowledge, so in what follows we shall simply accept Russell’s view as given, without examining the doctrine of acquaintance on which it ultimately rests. Although there is general agreement among commentators on Russell that he held the view quoted at the time of The Principles of Mathematics, and the passage above shows unequivocally that he held the view in 1903, there is some disagreement as to whether he held the view in 1905, when he wrote ‘On Denoting’. In a paper (1994) coauthored with Judy Pelham we maintain that Russell stuck to this view of propositions throughout 1905, and also in later years. The main reason for thinking this is that it seems otherwise impossible to make sense of the manuscripts on the substitutional theory from the same year. All of these unpublished writings of Russell are based on a primitive notion of substitution that is not the modern notion, in which one syntactical entity is substituted for another, but rather a notion of entity substitution, in which one individual is substituted for another. To understand what is at issue here, it is helpful to consider a set-theoretical analogy. If S is a set (let us say, of natural numbers), we can define the set

to be ( S\{y})

{x}, provided y S, otherwise

= S. In other words, is the result of replacing one member of S by another. For example, if S is the set {2, 3, 7}, then = {2, 5, 7}. The substitution in question acts on complex abstract objects and produces another complex abstract object by replacing one constituent by another. This is exactly the kind of process that Russell had in mind in his substitutional theory of propositions; it is also the notion of substitution given above in ‘Complexes’ in the list of primitive logical notions . Although Russell ultimately abandoned his earlier view of propositions as entities, his commitment to the view that objects form part of the complexes

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Page 16 expressing the meanings of statements about them remained in a modified form. Thus in his later multiple-relation theory of judgement, individuals are constituents of judgement-complexes, just as they are constituents of propositions in the earlier theory. Hence, it appears that the principle that individuals occur in the semantic values of statements about them is more fundamental for Russell than his commitment to propositions as such. Gappy Objects and Variables It is a well-known fact that Frege held to a view that included ‘gappy’ objects among the entities over which his quantifiers range. More specifically, Frege held that just as a free variable can be considered as a ‘gap’ in a formula to be filled by the name of an entity, so there are ‘gappy’ or ‘unsaturated’ entities corresponding to formulas with free variables. He writes in his 1904 paper ‘What is a Function?’: The peculiarity of functional signs, which we here called ‘unsaturatedness’, naturally has something answering to it in the functions themselves. They too may be called ‘unsaturated’, and in this way we mark them out as fundamentally different from numbers. (Frege 1984:292) The functions themselves are ‘gappy’, and are to be sharply distinguished from the ‘courses of values’ corresponding to the functions. (Frege uses the term ‘ Werthverlauf ’, rendered by Russell as ‘range’, Russell 1937, Appendix A: 511.) It doesn’t seem to be generally recognized that gappy objects fit naturally into Russell’s logical universe at this time. In my paper (1994) with Judy Pelham, we included such entities, which we called ‘propositional forms’, though we did not provide detailed historical arguments for their inclusion. I would now like to argue that the appearance of such strange-seeming entities in Russell’s logical ontology appears very plausible, given his other assumptions. Let us ask the question: What are the immediate constituents of a universally quantified proposition such as ( x)φ(x)? There appear to be three reasonable answers to this. The first is that the immediate constituents are all the Russellian propositions of the form φ( a ), where a is an individual. Although this view has a lot to recommend it, it does not seem to fit with Russell’s general views of complexes. If we take this view, then we are treating a universally quantified proposition essentially as an infinite conjunction, and so it would (assuming the axiom of infinity, which Russell at this period held to be a logical truth) be a complex with infinitely many constituents. However, though Russell admitted the bare logical possibility of such complexes, he insisted that the complexes arising in practice were all finite (Russell 1937:145–46). It was Russell’s view that we grasp the meaning of propositions by grasping the meaning of their constituents (that is to

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Page 17 say, Russellian propositions correspond quite closely in their epistemological function to Fregean senses). This is necessarily a finite process—that is to say, we can grasp the meaning of a universal proposition without explicitly grasping the meaning of all of its instances (since we might not be acquainted with all of the individuals in the universe). Hence, this view of the constituents of universal propositions cannot possibly be maintained as a plausible interpretation of Russell’s views. The second view is that the universal proposition has the propositional function φ as an immediate constituent. This is an attractive viewpoint, and probably represents the way that Russell thought about propositions early in his career. However, Russell lost his logical innocence with the discovery of the Contradiction, and this view seems to be made untenable by the paradoxes. The difficulty is this: there are complexes such as for which no corresponding function exists. We seem to be stuck with thinking of them just as complexes, without being allowed to think of the function itself as a legitimate constituent. Such complexes seem to form part of Russell’s universe at this time. For example, consider the primitive proposition stated at the end of ‘Complexes.’ What are the entities over which the variable ‘X’ ranges? It appears reasonable to guess that these are unsaturated entities in the style of Frege. Hence, we are led to adopt the third view that the ‘gappy’ or ‘unsaturated’ object corresponding to the expression φ( x) must be part of Russell’s logical universe. If we push the analysis a little farther, we can ask: What are the constituents of φ( x)? It seems as if the variable x must be a constituent of the gappy object φ( x), just as Arthur Balfour is a constituent of the proposition expressed by the sentence ‘Arthur Balfour advocates retaliation.’ Furthermore, it would appear that his universe must include infinitely many distinct variables x, y, z ,…, since we have to distinguish the propositional form ψ(x, y) from ψ(x, x). We must be able to identify and distinguish the gaps themselves. I have just argued that, given certain general principles accepted by Russell from 1903 to 1905, he ought to have been committed to gappy or unsaturated objects, just like Frege. Moreover, we can also find direct textual evidence that Russell saw the necessity of these odd-seeming entities himself. In the set of rough manuscript notes from 1903 entitled ‘Points about Denoting’, he writes: Consider e.g. p q. This contains two variables. The attitude is, at present, that there is such an object as ‘ p q’, distinct from all the values obtained by giving definite values to p and q. Similarly, and more fundamentally, there is such an object as p, distinct from all the values of p. (Russell 1994:311) This passage shows Russell committing himself to the existence of propositional forms, and to variables as entities.

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Page 18 It is significant that G. E. Moore saw some of the difficulties involving unsaturated objects and variables as entities. In a letter of 23 October 1905, Moore wrote to Russell: I was very interested in your article in Mind, and ended by accepting your main conclusions (if I understand them) though at first I was strongly opposed to one of them. What I should chiefly like explained is this. You say ‘ all the constituents of propositions we apprehend are entities with which we have immediate acquaintance’? Have we, then, immediate acquaintance with the variable? and what sort of entity is it? (Russell 1994:311) These remarkably penetrating remarks show that Moore too saw the difficulties in Russell’s view of quantified propositions and their constituents. Yet the sentence immediately following the passage quoted above shows uneasiness connected with the necessary commitment to infinitely many variable entities: ‘But the difficulty lies in this: p is not a definite object, for if it were, it would be the same as q; p is any term, and q is any term, and each is merely and solely any term, and yet they are not identical’ (311). In fact, although it seems that Russell should have accepted propositional forms and variables as entities, he always showed considerable uneasiness about these equivocal inhabitants of the logical universe. This uneasiness already showed itself in Appendix A of Principles of Mathematics. Here Russell makes a somewhat comical objection to Frege’s notion of function as an unsaturated entity: Frege’s general definition of a function, which is intended to cover also functions which are not propositional, may be shown to be inadequate by considering what may be called the identical function, i.e. x as a function of x. If we follow Frege’s advice, and remove x in hopes of having the function left, we find that nothing is left at all; yet nothing is not the meaning of the identical function. (Russell 1937, Appendix A: 509) Although I have argued that the most coherent interpretation of Russell’s ontology at this time is given by a universe containing gappy objects, it is a moot point whether Russell himself showed real commitment to these entities, and evidence can be provided on both sides of the ledger. This question, however, is not central to the basic points that I am trying to make here. What I am trying to emphasize in this sketch of the ontology of the period is that Russell was struggling with problems that concern very abstract and complex entities of an unfamiliar kind. In particular, the difficulty of dealing with denoting phrases containing free variables, such as those defining functions, is central for his research at this time. This point is driven home by Russell’s own remarks in the paper ‘On Meaning and Denotation’:

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Page 19 We have next to consider a far more difficult class of problems, the problems, namely, which result from variable denotation. In all the cases of denoting complexes hitherto discussed, there was a perfectly definite entity denoted in an unambiguous manner, and the only difficulty involved was that of disentangling and characterizing the fact of denoting. But now we have also to consider the special and formidable problems involved in the nature of the variable. (Russell 1994:328) It was the intimate connection between variable denotation and the problem of the paradoxes that led Russell to conjecture that the solution of the latter would be found in understanding the true nature of meaning and denotation. MEANING AND DENOTATION If we are to understand the importance of the emergence of the theory of denoting in 1905, we need to have some grasp of the theory of meaning and denotation that immediately preceded it. In the critical parts of ‘On Denoting’, Russell discusses the theory of meaning and denotation as ‘Frege’s theory’ (Russell 1905a: 483; 1994:418). Peter Geach (1958–59) seems to have been the first to suggest that these notoriously difficult passages are better interpreted as referring to Russell’s own earlier theory of meaning and denotation. Chrystine Cassin (1970) also followed this suggestion in her detailed analysis of the notorious ‘Gray’s Elegy’ passage of ‘On Denoting’. This suggestion is definitely correct, in the sense that these parts of ‘On Denoting’ are derived from similar passages in the manuscripts of 1903 to 1904. However, it should be added that Russell himself failed to distinguish between his theory and Frege’s. In a letter to Alexius Meinong of 15 December 1904 (Russell 1994: xxxiv), Russell explicitly embraces Frege’s theory of sense and reference, while in a review of articles by members of Meinong’s school (Russell 1905b: 533; 1994:599), published in the same number of Mind as (Russell 1905a), Russell identifies the ‘theory of denoting’ with Frege’s theory of Sinn and Bedeutung . So, let us proceed to examine the main ideas of Russell’s theory of 1903 to 1904, while bearing in mind that it is similar to, but not identical with, the theory of Frege. Before plunging into deep philosophical waters, it might be a good idea to see what Russell’s formal practice was at this time, with respect to descriptions. Let us recall that Frege employs a primitive description operator in his Grundgesetze der Arithmetik (Frege 1893: §11). This operator takes objects as inputs, and has objects as outputs. The rule for the operator is that if the input is a course-of-values that has exactly one element, then the output is that element. If the input does not satisfy this condition, then the output is the empty courseof-values.

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Page 20 Russell’s logical practices of 1903 to 1904 are similar, in that he has a primitive description operator ι, mentioned above in connection with one of the 1903 manuscripts. The meaning of the ι operator, derived from a corresponding operator of Peano, is that it is the inverse of the unit class operator ι. That is to say, it satisfies the condition ι(ιx) = x (Russell 1994:61). Later, in 1904, Russell introduced a notation similar to that of the 1905 theory, namely, a variable-binding description operator (Russell 1994:127); this new notation is an important step towards the 1905 theory of descriptions. This seemingly minor notational shift has a real importance for Russell. As long as he was using a description operator in the style of Frege and Peano, the theory of descriptions was dependent on the theory of set abstraction. Both Frege and Peano use such set abstractions freely, but with the emergence of the paradoxes, this was no longer an option for Russell. Hence, the change in notation is a step towards freeing the theory of descriptions from its dependence on the theory of set abstraction. After these notational preliminaries, let us set down an outline of the 1903 theory of meaning and denotation. Names and Descriptions Here is a rough sketch of the 1903 theory, as presented in the manuscript notes of 1903 ‘On the Meaning and Denotation of Phrases’ (Russell 1994:283–96). Proper names are devoid of meaning, but denote an individual—this is of course already an important divergence from the theory of Frege. Verbs and adjectives have meaning but no denotation. Adjectival nouns, on the other hand, have denotation. ‘The table is black’, for example, contains the words is and black , which, as they occur in this sentence, mean, but do not denote, the objects to which they refer. The word blackness, on the contrary, denotes, but does not mean, the very same object as that which the word black means without denoting. (Russell 1994:284) It appears from this passage that the difference between meaning and denotation is a difference in the relationship between parts of speech and the objects corresponding to them. However, later in the same paper, Russell indicates that there may be a difference in the objects themselves. He writes: Words and phrases are of three kinds: (1) those that denote without meaning; (2) those that mean without denoting; (3) those that both mean and denote. Socrates belongs to (1), is to (2), the death of Socrates to (3). Objects also are of three kinds: (1) those that can only

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Page 21 be denoted; (2) those that can only be meant; (3) those that can be either meant or denoted. The second kind is doubtful, and raises grave logical problems. The first kind of objects I propose to call individuals; the third shall be called functions ; the second and third together shall be called concepts , and the second alone shall be called non-functional concepts . (Russell 1994:287) This passage is quite puzzling, but I believe that it can be interpreted by thinking over some of the things we said earlier about gappy objects and functions. The difficult category here is the second one. What did Russell have in mind here? The example that he gives is the meaning of is. Assuming that this is the ‘is’ of predication, Russell is referring to the membership relation . Now at this time in Russell’s logical research, x y is a typical example of a nonfunctional complex, since there can be no function ( x y), on pain of contradiction. Hence, it seems that the objects in the second category are nonfunctional complexes, which would explain why Russell says that they ‘raise grave logical problems’. Russell’s basic idea that individuals are constituents of true propositions about them obviously causes him big headaches when it comes to fictional names. The view he takes is that imaginary proper names are really substitutes for descriptions (Russell 1994:285). This leads him on to consider sentences containing descriptions that do not denote. He eventually concludes that they lack truth values, and that phrases such as ‘the present King of France is bald’ are neither true nor false (Russell 1994:286). (Russell never seems to have thought Frege’s trick of assigning such descriptions a conventional denotation, such as the empty set, to be plausible.) The theory of meaning and denotation makes contact with Russell’s project of logical foundations through the mechanism of functional abstraction. The operation that transforms the complex X into the function, ( X ) is seen by Russell as a move akin to that of forming an adjectival noun from an adjective: The method of obtaining the function ( X ) is this: If x is not already the subject of X , substitute for X (if possible) a formally equivalent complex in which x is subject, and does not occur except as subject. Then what is said about x is the function ( X ), i.e. what is meant by the rest of X is what is denoted by ( X ). (Russell 1994:291–92) The parallel here is with the formation of the adjectival noun blackness from the adjective black described in the earlier quotation. The operation of functional abstraction takes us from an expression that means a certain entity to another expression that denotes the same entity. This description of what is happening is, of course, problematic in the case of nonfunctional complexes.

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Page 22 THE EMERGENCE OF THE THEORY OF DESCRIPTIONS The birth of Russell’s new theory of denoting is chronicled in full detail in the 1904 manuscript entitled ‘On Fundamentals’ (Russell 1994: Paper 15). This set of working notes begins with a theory of meaning and denotation similar to the theory of 1903 described above. Russell distinguishes between entityoccurrences and meaning-occurrences in complexes. The bulk of the paper consists of a series of numbered paragraphs in which the new theory gradually takes shape. In paragraphs 21 to 23 (Russell 1994:373–76), certain problems lead Russell to an even more complex set of distinctions about occurrences; the distinction between primary and secondary occurrences emerges for the first time in paragraph 23. In paragraphs 40 to 42 (Russell 1994:383–85), the basic ideas of the new theory of denoting finally emerge. I shall not go into detail here about the subtle and complicated reasoning about occurrences and complexes that leads Russell to his final theory. Rather, I would like to emphasize again the connection in Russell’s mind between the theory and his principal foundational problems. The first application that Russell finds for his new notions is in the theory of classes. Paragraph 41 introduces the contextual definition for descriptive phrases, and in paragraph 42, Russell immediately applies the idea to give a contextual elimination of class abstracts. This treatment, of course, in a more complex and sophisticated version, is a fundamental idea in Principia Mathematica (Whitehead and Russell 1910: *20). For Russell, as for Quine, the important feature of his new theory was the reduction in the number of primitive concepts of logic. Why Ontological Reduction? Ontological reduction is sometimes considered as an end in itself, rather as if we are looking for the basic logical particles making up the mathematical universe, like physicists searching for the basic constituents of matter. For Russell, in the period we are discussing, there was a more pragmatic aspect to the quest for ontological simplicity. The hope that he nursed was that by simplification, the basic structure of the paradoxes would be revealed, and the true solution made manifest. We can see this idea of simplification as a road to the solution of the paradoxes in a letter that Whitehead wrote to Russell on 28 September 1905. Russell had found a very general form of the paradoxes that encompassed most of the known forms, and had described his discovery in a letter to Couturat of 24 September 1905 (Russell 1994: xxxvi–xxxvii). The argument for this generalized form of the Contradiction was later published in Russell’s paper surveying possible solutions to the paradoxes of logic and set theory (Russell 1906). Whitehead was pleased by Russell’s discovery, and wrote to Russell on 28 September 1905: ‘I think your simplification of

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Page 23 the Contradiction most important. All your enemies have now one neck. But in a way this makes them harder to subdue; for your solution ought to have one neck also’ (Russell 1994: xxxvii). In October 1905, Russell had reached the conclusion that the radical ontological reduction promised by his theory of descriptions was also the key to the solution of the paradoxes. His first published remark on this new idea was a footnote that he added to Couturat’s French translation of his polemical reply to Pierre Boutroux (Russell 1905c; 1994: Paper 23). The footnote refers to a passage describing the notion of propositional functions, and reads, in part: I believe that this notion may even be replaced by the more primitive notion of the substitution of a variable for a constant, and that by this means we can avoid the contradictions arising from certain paradoxical classes, for example the contradiction discovered by Burali-Forti. (Russell 1994:524) In the letter providing the corrections and additions to Couturat’s translation, dated 23 October 1905, Russell gives more details of the idea: I find that to avoid contradiction, and make the elements of mathematics rigorous, it is absolutely necessary not to employ a single letter, such as φ or f , for a variable which cannot become an arbitrary entity, but which is really a dependent variable…. Instead of φ!x, we can put , which is to mean ‘the result of substituting x for a in p’… Thus we shall have only one type of independent variable… I think once more that the solution of the contradictions is to be found in maintaining that there are no classes or relations. (Russell 1994: xxxvii–xxxviii) Thus by the end of 1905, Russell, starting from his theory of descriptions, had arrived at a radical ontological simplification of logic. First, classes were to be eliminated in favour of propositional functions, using the ideas of ‘On Fundamentals’. Secondly, propositional functions themselves were to be eliminated by reducing them to the more primitive notions of propositions and substitution. The resulting substitutional theory, based on just these two primitive notions, together with the basic notions of predicate logic, is a remarkably elegant and economical theory, which Russell hoped would provide the final solution to the tormenting problem of the paradoxes he had first encountered in 1901. Did it Work? We may well ask whether the optimistic attitude Russell showed in October 1905 was in fact justified. Did the radical ontological reduction of the

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Page 24 substitutional theory lead to the solution of the paradoxes, as he hoped it would in his letter to Couturat? Unfortunately, the answer is ‘no’. The paradoxes re-emerged in the form of a substitutional paradox (Landini 1989, 1998; Pelham and Urquhart 1994; Linsky 2003) that Russell battled by producing more and more complicated forms of the substitutional theory, but ultimately in vain, as the paradox kept popping up again in more and more complex forms. Even though Russell had jettisoned classes, relations and fi** nally even propositional functions, the paradox kept returning like an unkillable monster in a horror movie. In the end, the solution was found by returning to the old idea of types, a solution that Russell had advocated, and then abandoned, in Appendix B of the Principles of Mathematics. Although the apparatus of ontological reduction, in the form of the theory of descriptions, the doctrine of incomplete symbols, and the reduction of classes to propositional functions, is retained in Principia Mathematica , ultimately it is the theory of types that must take the credit for holding the paradoxes at bay. In Church’s famous ‘Bibliography of Symbolic Logic’ (1936), ‘On Denoting’ is accorded one of Church’s rare asterisks, as a publication ‘of especial interest or importance from the point of view of symbolic logic’; however, ‘Mathematical logic as based on the theory of types’ (Russell 1908) rates one of Church’s even rarer double asterisks, as one of a small number of publications ‘which mark the first appearance of a new idea of fundamental importance’ (Church 1936:122). Church’s entire bibliography, starting from Leibniz and containing 547 items, contains only eleven double asterisks; Boole, Brouwer, De Morgan, Gödel, Hilbert and Russell each earn a single double asterisk, Zermelo scores two, while Frege is the clear winner with three double asterisks. As I indicated in the opening section of this paper, Church’s judgement on the relative importance of the theory of descriptions and the theory of types accords closely with the general point of view current among professional logicians. The theory of descriptions is an interesting and historically important proposal for formalizing logical notions, but not truly fundamental in the same sense as the theory of types, which remains one of the few really essential ideas of modern logic. What is more, Russell’s original idea, that the theory would lead to the fi** nal solution of the conundrum posed by the paradoxes, eventually led to a blind alley. Although Russell hoped again and again that the present King of France would solve the Contradiction, it eventually became clear that the royal intellect was in fact not up to that standard. NOTES 1. I would like to thank Peter Koellner for comments on this and the next section that resulted in substantial improvements.

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Page 25 REFERENCES Barendregt, H. P. (1984) The Lambda Calculus: Its Syntax and Semantics, Studies in Logic and the Foundations of Mathematics, vol. 103, Amsterdam: North Holland. Cassin, C. E. (1970) ‘Russell’s Discussion of Meaning and Denotation: A Re-Examination’, in E. D. Klemke (ed.) Essays on Bertrand Russell, Chicago/London: University of Illinois Press: 256–72. Church, A. (1936) ‘A Bibliography of Symbolic Logic’, The Journal of Symbolic Logic 1: 121–218. Frege, G. (1893) Grundgesetze der Arithmetik, begriffsschriftlich abgeleitet, vol. 1, Jena: Pohle. ——. (1984) Collected Papers on Mathematics, Logic, and Philosophy , ed. B. F. McGuinness, Oxford: Blackwell. Geach, P. T. (1958–59) ‘Russell on Meaning and Denoting’, Analysis 19: 69–72. Grattan-Guinness, I. (1977) Dear Russell—Dear Jourdain , New York: Columbia University Press. Landini, G. (1989) ‘New Evidence Concerning Russell’s Substitutional Theory of Classes’, Russell, n.s. 9: 26–42. ——. (1998) Russell’s Hidden Substitutional Theory , New York/Oxford: Oxford University Press. Linsky, B. (2003) ‘The Substitutional Paradox in Russell’s 1907 Letter to Hawtrey’, Russell, n.s. 22: 151– 60. Pelham, J. and Urquhart, A. (1994) ‘Russellian Propositions’, in Logic, Methodology and Philosophy of Science IX: Proceedings of the Ninth International Congress of Logic, Methodology, and Philosophy of Science, Uppsala, Sweden, August 7–14, 1991, Amsterdam: North Holland: 307–26. Quine, W. V. O. (1963) From a Logical Point of View , 2nd edn, rev., New York: Harper and Row. Ramsey, F. P. (1931) The Foundations of Mathematics and Other Logical Essays, ed. R. B. Braithwaite, with a preface by G. E. Moore, London: Routledge and Kegan Paul. Russell, B. (1905a) ‘On Denoting’, Mind 14: 479–93. ——. (1905b) Review of Untersuchungen zur Gegenstandstheorie und Psychologie , ed. A. Meinong, Mind 14: 530–38. ——. (1905c) ‘Sur la relation des mathématiques à la logistique’, Revue de métaphysique et de morale 13: 906–16. ——. (1906) ‘On Some Difficulties in the Theory of Transfinite Numbers and Order Types’, Proceedings of the London Mathematical Society, Series 2, 4: 29–53. ——. (1908) ‘Mathematical Logic as Based on the Theory of Types’, American Journal of Mathematics 30: 222–62. ——. (1937) The Principles of Mathematics, 2nd edn (first published 1903), London: George Allen and Unwin. ——. (1985) My Philosophical Development, Unwin Paperbacks (first published 1959), London: George Allen and Unwin. ——. (1994) Collected Papers of Bertrand Russell, vol. 4, Foundations of Logic, 1903–05 , ed. A. Urquhart with the assistance of A. C. Lewis, London: Routledge. Urquhart, A. (1995) ‘G. F. Stout and the Theory of Descriptions’, Russell, n.s. 14: 163–71. Whitehead, A. N. and Russell, B. (1910) Principia Mathematica , vol. 1, Cambridge: Cambridge University Press.

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Page 26 2 Antirealism and the Theory of Descriptions Graham Stevens According to Michael Dummett’s celebrated characterization of the realism debate, the defining feature of realism with regard to any particular domain of discourse is a commitment to the principle of bivalence applied to statements of that domain. As Dummett has noted, however, Russell’s theory of descriptions somewhat complicates such a characterization of the issue by offering a means of retreating from realism while retaining the principle of bivalence. To give perhaps the most obvious example, the theory of descriptions allows one to resist the temptation to posit any Meinongian entities corresponding to definite descriptions such as ‘the present King of France’ (used at a time when France has no King), while maintaining that statements containing those phrases, such as ‘the present King of France is bald’ or ‘the present King of France is not bald’ are nonetheless determinately true or false. Dummett therefore expands his characterization of realism to admit the possibility of resisting realism without violation of bivalence offered by the theory of descriptions by holding that integral to any given version of realism is not just the principle of bivalence for the statements of the relevant class but also an ‘interpretation of those statements at face value, that is to say, as genuinely having the semantic form that they appear on their surface to have’ (Dummett 1991:325). Relinquishing commitment to either principle constitutes, according to Dummett, a concessionary move in the direction of antirealism. A little reflection should persuade one that Dummett’s modification of his original claim is well advised, for Russell’s theory of descriptions is not the only example of a theory which effects a retreat from realism by refusing to uncritically read the semantic value of an expression off of its surface grammatical form. Early versions of expressivism, for example, in holding that certain sentences (most commonly those uttered in moral discourse) are sometimes used to express nonrepresentational states of a speaker and are thus devoid of any truth-evaluable content, present an antirealist alternative by refusing to interpret those sentences at face value. It would be a mistake to view the expressivist’s position as being driven by a concern about the legitimacy of bivalence. Expressivism is quite compatible with bivalence for the simple reason that the statements which induce antirealist

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Page 27 sympathies in the expressivist are not, strictly speaking, truth- (or falsehood-) bearers at all. Hence their lack of a truth-value poses no more threat to classical bivalent semantics than does the fact that the sentence ‘What is antirealism?’, being a question, lacks a truth-value. By reinterpreting the statements of the disputed class contrary to their surface grammar, the expressivist, like the Russellian, is suitably positioned to resist the pull of realism without being forced to abandon bivalence. Russell himself did not, at least originally, intend to use the theory of descriptions to retreat from realism regarding anything more than classes. Contrary to a popular myth, partly propagated by Russell himself in some later writings, the theory of descriptions was not required in order to escape from the Meinongian excesses commonly thought to infect the Principles of Mathematics. In that work, Russell did indeed take the logical form of the semantic values of sentences as reflective of those sentences’ grammatical form. According to this early position, to every significant declarative sentence corresponds a Russellian proposition and, furthermore, to every grammatical unit of the sentence corresponds a constituent of the proposition. Thus there must, in the proposition expressed by the sentence ‘the present King of France is bald’, be something corresponding to the denoting phrase ‘the present King of France’. Meinongian nonexistent objects, that is, objects which, despite their lack of existence, nonetheless retain a form of being, quickly start to loom on the horizon and seem to be endorsed in passages such as the following: Numbers, the Homeric gods, relations, chimeras and four-dimensional spaces all have being, for if they were not entities of a kind, we could make no propositions about them. Thus being is a general attribute of everything, and to mention anything is to show that it is… Existence , on the contrary, is the prerogative of some only amongst beings… what does not exist must be something, or it would be meaningless to deny its existence; and hence we need the concept of being, as that which belongs even to the non-existent. (Russell 1903: §427) Confronted by such outlandish remarks, it has been customary for commentators on Russell to assume that only with the theory of descriptions was Russell saved from the perils of Meinongianism. Russell’s own words in this passage should not be interpreted at face value, however. Russell did not discover the theory of descriptions until 1905, but this did not leave him silent regarding the semantics of denoting phrases in the Principles . According to the theory of denoting forwarded in the Principles , there is no need to invoke a shadowy nonexistent being to sit on the shadowy nonexistent throne of France in order to explain the semantics of the sentence ‘the present King of France is bald’. According to the Principles , every (meaningful) declarative sentence expresses a Russellian proposition. Furthermore, there is no evidence that Russell doubted at this time the

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Page 28 principle that the Russellian proposition expressed by a sentence will also contain constituents corresponding to all the constituents of that sentence. Thus, of course, some entity is required to inhabit the place of the subject in the Russellian proposition that the present King of France is bald. Russell does not, however, seek to fill this place with a Meinongian nonexistent being. Rather, sentences containing denoting phrases express propositions containing denoting concepts . The mark of a denoting concept is that it can occupy the subject position of a Russellian proposition without being the logical subject of that proposition. The proposition that the present King of France is bald thus contains a denoting concept in place of the thing that it is about. Russell’s theor y of denoting concepts provides him with enough resources to avoid Meinongianism by allowing for cases where a denoting concept fails to denote anything in reality (that is, where the thing it is about does not exist). Indeed Russell explicitly appeals to this kind of case in order to find a way out of the apparent paradox suggested by his remark that ‘in some sense nothing is something’: We may now reconsider the proposition ‘nothing is not nothing’—a proposition plainly true, and yet, unless carefully handled, a source of apparently hopeless antinomies. Nothing is a denoting concept, which denotes nothing. The concept which denotes is of course not nothing, i.e., it is not denoted by itself. The proposition which looks so paradoxical means no more than this: Nothing , the denoting concept, is not nothing, i.e., is not what itself denotes. (§73) It is important to note that this does not simply bring us back full circle to the need for a present King of France to have being in order for the denoting concept the present King of France to be significant. This is why the passage quoted from §427 of the Principles is misleading. Russell’s point there is that something must exist to fill the subject position in a proposition if there are meaningful propositions about the sorts of things he lists. This requirement, however, is met by the presence of a denoting concept in the proposition; there is no need to make the further demand that the thing denoted by the concept must have either full-blooded existence or the more diluted being. All that matters is that Russell’s ontology extends to denoting concepts. Thus Russellian propositions are guaranteed constituents corresponding to the constituents of the sentences expressing them without recourse to Meinongianism. The theory of descriptions hardly deserves credit for ridding Russell of ontological commitments he did not actually have. Once we see the early theory of denoting in the correct light, however, it becomes evident that, far from being a deliberate retreat from realism, the theory of descriptions is in fact an effective method of preserving Russell’s realistic theory of propositions. Peter Hylton, who has recently argued in detail for such an

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Page 29 interpretation of the theory of descriptions, extends the familiar use of the term ‘direct realism’ so as to describe ‘both Russell’s insistence on a direct and unmediated relation between the mind and the known object and the idea that propositions paradigmatically contain the entities they are about’ (Hylton 2003:209). The term helpfully unites Russell’s propositional realism—a certain take on the kinds of entities that propositions are taken to be—and the epistemological thesis, often referred to as Russell’s ‘principle of acquaintance’, that ‘in every proposition that we can apprehend… all the constituents are really entities with which we can have immediate acquaintance’ (Russell 1905:56). As Hylton correctly points out, the problem of denoting forces an uncomfortable split between these two principles in 1903. If the present King of France is a constituent of the proposition that the present King of France is bald, then it seems that we can understand some propositions containing constituents (such as the present King of France) that we are not acquainted with. Thus, Russell’s propositional realism is preserved, as every proposition contains the entities it is about, but only at the expense of the principle of acquaintance. Alternatively, one can reject, as Russell did in 1903, the claim that every proposition must contain the entities it is about. This allows for the preservation of the principle of acquaintance (we are acquainted with the denoting concept the present King of France , but not with its denotation), but only at the expense of a key component of Russellian propositional realism. The problem with the theory of denoting, then, is not that it falls prey to a naïve realism that is forced to admit Meinongian objects; it is that it is forced to depart from realism of the Russellian variety regarding the nature of propositions and of what it is for us to understand them. The theory of denoting simply presents a class of exceptions to Russell’s direct realism with no decent account of why such exceptions should be admitted. The theory of descriptions, evidently, overcomes this difficulty.1 By analysing the sentence ‘the present King of France is bald’ into the Russellian proposition that there is one and only one x that is presently King of France and x is bald, the theory allows for us to be acquainted with all of the constituents of the proposition, and for the proposition to contain the things it is about—for the theory states that the proposition , contrary to what a face-value interpretation of the sentence suggests, is not about some nonexistent figure at all; rather, it is about the instantiation of its constituent concepts (and the concept of instantiation is, of course, itself a further constituent represented by the existential quantifier). The theory of descriptions, then, played an important role in the preservation of Russell’s realism. Contrary to what Dummett suggests, the theory in fact does so precisely because it refuses to interpret sentences at face value. The very thing Dummett takes to betray the theory’s antirealist leanings enables it to defend Russell’s realist metaphysics. This is somewhat surprising when one recalls the uses that the theory of descriptions has been put to, both by Russell and by followers such as

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Page 30 Quine, in disposing of ontological commitments. Those uses are doubtless the uses that Dummett has in mind when viewing the theory as driven by antirealist motivations. Russell, of course, put the theory to a use of that sort almost immediately, appealing to it when arguing against the reality of classes as a means of avoiding the Russell paradox. However, even as he was retracting his earlier unblinking realism about classes, Russell was doing so as part of a wider philosophical project designed to preserve more fundamental realist ambitions. That Russell intended from the outset to use the theory of descriptions in attacking the Russell paradox is evident from his comment in a 1904 letter to his wife that he and Whitehead had ‘had a happy hour yesterday, when we thought the present King of France had solved the Contradiction; but it turned out finally that the royal intellect was not quite up to that standard. However, we made a distinct advance’ (Russell to Alys Russell, 14 April 1904, in Russell 1992:269), as well as from his remark in the first volume of his autobiography that the discovery of the theory in 1905 ‘was the first step towards overcoming the difficulties that baffled me for so long’ (Russell 1967:152). Russell goes on to say: ‘In 1906 I discovered the Theory of Types. After this it only remained to write the book [ Principia Mathematica ] out’ (152). In fact, the theories of descriptions and types are more closely related than many have realized. Recent interest in the period between 1905 and 1908 has shown the ‘substitutional theory of classes and relations’ that Russell developed during this time to be the missing link between the two theories.2 In an autobiographical piece written for the Library of Living Philosophers volume dedicated to him in 1944, Russell makes it plain that the real importance of the theory of descriptions is to be found in its application to the theory of classes: What was of importance in this theory was the discovery that, in analysing a significant sentence, one must not assume that each separate word or phrase has significance on its own account. ‘The golden mountain’ can be part of a significant sentence, but is not significant in isolation. It soon appeared that class-symbols could be treated like descriptions, i.e., as non-significant parts of significant sentences. This made it possible to see, in a general way, how a solution of the contradictions might be possible. (Russell 1944:13–14) The treatment of class-symbols as nonsignificant parts of significant sentences was first tentatively explored under the name ‘The No Classes Theory’ as one of three possible solutions to the contradictions in a paper presented in 1905. By the time that the paper was published in 1906, however, Russell was prepared to attach to it the following note: ‘From further investigation I now feel hardly any doubt that the no-classes theory affords the complete solution of all the difficulties stated in the first section of this paper’ (Russell 1906a: 164). In another paper presented in 1906 Russell

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Page 31 further developed the theory, now under the name shared by the paper ‘The Substitutional Theory of Classes and Relations’. The substitutional theory avoids all mention of classes as entities, replacing talk of classes with reference to matrices expressed by symbols of the form ‘ p/ a ’. Here both ‘ p’ and ‘ a ’ are understood to be names of entities. The nature of a matrix is best explained by the fact that a matrix features in propositions such as that expressed by ‘ p/ a ;x! q’ which can be read as ‘ q results from the substitution of x for a in all those places, if any, where a occurs in p’. Admitting, as of course Russell did at this time, that Russellian propositions are entities, either p or a may be propositions (though neither has to be). This allows Russell to treat a matrix as if it were a class and thus ensure that all talk of actual classes is eliminable in favour of talk of matrices. The condition under which an entity x is a member of the ‘class’ p/ a is just that there is a true proposition resulting from the substitution of x for a in p. The connection forged by the substitutional theory between the theories of descriptions and types is evident when we reflect on the form that the Russell paradox would need to take in the substitutional calculus. About the closest we could get would be to write something like ‘ p/ a ;p/ a ’. But this is mere nonsense, amounting to something like ‘the result of replacing a in p by the result of replacing a in p by’. Self-membership becomes impossible according to the substitutional analysis of classes. As Russell says: ‘now “ x is an x” becomes meaningless, because “ x is an α” requires that α should be of the form p/ a , and thus not an entity at all. In this way membership of a class can be defined, and at the same time the contradiction is avoided’ (Russell 1906b: 172). In brief, the grammar of substitution yields the kinds of distinctions placed on a standard theory of classes by simple type-theory and, indeed, it is best understood as the original foundation for Russell’s mature theory of types. A commonly voiced objection to Russellian type-theory is that Russell outlaws certain apparent propositions as nonsense on purely ad hoc grounds. However, once one sees that the theory of types has its origins in the substitutional theory it is evident that this criticism is unfair. From the perspective of the logic of substitution, violations of type-distinctions are clearly nonsense in a quite unobjectionable way. Furthermore, it is because ‘classes’ are incomplete symbols that violations of type-distinctions are violations of sense; thus the substitutional theory provides the link between the theory of descriptions and the theory of types. The application of the theory of descriptions in the substitutional theory, at least from a first glance, appears to comport better with Dummett’s interpretation of the theory of descriptions. With classes eliminated in favour of matrices, classes become what Russell sometimes called ‘logical fictions’. However, the definition of cardinal numbers as classes of similar classes is retained, thus it seems that numbers must also be logical fictions. Confirmation of this interpretation can be found in ‘The Substitutional Theory of Classes and Relations’:

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Page 32 The theory which I wish to advocate is that classes, relations, numbers, and indeed almost all the things that mathematics deals with, are ‘false abstractions’, in the sense in which ‘the present King of England’, or ‘the present King of France’ is a false abstraction. Thus e.g. the question ‘what is the number one ?’ will have no answer; the question which has an answer is ‘what is the meaning of a statement in which the word one occurs?’ And even this question only has an answer when the word occurs in a proper context. (Russell 1906b: 166) There is a striking similarity between this passage and §62 of Frege’s Grundlagen der Arithmetik . The similarity should not blind us to the differences, however. For Frege, the contextual definition of number is the first step towards grasping the concept of numbers as objects which are neither psychological nor physical in nature. The final step is taken later, however, when the notion of a class (extension of a Fregean concept) is introduced. With classes expelled from his ontology, however, Russell is no longer able to complete the same manoeuvre. Thus the contextual definition of number given in Russell’s substitutional theory serves an opposite purpose to that of Frege’s earlier definition. Whereas Frege was seeking to establish the self-subsistence of numbers as logical objects, Russell is seeking to demonstrate their lack of that same status. It is perhaps unsurprising, then, that the substitutional theory left Whitehead feeling somewhat uneasy when Russell first presented it to him. Dismayed by Russell’s apparently drastic retreat from the realist philosophy of the Principles , Whitehead complained: ‘It founds the whole of mathematics on a typographical device and thus contradicts the main doctrines of [ The Principles of Mathematics]’ (Whitehead to Russell, 22 February 1906, quoted in Russell 1973:131). Whitehead at this point saw the substitutional theory as retreating from realism in just the same way that Dummett holds the theory of descriptions (which, as we have seen, was the engine that drove the substitutional theory) to be naturally inclined towards doing. Again, however, Russell’s intentions here are more sophisticated than they first appear. What Whitehead had failed to realize when he wrote the letter quoted from above was the extent to which Russell was once again going to great lengths to secure a way of retaining his realist metaphysics. To view the substitutional theory as founding mathematics on a typographical device is simply to mistake the formulas of the substitutional calculus for the Russellian propositions they represent. It is these latter entities that provide the foundations for mathematics according to the substitutional theory. Far from beating a retreat into antirealism, Russell was seeking to draw on his robust propositional realism in order to avoid the need for any ontology of classes or functions. The original use of the theory of descriptions, we saw above, allowed for the rejection of denoting concepts without rejecting realism. Indeed, following Hylton, I have argued that the introduction of the theory of

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Page 33 descriptions allows for Russell to maintain his direct realism without recourse to the ad hoc exceptions demanded by the theory of denoting concepts. The application of the theory of descriptions to classes in the substitutional theory can be viewed in much the same way. Russell’s paradox, and its close relatives, showed that Russell’s realist ontology of classes cannot be maintained without alteration from the form it took in the Principles . The ‘doctrine of logical types’ sketched in the second appendix to that book, however, simply suggests a new set of ad hoc exceptions to an uncritical realist stance towards classes and functions. Without a philosophical explanation of why classes and/or functions must be typestratified, a theory of types is no more than a technical fix for the contradictions. And a technical fix is no defence of a realist metaphysics. With classes and functions understood as logical fictions derived from matrices in substitution, however, types can be understood as arising out of the grammatical distinctions of the substitutional theory in the manner explained above, and the classes required for mathematics can be eliminated in favour of a more basic ontology of Russellian propositions that remains free of the contradictions. Yet, as Russell is eager to stress, the only significant alteration to his view of what mathematical objects there are is that those entities which had already been shown to lead to contradiction are now avoided, thanks to ‘the delicate discrimination with which the substitutional method just avoids the results that lead to contradictions, while leaving everything else intact’ (Russell 1906b: 189). Thus the threat to realism engendered by the paradoxes is met squarely by placing the emphasis on an unrestrained realism of propositions rather than classes, relations, or functions. Russell’s ‘gradual retreat from Pythagoras’ (Russell 1959:208), as he was fond of calling his evolving attitude towards the philosophy of mathematics as his career progressed, had not retreated very far at this time. Classes and functions may have been expelled from his ontology, but propositions were construed in sufficiently robust terms to take up the slack, as is evident from Russell’s insistence that ‘it is very hard to believe that there are no such things as propositions, or to see how, if there were no propositions, any general reasoning would be possible’ (Russell 1906b: 189). Unfortunately for Russell, these words turned out to be portentous. Shortly after writing them, he discovered a paradox in the substitutional theory whose eventual solution brought to an end Russell’s ontological commitment to propositions. Thus ended Russell’s propositional realism but, again, it would be a mistake to interpret this turn of events as marking a general retreat from realism. Russell rejected his theory of propositions in favour of the multiple relation theory of judgement. Yet again, the theory of descriptions was called on to find replacements for propositions just as it had previously furnished replacements for classes. Propositions now took their turn as ‘incomplete symbols’ (Whitehead and Russell 1910:44) contextually eliminable in favour of judgement complexes composed

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Page 34 of what were previously taken to be the non-propositional constituents of propositions. These constituents, it should be noted, include qualities and relations as well as particulars (see 43). As Russell put the view a few years later: ‘A complete description of the existing world would require not only a catalogue of the things, but also a mention of all their qualities and relations’ (Russell 1914:60). The new theory of judgement lay at the heart of a staunchly realist correspondence theory of truth. The multiple-relation theory was not without major flaws, of course, but it was nonetheless another ingenious application of the theory of descriptions in order to allow Russell to make ontological cutbacks without weakening his realist resolve. Clearly, then, Dummett’s characterization of the place of the theory of descriptions within the realism debate faces some difficulty. Of course, the fact that Russell himself did not use the theory of descriptions (at least in the cases I have drawn attention to) as part of an antirealist programme does not pose a serious challenge to Dummett’s claim that one could so use it. However, Dummett’s claim must be stronger than this in order to support his analysis of the realist’s position regarding a particular class of statements as being committed to both the principle of bivalence as holding for them and a face value interpretation of the singular terms they contain: We may thus characterize a realistic interpretation of a given class of statements as one which applies to them, in accordance with the structure they appear on the surface to have, the classical two-valued semantics, in particular treating the (apparent) singular terms occurring in them as denoting objects (elements of the relevant domain) and the statements themselves as being determinately true or false. (Dummett 1991:326) This is obviously problematic in light of the foregoing discussion. To be fair to Dummett, he freely admits that this is ‘a narrow understanding of the term realism ’ (326). The question that we must ask is whether it is too narrow. Russell does not fit this picture, even during a period when he was at pains to mount a strident defence of realism. In discussing why commitment to the principle of bivalence is an insufficient condition for a realist perspective on arithmetic, Dummett states that, in addition to maintaining bivalence, a mathematical realist must reject the ‘nominalist’ thesis that numerical terms do not denote objects (see 326). On the envisaged nominalist interpretation of number theory, arithmetical statements will be recast in forms that do not contain numerical terms at all but will contain in their place numerically definite quantifiers of the form ‘there are n…’. Clearly, Dummett is correct to count the nominalist position offered as a rejection of mathematical realism. But the question to be addressed is whether he is right to do so solely on the grounds that the interpretation refuses to treat arithmetical sentences at face value.

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Page 35 The problem with doing so is that Russell offers a particularly vivid example of one who offers an interpretation of the sentences of number theory which refuses to take them at face value, yet is clearly not motivated by any sympathy towards nominalism.3 Throughout the many changes of opinion to be found in Russell’s writings, there is not (at least to my knowledge) a single note of sympathy expressed towards nominalism.4 Russell’s realism regarding universals was never retracted. Indeed, in 1948’s Human Knowledge , Russell adopted a position wholly antithetical to nominalism by arguing that only universals, not particulars, exist.5 Of course, one might well argue that Dummett’s claim holds, in a strict sense, even when applied to Russell. Russell, despite his clear commitment to realism in a global sense, is surely repudiating realism regarding local areas of his ontology. By rejecting the existence of classes, say, or functions, Russell is retreating from realism about those objects and, consequently, retreating from realism generally even if only by a small distance. This certainly seems to be the defence Dummett is likely to offer, if his justification for viewing Frege’s retreat from Meinongian ‘ultra-realism’ as a retreat from realism all the same is anything to go by (see Dummett 1991:324–25). The problem with this defence, however, is that it deprives Dummett’s characterization of realism of the very quality that originally stood in its favour— namely, its ability to pick out a common feature of the realism debate which offers the promise of a coherent means of refereeing the debate between realists and antirealists. With the characterization of realism reduced to the conjunctive commitment to the principle of bivalence and the principle that statements are to be interpreted at face value, the defining feature starts to look just as trivial as the claim that realists believe in the mind-independent existence of something which antirealists may deny. If the definition of realism leaves Russell as an antirealist simply because he was prepared to make ontological cutbacks at certain points, the term ‘antirealist’ is unlikely to remain useful in picking out a particularly homogenous class of philosopher. If Dummett is overly hasty in his interpretation of the theory of descriptions as a means of repudiating realism, he is certainly not alone in doing so. Interpretations of Russell’s philosophy have, for the most part, assumed the same interpretation. In recent years, that assumption has been challenged in key areas, two of which, the issues of Russell’s alleged Meinongianism in 1903 and his alleged retreat from realism in 1905, I have covered in some detail here. It is a mark of how central the theory of descriptions is to Russell’s work that rejecting the traditional interpretation of the role played by the theory in that work leads to a dramatic shift in the overall interpretation of Russell’s philosophy. The assumption that the theory of descriptions marks Russell’s point of departure from realism comports well with Russell’s own description of his philosophical development as a gradual retreat from Pythagoras. There is a significant danger, however, of allowing our assumptions about the theory of descriptions to tempt us into inaccurately

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Page 36 accelerating the rate at which Russell retreated from Pythagorean realism. This is likely to lead, on the one hand, to an interpretation of Russell’s position in the Principles as largely indistinguishable from the ‘ultra-realism’ of Meinong, and, on the other hand, to an exaggerated depiction of the extent to which Russell retracted his early realism. Russell’s attitude towards the second component in Dummett’s depiction of the realist’s position reveals more about Russell’s position in the realism debate. Dummett’s positioning of the principle of bivalence at the centre of the debate was, at least to a minor degree, pre-empted by Russell.6 His longest discussion of the topic is to be found in 1940’s Inquiry into Meaning and Truth . Russell’s discussion lacks the sophistication of Dummett’s analysis, to be sure, but the claim that adherence to the law of excluded middle (which Russell does not clearly separate from the principle of bivalence) results in commitment to realism is repeatedly made. Like Dummett, Russell takes the failure of the law of excluded middle in intuitionistic mathematics as his starting point, and then extends the same reasoning to nonmathematical domains as a way of formulating a coherent antirealist position. Despite some sympathetic considerations of the antirealist position, characterized in strikingly Dummettian terms as a conception of truth as ‘what can be known’ (Russell 1940:275), Russell eventually rejects the position, deciding to ‘accept the law of excluded middle without qualification’ (305). What sympathy Russell expresses for the antirealist position stems from his belief that ‘if we adhere to the law of excluded middle, we shall find ourselves committed to a realist metaphysic which may seem, in the spirit if not in the letter, incompatible with empiricism’ (274). Pure empiricism, according to Russell, requires us to abandon both realism and ‘common sense’ (284), however, and it is the combination of these two views that leads us to take the law of excluded middle as self-evident. Russell, thankfully, was never one of those philosophers held hostage to common sense, but he was less inclined to waver from realism. Russell’s desire to defend a fundamentally realist perspective is revealed in his desire to retain the law of excluded middle. This desire in turn is evidence that Russell shared Dummett’s view of the status of the law as illustrative of one’s position in the realism debate. As a consequence, rejecting the law of excluded middle is treated very differently than embracing the theory of descriptions. The theory of descriptions was embraced by Russell because, contrary to Dummett’s analysis of the matter, it allowed Russell to defend realism. The law of excluded middle is not rejected by Russell because, as Dummett’s analysis of the matter correctly has it, such a rejection shifts one dramatically away from realism. It was for just this reason that Russell refused to yield to the pressure that he clearly recognized was placed on the law in the context of a broadly empiricist philosophy. Rather than bow to that pressure and abandon the law of excluded middle, he chose to reign in his commitment to empiricism. In 1936 Russell published

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Page 37 a paper entitled ‘The Limits of Empiricism’ which specified clearly where his own commitment to empiricism stopped. Russell makes it abundantly clear in that paper that the failure of the law of excluded middle in pure empiricism is the point of departure from the degree of empiricism he is willing to endorse. There is much more to be said about Russell’s attitude towards bivalence and the law of excluded middle during this period than I have said here. For the purpose of concluding this paper, I only want to reiterate the asymmetry in Russell’s attitudes towards the two positions that Dummett would later take to characterize the realist’s position. By bringing the status of the principle of bivalence to the fore in discussions of realism, Dummett has uncovered an (perhaps the) essential commitment of the realist. Russell did not recognize the point with anything like the clarity and insight that Dummett has, but he did recognize it all the same. Furthermore, it is because he recognized that the principle of bivalence was essential to realism that he was not prepared to renounce his commitment to the principle. Rejection of the law of excluded middle was certainly viewed by Russell as a retreat from realism. Endorsement of the theory of descriptions was not. To mistake the theory of descriptions as a rejection of realism is to invite both a misinterpretation of Russell’s philosophy and a misinterpretation of the realism debate in general. Russell did not introduce the theory of descriptions in order to purge his philosophy of a Meinongian ‘ultra-realism’ in 1905. Nor did he use it to make any particularly radical move away from realism in later years. Russell’s philosophy is realist in spirit from start to finish, and the true importance of the theory of descriptions lies in the way it enabled Russell to retain that spirit in the face of otherwise seemingly insurmountable difficulties.7 NOTES 1. This is not to say that the theory was originally intended to overcome this difficulty. As I have argued elsewhere (Stevens 2005: Ch. 2), the driving motivation behind the development of the theory of descriptions was Russell’s desire to solve the paradox. Nonetheless, it is evident that there were numerous other consequences of the theory that further enthused Russell. The distinction between knowledge by acquaintance and knowledge by description was one such consequence; the reconciliation of the principle of acquaintance with Russell’s propositional realism was another. 2. The substitutional theory went largely unstudied until very recently. Russell’s most important papers on the subject were not widely available until they were published in Russell (1973), and his manuscripts on the subject have only recently been studied in detail, largely thanks to Landini’s pioneering (1998) study. 3. Some, myself included (Stevens 2005: Ch. 3), have argued for a ‘nominalist’ interpretation of propositional functions in Principia Mathematica . Lest any confusion should arise here, let me make it plain that the attribution of a nominalist semantics to Principia is not intended to attribute any philosophical

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Page 38 commitment to nominalism in general but is only intended to be a denial that functions survived in Russell’s ontology by 1910. Nominalism as a philosophical thesis (that only particulars exist) is wholly at odds with Russell’s ontology at any time in his career. 4. One might be tempted to think that nominalist sentiments were expressed in some of Russell’s later writings when he voiced his opinion, inherited from Wittgenstein, that mathematics (being part of logic) was purely ‘linguistic’ (see, for example, Russell ca. 1950). Again, however, there is nothing in these writings to suggest that Russell had retracted his commitment to the reality of universals, only that he had accepted a Tractarian conception of logic as analytic. This was certainly an enormous departure from his 1903 philosophy of logic, but it was not a rejection of realism. See Stevens (2004:56–58) for further discussion of the impact of Wittgenstein’s theory of logic on Russell. 5. See Russell’s footnote added to the 1956 reprint of Russell (1911:124). 6. This point is noted by Griffin (2003:36–37). 7. An earlier version of this paper was presented at the ‘Russell vs. Meinong: 100 Years After On Denoting ’ conference at the Bertrand Russell Research Centre, McMaster University, 14–18 May 2005. I am grateful to the audience for comments and would also like to thank Harm Boukema, Gregory Landini, Gideon Makin and Stefan Andersson for helpful discussions of the paper. REFERENCES Dummett, M. (1991) The Logical Basis of Metaphysics , London: Duckworth. Griffin, N. (2003) ‘Introduction’, in Griffin (2003): 1–50. ——., ed. (2003) The Cambridge Companion to Bertrand Russell, Cambridge: Cambridge University Press. Hylton, P. (2003) ‘The Theory of Descriptions’, in Griffin (2003): 202–40. Landini, G. (1998) Russell’s Hidden Substitutional Theory , New York/Oxford: Oxford University Press. Russell, B. (1903) The Principles of Mathematics, Cambridge: Cambridge University Press, 2nd edn, London: Allen and Unwin, 1937. ——. (1905) ‘On Denoting’, reprinted in Russell (1956). ——. (1906a) ‘On Some Difficulties in the Theory of Transfinite Numbers and Order Types’, reprinted in Russell (1973). ——. (1906b) ‘On the Substitutional Theory of Classes and Relations’, reprinted in Russell (1973). ——. (1914) Our Knowledge of the External World , London: Routledge. ——. (1936) ‘The Limits of Empiricism’, Proceedings of the Aristotelian Society 30: 131–59 reprinted in B. Russell, The Collected Papers of Bertrand Russell, vol. 9, A Fresh Look at Empiricism 1927–42 . ed. J. Slater, London: Routledge. ——. (1940) An Inquiry into Meaning and Truth , London: Allen and Unwin. ——. (1944) ‘My Mental Development’, in Schilpp (1944): 3–20. ——. (1948) Human Knowledge: Its Scope and Limits , London: Allen and Unwin. ——. (ca. 1950) ‘Is Mathematics Purely Linguistic?’, reprinted in Russell (1973). ——. (1956) Logic and Knowledge: Essays 1901–1950, ed. R. C. Marsh, London: Allen and Unwin. ——. (1959) My Philosophical Development, London: Allen and Unwin.

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Page 39 ——. (1967) The Autobiography of Bertrand Russell, vol. 1 (in 3 vols. 1967, 1968, 1969), London: Allen and Unwin. ——. (1973) Essays in Analysis , ed. D. Lackey, London: Allen and Unwin. ——. (1992) The Selected Letters of Bertrand Russell: The Private Years, 1884–1914 , ed. N. Griffin, London: Routledge. Stevens, G. (2004) ‘From Russell’s Paradox to the Theory of Judgement: Wittgenstein and Russell on the Unity of the Proposition’, Theoria , vol. 70, pt 1: 28–61. ——. (2005) The Russellian Origins of Analytical Philosophy , London: Routledge. Whitehead, A. N., and Russell, B. (1910) Principia Mathematica , vol. 1, Cambridge: Cambridge University Press.

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Page 40 3 Russell vs. Frege on Definite Descriptions as Singular Terms* Francis Jeffry Pelletier and Bernard Linsky INTRODUCTION In ‘On Denoting’ and to some extent in ‘Review of Meinong and Others, Untersuchungen zur Gegenstandstheorie und Psychologie ’, published in the same issue of Mind (Russell, 1905a,b), Russell presents not only his famous elimination (or contextual definition) of definite descriptions, but also a series of considerations against understanding definite descriptions as singular terms. At the end of ‘On Denoting’, Russell believes he has shown that all the theories that do treat definite descriptions as singular terms fall logically short: Meinong’s, Mally’s, his own earlier (1903) theory, and Frege’s. (He also believes that at least some of them fall short on other grounds—epistemological and metaphysical—but we do not discuss these criticisms except in passing). Our aim in the present paper is to discuss whether his criticisms actually refute Frege’s theory. We first attempt to specify just what Frege’s theory is and present the evidence that has moved scholars to attribute one of three different theories to Frege in this area. We think that each of these theories has some claim to be Fregean, even though they are logically quite different from each other. This raises the issue of determining Frege’s attitude towards these three theories. We consider whether he changed his mind and came to replace one theory with another, or whether he perhaps thought that the different theories applied to different realms, for example, to natural language versus a language for formal logic and arithmetic. We do not come to any hard and fast conclusion here, but instead just note that all these theories treat definite descriptions as singular terms, and that Russell proceeds as if he has refuted them all. After taking a brief look at the formal properties of the Fregean theories (particularly the logical status of various sentences containing nonproper definite descriptions) and comparing them to Russell’s theory in this regard, we turn to Russell’s actual criticisms in the above-mentioned articles to examine the extent to which the criticisms hold. Our conclusion is that, even if the criticisms hold against some definitedescriptions-as-singular-terms theories, they do not hold against Frege, at least not in the form they are given.

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Page 41 THREE FREGEAN THEORIES OF DEFINITE DESCRIPTIONS We start with three types of theories that have been attributed to Frege, often without acknowledgement of the possibility of the other theories.1 Frege’s views on definite descriptions are contained pretty much exclusively2 in his 1892 ‘Über Sinn und Bedeutung’ and his 1893 Grundgesetze der Arithmetik , volume 1.3 In both of these works Frege strove to make definite descriptions singular terms, by which we mean that they are not only syntactically singular but also that they behave semantically like such paradigmatic proper names as ‘Rudolf Carnap’ in designating some item of the domain of discourse. Indeed, Frege claims that definite descriptions are proper names: ‘The Bezeichnung [indication] of a single object can also consist of several words or other signs. For brevity, let every such Bezeichnung be called a proper name’ (1892:57). And although this formulation does not explicitly include definite descriptions (as opposed, perhaps, to compound proper names like ‘Great Britain’ or ‘North America’), the examples he feels free to use (for example, ‘the least rapidly convergent series’, ‘the negative square root of 4’) make it clear that he does indeed intend that definite descriptions are to be included among the proper names. In discussing the ‘the negative square root of 4’, Frege says ‘We have here the case of a compound proper name constructed from the expression for a concept with the help of the singular definite article’ (1892:71). A Frege-Strawson Theory In ‘Über Sinn und Bedeutung’ Frege considered a theory in which names without Bedeutung might nonetheless be used so as to give a Sinn to sentences employing them. He remarks, It may perhaps be granted that every grammatically well-formed expression figuring as a proper name always has a Sinn . But this is not to say that to the Sinn there also corresponds a Bedeutung . The words ‘the celestial body most distant from the Earth’ have a Sinn , but it is very doubtful they also have a Bedeutung …. In grasping a Sinn , one is certainly not assured of a Bedeutung . (1892:58) Is it possible that a sentence as a whole has only a Sinn , but no Bedeutung ? At any rate, one might expect that such sentences occur, just as there are parts of sentences having Sinn but no Bedeutung . And sentences which contain proper names without Bedeutung will be of this kind. The sentence ‘Odysseus was set ashore at Ithaca while sound asleep’ obviously has a Sinn . But since it is doubtful whether the name ‘Odysseus’, occurring therein, has a Bedeutung , it is also doubtful whether the whole sentence does. Yet it is certain, nevertheless, that anyone who seriously took the sentence to be true or false would

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Page 42 ascribe to the name ‘Odysseus’ a Bedeutung , not merely a Sinn ; for it is of the Bedeutung of the name that the predicate is affirmed or denied. Whoever does not admit a Bedeutung can neither apply nor withhold the predicate. (1892:62) The thought loses value for us as soon as we recognize that the Bedeutung of one of its parts is missing…. But now why do we want every proper name to have not only a Sinn , but also a Bedeutung ? Why is the thought not enough for us? Because, and to the extent that, we are concerned with its truthvalue. This is not always the case. In hearing an epic poem, for instance, apart from the euphony of the language we are interested only in the Sinn of the sentences and the images and feelings thereby aroused…. Hence it is a matter of no concern to us whether the name ‘Odysseus’, for instance, has a Bedeutung , so long as we accept the poem as a work of art. It is the striving for truth that drives us always to advance from the Sinn to Bedeutung . (1892:63) It seems pretty clear that Frege here is not really endorsing a theory of language where there might be ‘empty names’, at least not for use in any ‘scientific situation’ where we are inquiring after truth; nonetheless, it could be argued that this is his view of ‘ordinary language as it is’—there are meaningful singular terms (both atomic singular terms like ‘Odysseus’ and compound ones like ‘the author of Principia Mathematica ’) which do not bedeuten an individual. And we can imagine what sort of theory of language is suggested in these remarks: a Frege-Strawson theory4 in which these empty names are treated as having meaning (having Sinn ) but designating nothing (having no Bedeutung ), and sentences containing them are treated as themselves meaningful (have Sinn ) but having no truth-value (no Bedeutung )—the sentence is neither true nor false. As Kaplan (1972) remarks, if one already had such a theory for ‘empty’ proper names, it would be natural to extend it to definite descriptions and make improper definite descriptions also meaningful (have Sinn ) and sentences containing them treated as themselves meaningful (have Sinn ) but having no truth-value (no Bedeutung ). A natural formalization of such a theory is given by the kind of ‘free logics’ which allow singular terms not to denote anything in the domain, thereby making sentences containing these truth-valueless. (See Lambert and van Fraassen 1967; Lehmann 1994; and especially Morscher and Simons 2001 for a survey and recommendation of which free logic Frege should adopt.) In these latter theories there is a restriction on the rules of inference that govern (especially) the quantifiers and the identity sign, so as to make them accord with this semantic characterization of the logic. Even though Frege does not put forward the Frege-Strawson theory in his formalized work on the foundations of mathematics, it has its own interesting formal features, which we mention below. And some scholars think of this theory as accurately describing Frege’s attitude towards natural language.

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Page 43 A Frege-Carnap Theory Frege also mentions a ‘chosen object’ theory in ‘Über Sinn und Bedeutung’. In initiating this discussion Frege gives his famous complaint (1892:69): ‘Now, languages have the fault of containing expressions which fail to bezeichnen an object (although their grammatical form seems to qualify them for that purpose) because the truth of some sentence is a prerequisite’, giving the example ‘Whoever discovered the elliptic form of the planetary orbits died in misery’, where he is treating ‘whoever discovered the elliptic form of planetary orbits’ as a proper name that depends on the truth of ‘there was someone who discovered the elliptic form of the planetary orbits’. He continues: This arises from an imperfection of language, from which even the symbolic language of mathematical analysis is not altogether free; even there combinations of symbols can occur that seem to bedeuten something but (at least so far) are without Bedeutung [ bedeutungslos ], e.g., divergent infinite series. This can be avoided, e.g., by means of the special stipulation that divergent infinite series shall bedeuten the number 0. A logically perfect language ( Begriffsschrift) should satisfy the conditions, that every expression grammatically well constructed as a proper name out of signs already introduced shall in fact bezeichne an object, and that no new sign shall be introduced as a proper name without being secured a Bedeutung . (1892:70) In discussing the ‘the negative square root of 4’, Frege says: We have here the case of a compound proper name constructed from the expression for a concept with the help of the singular definite article. This is at any rate permissible if one and only one single object falls under the concept. [footnote] In accordance with what was said above, an expression of the kind in question must actually always be assured of a Bedeutung , by means of a special stipulation, e.g., by the convention that its Bedeutung shall count as 0 when the concept applies to no object or to more than one. (1892:71) Frege is also at pains to claim that it is not part of the ‘asserted meaning’ of these sorts of proper names that there is a Bedeutung ; for, if it were, then negating such a sentence would not mean what we ordinarily take it to mean. Consider again the example ‘Whoever discovered the elliptic form of the planetary orbits died in misery’ and the claim that ‘whoever discovered the elliptic form of planetary orbits’ in this sentence depends on the truth of ‘there was a unique person who discovered the elliptic form of the planetary orbits’. If the sense of ‘whoever discovered the elliptic form of planetary orbits’ included this thought, then the negation of the sentence would

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Page 44 be ‘Either whoever discovered the elliptic form of the planetary orbits did not die in misery or there was no unique person who discovered the elliptic form of the planetary orbits’. And he takes it as obvious (1892:70) that the negation is not formed in this way.5 Securing a Bedeutung for all proper names is an important requirement, not just in the case of abstract formal languages, but even in ordinary discourse; failure to adhere to it can lead to immeasurable harm. The logic books contain warnings against logical mistakes arising from the ambiguity of expressions. I regard as no less pertinent a warning against proper names without any Bedeutung . The history of mathematics supplies errors which have arisen in this way. This lends itself to demagogic abuse as easily as ambiguity does—perhaps more easily. ‘The will of the people’ can serve as an example; for it is easy to establish that there is at any rate no generally accepted Bedeutung for this expression. It is therefore by no means unimportant to eliminate the source of these mistakes, at least in science, once and for all. (1892:70) These are the places that Frege puts forward the Frege-Carnap theory.6 It should be noted that there is no formal development of these ideas (nor of any other ideas) in ‘Über Sinn und Bedeutung’; but the theory has been developed in Kalish and Montague (1964). It remains, however, a bit of a mystery as to why Frege comes to put both theories into his article without remarking on their differences. Does the Frege-Strawson theory perhaps apply to natural language while the Frege-Carnap theory applies to formal languages? Perhaps, but if so, what are we to make of the different theory proposed in the Grundgesetze? We compare the formal properties of the Frege-Strawson and Frege-Carnap theories below, and also compare both these with the Grundgesetze theory. The Frege-Grundgesetze Theory In the 1893 Grundgesetze, where Frege develops his formal system, he also finds room for definite descriptions—although his discussion is disappointingly short. The relevant part of the Grundgesetze is divided into two subparts: a rather informal description that explains how all the various pieces of the language are to be understood, and a more formal statement that includes axioms and rules of inference for these linguistic entities.7 Frege maintains the central point of the Frege-Carnap theory that he had put forward in ‘Über Sinn und Bedeutung’ by proclaiming (1893, §28, p. 83) ‘the following leading principle: Correctly-formed names must always bedeuten something ’, and (§33, p. 90) ‘every name correctly formed from the defined names must have a Bedeutung ’. In the Grundgesetze, Frege uses the symbols ‘ ’ to indicate the course of values ( Werthverlauf ) of F , roughly, the set of things that are F . The

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Page 45 Grundgesetze (§11, p. 50) introduces the symbol ‘\ξ’, which is called the ‘substitute for the definite article’.8 He distinguishes two cases (pp.49–50): 1. If to the argument there corresponds an object Δ such that the argument is (Δ = ε), then let the value of the function \ξ be Δ itself; 2. If to the argument there does not correspond an object Δ such that the argument is (Δ = ε), then let the value of the function be the argument itself. And he follows this up with the exposition (p. 50): Accordingly \ (Δ = ε) = Δ is the True, and ‘\ Φ(ε)’ bedeutet the object falling under the concept Φ(ξ), if Φ(ξ) is a concept under which falls one and only one object; in all other cases ‘\ Φ(ε)’ bedeutet the same as ‘ Φ(ε)’. He then gives as examples: (a) ‘the item when increased by 3 equals 5’ designates 2, because 2 is the one and only object that falls under the concept being equal to 5 when increased by 3; (b) the concept being a square root of 1 has more than one object falling under it, so ‘the square root of 1’ designates (ε2 = 1) 9; (c) the concept not identical with itself has no object falling under it, so it designates (ε ≠ ε);10 and (d) ‘the x plus 3’ designates (ε + 3)11 because x plus 3 is not a concept at all (it is a function with values other than the True and the False). In the concluding paragraph of this section, Frege says his proposal has the following advantage: There is a logical danger. For, if we wanted to form from the words ‘square root of 2’ the proper name ‘the square root of 2’ we should commit a logical error, because this proper name, in the absence of further stipulation, would be ambiguous, hence even without Bedeutung [ bedeutungslos ]…. And if we were to give this proper name a Bedeutung expressly, this would have no connection with the formation of the name, and we should not be entitled to infer that it was a … square root of 2, while yet we should be only too inclined to conclude just that. This danger about the definite article is here completely circumvented, since ‘\ Φ(ε)’ always has a Bedeutung , whether the function Φ(ξ) be not a concept, or a concept under which falls no object or more than one, or a concept under which falls exactly one object. (1893, §11:50–51) There seem to be two main points being made here. First, there is a criticism of the Frege-Carnap theory on the grounds that in such a theory the stipulated entity assigned to ‘ambiguous’ definite descriptions ‘would have no connection to the formation of the name’. This would pretty clearly suggest that Frege’s opinion in Grundgesetze was against the Frege-Carnap

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Page 46 view of definite descriptions. And, second, there is the apparent claim that in his theory the square root of 2 is a square root of 2, or more generally that the denotation of improper descriptions, at least in those cases where the description is improper due to there being more than one object that satisfies the predicate, manifests the property mentioned in the description. At this point there is a mismatch between Frege’s theory and his explanation of the theory. According to this theory, in fact, the square root of 2 is not a square root of 2—it is a course of values, that is to say, a set. So, on the Grundgesetze theory, it looks like we cannot ‘infer that it [the square root of 2] was a … square root of 2’ even though ‘we should be only too inclined to conclude just that’. [On Frege’s behalf, however, we could point out that everything in (= which is a member of) that course of values will be a square root of 2; so there is some connection between the object that the definite description refers to and the property used in the description. But the course of values itself will not be a square root of 2. Thus, the connection won’t be as close as saying that the Bedeutung of ‘the F ’ is an F .] Is that which we are ‘only too inclined to conclude’ something that we in fact shouldn’t? But if so, why is this an objection to the proposal to just stipulate some arbitrary object to be the Bedeutung ? We don’t know what to make of Frege’s reason to reject the Frege-Carnap account in this passage, since his apparent reason is equally a reason to reject the account being recommended. At any rate, this is the general outline of Frege’s theory in the Grundgesetze. We compare the logical properties of this theory with those of the Frege-Strawson and the Frege-Carnap theories below. TO WHAT DO THE DIFFERENT THEORIES APPLY? It is not clear to us whether Frege intended the Frege-Carnap and Frege-Grundgesetze theories to apply to different realms: the ‘Über Sinn und Bedeutung’ theory perhaps to a formalized version of natural language and the Grundgesetze theory to a formal account of mathematics? Frege himself never gives an explicit indication of this sort of distinction between realms of applicability for his theories of descriptions, although it is very easy to see him as engaging simultaneously in two different activities: constructing a suitable framework for the foundations of mathematics, and then a more leisurely reflection on how these same considerations might play out in natural language. Various attitudes are possible here; for example, one who held that the Frege-Strawson theory represented Frege’s attitude to natural language semantics would want to say that both the FregeCarnap and the Frege-Grundgesetze theories were relevant only to the formal represen tation of arithmetic. This then raises the issue of how such a view would explain why Frege gave both the Carnap and the Grundgesetze theories for arithmetic.

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Page 47 Possibly, such an attitude might maintain, the Grundgesetze theory was Frege’s ‘real’ account for arithmetic, but in ‘Über Sinn und Bedeutung’ he felt it inappropriate to bring up such a complex theory (with its courses of values and the like) in those places where he was concerned to discuss formal languages—as opposed to those places where he was discussing natural language (and where he put forward the Frege-Strawson account). So instead he merely mentioned a ‘simplified version’ of his theory. In this sort of picture, the Frege-Carnap theory is an inappropriate account of Frege’s views, since it is a mere simplified account meant only to give nonformal readers something to fasten on while he was discussing an opposition between natural languages and Begriffsschriften . According to this attitude, the real theories are Strawson for natural language and Grundgesetze for arithmetic. Another attitude has Frege being a language reformer, one who wants to replace the bad natural language features of definite descriptions with a more logically tractable one. In this attitude, Frege never held the Strawson view of natural language. His talk about Odysseus was just to convince the reader that natural language was in need of reformation. And he then proposed the Frege-Carnap view as preferable in this reformed language. According to one variant of this view, Frege thought that the Carnap view was appropriate for the reformed natural language while the Grundgesetze account was appropriate for mathematics. Another variant would have Frege offer the Carnap view in ‘Über Sinn und Bedeutung’ but replace it with a view he discovered later while writing the Grundgesetze. As evidence for this latter variant, we note that Frege did seem to reject the Carnap view when writing the Grundgesetze, as we discussed above. However, a consideration against this latter variant is that Frege would most likely have written the relevant portion of the Grundgesetze before writing ‘Über Sinn und Bedeutung’. And a consideration against the view as a whole in both of its variants is that Frege never seems to suggest that he is in the business of reforming natural language. One might assume that ‘Über Sinn und Bedeutung’, because it was published in 1892, would be an exploratory essay, and that the hints there of the Frege-Carnap view were superseded by the final, official Grundgesetze view. Yet clearly the Grundgesetze was the fruit of many years’ work, and it is hard to imagine that by 1892 Frege had not even proved his Theorem 1 of Grundgesetze, in which the description operator figures.12 SOME FORMAL FEATURES OF THE THREE THEORIES In this section we mention some of the consequences of the different theories; particularly, we look at some of the semantically valid truths guaranteed in the different theories, as well as some valid rules of inference. To do this fully we should have a formal development of the three Fregean theories and the Russell theory before us. But we do not try to provide

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Page 48 such a careful development and rely instead on informal considerations of what the semantics are for a theory that embraces the principles given in the last section for the different views on definite descriptions. With regards to Russell’s approach, it is well known what this theory is classical first-order logic plus some method of eliminating descriptions (that we discuss shortly). The Frege-Carnap theory is developed in Chapter 7 of Kalish and Montague (1964),13 but we needn’t know the details in order to semantically evaluate our formulas. All we need to do is focus on the sort of interpretations presumed by the theory: namely, those where, in any one domain and interpretation, every improper description designates the same one thing in the domain, and this thing might also be designated in more ordinary ways. The Frege-Grundgesetze theory can be similarly conceived semantically as containing objects and courses-of-values of predicates (sets of things that satisfy the predicate). And we can informally evaluate the formulas simply by reflecting on these types of interpretations: improper descriptions designate the set of things that the formula is true of—which will be the empty set, in the case of descriptions true of nothing, and will be the set of all instances, in those cases where the descriptions are true of more than one item in the domain.14 There might be many ways to develop a FregeStrawson theory, but we concentrate on the idea that improper definite descriptions do not designate anything in the domain and that this makes sentences containing such descriptions neither true nor false. This is the idea developed by (certain kinds of) free logics: atomic sentences containing improper descriptions are neither true nor false because the item designated by the description does not belong to the domain. (It might, for example, designate the domain itself, as in Morscher and Simons 2001, and Lehmann 1994.)15 In a Frege-like development of this idea, we want the lack of a truth-value of a part to be inherited by larger units. Frege wants the Bedeutung of a unit to be a function of the Bedeutungen of its parts, and if a part has no Bedeutung , then the whole will not have one either. In the case of sentences, the Bedeutung of a sentence is its truth-value, and so in a complex sentence, if a subsentence lacks a truth-value, then so will the complex. In other words, the computation of the truthvalue of a complex sentence follows Kleene’s (1952:334) ‘weak 3-valued logic’, where being neither true nor false is inherited by any sentence that has a subpart that is neither true nor false.16 We start by listing a series of formulas and argument forms to consider because of their differing interactions with the different theories. The formulas and answers given to them by our three different Fregean theories and Russell’s theory are summarized in Table 3.1. It should be noted that in Table 3.1 we are always talking about the case where the descriptions mentioned are improper. So, when looking at the formula under consideration, one must always take the description(s) therein to be improper. Since we are always looking at the cases where the descriptions are improper, every interpretation we consider is called an i-interpretation (for

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Page 49 ‘improper description interpreta tion’). In an i-interpretation for a particular formula, all definite descriptions mentioned in the formula are improper. If it should turn out that the formula under consideration is false in every i-interpretation (of the sort relevant to the theory under consideration), then we call it i-false, that is, false in every interpretation for the theory where the descriptions mentioned are improper. Similarly, we call some formulas i-true if they are true in every i-interpretation that is relevant to the theory. Of course, if a formula is true (or false) in every interpretation (not restricted to i-interpretations) for the theory, then it will also be i-true (or i-false); in these cases we say that the formula is ‘logically true’ or ‘logically false’ in the theory. If a formula is true in some iinterpretations and false in other i-interpretations, then it is called i-contingent . Of course, an icontingent formula is also simply contingent (without the restriction to i-interpretations). Similar considerations hold about the notion of i-validity and i-invalidity . An argument form is i-valid if and only if all i-interpretations where the premises are true also make the conclusion true. If an argument form is valid (with no restriction to i-interpretations), then of course it is also i-valid. In the case of the Frege-Strawson theory, sentences containing an improper description are neither true nor false in an i-interpretation. We therefore call these i-neither . When we say that an argument form is i-invalid * (with an *), we mean that in an i-interpretation the premise can be true while the conclusion is neither true nor false (hence, not true). Things are not so simple in Russell’s theory. For one thing, the formulas with definite descriptions have to be considered ‘informal abbreviations’ of some primitive sentence of the underlying formal theory. And there can be more than one way to generate this primitive sentence from the given ‘informal abbreviation’, depending on how the scope of the description is generated. If the scope is ‘widest’, so that the existential quantifier corresponding to the description becomes the main connective of the sentence, then generally speaking,17 formulas with improper descriptions will be i-false because they amount to asserting the unique existence of a satisfier of the description and by hypothesis this is not satisfied. But often they will be contingent because there will be non-i-interpretations in which there is such an item and others in which there is not. But it could be that the description itself is contradictory and therefore the sentence is logically false, and hence i-false. Furthermore, there might be definite descriptions that are true of a unique object as a matter of logic, such as ‘the object identical to a ’; and in these latter cases, if the remainder of the sentence is ‘tautologous’ then the sentence could be logically true—for example, ‘Either the object identical with Adam is a dog or the object identical with Adam is not a dog’, whose wide scope representation would be (approximately) ‘There exists a unique object identical with Adam which either is a dog or is not a dog.’18 We therefore take all descriptions in Russell’s theory to have narrow scope, and so our claims in Table 3.1 about i-truth, i-falsity, i-contingency,

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Page 50 i-validity, and i-invalidity should be seen as discussing the disambiguation of the ‘informal abbreviation’ with narrowest scope for all the descriptions involved, and then assuming that these descriptions are improper. One final remark should be made about the interpretation of the table. It was our intent that the various F s and Gs that occur in the formulas should be taken as variables or schema, so that any sentence of the form specified would receive the same judgement. But this won’t work for some of our theories, since predicate substitution does not preserve logical truth in them. For example, in a Frege-Strawson theory, if we substitute a complex predicate containing a nondenoting definite description for F in a logical truth, a logical falsehood, or a contingent formula, then the result becomes neither true nor false. So the Frege-Strawson theory does not preserve logical truth under predicate substitution. In Russell’s theory, substitution of arbitrary predicates for the F s and Gs can introduce complexity that interacts with our decision to eliminate all descriptions using the narrowest scope. For example, formula 3, when F stands for ‘is a round square’, generates Russell’s paradigm instance of a false sentence: ‘The round square is a round square’. And this is the judgement generated when we eliminate the definite description in Russell’s way, and is what we have in our table. But were we to uniformly substitute ‘~ F ’ for ‘ F ’ in formula 3, we generate ~F ι x~Fx ; and now eliminating the description by narrowest scope yields   It can be seen that the formula inside the main parentheses is logically false (regardless of whether the description is or isn’t proper), and so there can be no such x. And therefore the negation of this is logically true. Yet, we followed Russell’s rule in decreeing that the original formula 3 is false when the description is eliminated with narrowest scope. This example shows that Russell’s theory allows one to pass from logical falsehood to logical truth; adding another negation to the premise and conclusion will show that it does not preserve logical truth under predicate substitution, unless one is allowed to alter scope of description-elimination. Therefore, we restrict our attention to the case where the F s and Gs are atomic predicates in the theories under consideration here. And so we are not able to substitute ~F for F in 3, with this restriction. We do not intend to prove all the entries in the table, but instead merely to indicate why a few chosen ones have the values they do and thereby give a method by which the reader can verify the others. We start with the Frege-Strawson theory. The idea is that improper descriptions have no designation (at least, not in the universe of objects), and sentences containing such descriptions have no truth-value. As stated, this principle would decree that, when ιxFx is improper, no formula containing such a description is either true or false. Hence all the entries of individual formulas in the table will be i-neither. This is because of Frege’s

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Page 51 Table 3.1. How Four Theories of Descriptions View Some Arguments and Formulas   Formula or Rule F-S F-C F-Gz Russell 1 a) xFx F ι xGx i-invalid* valid valid i-invalid b) F ι xGx xFx valid valid valid valid c) xFx F ι xGx i-neither logically true logically true i-false d) F ι xGx xFx i-neither logically true logically true logically true 2 y y = ι xFx i-neither logically true logically true i-false 3 F ι xFx i-neither i-contingent i-false i-false 4 ( P ~P) G ι xFx i-neither logically true logicallytrue logically true 5 F ι xFx ~F ι x~Fx i-neither logically true i-false logically true 6 ( y x(Fx ≡ x = y) i-neither logically true logically true logically true F ι xFx) 7 G ι xFx ~G ι xFx i-neither logically true logically true logically true 8 ι xFx = ι xFx i-neither logically true logically true i-false 9 ι x x ≠ x = ι x x ≠ x i-neither logically true logically true logically false 10 ι x x = x = ι x x ≠ x i-neither logically true i-false logically false 11( ι xFx = ι x x ≠ x) i-neither logically true i-contingent logically false ( ι x~Fx = ι x x ≠ x) logically true i-contingent logically true 12( G ι xFx & G ι x~Fx) i-neither G ι xGx i-contingent i-false logically true 13( ι xFx = ι xGx ) G ι i-neither xFx valid valid i-invalid 14 x ( Fx ≡ Gx) ι xFx i-invalid* = ι xGx 15a) x ( Sxa ≡ x = b) Interderivable; Not interderivable; soNot interderivable; Logically equivalent; not i-equivalent not i-equivalent19 so, not i-equivalent hence interderivable b) b = ι xSxa insistence that the Bedeutung of the whole is determined by the Bedeutungen of the parts; and so if the parts are missing some Bedeutungen then so will the whole be missing its Bedeutung , even in formulas like 4. Entries 1a and 14 are arguments, and in every i-interpretation where the premise is true the conclusion will be neither true nor false, and so we call it i-invalid*. Entry 1b is valid, because if the premise is true then the description must be proper and therefore designate some item in the domain. But

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Page 52 in that case the conclusion must be true, making the argument valid. Note therefore that since 1d is not a theorem, it follows that the Frege-Strawson system does not have a deduction theorem. Formula 15 is interesting because if 15a is true, then that is precisely the information required to show that the description is proper and so 15b would follow; and if 15b is true then the description is presupposed to be proper and hence 15a would follow. So 15a and 15b are interderivable. But the biconditional formula between the two contains a definite description, and any description might be improper. So the two formulas cannot be i-equivalent. (Again, this is a case where the deduction theorem fails.) A basic feature of the Frege-Carnap theory is that there is always a referent for any description (formula 2), even ι x x ≠ x, and so this means that rules of universal instantiation and existential generalization can be stated in full generality; thus 1a and 1b are valid, and furthermore the theory has a deduction theorem so that 1c and 1d are logically true. It follows from formula 2, which is just a restatement of the fundamental intuition, that formulas like 7 must be logically true. It also follows that a law of selfidentity can be stated in full generality, and thus 8 and 9 are true. Furthermore, in Frege-Carnap, all improper descriptions designate the same item of the domain in any interpretation (namely, whatever the guaranteed-to-be-improper ι x x ≠ x does), and so formulas like 10 must be true and arguments like 14 must be valid.20 We note that the crucial formula 3 is i-contingent. For, in the improper case the description designates some element of the domain, and in some interpretations this element will be an F while in other interpretations it won’t. Note also that if the description is proper then 3 must be true; therefore 6 will turn out to be not just i-true, but logically true (since the antecedent guarantees the propriety of the description). The status of the other formulas can be established by arguments like the following for 5. Formula 5 is certainly i-true in Frege-Carnap, because if both descriptions are improper, then they both designate the same item of the domain, and this item is either F or ~F . But furthermore, it is even true when at least one of the descriptions is proper, because then 3 will be in play for whichever description is proper and hence that disjunct will be true. And hence the entire disjunction will be true. There are some difficulties of representing natural language in the Frege-Carnap theory. Consider 15a and b, under the interpretation ‘Betty is Alfred’s one and only spouse’ and ‘Betty is the spouse of Alfred’, represented as   While the two English sentences seem equivalent, the symbolized sentences are not, in Frege-Carnap: consider Alfred unmarried and Betty being the designated object. Then the first sentence is false but the second is true.

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Page 53 Since they are not i-interderivable, they are therefore not i-equivalent, contrary to our intuitions about the natural language situation they are intended to represent. Many of the logical features of the Frege-Carnap theory hold also in the Frege-Grundgesetze theory, since there is always a Bedeutung for every definite description: formula 2 holds, and so 7 holds. And once again, 6 will be not just i-true but logically true. Because the Bedeutung of a description is a function of what F is true of (as in the Frege-Carnap theory), formulas 8 and 9 are i-true and 14 is valid. In Frege-Carnap the critical 3 is i-contingent, while in Frege-Grundgesetze it is i-false. In Frege-Carnap, the improper description designates some ‘arbitrarily chosen’ element of the domain, and in some interpretations this element will be F while in some other interpretations it will be ~F . But surprisingly, in the Frege-Grundgesetze theory, since the improper description designates the set consisting of all the elements that are F , this set cannot be F . For, to be F in the Grundgesetze theory is to be an element of the set {x: Fx }. If the improper ι xFx were to be F , then {x: Fx } {x: Fx }, which contradicts the axiom of foundation. So formula 6 has to be false for all improper descriptions. Formula 13 will be i-false for much the same reason: the consequent cannot be true, but the antecedent can be, as for example when predicates F and G are coextensive but not true of a unique individual. The Frege-Carnap and Frege-Grundgesetze theories differ on formulas 5, 10 and 11. This is because in Frege-Carnap all improper descriptions bedeuten the same items in the domain of any one interpretation, while in Frege-Grundgesetze different descriptions bedeuten different entities if the predicates are true of different classes of things in the domain, even of the same interpretation. So for example, in 10 on the Frege-Carnap theory, ι x x ≠ x is necessarily improper and therefore bedeutet the chosen individual. But unless there is just one entity in the domain, ι x x = x is also improper and bedeutet that very same entity. On the other hand, if the domain does contain only one element, so that ι x x = x bedeutet it, then that element is forced to serve as the chosen object also and again 10 is true. However, on the Frege-Grundgesetze theory, the description ι x x = x will bedeuten the set of all things in the domain21 while the description ι x x ≠ x will bedeuten the empty set. So there are i-models where 10 fails. (It does not fail in every interpretation, since the domain that contains just the empty set will make ι x x = x be proper and bedeuten the empty set, while ι x x ≠ x will also bedeuten the empty set.)22 On the whole, the Russell answers for our formulas and arguments in the table are quite easily computed (so long as we focus on the narrow scope for the description). As with the other theories, many of the formulas follow from the basic formula 2. It is a hallmark of Russell’s theory that if there is no F in the domain then the critical formula 3 will be false. Argument 1a is i-invalid because if there is no G in the domain then it is certainly possible for everything in the domain to be F and yet not have ‘the G’ be one of

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Page 54 them. Formula 8 will be i-false because when we eliminate the descriptions we are left with a sentence saying that ‘there is an x which is an F … ’, and since the descriptions are improper, this will always be false in an i-model. Formulas such as 5 and 7 will come out as i-true because of the negated disjunct. Formulas 9, 10 and 11 will be logically false because the descriptions are impossible and so their elimination will amount to asserting the existence of something that has an impossible collection of properties. When the description embedded in this disjunct is eliminated with narrow scope, we will have a negation of something that is i-false. Hence that disjunct will be i-true and the entire formula will thereby be i-true. Formulas 15a and 15b will be equivalent because they are interderivable and the deduction theorem holds for Russell (unlike the Frege-Strawson case). RUSSELLIAN CRITICISMS OF SINGULAR TERM ANALYSES Russell criticizes Frege as follows (where Russell says ‘denotation’ understand ‘ Bedeutung ’ where he says ‘meaning’ understand ‘ Sinn ’): If we say, ‘the King of England is bald’, that is, it would seem, not a statement about the complex meaning of ‘the King of England’, but about the actual item denoted by the meaning. But now consider ‘the King of France is bald’. By parity of form, this also ought to be about the denotation of the phrase ‘the King of France’. But this phrase, though it has a meaning, provided ‘the King of England’ has a meaning, has certainly no denotation, at least in any obvious sense. Hence one would suppose that ‘the King of France is bald’ ought to be nonsense; but it is not nonsense, since it is plainly false. (1905a: 419) This sort of criticism misses the mark. It is not part of the Frege-Grundgesetze theory, nor of the FregeCarnap theory, that ‘the King of France is bald’ is nonsense. It is, of course, a feature of the FregeStrawson account that it lacks a truth-value, which is still some way from nonsense, for although it lacks a Bedeutung it still has a Sinn . A further criticism of the Frege-Strawson view is contained in these sentences: Or again consider such a proposition as the following: ‘If u is a class which has only one member, then that one member is a member of u’, or, as we may state it, ‘If u is a unit class, the u is a u’. This proposition ought to be always true, since the conclusion is true whenever the hypothesis is true…. Now if u is not a unit class, ‘the u’ seems to denote nothing; hence our proposition would seem to become nonsense as soon a u is not a unit class. Now it is plain that such propositions do not become nonsense merely because their hypotheses are false. The King in The Tempest

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Page 55 might say, ‘If Ferdinand is not drowned, Ferdinand is my only son’. Now ‘my only son’ is a denoting phrase, which, on the face of it, has a denotation when, and only when, I have exactly one son. But the above statement would nevertheless have remained true if Ferdinand had been in fact drowned. Thus we must either provide a denotation in cases which it is at first absent, or we must abandon the view that the denotation is what is concerned in propositions which contain denoting phrases. (1905a: 419) Russell here is arguing against the Frege-Strawson view on which sentences with non-denoting descriptions come out neither true nor false (Russell’s ‘meaningless’?), because if the antecedent of a conditional hypothesizes that it is proper then the sentence should be true. (Our formula 6 captures this.) But as Russell himself says, one needn’t abandon all singular term analyses in order to obey this intuition. So it is strange that he should think he has successfully argued against Frege, unless it is the Frege-Strawson view that Russell is here attributing to Frege. And yet Russell had read the relevant passages in ‘Über Sinn und Bedeutung’ as well as Grundgesetze in 1902, making notes on them for his Appendix A on ‘The Logical Doctrines of Frege’ for his Principles of Mathematics. Indeed, just later in ‘On Denoting’ he does in fact attribute the Grundgesetze theory to Frege: Another way of taking the same course [a singular term analysis that is an alternative to Meinong’s way of giving the description a denotation] (so far as our present alternative is concerned) is adopted by Frege, who provides by definition some purely conventional denotation for the cases in which otherwise there would be none. Thus ‘the King of France’, is to denote the null-class; ‘the only son of Mr. So-andso’ (who has a fine family of ten), is to denote the class of all his sons; and so on. But this procedure, though it may not lead to actual logical error, is plainly artificial, and does not give an exact analysis of the matter. (1905a: 420) Even granting Russell’s right to call it ‘plainly artificial’, he does not here find any logical fault with Frege’s Grundgesetze theory. In any case, he joins the other commentators in not remarking on the different theories of descriptions Frege presented in different texts. Indeed he states two of them without remarking on their obvious difference. On the other hand, Russell’s presentation of one of his ‘puzzles’ for a theory of descriptions does touch on Frege (compare our formula 7): (2) By the law of excluded middle, either ‘ A is B ’ or ‘ A is not B ’ must be true. Hence either ‘the present King of France is bald’, or ‘the present King of France is not bald’ must be true. Yet if we enumerated the things that are bald, and then the things that are not bald, we should

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Page 56 not find the present King of France in either list. Hegelians, who love a synthesis, will probably conclude that he wears a wig. (1905a: 420) The empty set, which is the Frege-Grundgesetze theory’s Bedeutung for ‘the present King of France’, will be in the enumeration of things that are not bald. With the Frege-Carnap view we just don’t know which enumeration it will be in (but it will be in one of them). So, both the Frege-Grundgesetze and the FregeCarnap theories make the law of excluded middle (in the form our formula 7) true, just as Russell’s theory does, and it is only the Frege-Strawson theory which does not. And it seems that Russell is attributing the Frege-Strawson theory to the Hegelians. (It is neither true nor false that the present King of France is bald … so he must be wearing a wig!) Russell’s discussion is unfair to Frege’s various accounts. Russell’s main arguments are directed against Meinong, and since both Meinong and Frege take definite descriptions to be designating singular terms, Russell tries to paint Frege’s theory with the same brush he uses on Meinong’s theory. Although there is some dispute about just how to count and individuate the number of different Russell arguments against Meinong in Russell’s various writings on the topic, basically we see five logical objections23 against singular term theories of descriptions raised in Russell’s 1905 works: (a) Suppose that there is not a unique F . Still, the sentence ‘If there were a unique F , then F ι xFx ’ would be true (compare our formula 6). (b) The round square is round, and the round square is square. But nothing is both round and square. Hence ‘the round square’ cannot denote anything. (c) If ‘the golden mountain’ is a name, then it follows by logic that there is an x identical with the golden mountain, contrary to empirical fact. (d) The existent golden mountain would exist, so one proves existence too easily. (e) The nonexisting golden mountain would exist according to consideration (c) but also not exist according to consideration (b). Russell’s conclusion from all these criticisms was that no singular term account of descriptions could be adequate. As we quoted before, he thinks of Frege as ‘another way of taking the same course’ as Meinong. And as for his ‘quantificational analysis’ of descriptions, while he admits that the account is counter-intuitive, he challenges others to come up with a better account that avoids these considerations.24 But however much these considerations hold against Meinong, Ameseder and Mally (who are the people that Russell cites), they do not hold with full force against Frege.25 Against the first consideration, we should note that formula 6 is i-true, indeed logically true, in both Frege-Carnap and Frege-Grundgesetze. It is only the Frege-Strawson theory that this objection holds against, since it judges the sentence to be neither true nor false when the description is improper. As for the second point, Frege has simply denied that F ι xFx is i-true (and it might be noted that Russell’s method has this effect also, decreeing it to be i-false), and that is required to make the consideration have any force. Against the third consideration, Frege could have said that there was nothing wrong with the golden mountain existing, so long

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Page 57 as you don’t believe it to be golden or a mountain. Certainly, whatever the phrase designates does exist, by definition in the various theories of Frege. And against the fourth consideration, Frege always disbelieved that existence was a predicate, so he would not even countenance the case. Nor would the similar case of (e) give Frege any pause. So, Russell’s considerations do not really provide a conclusive argument against all singular term accounts of definite descriptions, and in particular they do not hold against Frege’s various theories (except the one objection to the Frege-Strawson theory). And it is somewhat strange that Russell should write as if they did. For, as we mentioned earlier, in 1902 he had read both ‘Über Sinn und Bedeutung’ and Grundgesetze, making notes on Frege’s theories.26 Yet he betrays no trace here of his familiarity with them, saying only that they do not provide an ‘exact analysis of the matter’, but never saying how they fall short. In fact, a glance at Table 3.1 reveals that there is one commonality among all the theories of descriptions we have discussed: they never treat the critical formula 3, F ι xFx, as logically true, or even i-true, unlike Meinong and his followers. (When the description is improper, the Frege-Carnap theory treats it as i-contingent—sometimes true, sometimes false—and the Frege-Grundgesetze theory treats it as false for every atomic predicate, just like Russell’s theory.27 The Frege-Strawson theory also treats it as not always true.) It is this feature of all these theories that allows them to avoid the undesirable consequences of a Meinongian view; and it is rather unforthcoming of Russell to suggest that there are really any other features of his own theory that are necessary in this avoidance. For, each of Frege’s theories also has this feature. WHERE RUSSELL’S THEORY DIFFERS FROM FREGE’S We have seen that there are various ways to present a theory of definite descriptions as singular terms, and that they give rise to assignments of different logical statuses to different formulas. We’ve also seen that Russell’s theory and Frege’s theory in fact essentially agree on the critical formula 3, which is all that is required to avoid Russell’s explicit objections to the singular term theory of definite descriptions. In this section we compare some of our test sentences with the formal account of definite descriptions in Principia Mathematica *14, so that one can see just what differences there are in the truth-values of sentences employing definite descriptions between Russell’s theory and the various Frege theories, as summarized in Table 3.1. Our idea is that another test of adequacy of a theory of definite descriptions will be the extent to which the theory agrees with intuition on these sentences. And so we are interested in the ways in which Russell’s theory differs from the Frege-Carnap and Frege-Grundgesetze theories. As can be seen from the table, there are many such places. The places where both of these Frege theories agree with one another and disagree with Russell are:

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Page 58 Table 3.2. Where Frege-Carnap and -Grundgesetze Agree and Disagree with Russell   Forward or Rule Frege Russell 1 a) xFx F ι xGx valid i-invalid logically true i-false c) xFx F ι xGx 2 logically true i-false y y = ι xFx 8 ι xFx = ι xFx logically true i-false 9 ιxx≠x=ιxx≠x logically true logically false 13 ( ι xFx = ι xGx ) G ι xFx i-contingent logically true 14 x ( Fx ≡ Gx) ι xFx = ι xGx i-valid i-invalid 15 a) x ( Sxa ≡ x = b) not interderivable logically equivalent b) b = ι xSxa Most of these differences are due to the fundamental 2. Given that different choice, it is clear that 1a and 1c must differ as they do. And Russell’s interpretation of a definite description as asserting that there exists a unique satisfier of the description (and his related ‘contextual definition’) will account for all the cases where the formula (or argument) is i-false (or i-invalid) in Russell. However, since it is logically impossible that there be a non-self-identical item, 9 must be logically false. The two places where these three theories provide different answers are 3, which we have already discussed, and 13. Formula 13 is logically true in Russell because if the descriptions are improper then the antecedent is false (and hence 13 is true), but if the antecedent is true then both descriptions must be proper … and hence the consequent must be true. As we mentioned before, in Frege-Carnap, when the descriptions are improper then the antecedent is true. But whether the consequent is true or not depends on whether the chosen object has the property G or not. In Frege-Grundgesetze, if the descriptions are improper and the predicates F and G are coextensive, then the antecedent is true, but in that case the predicate G could not be true of ι xFx , for then it would have to be true of ι xGx … which we showed above to be impossible. But 13 is not logically false in Frege-Grundgesetze because it is true when the descriptions are proper. Supporters of Frege’s singular term theory or of Russell’s quantificational analysis should ask themselves what they think of these differences in the logic between Frege and Russell. For example, if one is drawn to the idea that every thing is self-identical, and infers from this claim that every statement of self-identity must be true, then one will be in agreement with Frege on formulas 8 and 9, and opposed to Russell. If, like Morscher and Simons (2001:21), one thinks that 14 is an obvious truth that must be obeyed by any theory of definite descriptions, then one will side with Frege against Russell. And conversely, of course. There should be some discussion among

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Page 59 the proponents of these two theories as to which way they prefer to tilt, and why, concerning the many formulas that are treated differently in Frege’s theories vs. Russell’s theory. As we mentioned, most of the differences can be traced to the basic formula 2. But this, in fact, is just a restatement of the difference between a singular term analysis of definite descriptions and a quantificational analysis. Once you have made the choice to adopt 2, the main further differences among singular term analyses concern whether or not to differentially treat descriptions where nothing satisfies the predicate from those where the predicate is true of more than one thing. If you choose not to treat them differently, then the most natural theory is Frege-Carnap. If you do wish to treat them differently, the Frege-Grundgesetze theory offers one direction (although as we mentioned earlier, there is a difficulty in mixing individuals in the domain with sets of these individuals, and making the result all be in the same domain). There are other ways to carry this general strategy out, some of them following from the epsiloncalculus (for example, von Heusinger 1997), others looking like the ‘Russellian theory’ of Kalish, Montague, and Mar (1980: Chapter 8). But we won’t go into those sorts of theories now. In any case, given that 2 is just a restatement of the fundamental difference between singular term theories and quantificational theories, and given that the remaining logical differences basically follow from this choice, it seems to follow that the only real way to favour one theory over the other is to see which of the other formulas and arguments are more in accord with one’s semantic intuitions. Russell has not done this, despite his belief to the contrary. He focused basically on 3; but this formula is not treated differently in any important way between Russell and the Frege theories. Instead, it only separates the Meinongian singular term theory from both Frege’s and Russell’s theories. CONCLUDING REMARKS The fundamental divide in theories of descriptions now, as well as in Russell’s time, is whether definite descriptions are ‘really’ singular terms, or ‘really’ not singular terms (in some philosophical ‘logical form’ sense of ‘really’). If they are ‘really’ not singular terms then this might be accommodated in two rather different ways. One such way is that of the classical understanding of Russell: there is no grammatically identifiable unit of any sentence in logical form that corresponds to the natural language definite description. Instead, there is a grab-bag of chunks of the logical form which somehow coalesce into the illusory definite descriptions. A different way is more modern and stems from theories of generalized quantifiers in which quantified terms, such as ‘all men’, are represented as a single unit in logical form and this unit can be semantically evaluated in its own right—this one

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Page 60 perhaps as the set of all those properties possessed by every man. In combining this generalized quantifier interpretation of quantified noun phrases into the evaluation of entire sentences, such as ‘All men are mortal’, the final, overall logical form for the entire sentence becomes essentially that of classical logic. So, although quantified noun phrases are given an interpretable status on their own in this second version, neither does their resulting use in a sentence yield an identifiable portion of the sentence that corresponds to them nor does the interpretation of the quantified noun phrase itself designate an ‘object’ in the way that a singular term does (when it is proper). It instead denotes some set-theoretic construct. If we treat definite descriptions as a type of generalized quantifier (as in Neale, 2001), and thereby take this second way of denying that definite descriptions are ‘really’ singular terms, the logical form of a sentence containing a definite description that results after evaluating the various set-theoretic constructions will (or could, if we made Russellian assumptions) be that which is generated in the purely intuitive manner of Russell’s method. So these two ways to deny that definite descriptions are singular terms really amount to the same thing. The only reason the two theories might be thought different is because of the algorithms by which they generate the final logical form in which definite descriptions ‘really’ are not singular terms, not by whether the one has an independent unit that corresponds to the definite description. In this they both stand in sharp contrast to Fregean theories. These latter disagreements are pretty much orthogonal to those of the earlier generation. The contemporary accounts, which have definite descriptions as being ‘nearly’ a classical quantifier phrase, agree with the Russellian truth conditions for sentences involving them. Although these truth conditions might be suggested or generated in different ways by the different methods (the classical or the generalized quantifier methods) of representing the logical form of sentences with descriptions, this is not required. For one could use either the Russellian or Frege-Strawson truth conditions with any contemporary account. It is clear, however, that we must first settle on an account of improper descriptions. We remarked already on the various considerations that might move theorists in one direction or another as they construct a theory of definite descriptions. We would like to point to one further consideration that has not, we think, received sufficient consideration.28 It seems to us that a logical theory of language should treat designating and empty proper names in the same way, since there is no intuitive syntactic way to distinguish denoting from nondenoting proper names in natural language. We also find there to be much in common between empty proper names and improper descriptions, from an intuitive point of view—so that their semantics should be the same. And of course there is no intuitive way to distinguish (empirically) nonproper vs. proper descriptions in general. So, all these apparent singular terms should be dealt with in the same way. If definite

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Page 61 descriptions are to be analysed away à la Russell, then the same procedure should be followed for ‘Pegasus’ and its kin. And if for ‘Pegasus’, then for ‘Benjamin Franklin’ and its kin. (A strategy taken by Russell, in other works.) If, on the other hand, these latter are taken to be singular terms, then so too should definite descriptions. And whatever account is given for nondenoting proper names should also be given for improper descriptions: if nondenoting names have a sense but no denotation in the theory, then we should adopt the Frege-Strawson theory of improper descriptions. If we think we can make meaningful and true statements using ‘Pegasus’ and its cohort, then we should adopt either the FregeCarnap or the Frege-Grundgesetze theory of improper descriptions. In any case, we should care about the present King of France.29 NOTES * This paper is a shortened version of our Pelletier & Linsky (2005). The earlier paper has more material on Fregean theories of descriptions, and the present paper has more material on Russell’s considerations concerning singular term analyses of definite descriptions. 1. But we do not attempt to make careful attributions in this regard. 2. An exception is a longish aside in Frege’s Grundlagen (1884: §74, n1). The theory he puts forward there is rather different from the ones we consider in this paper. For further details see our ‘What is Frege’s Theory of Descriptions?’ (2005). 3. In our quotations, we leave Bedeutung , Sinn and Bezeichnung (and cognates) untranslated in order to avoid the confusion that would be brought on by using ‘nominatum’, ‘reference’ and ‘meaning’ for Bedeutung . We got this idea from Russell’s practice in his reading notes (see Linsky 2004–5). Otherwise, we follow Max Black’s translation of ‘Über Sinn und Bedeutung’ and Montgomery Furth’s translation of Grundgesetze der Arithmetik . 4. The name ‘Frege-Strawson’ for this theory is from Kaplan (1972), thinking of Strawson (1950, 1952). 5. Contrary, perhaps, to Russell’s opinion as to what is and isn’t obvious. 6. Once again, the name is from Kaplan (1972), referring to Carnap (1956, especially 32–38). 7. Amazingly, in the formal part of the Grundgesetze there is no axiom covering the case of improper descriptions! For further discussion of this and of the formal problems with the Grundgesetze theory see our (2005) ‘What is Frege’s Theory of Descriptions?’ 8. Morscher and Simons (2001:20) take this turn of phrase to show that Frege did not believe that he was giving an analysis of natural language. To us, however, the matter does not seem so clear: How else would Frege have put the point if in fact he were trying to give a logical analysis of the natural language definite article? 9. That is, it bedeutet the course of values of ‘is a square root of 1’, i.e., the set {-1,1}. 10. The course of values of ‘is non-self-identical’, i.e., the empty set. 11. The course of values of the function of adding 3, roughly, the set of things to which three has been added.

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Page 62 12. On the other hand, it might be noted that in the Introduction to the Grundgesetze (p. 6) Frege remarks that ‘a sign meant to do the work of the definite article in everyday language’ is a new primitive sign in the present work. And it is of course well known that Frege says that he had to ‘discard an almostcompleted manuscript’ of the Grundgesetze because of internal changes brought about by the discovery of the Bedeutung-Sinn distinction. 13. And also as Ch. 6 in Kalish, Montague and Mar (1980). 14. There are difficulties in giving a complete and faithful account of the FregeGrundgesetze theory, since its formal development is contradictory because of Basic Law V. Even trying to set this aside, there are difficulties in giving an informal account of improper descriptions, because they are supposed to denote a set. And then this set must be in the domain. But we would then want to have principles in place to determine just what sets must be in a domain, given that some other sets are already in the domain. A simple example concerns the pair of descriptions ι xFx and ι x~Fx , when the descriptions are both improper. The former description is supposed to designate the set of things that are F , and the latter description is supposed to designate the complement of this set. But this leads directly to a contradiction, since it presumes the existence of the complement of any set. So we cannot have both descriptions be improper! None of this is discussed by Frege, and he offers no answers other than by his contradictory Basic Law V. Some of our evaluations of particular sentences run afoul of this problem; but we try to stick with the informal principles that Frege enunciates for this theory, and give these ‘intuitive’ answers. 15. Kalish, Montague, and Mar (1980: Ch. 8), have what they call a ‘Russellian’ theory that is formally similar to this in that it takes ‘improper’ terms to designate something outside the domain. But in this theory, all claims involving such terms are taken to be false, rather than ‘neither true nor false’. (It seems wrong to call this a ‘Russellian’ theory, since singular terms are not eliminated. It might be more accurate to say that it is a theory that whose sentences have the same truth value as the Russellian sentences when the descriptions are eliminated.) 16. There are certainly other 3-valued logics, but Frege’s requirement that the Bedeutung of a whole be a function of the Bedeutungen of the parts requires the Kleene ‘weak’ interpretation. 17. But not always; see for example formula 4 in Table 3.1. 18. Principia Mathematica had no individual constants, so this description could not be formed. It is not clear to us whether there is any formula that can express the claim that it is logically true that exactly one individual satisfies a formula, if there are no constants. Since Russell elsewhere thinks that proper names of natural languages are disguised descriptions, it is also not clear what Russell’s views about forming these ‘logically singular’ descriptions in English might be. 19. In both Frege-Carnap and Frege-Grundgesetze, 15a entails 15b, but not conversely. 20. Morscher and Simons (2001:21) call formula 14 ‘the identity of coextensionals’ and say it is an ‘obvious truth’ that should be honoured by any theory of descriptions. 21. This illustrates a problem in the Frege-Grundgesetze theory: Since the Bedeutung of any description has to be in the domain, it follows that, in the case of a ‘universally applicable’ description such as ι x x = x, the set of all things in the domain has to be in the domain. But then a set is an element of itself, contrary to the principle of well-foundedness.

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Page 63 22. It is not at all clear that there can be a domain that contains only the empty set, in the Grundgesetze framework. But once again, we will not go into the details of this difficult issue. 23. There is also a nonlogical objection embedded in the ‘Gray’s Elegy’ consideration, to the effect that we would need an infinite hierarchy of names of the content of definite descriptions. It is not so clear to us how this is supposed to tell against Frege, who does embrace such an infinite hierarchy of indirect Sinn , although others, such as Salmon (in this volume) find this objection to be the core of the Gray’s Elegy argument. Furthermore, as a second point, arguments that descriptions and logically proper names must differ appear in Russell’s work after ‘On Denoting’, but specifically address logically proper names rather than the arguably more general notion of singular term. 24. ‘I … beg the reader not to make up his mind against the view—as he might be tempted to do, on account of its apparently excessive complication—until he has attempted to construct a theory of his own on the subject of denotation.’ (p. 427) 25. Perhaps the arguments do not hold against Meinong, Ameseder and Mally either. But that is a different topic. 26. Russell’s notes on Frege are in the Bertrand Russell Archives at McMaster University, item RA 230.030420. They are published in Linsky (2004–5). 27. It is also false for all conjunctions of atomic predicates (as in ‘is a golden mountain’). As remarked above, it is not always false when the predicate has certain ‘inherently negative’ constructions, such as explicit negation (‘is not a golden mountain’) and conditionals (‘if a golden mountain, then valuable’). 28. Except from certain of the free logicians, who take the view that sentences which contain nondenoting names are neither true nor false, and this ought to be carried over to nondenoting definite descriptions as well. 29. We thank many people for discussions of the topic of this paper, especially Harry Deutsch, Mike Harnish, Greg Landini, James Levine, Nathan Salmon, an anonymous referee and the audience at the Russell-Meinong conference at McMaster University, May 2005. REFERENCES Carnap, R. (1956) Meaning and Necessity , 2nd edn, Chicago: University of Chicago Press. Frege, G. (1884) Grundlagen der Arithmetik, eine logisch-mathematische Untersuchung über den Begriff der Zahl, Breslau: Koebner. ——. (1892) ‘Über Sinn und Bedeutung’, Zeitschrift für Philosophie und philosophische Kritik 100: 25–50. Translated by M. Black (1952). Selections from the Philosophical Writings of Gottlob Frege, 3rd edn, as ‘On Sense and Meaning’, Oxford: Blackwell, 1980: 56–78 . Quotations and page references are to this translation. ——. (1893) Grundgesetze der Arithmetik, begriffsschriftlich abgeleitet , vol. 1, Jena: Pohle. Translated by M. Furth as The Basic Laws of Arithmetic: Exposition of the System , Los Angeles: University of California Press, 1964. Quotations and page references are to this translation. Kalish, D. and Montague, R. (1964) Logic: Techniques of Formal Reasoning, New York: Harcourt Brace Jovanovich. Kalish, D., Montague, R. and Mar, G. (1980) Logic: Techniques of Formal Reasoning, 2nd edn, New York: Harcourt Brace Jovanovich.

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Page 64 Kaplan, D. (1972) ‘What is Russell’s Theory of Descriptions?’, in D. F. Pears (ed.), Bertrand Russell: A Collection of Critical Essays, Garden City, NY: Doubleday Anchor: 227–44. Kleene, S. (1952) Introduction to Metamathematics , New York: Van Nostrand. Lambert, K. and van Fraassen, B. (1967) ‘On Free Description Theory’, Zeitschrift für Mathematische Logik und Grundlagen der Mathematik 13: 225–40. Lehmann, S. (1994) ‘Strict Fregean Free Logic’, Journal of Philosophical Logic 23: 307–36. Linsky, B. (2004–5) ‘Bertrand Russell’s Notes for Appendix A of The Principles of Mathematics’, Russell: The Journal of Bertrand Russell Studies , n.s. 24: 133–72. Morscher, E. and Simons, P. (2001) ‘Free Logic: A Fifty-Year Past and Open Future’, in E. Morscher and A. Hieke (eds), New Essays in Free Logic: In Honour of Karel Lambert , Dordrecht: Kluwer: 1–34. Neale, S. (2001) Facing Facts, New York: Oxford University Press. Pelletier, F. J. and Linsky, B. (2005) ‘What is Frege’s Theory of Descriptions?’, in B. Linsky and G. Imaguire (eds), On Denoting: 1905–2005, Munich: Philosophia Verlag: 195–250. Russell, B. (1903) Principles of Mathematics, Cambridge: Cambridge University Press. ——. (1905a) ‘On Denoting’, Mind 14: 479–93, reprinted in The Collected Papers of Bertrand Russell, vol. 4, Foundations of Logic, 1903–05 , eds. A. Urquhart and A. C. Lewis, London: Routledge, 1994: 414–27. Page references to this reprint. ——. (1905b) ‘Review of Meinong and Others, Untersuchungen zur Gegenstandstheorie und Psychologie ’, Mind 14: 530–38. Strawson, P. (1950) ‘On Referring’, Mind 59: 320–44. ——. (1952) Introduction to Logical Theory , London: Methuen. von Heusinger, K. (1997) ‘Definite Descriptions and Choice Functions’, in S. Akama (ed.) Logic, Language and Computation, Dordrecht: Kluwer: 61–91. Whitehead, A. N. and Russell, B. (1910) Principia Mathematica , Cambridge: Cambridge University Press, 2nd edn, 1925–27. Reprinted in paperback as Principia Mathematica to *56 , Cambridge: Cambridge University Press, 1962.

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Page 65 4 A Cantorian Argument Against Frege’s and Early Russell’s Theories of Descriptions Kevin C. Klement It would be an understatement to say that Russell was interested in Cantorian diagonal paradoxes. His discovery of the various versions of Russell’s paradox—the classes version, the predicates version, the propositional functions version—had a lasting effect on his views on philosophical logic. Similar Cantorian paradoxes regarding propositions—such as that discussed in §500 of The Principles of Mathematics—were surely among the reasons Russell eventually abandoned his ontology of propositions.1 However, Russell’s reasons for abandoning what he called ‘denoting concepts’, and his rejection of similar ‘semantic dualisms’ such as Frege’s theory of sense and reference—at least in ‘On Denoting’—made no explicit mention of any Cantorian paradox. My aim in this paper is to argue that such paradoxes do pose a problem for certain theories such as Frege’s, and early Russell’s, about how definite descriptions are meaningful. My first aim is simply to lay out the problem I have in mind. Next, I turn to arguing that the theories of descriptions endorsed by Frege and by Russell prior to ‘On Denoting’ are susceptible to the problem. Finally, I explore what responses a contemporary ‘semantic dualist’ with commitments similar to Frege or early Russell could give that might have some plausibility. AN OVERVIEW OF THE PROBLEM Here’s the core difficulty: by Cantor’s powerset theorem, every set has more subsets than members. Given a sufficiently abundant metaphysics of properties, concepts, ‘propositional functions’ or suchlike, a result similar to Cantor’s theorem applies to them: for a given logical category of entity, the number of properties applicable (or not) to entities in that category must exceed the number of entities in that category (see Russell 1903: §§102, 348). If, like Frege and early Russell, we believe that a descriptive phrase of the form has a sense or meaning which is a distinct entity from its denotation, and believe that such a sense exists for every property φ, we come to the brink of violating Cantor’s theorem. If we now consider those properties applicable or not to senses or meanings, and are committed to

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Page 66 a distinct sense, as a self-standing entity, for each such property, we risk positing as many senses as properties applicable to them, in violation of Cantorian principles.2 In order to state the problem more precisely, it is worth listing those principles that together generate the problem. In stating the principles, let us use the label descriptive sense for those senses—assuming there are any—that either are the senses of definite description phrases or are appropriate for playing this role, that is, they have as part of their nature some property φ such that they present as denotation the unique entity of which φ holds, if there is such a unique entity, and otherwise lack denotation (or present some special chosen object as denotation).3 Let us furthermore use the notation ‘[[the φ]]’ to speak about such a sense itself (as opposed to its denotation). Hence, according to the usual story, (A) is true but (B) is false: (A) the author of Frankenstein = the second daughter of Mary Wollstonecraft (B) [[the author of Frankenstein ]] = [[the second daughter of Mary Wollstonecraft]] I use the word ‘expresses’ for the relation between a phrase and its sense, the word ‘presents’ for the relation between a sense and the denotation it picks out, and the word ‘designates’ for the relation between a phrase and its denotation, so we have: (C) ‘the author of Frankenstein ’ expresses [[the author of Frankenstein ]] (D) [[the author of Frankenstein ]] presents the author of Frankenstein (E) ‘the author of Frankenstein ’ designates the author of Frankenstein Consider then, the following set of assumptions: Comprehension Principle (CP): For every open sentence ‘ … x … ’ not containing ‘φ’ free, the corresponding instance of the following schema is true: There exists a property φ such that any entity x has φ if and only if … x … Descriptive Sense Principle (DSP): For every property φ, there is at least one descriptive sense, that is, at least one sense taking the form [[the φ]]. Sense Uniqueness Principle (SUP) : A descriptive sense involves only one property, that is: for any descriptive senses [[the φ]] and [[the ψ]], [[the φ]] is identical to [[the ψ]] only if φ is the same property as ψ.

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Page 67 Sense Property Principle (SPP): (i) Descriptive senses themselves have or lack properties and can be presented by other descriptive senses in virtue of these properties, and (ii) descriptive senses are not divided into logical subtypes: those properties applicable (or not) to some descriptive senses are applicable (or not) to all of them. Applying Cantorian diagonal argumentation, from these principles we obtain a Russell-style paradox. Certain descriptive senses do not have their corresponding properties. For example, [[the author of Frankenstein ]] did not author Frankenstein, and [[the sense that presents the Eiffel Tower]] does not present the Eiffel Tower.4 On the other hand, [[the sense]] is a sense, and [[the self-identical thing]] is a self-identical thing. Let us now introduce terms for certain properties, autopredicability and heteropredicability , as follows: Definition: x is heteropredicable if and only if there is a property φ such that x is identical to a descriptive sense of the form [[the φ]] and x does not have φ. Definition: x is autopredicable if and only if x is not heteropredicable, or equivalently, for all properties φ, if x is identical to a descriptive sense of the form [[the φ]], then x has φ. Notice that in order to be autopredicable, a sense does not have to present itself: a descriptive sense [[the φ]] can be autopredicable even if other entities besides it have the property φ. For example, assuming a plurality of senses, [[the sense]] is autopredicable, because it is a sense, and this does not require it to be the only sense. However, if there are any senses that present themselves, they are autopredicable. If the sense Sally loves most is [[the sense Sally loves most]], then [[the sense Sally loves most]] is autopredicable. All descriptive senses derived from uninstantiated properties, for example, [[the King of France in 1905]] are heteropredicable. You may have guessed where this is going, but let’s walk through it carefully: (1) By (CP), there is a property H such that any entity x has H if and only if there is a property φ such that x is identical to a descriptive sense of the form [[the φ]] but x does not have φ. (2) By (1) and (DSP), there is a descriptive sense, [[the H]].5 (3) By (SPP), the question as to whether or not [[the H]] has property H arises. However, both assumptions are impossible: (4) First let’s show that [[the H]] cannot have property H. (4a) Assume for reductio ad absurdum that [[the H]] has property H.

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Page 68 (4b) By (4a) and (1), there is a property φ such that [[the H]] is identical to a descriptive sense of the form [[the φ]] but [[the H]] does not have φ. (4c) Let us call the property posited in (4b) ‘ G’. Hence, [[the H]] is identical to a descriptive sense [[the G]], and [[the H]] does not have G. (4d) By (SUP) and the first conjunct of (4c), G is the same property as H. (4e) By (4d) and the second conjunct of (4c), [[the H]] does not have H, which contradicts our assumption at (4a). (5) Likewise [[the H]] cannot not have H. (5a) Assume that [[the H]] does not have H. (5b) By (1) and (5a), it is not the case that there is a property φ such that [[the H]] is identical to a descriptive sense of the form [[the φ]] but [[the H]] does not have φ. (5c) By logical manipulations on (5b), we get: for all properties φ, if [[the H]] is identical to a descriptive sense of the form [[the φ]], then [[the H]] has φ. (5d) By (5c), if [[the H]] is identical to a descriptive sense of the form [[the H]], then [[the H]] has H. (5e) Certainly, [[the H]] is identical to a descriptive sense of the form [[the H]], and so by (5d), [[the H]] has H, which contradicts (5a). (6) Conclusion: At least one of the assumptions (CP), (DSP), (SUP) or (SPP) must be false. The process of reasoning given above is difficult to counter. Alleging that a logical mistake is made somewhere along the way would require, I think, toeing a fairly revisionist line with regard to certain logical principles, denying, for example, the indiscernibility of identicals, the principle of bivalence or the validity of reductio argumentation. There are more subtle concerns one might have, particularly with regard to the correct logic of the notation ‘[[the φ]]’ and whether it is legitimate to ‘quantify in’ to such a construction.6 However, when scrutinized, I believe such worries in the end would amount to a rejection of (CP), (DSP), (SUP) or (SPP), or at least advocacy of a precisification of one of these principles. The argument at least establishes that it would be naïve to accept all of these principles without further scrutiny. FREGE AND EARLY RUSSELL Next, I want to argue that Frege and early Russell either were committed to the principles (CP), (DSP), (SUP) and (SPP), or were at least committed to those instances necessary to generate the antinomy just described. (CP) is roughly the standard principle of comprehension for second order

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Page 69 logic; both Frege and Russell accepted a version of this principle within their logical systems. In Frege’s logical system, higher-order quantification is quantification over functions. Certain functions, called ‘concepts’, were understood as functions onto truth-values. Frege believed that if a proper name is removed from a sentence, what remains is a name of a concept (see Frege 1891, passim). Hence, if we take ‘property’ in ‘CP’ to mean Fregean concepts, Frege would have endorsed (CP). A caveat should be entered that Frege would only have accepted (CP) as a general principle for those logical languages that avoided vagueness and ensured that every wellformed name had a reference. Frege believed that a complex expression does not refer whenever it contains a subexpression that doesn’t refer. So in natural language, where nonreferring expressions are used, Frege might have demurred from something such as (CP). For example, he might have claimed that the open sentence ‘ x = Hercules’ would not correspond to any function. However, (CP) is only involved in the antinomy sketched above at step (1), where it is concluded that there is such a property as H, or heteropredicability. Even if Frege would have insisted upon exceptions to (CP) for ordinary language, these exceptions are not relevant to the issue under consideration, because there is nothing about our definition of H that involves expressions that do not refer, vague concept words or anything similar. In the case of early Russell, there is a complicating factor regarding whether (CP) should be taken as positing what he called ‘class-concepts’ or ‘predicates’, or what he called ‘propositional functions’.7 Unfortunately, Russell sometimes used the word ‘property’ synonymously with ‘predicate’, and sometimes synonymously with ‘propositional function’ (see Linsky 1988). On my own interpretation, by ‘predicate’ Russell meant the ontological correlate of an adjectival phrase, which he understood roughly as a Platonic universal devoid of complexity; whereas, by ‘propositional function’ he understood a complex proposition-like unity containing variables in place of definite terms (see Klement 2005). In The Principles of Mathematics, when responding to the very similar antinomy involving predicates that are not predicable of themselves, Russell came to the conclusion that there is no such predicate as ‘not predicable of oneself’ (Russell 1903: §101). This might make it seem as if he would have denied (CP) and reject any such predicate as H. However, early Russell distinguished between predicates and propositional functions. While he denied a common predicate , Russell admitted that there was a propositional function satisfied by all and only predicates not predicable of themselves, and also admitted a denoting concept derived from this propositional function denoting the class of all such predicates (Russell 1903: §84 chiefly, but compare §§77, 96, 488). Although the primary chapter on denoting concepts in Principles of Mathematics deals principally with denoting concepts derived from predicates, Russell’s final position admitted denoting ‘complexes’ derived from propositional functions. This is clearer in Russell’s 1903 through 1904 manuscripts, where a denoting complex was explicitly described as

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Page 70 derived from an indefinable ‘denoting function’, written ‘ ι’, along with a propositional function (Russell 1994:87–89, 355–56). Indeed, a denoting complex is portrayed in these manuscripts as a complex formed from the function ι and a propositional function. Hence, the relevant version of (CP) would involve propositional functions rather than simple predicates. Here, just as Russell accepted a propositional function satisfied by all and only predicates not predicable of themselves, there seems no barrier to supposing that he would have allowed a version of (CP), interpreted to deal with propositional functions, according to which H would be admitted as a propositional function. Given the description we have just given of a Russellian denoting complex as a complex formed by the operator ‘ ι’ and a propositional function, it is clear that he would have posited such a denoting complex for each propositional function; and hence, interpreting ‘descriptive sense’ to mean the same as ‘denoting complex’, early Russell would have accepted (DSP). With regard to (DSP), in the case of Frege the situation is a bit complicated in that the properties, or at least the properties posited by his version of (CP), are functions located at the level of reference. Frege applied the sense/reference distinction to concept and other function expressions as well. According to the little known theory of definite descriptions presented in Frege’s Grundgesetze, §11, an ordinary language description of the form the φ would be analysed with a term of the form , where represents Frege’s abstraction operator for forming a name of the extension of a concept, and ‘\’ represents a function on extensions that yields the sole object included in the extension if there is such a sole object, and returns its argument as value otherwise. Frege regarded the sense of a complex expression as a whole containing the senses of its subexpressions as parts; so the sense of the phrase ‘\ F (ε)’ would contain the sense of the concept phrase ‘F( )’ as part. Presumably, Frege would have regarded it as generally the case that a descriptive sense would contain as a part a sense presenting a concept, but would not contain the function or concept itself . Arguably, then, Frege might have room for claiming that only those concepts that are presented by some sense have descriptive senses corresponding to them. Certainly, Frege might have claimed that certain concepts, for example, those that map objects to the True or the False in an irregular fashion not corresponding to any condition specifiable in a finitely complex way, are not presented by any sense, and, hence, have no corresponding descriptive sense. Again, however, even if Frege is not committed to (DSP) in its strongest form, this will not provide a solution to the antinomy described above unless H is one of the concepts having no corresponding sense. Yet H does map objects to the True in a finitely specifiable way; indeed, the expression we used above to define H presumably expresses a sense, and this sense would present H. It is unlikely that Frege could have plausibly claimed that there is no such descriptive sense as [[the H]] without further argumentation.

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Page 71 With regard to (SUP), it seems clear that Russell would be committed to a one-to-one correlation between denoting complexes and propositional functions. Since a denoting complex simply is a complex containing the description operator and a propositional function, the denoting complex so-formed would be different for different propositional functions. In Frege’s case, again the situation is slightly more complicated, though not much. A Fregean descriptive sense would be a composite containing as a part a sense presenting some concept. Different descriptive senses would result for different concept senses. Since presumably a given concept sense would present at most one concept, (SUP) would hold for Frege as well. Moving to (SPP), part (i) is part and parcel of adopting a realism about meanings, denoting complexes or senses. If there are such entities, they must have properties and be presented by other senses. If not, then it would seem impossible for us to speak about them. The more interesting question would be whether or not Frege or Russell would have room for denying part (ii) of (SPP) by drawing upon some theory of logical types. Frege’s only division of logical type was that involved in the distinction between functions and objects and the hierarchy of functions of different levels. Descriptive senses are presumably all objects on Frege’s approach: an object was characterized by Frege as an entity the expression for which does not contain an empty spot (Frege 1891:140–41). According to Frege’s theory of indirect speech, descriptive senses are sometimes the referents of descriptive phrases, which would count as object expressions in Frege’s theory. There does not seem to be much room for dividing them into logical types. Russell’s views on logical types changed through his career, but early Russell (at least) was explicit that all singular entities—all ‘individuals’, as he would say—form a single logical type and can all be logical subjects in propositions. Indeed, he found it ‘self-contradictory’ to deny of any entity that it is not a logical subject (Russell 1903: §49). The short-lived theory of types presented in Appendix B to the Principles made a distinction between pluralities, or classes-as-many, and individuals, but classes-asmany were not regarded by Russell as singular entities at all.8 Denoting complexes, if taken to be unified entities, and not—as in Russell’s later thought—just roundabout ways of talking about multiple entities entering into propositions in more complicated ways, would presumably all count as the same logical type for Russell. POSSIBLE ALTERNATIVE RESPONSES I have just argued that the historical Russell and Frege were committed to the principles giving rise to the antinomy sketched earlier. It is nevertheless worth considering what routes would be available to those who might wish to attempt to preserve the core of a semantic dualist position similar to Frege’s or early Russell’s yet avoid the antinomy. Because the antinomy

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Page 72 is generated by accepting the conjunction of (CP), (DSP), (SUP) and (SPP), any adequate response would require rejecting one or more of these principles. Let us consider them in turn and, for each, consider the immediate benefits and costs of abandoning it. Again, (CP) is roughly the standard principle of comprehension of second-order logic. Of course, the merits and demerits of deviating from first-order logic are still matters of philosophical controversy.9 There are many rival views on the nature of properties, their existence conditions and the appropriate corresponding logic worth exploring. I cannot survey them here. However, it is not clear that the general problem wouldn’t also arise for those who think of properties as, say, functions from possible worlds to classes or some such. Whatever one’s view of properties, avoiding the contradiction above by rejecting (CP) would require saying something more about the relationship between properties and open sentences and discovering some principled reason not only why not every open sentence corresponds to a property, but in particular , why there is no such property as H. Of course, there are other reasons to prefer a ‘sparse’ rather than ‘abundant’ theory of properties besides blocking this paradox, but in the context of the present discussion, one must be willing to accept even that there is no derivative or less fundamental notion of ‘property’ relevant to the meaningfulness of descriptions that would generate the problem. After all, it would not be plausible to suppose that there is no such sense as [[the author of Frankenstein ]] simply because the trait of authoring Frankenstein is not metaphysically simple or fundamental. Still, this warrants further exploration.10 We have already seen that there might be room within a Fregean perspective for denying (DSP) in its full generality. Doubts about (DSP) multiply further if we deviate from the Fregean conception of a sense as an abstract object, and instead portray a sense as something psychological, linguistic or psycho-linguistic (for example, an item of the language of thought). Then surely, if our metaphysics of properties is abundant, we would not be committed to a sense for every property. This definitely makes the situation more Cantor-friendly. But as with the case of Frege himself, the advantages of scrapping (DSP) in the present context, are not what they might seem. Again, for this to serve as a solution to the paradox sketched above, we would have to conclude that H is one of the properties to which there corresponds no descriptive sense. It is difficult to exclude [[the H]] except by means of some ad hoc restriction. For example, without further elaboration, it is unclear how appeal to a psychological or linguistic conservatism about the existence of senses could help avoid [[the H]], since we at least seem to be able to have thoughts making use of this sense, and form linguistic expressions that express it. Someone wishing to use the falsity of (DSP) to avoid the problem needs a more subtle response.11 In examining (SUP), it is important not to confuse it with something like its converse. If properties are located at the level of denotation, or otherwise are given identity conditions governed by their extensions either in this

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Page 73 world or even across all possible worlds, then it would be implausible to suppose that a property could have only one descriptive sense. One might hold, for example, that the property being the 8th planet from the sun is the same property as being the (5 + 3)rd planet from the sun, and yet deny that the sense [[the 8th planet from the sun]] is identical to the sense [[the (5 + 3)rd planet from the sun]]. I have tried to formulate the argument above without assuming that for a given φ there is only one descriptive sense of the form [[the φ]]. However, notice that if the problem is that, by Cantor’s theorem, there must be more properties of descriptive senses than descriptive senses, allowing there to be more than one [[the φ]] for a given φ, if anything, makes the problem worse, not better. (SUP) itself would be very difficult to deny while maintaining both that descriptive senses present their denotation in virtue of the denotation’s unique possession of a certain property, and that the relationship between sense and denotation is determinate. Suppose there were a descriptive sense S*, such that S* took both the form [[the φ]] and the form [[the ψ]], but φ ≠ ψ. It would then seem possible for there to be one entity uniquely φ and a distinct entity uniquely ψ, and it would be indeterminate which entity would be presented by S*. The best hope for making good on a denial of (SUP) might come from a more sophisticated understanding of the nature of senses/intensions generally, whereupon a sense, understood as a linguistic meaning, does not by itself fix a denotation, and only does so in conjunction with features of the context in which a linguistic act is performed.12 One might then maintain, for example, that the description ‘the person I most admire’ has the same sense regardless of who utters it. However, if uttered by Sally, it has its denotation in virtue of that denotation having one property ( being admired most by Sally), but if uttered by Raoul it has its denotation in virtue of that denotation having a different property ( being most admired by Raoul). However, it is doubtful that this would avoid the problem altogether. The paradox above might still be reformulable by choosing one context of evaluation to consider throughout, or by focusing more narrowly on a certain subclass of descriptive senses (‘eternal senses’?) that are not so context-dependent. Again, in order for this strategy to solve the contradiction, we’d have to say that the descriptive sense [[the H]] from the argument above is one of the senses corresponding to more than one property. Yet there does not seem to be anything context-dependent about it. Of the four principles, (SPP) is the most difficult to fully evaluate. A realist about senses would be hard pressed to deny part (i). Indeed, even for a view on which senses are derivative or constructed entities —reducible to something more fundamental—it would be odd to claim that they don’t have properties, or cannot be presented by other senses. It would then become hard to see how the statements we make about senses when philosophizing about them could be possible.13 Part (ii) of (SPP) is more open to criticism. Notice, however, that it does not suffice simply to place

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Page 74 descriptive senses in a different logical category from concrete objects. All talk of properties in the argument above can be restricted to ‘properties of descriptive senses’ and the argument goes through just as well. One would need, instead, to divide descriptive senses and/or the properties applicable to them, into various ramified subtypes. Notice that the definition given of heteropredicability is what is sometimes called an ‘impredicative’ definition:14 it involves quantification over a range that includes that which is being defined. Someone might, therefore, claim either that the definition is illegitimate (which amounts to a rejection or modification of (CP)), or that the property so defined falls into a separate logical category from those it quantifies over. To solve the above contradiction, one would need argue, on the basis of this , either that the question as to whether or not [[the H]] is H does not arise (thus blocking step (3)), or that something goes wrong at steps like (5d), where a quantifier over properties using φ and ψ is instantiated to H. Typically, ramified type-theories derive their philosophical justification by appeal either to a Tarskian hierarchy of languages, or to some sort of vicious-circle principle.15 Without delving more into the nature of properties and their relationship to descriptive senses, the philosophical viability of ramification cannot be fully assessed. I, for one, am skeptical. While the paradox we have been discussing is a semantic paradox, involving meanings, the paradox deals most directly with properties and senses, and only indirectly with language. This makes it quite different from the Grelling or Liar paradoxes. If properties or senses are abstracta, it is not clear how a Tarskian hierarchy of languages would be relevant, nor exactly what would make impredicativity viciously circular.16 Although I am still somewhat undecided about the issue, I think this sort of paradox poses a definite challenge for the would-be defender of intensional entities such as senses or denoting concepts. It represents yet another reason in favour of theories such as that of the mature Russell’s theory of descriptions, in which differences between descriptive phrases intuitively having different meanings are respected without positing a special class of intensional entity. NOTES 1. For further discussion, see Landini 1998: Ch. 8. 2. This paradox is a new instance of a general category of Cantorian problems regarding senses which I discuss in Klement 2003. 3. In this paper, I do not assume anything about whether or not proper names or other individually referring expressions besides descriptions should be understood as expressing descriptive senses. For those who accept a Fregean descriptivist theory of names, the points made in this paper will have even more importance, but the argument itself does not presuppose any such thing. The last clause, with regard to ‘presenting a chosen object’, is meant to accommodate views such as Frege’s use of the sign ‘\’ as a ‘substitute for the

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Page 75 definite article’ in his logical language (see Frege 1893: §11), Carnap’s use of the sign ‘ ι’ (see Carnap 1956:32ff.), Church’s use of the sign ‘ι’ (see Church 1951:14), and similar devices. 4. This example may take some thought to figure out. Notice, we are not asking whether or not the sense that presents the Eiffel tower presents the Eiffel tower, but something more like whether or not the sense of the phrase ‘the sense that presents the Eiffel tower’ presents the Eiffel Tower. Presumably, if this sense were to present anything, it would present a sense, and not a monument in Paris. However, I think a Fregean should say that it lacks denotation altogether, since the uniqueness requirement is not fulfilled. 5. I should note that we need not assume that this sense is unique; if there are multiple descriptive senses for H, the contradiction results for any of them. More on this below. 6. Notice that I did not introduce ‘[[the φ]]’ as shorthand for ‘the sense of the phrase ’. If I had, then surely quantifying in would be illegitimate. I mean something closer to a function mapping properties to their descriptive senses. However, given the possibility of the falsity of the converse of (SUP), this way of understanding [[the φ]] might also be overly simplistic. This is merely an instance of the general sort of difficulty Russell himself drew attention to in ‘On Denoting’ regarding speaking about meanings as opposed to their denotations. (For a general discussion, see Klement 2002b.) The argument can be captured without using this notation and instead making use of a relation sign representing the presentation relation, such as Church’s ‘Δ’ (see Church 1951:16). However, the argument is much easier to follow for informal discussion with the notation ‘[[the φ]]’. 7. Unfortunately, it is still widely believed that Russell equated predicates/concepts and propositional functions. I have argued against this common misreading elsewhere. See Klement 2004, 2005. 8. See, e.g., his remarks to Jourdain, quoted in Grattan-Guinness 1977:78. 9. In particular, Quine’s criticism of the higher-order logic of Principia Mathematica as having been born in the sin of confusing metalinguistic schematic variables with object-language variables for ‘propositional functions’ understood realistically as complex attributes comes to mind. Quine suggests instead that the innocuous part of second-order logic can be reconstructed in a first-order set theory (see, e.g., Quine 1961, 1969). Of course, it is highly unlikely that someone wishing to maintain a Fregean intensionalist view of the meaningfulness of descriptions would look to a hyper-extensionalist like Quine for salvation; the theory of descriptions was one of the few Russellian doctrines Quine liked. 10. The sort of conservatism with regard to reifying universals and other intensional entities found in Cocchiarella’s work (e.g., Cocchiarella 1987, 2000) might represent a compromise worth exploring. I cannot do the issue justice here. 11. For further discussion of related issues, see Klement 2003. 12. Versions of such sophisticated understanding of senses, or intensions, abound in the philosophy of language literature from the past 30 years: see, e.g., Perry 1977, Stalnaker 1978, Burge 1979, Chalmers 2002, etc. The details of their views, and the terminology they use, vary widely. 13. Perhaps an adherent to a modified version of the early Wittgensteinian saying/showing distinction (see Wittgenstein 1922) could accept that we can’t actually ‘say anything’ about senses. The issue is too difficult to be broached here, and if there’s something to it, we can’t really discuss it anyway.

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Page 76 14. This notion generally comes from Whitehead and Russell 1925 (see Introduction, Ch. 2). For discussion, see Chihara 1973; Hazen 1983; Goldfarb 1989; Urquhart 2003 and others. 15. See Tarski 1933; Whitehead and Russell 1925; Church 1974, 1976; Anderson 1987 and others. 16. For influential criticisms of certain forms of ramification along these lines, see Gödel 1944 and Quine 1966; for a defence of the historical Russell, see Landini 1998: Ch. 10. For a discussion of the plausibility of ramification for Fregeans, see Klement 2002a: Ch. 7. REFERENCES Anderson, C. A. (1987) ‘Semantic Antinomies in the Logic of Sense and Denotation’, Notre Dame Journal of Formal Logic 28: 99–114. Burge, T. (1979) ‘ Sinn ing against Frege’, Philosophical Review 58: 398–432. Carnap, R. (1956) Meaning and Necessity , 2nd edn, Chicago: University of Chicago Press. Chalmers, D. (2002) ‘On Sense and Intension’, in J. Tomberlin (ed.), Philosophical Perspectives 16: Language and Mind, Oxford: Blackwell. Chihara, C. (1973) Ontology and the Vicious Circle Principle , Ithaca, NY: Cornell University Press. Church, A. (1951) ‘A Formulation of the Logic of Sense and Denotation’, in P. Henle, H. Kallen and S. Langer (eds), Structure, Method and Meaning: Essays in Honor of Henry M. Sheffer , New York: Liberal Arts Press. ——. (1974) ‘Outline of a Revised Formulation of the Logic of Sense and Denotation (Part 2)’, Noûs 8: 135–56. ——. (1976) ‘Comparison of Russell’s Resolution of the Semantical Antinomies with That of Tarski’, Journal of Symbolic Logic 41: 747–60. Cocchiarella, N. (1987) Logical Studies in Early Analytic Philosophy , Columbus, Ohio: Ohio State University Press. ——. (2000) ‘Russell’s Paradox of the Totality of Propositions’, Nordic Journal of Philosophical Logic 5: 25–37. Frege, G. (1891) Funktion und Begriff , translated as ‘Function and Concept’, in Frege (1984): 137–56. ——. (1892) ‘Über Sinn und Bedeutung’, translated as ‘On Sense and Meaning’, in Frege (1984): 155–77. ——. (1893) Grundgesetze der Arithmetik , vol. 1, translated in part as Basic Laws of Arithmetic , ed. M. Furth, Berkeley: University of California Press, 1964. ——. (1979) Posthumous Writings, trans. P. Long and R. White, Chicago: University of Chicago Press. ——. (1980) Philosophical and Mathematical Correspondence, ed. B. F. McGuinness, Chicago: University of Chicago Press. ——. (1984) Collected Papers on Mathematics, Logic and Philosophy , ed. B. F. McGuinness, New York: Blackwell. Gödel, K. (1944) ‘Russell’s Mathematical Logic’, in P. A. Schlipp (ed.), The Philosophy of Bertrand Russell, vol. 1, New York: Harper and Row. Goldfarb, W. (1989) ‘Russell’s Reasons for Ramification’, in C. W. Savage and C. A. Anderson (eds), Rereading Russell, Minneapolis: University of Minnesota Press. Grattan-Guinness, I. (1977) Dear Russell, Dear Jourdain, New York: Columbia University Press.

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Page 77 Hazen, A. (1983) ‘Predicative Logics’, in D. Gabbay and F. Guenthner (eds), Handbook of Philosophical Logic, vol. 1, Dordrecht: Reidel. Klement, K. (2001) ‘Russell’s Paradox in Appendix B of The Principles of Mathematics: Was Frege’s Reply Adequate?’ History and Philosophy of Logic 22: 13–28. ——. (2002a) Frege and the Logic of Sense and Reference, New York: Routledge. ——. (2002b) ‘Russell on Disambiguating with the Grain ‘, Russell, n.s. 21: 101–27. ——. (2003) ‘The Number of Senses’, Erkenntnis 58: 302–23. ——. (2004) ‘Putting Form Before Function: Logical Grammar in Frege, Russell and Wittgenstein’, Philosopher’s Imprint 4: 1–47. ——. (2005) ‘The Origins of the Propositional Functions Version of Russell’s Paradox’, Russell, n.s. 24: 101–32. Landini, G. (1998) Russell’s Hidden Substitutional Theory , Oxford: Oxford University Press. Linsky, B. (1988) ‘Propositional Functions and Universals in Principia Mathematica ’, Australasian Journal of Philosophy 66: 447–60. Quine, W. V. O. (1961) ‘Logic and the Reification of Universals’, in From a Logical Point of View , Cambridge, MA: Harvard University Press. ——. (1966) ‘Russell’s Ontological Development’, Journal of Philosophy 63: 657–67. ——. (1969) Set Theory and Its Logic , 2nd edn, Cambridge, MA: Harvard University Press. Perry, J. (1977) ‘Frege on Demonstratives’, Philosophical Review 86: 476–97. Russell, B. (1903) The Principles of Mathematics, New York: W. W. Norton (1996 paperback). ——. (1905) ‘On Denoting’, Mind 14: 479–93, reprinted in Russell (1994): 414–27. ——. (1994) Collected Papers of Bertrand Russell, vol. 4, Foundations of Logic, 1903–05 , ed. A. Urquhart, London: Routledge. Stalnaker, R. (1978) ‘Assertion’, in P. Cole (ed.), Syntax and Semantics: Pragmatics, vol. 9, New York: Academic Press. Tarski, A. (1933) ‘The Concept of Truth in Formalized Languages’, reprinted in Logic, Semantics, Metamathematics , 2nd edn, Indianapolis: Hackett Publishing, 1983. Urquhart, A. (2003) ‘The Theory of Types’, in N. Griffin (ed.), The Cambridge Companion to Bertrand Russell, Cambridge: Cambridge University Press. Whitehead, A. N. and Russell, B. (1925) Principia Mathematica , vol. 1, 2nd edn, Cambridge: Cambridge University Press. Wittgenstein, L. (1922) Tractatus Logico-Philosophicus , trans. C. K. Ogden, London: Routledge and Kegan Paul.

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Page 78 5 ‘On Denoting’ Appearance and Reality Gideon Makin One hundred years on, ‘On Denoting’ (OD) remains one of the most—if not the most—influential and celebrated essays in the analytic tradition in philosophy. And yet, as far as our understanding of its text is concerned, such notoriety may be something of a mixed blessing. A certain tradition regarding its philosophical morals has taken such deep root that it is now barely possible to read it with an open mind on what precisely it says or implies. This traditional view, which still dominates the secondary literature, gets things right on Russell’s positive account of propositions, expressed by sentences containing ‘the so and so’ phrases (in the singular)—which is a relatively straightforward matter. However, when one asks what precisely was his case for it, why was an analysis of this kind called for and what were the relevant alternatives? the matter is otherwise. In this paper I examine some features of the traditional view of OD, which I label ‘appearance’, and contrast them with what I claim is the far more complex ‘reality’ which emerges when some lesser known Russellian texts, as well as some of the finer details of OD itself, are given careful attention. Neglect of these sources is almost bound to lead to a distorted picture of what precisely the OD theory was trying to achieve, and what to avoid, as well as the philosophical agenda it was in the service of. On some of these matters OD is itself (as will emerge in the course of what follows) a somewhat misleading document. It appears to lend support to some later misunderstandings on particular points. I focus mainly on a single issue where, I suggest, the appearance/reality gap is particularly significant— though it is not the only one—namely, the ontological import of OD. What follows, however, is not an attempt at an exhaustive account of OD, and at least one exegetical issue which emerges from the view below as having cardinal importance is indicated only briefly at the very end. Ultimately, I argue that we are faced with the following choices: We can either stick to some variant of the traditional view: this leads to a neat and tidy picture of OD’s argument which is plainly false; or we can replace it with a messy, far more complex, picture, which leaves some loose ends, but has some prospect of being true.

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Page 79 THE ONTOLOGICAL BACKDROP: TWO GRADES OF MISCONCEPTION Having a clear view of the ontological import of OD is paramount because this issue is widely, if not universally, regarded as OD’s chief achievement and Russell’s principal case for recommending it. And although OD does indeed have some significant ontological import, I hope to show that careful examination reveals it as being quite different from what it has usually been taken to be. There are two varieties of the ‘appearance’ view on these matters to be distinguished. The first and more traditional of the two is what I refer to as the ‘crude’ view. Its criticism gives rise to a more sophisticated and refined alternative—alas, as I argue, still an appearance—which we then proceed to examine. Starting from the criticism of both these views, I then set out the alternative view I recommend (hopefully, ‘reality’). The crude view maintains that OD’s chief point is the demolition of an ‘unrestrained’ Meinongian ontology, which Russell had formerly subscribed to. In his ‘Russell’s Ontological Development’ Quine, perhaps one of the most influential propagators of this view,1 contrasts Russell’s former view with the one found in ‘On Denoting’ thus: ‘In the Principles of Mathematics, 1903, Russell’s ontology was unrestrained. Every word referred to something.’ While in OD, by contrast: ‘a reformed Russell emerges, … fed up with Meinong’s impossible objects’ (1967:291). A source not cited by Quine, but which seems to lend support to his claim, comes from no lesser an authority than Russell himself. In My Philosophical Development he says that Meinong had argued that if you say the golden mountain does not exist, it is obvious that there is something that you are saying does not exist—namely the golden mountain; therefore the golden mountain must subsist in some shadowy Platonic world of being, for otherwise your statement that the golden mountain does not exist would have no meaning. I confess that, until I hit upon the theory of descriptions, this argument seemed to me convincing . (1959:64, my emphasis) This would appear to be conclusive evidence that Quine’s view is (at least very nearly) right, but I regret to have to argue that it is completely wrong. It does not tally with very clear evidence much closer to the event than either Russell’s (1959) or Quine’s (1967) statements. Needless to say: what we take the ontological import of OD to have been depends on what we take Russell’s former ontological position to have been, and we cannot expect to understand the former unless we have a firm grip on the latter. But while the ontology of OD itself, at least by and large, is uncontroversial; the Russellian view which preceded it has, I believe, been widely misunderstood; and awkward as it may be to have to challenge

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Page 80 Russell’s authority on his own philosophical development, evidence to be cited shortly tells quite conclusively against it. Despite some not insignificant differences between them,2 it is convenient to bunch Quine’s and Russell’s 1959 accounts of the ontological impact of OD together as variants of a single ‘crude’ view, because they are flatly contradicted by a statement Russell had made before OD. In ‘The Existential Import of Propositions’ (a short polemical piece responding to Hugh MacColl, henceforth EIP) Russell wrote: ‘“the present King of France” is a complex concept denoting nothing … these words have a meaning, … but they have not a denotation : there is no entity, real or imaginary, which they point out’ (1905a: 100). This statement was not only written, but also published before OD, and its context makes it plain that Russell was then still endorsing the theory of denoting concepts set forth in his major earlier book The Principles of Mathematics (published in 1903, henceforth PoM), and which he repudiated in OD.3 The problem facing us now is this: If, as this evidence suggests, even before OD Russell did not admit empty phrases had referents, how could OD have marked his emancipation from an ‘unrestrained’ ontology which admits them? The answer is, I think, quite plain: it could not. The crude view on the ontological import of OD is thus untenable. Another, more refined view which is better informed about Russell’s pre-OD writings requires more elaborate discussion to show why the picture which it portrays, too, is only an ‘appearance’. It starts by conceding, in the light of the evidence just cited, that indeed on the eve of OD Russell was no longer committed to a Meinongian ontology (and hence that OD could not have marked his emancipation from it). Peter Hylton, who advocates such a view in his Russell, Idealism, and the Emergence of Analytic Philosophy, contends that ‘Russell’s ontological views undergo an important change between Principles and OD’ (1990:241). What then, on Hylton’s view, did this change consist in, and what precisely were Russell’s reasons for it? He contends there were two significant changes: First, Russell dropped his former commitment to referents of empty descriptions; and second, he modified his view on the distinction between existence and being (the evidence for the former, so far as I can tell, is none other than the passage just cited from EIP). Regarding the first of these, Hylton writes: Even though the theory of denoting concepts would enable Russell, in Principles , to deny that the present King of France has being, there is no sign that he realizes this fact. More important, perhaps, there is no sign there that he sees reason to deny being to the present King of France. In that book he is, notoriously, willing to attribute being to any putative object we can name. In section 427 he argues quite generally that: ‘ A is not’ must always be either false or meaningless…. This section is far from a grudging admission of the being of every putative

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Page 81 entity. On the contrary, outside the context of mathematics, Russell willingly asserts that every expression that seems to refer to something does in fact refer to a real entity, which has being even if it does not exist in space and time. (241, my emphasis) The difficulty confronting this view stems from the fact that the theory which enabled Russell to avoid the commitment to referents of empty descriptions—namely, the theory of denoting concepts, which is what Russell appealed to in EIP—was available to him long before this renunciation is supposed to have occurred. As Hylton is well aware, this theory was set forth as far back as PoM (finished, in fact, in December 1902). Why then did its impact have to wait until 1905 (albeit before OD)? Hylton responds to this by drawing on a difference in subject matter: he maintains that in EIP Russell extended to other putative entities a line of reasoning which in PoM was restricted to mathematical entities. On this reading, we might say, the change in EIP concerns the ‘boundary’ between mathematical and nonmathematical entities. The other, related, ontological change Hylton sees in EIP concerns the notions of existence and being (to be explained shortly). After PoM but before OD, he writes: Russell no longer accepts that there are objects, such as the putative present King of France, which are just like existent objects, except that they happen not to exist. Because there are no such objects, we no longer have to think of being and existence as two different ontological statuses which a given object may have. We can instead think of a single notion of existence which applies unequivocally to objects of two different sorts. (243) The change consists, then, in Russell no longer admitting (in EIP), as he did in PoM, entities of a kind which might have existed but (as a matter of fact) happened not to. The nature of the existence/being distinction thus changes, and becomes a distinction between the ontological status which one kind of object has, and that which another kind of object has. One kind of object is intrinsically non-spatio-temporal; if an object of this sort has any kind of reality it has being. Another sort of object is intrinsically spatio-temporal; if an object of this kind has any reality it exists. (243) The tenability of this account of the changes between PoM and EIP depends, like any other, inter alia , on what explanation it can offer on what brought them about—of Russell’s reasons for making them. Hylton suggests, though rather tentatively, that this role belongs to the impact of Meinong’s writings (243–44). Studying Meinong’s writings, Hylton

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Page 82 suggests, led Russell to see problems in his own former ontological position which he had not seen before. Chronologically at least, this makes good sense, because we know that Russell had indeed reviewed Meinong’s works at great length in the period between PoM and OD.4 Also (in a sense yet to be specified) Russell’s earlier view was at that time closer to Meinong’s than it was later to become. This then, in a nutshell, is how Hylton accommodates the evidence from EIP which contradicts the ‘crude’ view. The ontological change which freed Russell from the commitment to referents of empty phrases, and which had been mistakenly attributed to OD, had occurred in fact before (and thus, of course, independently of) it. Before turning to examine this view in detail, we might briefly indicate the general thrust of the view I argue for. While Hylton’s refined view and its cruder predecessor differ over when and why Russell withdrew his commitment to referents of empty phrases (that is, did this change come about only in OD or prior to, and thus independently of, it?), they share the underlying assumption that, in PoM at any rate, Russell was indeed committed to such entities. This assumption, I argue, is false. Russell was never committed to such an ontology, and when this correction is made not only does Russell’s ontological progression from PoM via EIP to OD transpire as quite different from what either of these views would have us believe, it also allows us to make better sense of the evidence considered by Hylton. But before we turn to set out this alternative let us first examine Hylton’s view. The grounds against it are independent of the broader alternative I propose, and its chief (though not only) failing is the want of textual evidence to support it. To begin with the point raised last, let us suppose for the sake of argument that the nature of change itself is indeed as Hylton contends. Yet still, what he proposes as Russell’s reasons for it strike me as quite unconvincing. He contends that Russell’s reading of Meinong’s writings, and his thinking through the problems of his expansive ontology, revealed to him that his own, similar, PoM ontology, suffered from serious difficulties. But he says precious little on what precisely these difficulties were. It is indeed true that in his tripartite review Russell not only reports Meinong’s views, but criticizes them and advances his own arguments as well; but the discussion is at least primarily (if not exclusively) epistemological, and Russell refrains from articulating his own positive views even when—as we know them from other writings—they are clearly relevant. The only citation Hylton provides in support of his view is a comment Russell makes on the phrase ‘the difference between a and b’ when a and b do not differ. But closer examination of the context in which it occurs reveals that Russell is at that point expressing not his own view on the matter (as one might conclude from Hylton’s pages) but rather something that might be said in support of the view he is arguing against5—and the matter is ultimately left unresolved.

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Page 83 This comment can hardly establish a causal link between the impact of Meinong and the (alleged) change in Russell’s ontology. For my part, I am inclined to be sceptical of claims about anyone having thought through the implications of a Russellian position more thoroughly than Russell himself (at least in this period). Such a claim could, in principle, be made good, but it would require far more substantial evidence than Hylton offers us. Turning to Hylton’s view on the nature of the ontological change, he discerns two strands. The first consists in Russell recognizing that a certain line of reasoning which he formerly applied only to the mathematical domain can be applied outside it as well (though he may well have recognized this in PoM). It is worth noting that the alleged oversight is supposed to have occurred in the very same work where the overlooked theory (that is, of denoting concepts) was first put forth. Now such a course strikes me—as I think it should anyone well versed in Russell’s writings—as so uncharacteristic of Russell that it renders such a hypothesis prima facie suspect; particularly when one bears in mind that Russell shows no sign that he is aware either of there being such a restriction in PoM, or of having lifted it in EIP. Indeed, in EIP Russell’s reasoning is applied indiscriminately to mathematical and nonmathematical entities. But I contest Hylton’s assumptions that things stood otherwise in PoM. Consider the following passage from PoM: Consider, for example, the propositions ‘chimeras are animals’ or ‘even primes other than 2 are numbers’. These propositions appear to be true, and it would seem that they are not concerned with the denoting concepts, but with what these concepts denote; yet that is impossible, for the concepts in question do not denote anything. (73) Russell’s practice, when discussing propositions in general, of grouping mathematical and nonmathematical instances together is prevalent throughout PoM. Nor is this feature accidental. It is an expression of one of the most fundamental tenets underlying this work as a whole (as well as OD itself). The notion of a proposition as Russell uses it, which is so central to almost everything relevant to our interests in PoM, is neutral, or applies indiscriminately, in precisely this way. To conclude, I find no evidence in EIP of an ontological change concerning the mathematical/nonmathematical boundary. Coming now to the other ontological change: Hylton maintains that Russell had changed his position in no longer admitting nonexistents which might have existed. Here again, there is a want of supporting textual evidence. The passage quoted above from EIP (about ‘the present King of France’ having meaning but not a denotation) must be what Hylton has in mind but, as before, this is no direct , nor in any sense, compelling,

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Page 84 evidence of such a change. There is not even a hint in Russell’s statement of anything so general, and Hylton makes no real case for his claim: he merely states it. But there is also another, deeper and more general consideration which tells against such a view. The change is couched in modal terms: the new view, we are told, leaves no room for entities which do not exist but might have existed. But Russell, on a number of occasions in this period (starting in PoM, and up until after OD) makes it plain that he rejects the logical (and hence, by implication, metaphysical) status of modal distinctions altogether. He argues, quite generally, that there is no sense in saying of anything that isn’t the case that it might have been the case (except as an implicit statement of our ignorance). In the course of his onslaught on Lotze’s view of space, in PoM, he writes: there seems to be no true proposition of which there is any sense in saying that it might have been false. One might as well say that redness might have been a taste and not a colour. What is true, is true; what is false, is false; and concerning fundamentals there is nothing more to be said. (454) Thus, talk of some entities being ‘intrinsically spatio-temporal’ (or, for that matter, intrinsically anything) is out of step with Russell’s broader outlook both in PoM and at least as late as 1905:6 since he rejects modal notions, he rejects the very distinction between intrinsic and nonintrinsic properties. In PoM Russell makes it plain that he regards existence as a subclass of beings (449), and nothing he says in the period leading up to OD, so far as I can discover, gives reason to believe this had changed. On what textual grounds Hylton maintains the contrary is not made clear.7 While I agree (as becomes clear below) that EIP marks a change in Russell’s position with regard to some special cases which, in PoM, he regarded as having being; there was no general change regarding existence and being of the kind Hylton proposes. In fact, the very talk of existence and being as ‘ontological statuses’ seems to me misguided. Being is an ontological status; but existence, on Russell’s view, is merely a property (more accurately, a relation) which only some beings have, and which does not differ, from a logical point of view, from other, more ordinary properties. To sum up, although I agree with Hylton about EIP marking some ontological change (and therefore one which is independent of OD), I remain unconvinced by his accounts both of its nature and of Russell’s reasons for making it. On neither of these points is his claim supported by substantial textual evidence, and it attributes to Russell a rather spectacular oversight. It should therefore be regarded as a hypothesis of last resort to be conceded only in the absence of any alternative explanation. A much simpler and more plausible explanation of the same data is, I think, available, as I try to show.

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Page 85 THE ONTOLOGICAL BACKDROP: RE-EXAMINING THE EVIDENCE I first lay out an alternative reading of Russell’s ontological course, and this leads to my positive view on the questions to which I found Hylton’s answers wanting. To anticipate: the ontological change in EIP was driven by a change in Russell’s view concerning the divide not between the mathematical and nonmathematical, nor that between existence and being, but rather between two kinds of expressions , namely, definite descriptions and proper names (more precisely, I would rather say, their epistemic corollaries). One cannot get a clear view of the ontological moves manifest in EIP, or in OD, unless one has a firm grip on Russell’s ontological view in PoM. Our task is to sort out, and reach a clear view on how four ontological ‘stations’ are related: a Meinongian position—I consciously use this label rather loosely, with little concern for fairness to Meinong—and three Russellian ‘stations’, namely, PoM, EIP and OD (the latter is discussed in the following section). I contest the assumption that the PoM ontology was Meinongian by reexamining the textual evidence on which it is based; and the first step on that course must be to clear the ground of what may be seen as a terminological point, but one which tends to breed philosophical confusion, namely, Russell’s use of the terms ‘being’ and ‘existence’ in the period from PoM to (and including) OD. These terms are used with specific technical senses which it is vital that we have a secure grip on. ‘Being’ (which Russell uses as synonymous with ‘subsistence’),8 the weakest among the three notions under consideration, holds of anything whatsoever, and denying being of anything is always false. This is no indication of an extravagant ontology, but plainly a tautology. If we bear in mind that it is propositions and their constituents, not sentences and words, that are at stake, it becomes clear that unless something occupies the subject position of a proposition of the form ‘ x does not have being’ (or, for that matter, any subject-predicate proposition) then there just is no proposition to begin with. If, on the other hand, something does occupy this position, then it must be an entity of some sort, that is, it must have being. Hence it follows that any denial of being, of anything whatsoever, must be either false (if it is meaningful, that is, expresses some proposition at all) or meaningless (fails to express a proposition, even if it resembles sentences which do). Such a notion is called for, in the first place, by anyone wishing to admit abstract entities (concepts, classes and propositions are paradigm cases). One needs a categorical distinction to set them apart from entities which occupy particular regions of space and time—that is, concrete ones; for this distinction Russell uses the labels ‘being’ and ‘existence’. Only entities which are not abstract are said to exist in this sense. To avoid confusion, I henceforth use ‘exist1’ when using the term in this sense. Russell (and Frege too) regarded existents1 as a subclass of beings: everything has being, but only some beings have the additional property

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Page 86 of existence1. It is vital to notice that existence1 is a property which can only be had by (or meaningfully be applied to) individuals; and since logic and mathematics are concerned with all beings regardless of whether they exist1, it is not a property that has any particular logical significance. But Russell uses ‘existence’ in another sense too, which I distinguish by using the subscript ‘exist2’. Exist2 is not applicable (that is, its application does not even make sense) to individuals, and requires a class, or class-concept, or propositional function, for its meaningful application. To say of a class that it exists is to say that it has at least one member (or of a class concept, that at least one entity falls under it, or of a propositional function, that at least one of its values is true). It is in this sense that we speak of existence theorems in mathematics, and this sense which has a special position in logic. Notice that saying of a class that it exists, that is, has members, leaves entirely open whether or not those members exist1. At the outset, then, these two meanings of ‘exist’ are, as Russell puts it in EIP, ‘as distinct as stocks in the flower-garden and stocks in the stock exchange’ (98). These distinctions are clearly observed throughout PoM,9 and there is nothing to suggest they were abandoned after PoM nor indeed, contrary to common wisdom, that they were affected by the advent of the theory of descriptions. Not only is ‘subsist’ (which Russell uses as a synonym of ‘being’) used in OD itself, but he goes on to use ‘being’, in the sense just specified, at least as late as The Problems of Philosophy (towards the end of Chapter 9) in 1912. But Quine, for one, is clearly oblivious to these distinctions when he writes: take impossible numbers: prime numbers divisible by 6. It must in some sense be false that there are such; and this must be false in the same sense in which it is true that there are prime numbers. In this sense are there chimeras? Are chimeras then as firm as the good prime numbers and firmer than the primes divisible by 6? (1967:292) The sense in which Russell would have maintained that there are prime numbers, but none divisible by 6 (since ‘prime number’ and ‘prime number divisible by 6’ are both class concepts) is, clearly, exist2. But this is precisely the sense in which he denies , even in PoM, that chimeras exist (though special complications apply to this case, discussed shortly). Similarly, when he claims that ‘in PoM classes occupied, however uneasily, the existential zone of being. To hold that classes, if there be any, must exist, while attributes at best subsist, does strike me as arbitrary; but such was Russell’s attitude’ (297). But classes (like other mathematical entities) were, as just mentioned, Russell’s chief reason for admitting a distinct notion of subsistence—he never held them to exist1. (On the other hand, if we take Quine to mean existence2, then Russell would have said that not all classes do.)

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Page 87 Indeed, Russell’s ontology can be made to appear very arbitrary when these distinctions are confused. Hylton, too, is not as meticulous as might be expected when dealing with these distinctions. He speaks about a denial of the being of the present King of France, something which (as we have already seen) is ruled out on Russell’s view. The closest one can come to this is to deny that the phrase (or the denoting concept it expresses) denotes. But this, though equivalent to a denial of being, is not the same proposition. The relevant notion in such cases is existence2. Russell puts the matter very crisply in PoM when he writes (where ‘ a ’ stands for a class-concept): ‘The denoting concept associated with a will not denote anything when and only when “ x is an a ” is false for all values of x’ (§73). The statement should be understood as encompassing definite descriptions, which are a species of denoting phrases, and it is existence2, not being, which is therefore relevant in this case. The same quotation may also—to anticipate a topic we come to shortly—serve to illustrate Russell’s recognition, in PoM, of meaningful yet empty denoting phrases.10 Important though these distinctions are, carelessness with regard to them does not seem to be the chief reason leading to the perception of the PoM ontology as Meinongian. This role belongs to a small number of well-known passages from this work. These statements—two of which are alluded to in our earlier quotations from Hylton and from Quine—are invariably appealed to as evidence. Let us begin by listing them: a. ‘ A is not’ is always false. For if A were nothing, it could not be said not to be (449). b. Every term has being, i.e. is in some sense. A man, a moment, a number, a class, a relation, a chimera, or anything that can be mentioned is sure to be a term; and to deny that such and such is a term must always be false (47). c. Points and instants, bits of matter, particular states of mind and particular existents generally are things in the above sense, and so are many terms which do not exist, for example, the points in a nonEuclidean space and the pseudo-existents of a novel (45). d. Numbers, the Homeric gods, relations, chimeras, and four-dimensional spaces all have being, for if they were not entities of a kind, we could make no propositions about them (449). e. Every word occurring in a sentence must have some meaning: a perfectly meaningless sound could not be employed in the more or less fixed manner in which language employs words (p. 42). As we have already seen, Hylton takes (a) as evidence that Russell ‘willingly asserts that every expression that seems to refer to something does in fact refer to a real entity, which has being even if it does not exist in space and time’ (a reading which is by no means peculiar to him). But what does

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Page 88 Hylton mean by ‘expression that seems to refer to something’ occurring in his statement? I take him to mean what in current philosophical discourse are called ‘singular terms’, a label which bunches together definite descriptions and proper names—as Hylton does throughout his discussion. But I think there are strong reasons against reading Russell in this way, because in PoM, at any rate, Russell recognized no such category. Throughout that work he regards proper names and denoting phrases (of which definite descriptions are a special case), as logically distinct categories. The proposed reading amalgamates kinds of expressions which Russell was careful to keep apart, and it thus seems to me highly implausible.11 Instead, I suggest that we read this statement as asserting (more precisely, implying, since it is not really concerned with linguistic entities) that ‘ A is not’ (understood as a denial of being) must be false not for any referring expression ‘ A’, but rather, for any proper name ‘ A’. On Russell’s use of ‘proper name’ such an assertion is very nearly a tautology, because (as we have already seen when discussing the Russellian notion of being) if it was not false, then ‘ A’ would not be a name, but an empty sound. This is indeed the line which Russell proceeds to take in the very passage from which this dictum is taken. Speaking of ‘ A is not’ being either false or meaningless he continues: ‘For if A were nothing, it could not be said not to be; “ A is not” implies that there is a term A whose being is denied, and hence that A is. Thus unless “ A is not” be an empty sound, it must be false—whatever A may be, it certainly is’ (449).12 On this reading, ‘the present King of France is not’ is not an instance of ‘ A is not’ in the sense Russell is concerned with, and it is not of such sentences that he maintains they must be either false or meaningless. Had that been his view, he would not have offered an interpretation (and a very different one) of empty denoting phrases, like the one we have just seen from PoM (§73). This statement makes it evident that he clearly recognized that a phrase of this kind does not become nonsense merely because nothing answers to it. Its intelligibility flows from its consisting of meaningful parts (that is, words) combined in accordance with some general syntactic rules. Indeed, each of those parts will either stand for something or be an empty noise, but this is quite obviously not the case with the complex phrase itself. (We come across further evidence for this understanding of Russell’s position when we turn to his discussion of phrases such as ‘all chimaeras’ and the like below.)13 To sum up, whatever the merits of other textual evidence to the same effect, Russell’s statement that ‘ A is not’ must be either false or meaningless is no ground for thinking that he admitted entities corresponding to empty denoting phrases, and thus for viewing his PoM ontology as ‘Meinongian’. The key to most of what I have to say on this topic is the observation that from the very start Russell was very attentive to the logical (and epistemic) difference between proper names and definite descriptions. He never amalgamated them or assumed they would be given the same analysis.

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Page 89 The next three items on our list (b, c and d) are customarily cited as evidence for the Meinongian nature of PoM ontology. But we ought to begin by examining the context of each. The first occurs when Russell explains that he uses the word ‘entity’ as synonymous with ‘term’. The second occurs when he is explaining his use of ‘thing’ (as opposed to ‘concept’). Lastly, (d) occurs in the same context as, and immediately following (a), where Russell explains the notion of being (as opposed to existence1). Do these passages constitute substantial evidence in favour of the ‘appearance’ view? None of them occurs in the context of an ontological discussion proper. Russell’s point in each of them is only to explain his use of certain bits of technical terminology. The particular items featuring in each serve merely as illustrations: any other set of similar examples would have served just as well. The point being made in each is exclusively negative, namely, that the range of entities logic (and hence mathematics) considers is not restricted to existents, that is, to spatio-temporal objects. Next, we need to remember why Russell admits beings which do not exist in the first place. It is in order to allow mathematical and logical entities into his ontology. As he explains in the last of the three passages, numbers do not exist, and yet they are not mental entities, thus we must admit entities which have being but do not exist. If admitting nonexistent entities were a valid ground for claiming that Russell’s PoM ontology is Meinongian, then the same holds of his ontology in OD. In that essay he uses the term ‘being’ (or its synonym ‘subsist’) in precisely the sense it had in PoM. Clearly, what really matters for advocates of the view that PoM is Meinongian is which (kinds of) entities are admitted in this category, not the mere fact that any are admitted at all. Mathematical entities are not the problem (if they were, the same conclusion would follow for Quine’s ontology too). Admitting abstract entities is admitting nonexistent entities, and this cannot be what the claim of those who assimilate Russell’s PoM ontology with Meinong’s rests on. Bearing this in mind, let us distinguish among the nonexistent items on these lists between those which are broadly speaking, logico-mathematical entities (points, spaces, numbers, relations), and those we may call fictional entities. Since with regard to the former Russell was no less Meinongian in (and after) OD than he was before, our concern must focus on the non-mathematical cases (chimeras, Homeric gods, pseudo-existents of a novel). Indeed, there is no room for doubt that in PoM Russell admits such entities as beings, subsistent things;14 but why did he? I propose that it was not on account of the intelligibility of sentences containing phrases like ‘the Homeric gods’ or ‘the pseudo-existents of a novel’—this line of reasoning had been clearly disposed of by the theory of denoting—but rather on account of sentences containing proper names of individual Homeric gods or individual fictional characters. At this point our earlier discussion of ‘ A is not’ being always false (where ‘ A’ is understood as being confined to proper names) comes into play.

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Page 90 Given that Russell’s view, as we saw earlier, was that denials of being are either false or meaningless, sentences containing fictional proper names would have confronted him with the following dilemma: he could deny that such apparent names are names at all, dismiss them as empty noises and deny that uttering such a sentence expresses a proposition.15 Such a conclusion is indeed hard to swallow, and I think it is not hard to find reasons why Russell should have sought to avoid it if he only could. Not only can such sentences be palpably meaningful, but at least in some cases we are able to distinguish among them some which are (in some sense) true. Alternatively—and this, crucially, was the only alternative open to him—he could admit they had being, the kind of nonexistent being had by mathematical entities. Within the conceptual resources available to him in PoM there was no third option —though such an option did emerge, as we shall see, before OD. To sum up: I suggest that it was on account of their proper names , not of any descriptive phrases that Russell admitted such beings, and that his doing so flowed from the principle considered earlier regarding ‘ A is not’—a principle he was explicitly committed to (and, to the best of my knowledge, never abandoned). In this respect Russell’s PoM ontology was indeed closer to Meinong’s than it was later to become, but ultimately the similarity is, I think, superficial, and the differences deep. It is indeed true that there is a class of highly controversial entities which both Russell at the time of writing PoM and Meinong admit; but their respective grounds of doing so are entirely different. Even at his most ontologically expansive moment, Russell was driven by considerations which are sensitive to the difference between proper names and definite descriptions. Meinong’s route, by contrast, was not. The difference is crucial not so much because Meinong’s route leads to admitting more kinds of entities than does Russell’s but, far more importantly, because it leads in turn to admitting nonsubsistent and contradictory entities—something Russell never admitted. Russell avoided this route not just for the sake of parsimony, but rather because it flowed from a reasoned view which avoided the assumption that every meaningful description must have a referent in some sense (this is evident from Russell’s categorical phrasing in EIP). The theory of denoting concepts made it unnecessary for him to set foot on this slippery slope.16 The case made so far for disentangling Russell’s PoM ontology from Meinong’s, and the allied diagnosis of Russell’s underlying reasons for admitting fictional beings, may well be regarded, on the evidence considered thus far, as a mere hypothesis resting on somewhat indirect evidence. But this is no longer the case once we move on to his position in EIP. This discussion, like an experiment designed to test this hypothesis, demonstrates what happens to the commitment to fictional entities once their tie with proper names is removed. As soon as a way of interpreting such names as being other than ‘real’ proper names, the commitment vanishes.

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Page 91 The crucial passage in EIP occurs after Russell explains that ‘there are no Centaurs’ is to be understood as meaning ‘ x is a Centaur is false whatever value we give x’—which rehearses the line familiar from PoM—at which point Russell proceeds: The case of nectar and ambrosia is more difficult, since these seem to be individuals, not classes. But here we must presuppose definitions of nectar and ambrosia: they are substances having such and such properties, which, as a matter of fact, no substances do have. We have thus merely a defining concept for each, without any entity to which the concept applies. In this case the concept is an entity, but it does not denote anything. To take a simpler case: ‘The present King of England’ is a complex concept denoting an individual; ‘The present King of France’ is a similar complex concept denoting nothing. The phrase intends to point out an individual, but fails to do so: it does not point out an unreal individual, but no individual at all. The same explanation applies to mythical personages, Apollo, Priam, etc. These words have a meaning, which can be found by looking them up in a classical dictionary; but they have not a denotation : there is no entity, real or imaginary, which they point out. (100) Russell here discovers the possibility of taking fictional names as only apparent names and can offer an alternative understanding of them as descriptions in disguise. This is enough for the associated ontological commitment to vanish. Since Russell already has a solution for definite descriptions which frees him from the commitment to corresponding denotations, all he needs do is slot those descriptions into this theoretical machine.17 It is vital to note that EIP involves no change of ontological principle, but rather the reinterpretation of a certain class of names. The principle that ‘ A is not’ must be either false or meaningless—which I suggested drove Russell to making the problematic commitment in the first place—remains intact. What does change is the assumption that fictional names are to count as legitimate values of the ‘ A’ in that statement. Having found an alternative interpretation of such names, the earlier commitment to corresponding referents disappears. It is in this sense that the ontological change in EIP, modest though it was, is an effect of a shift involving the proper names/definite descriptions boundary, rather than on either of those boundaries (mathematical/non-mathematical or existence and being) proposed by Hylton. In OD Russell was to take this line further, by considering the possibility of nonfictional names being, in some cases, disguised descriptions—depending on the speaker’s epistemic relation to the name bearer. It is vital to observe too, that this elimination is independent of the theory of descriptions. Indeed, the theory of descriptions eventually took over the role which the former theory of denoting had played with regard to

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Page 92 fictional names in EIP; but the essential move does not depend on which theory of descriptions takes over so long as it is one which avoids the ontological commitment. (On Meinong’s view, by contrast, this reinterpretation would not have such consequences, since he does not have a theory of descriptions— here, in a generalized sense—which distinguishes them from proper names.) On this point, as well as on a number of other matters we soon come to, OD is somewhat misleading. Because of the marginal place allotted to the former theory of denoting in its discussion, a reader relying on OD alone is likely to form the impression that these two moves (that is, the new theory of descriptions and the reinterpretation of some names as descriptions in disguise) are so related that the one could not be made without the other. But not only can the two moves be separated—as a way of saying that they are logically independent of each other—they were , as a matter of brute historical fact, separate. As far as the commitment to referents of fictional names is concerned, the change from the old theory to the new was of no consequence— both avoided it. Appreciating this is, I think, vital for a true understanding of OD. Returning now to the items on the three lists, it remains for us to discuss chimeras (occurring in (b) and in (d)). They cannot be accounted for in the same manner as fictional name-bearers because ‘chimera’ is a class concept, not a name, and it is unlikely that Russell had names of particular chimeras in mind, as he would have had of Homeric gods or of characters in works of fiction. This problem invites us to turn to Russell’s discussion of this very same example in §73 of PoM, which was mentioned earlier. The section heading (in the table of contents) is ‘There are null class concepts, but there is no null class’. The section itself comes closer to being an explicit ontological discussion than do any of the passages (b) to (d) which were considered earlier. Russell says, for example, ‘It is necessary to notice that a concept may denote although it does not denote anything’ (74). The section is an attempt to find an acceptable interpretation of ‘chimeras are animals’ which is only problematic precisely on the assumption that there are no chimeras. And indeed, the section as a whole leaves one in no doubt that Russell does not take chimeras to have any sort of ontological status whatsoever (though the concept ‘chimera’ and the denoting concepts which derive from it, do). I therefore propose that Russell’s listing of chimeras in two of the lists is a slip, because it is inconsistent with what he himself clearly implies in a much more focused and self-conscious discussion of this very example elsewhere.18 All this is consistent with the interpretation according to which Russell admitted nonexistent beings (other than mathematical objects) only because there are (apparently intelligible) names for them, and not on account of the intelligibility of any descriptions, and that therefore the assimilation of his ontology with Meinong’s is mistaken.

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Page 93 I come now to (e), the fifth and last item on our list: ‘Every word has some meaning.’ This statement seems to have played a role in persuading Quine and others that Russell’s PoM ontology was unrestrained, and it is the source of Hylton’s talk of Russell ‘willingly asserting that every expression that seems to refer to something does in fact refer to a real entity’, discussed earlier. It is specifically echoed in an earlier quoted passage from Quine: ‘In PoM, 1903 Russell’s ontology was unrestrained. Every word referred to something.’ But when compared with Russell’s original words, we notice a difference. Russell wrote: ‘every word occurring in a sentence must have some meaning: a perfectly meaningless sound could not be employed in the more or less fixed manner in which language employs words’ (42). Note that Russell speaks here not (as Quine does) of every word having a reference, but rather of its having a meaning. Bearing in mind that his PoM theory allows some expressions that have the latter but not the former, the difference is significant. But what did Russell really mean by this statement, and does it indeed imply the ‘unrestrained’ ontology it seems to? Does the principle that every word must have some meaning conflict with, and thus likely to get swept away by, the theory of descriptions? To answer these questions we need to consider a number of passages from elsewhere in PoM which have a bearing on this matter. In §72 Russell considers the question (which incidentally concerns denoting phrases): ‘If u is a class concept, is the concept “all u’s” analyzable into all and u or is it a new concept, defined by a certain relation to u and no more complex than u itself?’ He concludes that ‘all u’s’ is not so analysable and that ‘language in this case as in some others is a misleading guide. The same remark will apply to every, any, some, a and the’ (72–73). From this it follows that it is not the case that each of these words is considered to have a meaning of its own, as the principle seems to demand. Only the whole phrase they form part of is held to have meaning. A similar conclusion emerges from Russell’s discussion of the relation of a member to a class of which it is a member (77–78): language expresses this relation with two words (‘is a’ as in ‘Socrates is a man’), but logic regards this as a simple and indefinable relation (indicated by the Greek epsilon). So this case too shows that in such sentences not every word has a meaning—surely not in the sense of standing for something. These instances prompt us to take a closer look at the sentence immediately following Russell’s statement of the principle which Quine alludes to. It reads: ‘The correctness of our philosophical analysis of a proposition may therefore be usefully checked by the exercise of assigning the meaning of each word in the sentence expressing the proposition’ (42). If we give the locution ‘correctness of our philosophical analysis’ its due, the alleged conflict with the theory of descriptions disappears. The principle need not be taken to imply that in language as we find it every word has a meaning. What is meant, rather, is that this should hold true of the final stage of analysis (that is, after ‘is-a’ will have been replaced with an epsilon, ‘is’, in

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Page 94 other contexts, with ‘has being’, and so on). It is the output of the analytic process, not its input, that needs to stand this test (thus ‘simple symbol’ might have done better than ‘word’). True, OD provides a more striking case than others of a gap between pre- and post-analytic forms of sentences. (Because of a strong pre-theoretic inclination to think of definite descriptions as akin to proper names.) But ultimately, not only does the theory, when correctly understood, not conflict with this principle, it provides a remarkable vindication of it. The analytic form this theory provides for sentences containing definite descriptions is one where each word (or rather symbol) does have a meaning (and indeed, a reference). On this score too, then, the principle does not, to conclude, lend support to the view that OD embodies a fundamental change in Russell’s ontological view. This concludes our survey of the textual evidence which has been taken to support the view that in PoM Russell’s ontology was Meinongian. In the course of it we have also offered an account of the nature of, and reasons for, Russell’s dropping, in EIP, his earlier ontological commitment to fictional characters. This brings us, at long last, to a position from which we are able to address the question of the ontological impact of OD itself. ‘ON DENOTING’S MODEST ONTOLOGICAL IMPACT Should we maintain then, in the light of the discussion above, that OD had no ontological impact? Not quite. One more category of items is yet to be considered, namely denoting concepts (of which what in OD Russell calls ‘denoting complexes’ are, as I understand it, a special case). Since the theory in OD superseded the former theory of denoting, and Russell makes no further mention of denoting concepts in subsequent works, one is inclined to think that these entities had been made redundant. Since the reason for positing them was merely to serve the theory of denoting, they must have become redundant as soon as that theory is replaced by the theory of descriptions. At the very least, one might think, this meagre ontological economy of eliminating denoting concepts may be credited to OD. This is by and large correct, but even here matters are not as straightforward as one might suppose. The analysis proposed in OD makes explicit use of the variable, and this, in view of the reading just proposed of ‘every word must have some meaning’ implies that the variable must have some meaning, since it occurs in the ultimate analytic form. What then is it? There seems little doubt that in PoM Russell conceived of the variable as standing for a denoting concept, namely, that expressed by ‘anything’. There is an interesting exchange with G. E. Moore (arising from his response to OD and conducted shortly after its publication) which points in the same direction (though adding an important epistemic twist). Moore asks Russell

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Page 95 whether, in view of the principle that we must be acquainted with each of the constituents of any proposition we understand, ‘Have we, then, immediate acquaintance with the variable? And what sort of entity is it?’ Russell’s answer is revealing: he wavers between two rather awkward replies to Moore’s question: that we have acquaintance with something which isn’t an entity, and that it is an indeterminate entity. This leads him to say: ‘I only profess to reduce the problem of denoting to the problem of the variable. This latter is horribly difficult, and there seem equally strong objections to all the views I have been able to think of’ (cited in Hylton: 256). Such an admission of there being a limitation on OD’s achievement takes another form in OD itself. In the very first sentence of his statement of the theory (after the three opening paragraphs) Russell says: ‘I take the notion of the variable as fundamental ; I use “ C( x)” to mean a proposition [more exactly, propositional function] in which x is a constituent, where x, the variable, is essentially and wholly undetermined’ (42, my emphasis). Admitting the variable as a fundamental notion is surely not a solution Russell could have been happy with. One of, and arguably the cardinal, driving force behind the whole discussion of denoting in PoM was to provide an account of this notion. So admitting it as a fundamental (that is, indefinable) notion is, in a sense, an admission of failure on Russell’s part.19 And yet, reducing all kinds of denoting concepts (of which there are six) to the single case of the variable is some achievement too. The economy at stake is not so much ontological, as it is a matter of reducing the number of fundamental logical constants. If before OD Russell’s list included the relation of denoting, as well as six kinds of denoting concepts (though probably not as logical constants) and five different kinds of combinations as their referents,20 all this machinery now becomes redundant. It ends up being ‘packed together’, so to speak, into the single indefinable notion of the variable.21 All sentences containing other denoting phrases have become definable by its means. I said earlier that OD is in some respects a misleading text. One instance of this which should, I think, be clear by now is the impression it gives that while Russell had indeed formerly endorsed a different theory of denoting—a most cursory mention of it is made in a footnote—it is not particularly pertinent to the discussion or to deciding the pros or cons of the new theory being proposed. As things are set out in OD, the contest seems to be between the theory of descriptions and Meinong’s theory on the one hand and Frege’s on the other. One is invited to perceive the theory of descriptions as the only viable way of handling the Meinongian difficulties (chief among them, the infringement of the law of contradiction), without getting into the ‘inextricable tangle’ as well as ‘plainly artificial’ devices of Frege’s solution. Another closely related, misleading impression encouraged by the text of OD is that Russell’s chief case for the theory hangs on its ability to solve the three puzzles he introduces. When introducing them, he writes:

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Page 96 A logical theory may be tested by its capacity for dealing with puzzles, and it is a wholesome plan, when thinking about logic, to stock the mind with as many puzzles as possible, since these serve much the same purpose as is served by experiments in physical sciences. I shall therefore state three puzzles which a theory as to denoting ought to be able to solve; and I shall show later that my theory solves them . (47, my emphasis) This statement, as well as the amount of space devoted to the discussion of the puzzles, creates an impression that Russell thinks, and seems to invite the reader to think, that solving the puzzles is a distinctive feature of the new theory he is advocating. Indeed, such a view is implicit in most presentations of OD on the traditional view. In the light of the text of OD alone, one would not be unreasonable to believe that Russell holds that none of the alternative theories can do the job. But Russell never quite says that, nor does he strictly imply it either. All he says is that the puzzles are ones ‘a theory as to denoting ought to solve’. In fact, this apparently tacit assumption is not at all true, and Russell would have been well aware of this, as he was himself the author of one of the alternative theories, and his abandoning it, as we know today, had nothing to do with any inadequacy in resolving these puzzles. Bunching together the PoM theory of denoting and Frege’s theory of sense and reference for this purpose—this, at any rate, was how things appeared to Russell both in PoM and in OD itself—we see that this theory too could solve the puzzles. A puzzle presenting essentially the same problem as the one about King George IV wanting to know whether Scott is the author of Waverley was employed in PoM to show the advantages of the theory of denoting concepts (64). The resolution of the other two rests on the appeal to the distinction between primary and secondary occurrences. This distinction cannot be found in PoM itself, but can, and in fact originated in, subsequent work on the theory of denoting concepts carried out before he struck upon the new theory, posthumously published under the title ‘On Fundamentals’ (1905c: 374ff.). The very terminology of ‘occurrences’ is one which has its origin in, and whose literal meaning is better suited to, the old theory where different kinds of occurrences a denoting complex might have in a proposition led Russell to devise a set of subtle and rather intricate distinctions. Of course, these solutions differ from those proposed in OD, and with hindsight the latter may well be regarded as superior; but we have absolutely no reason to think that dissatisfaction on this score played any role at all in leading Russell to abandon his former theory and propose a new one. It must be admitted, though, that discussing the puzzles is an effective expository device of the new theory. CONCLUSION: A THEORY WITHOUT A CAUSE? I will now try and bring together some of the strands of our discussion so far. I have argued that the traditional view according to which OD’s

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Page 97 chief achievement was the abolition of a former commitment to referents of empty denoting phrases is false, because Russell was never thus committed in the first place. I have further argued that another feature of Russell’s early ontology, namely, a commitment to referents of fictional names, resembles Meinong’s ontology only superficially. Russell’s reasons were quite different from Meinong’s; and because his reasons were different, discovering the possibility of interpreting such names as disguised descriptions led to shedding that commitment in his case, but would have no such effect in Meinong’s. Since this development occurred, prior to and independently of the theory of OD, the credit even for this later ontological change does not belong to OD either. This too, is an issue where confining one’s gaze to OD alone is likely to mislead. We have just noted further, and much more briefly, that most if not all the achievements (such as puzzle solving) which may be thought of as reasons for preferring the OD theory to its competitors—at least as far as the impression OD creates in the mind of an uninitiated reader—are not distinctive of the OD theory. Similar achievements may be attributed to at least one of the competing theories which Russell seems to be trying to persuade us is inferior to his new invention. Why then did Russell propose a new theory? Why should he have bothered? What was the problem he was trying to solve? This is a real (exegetical) puzzle, and recognizing its force strikes me as significant progress in understanding OD, even if, at first at least, it only replaces an erroneous presumption of knowledge with an admission of ignorance. Offering a solution to this puzzle falls outside the scope of the present paper; but I will venture a brief indication of where I think the solution lies. We know for sure that the theory of descriptions struck Russell in the course of preparatory work for what was eventually to become Principia Mathematica , and that the problem he was grappling with in those manuscript pages where the new solution emerged had initially appeared as a problem of notation. Subscribing, as he then was, to the theory of denoting concepts, he was trying to devise a coherent notational convention—his starting point was, in fact, indicated in the chapter on denoting in PoM—to mark the distinction between when one is talking about the denotation of the denoting concept, and when about the denoting concept (or meaning) itself. He soon recognized that he was confronting an insoluble problem, and that its root lay not in the want of notational ingenuity, but rather in the very conceptual structure the notation was trying to capture. In OD Russell speaks of these as ‘rather curious difficulties, which seem in themselves to prove that the theory that leads to such difficulties must be wrong’ (48). At this point OD tends to mislead us yet again. Without saying so explicitly, it creates the impression that the theory that leads to those curious difficulties is Frege’s. While this may be true too, anyone who has made a serious attempt to study the passage in question will have little doubt that it is first and foremost Russell’s own former theory of denoting that is under discussion and which breeds the ‘inextricable tangle’. Its discussion,

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Page 98 in OD, concludes with the words ‘Thus the point of view in question must be abandoned’ (51). OD ends up misleading further—though in this instance in a rather indirect manner—because a substantial chunk of it, where these difficulties are explained (best known by its least pertinent feature, the use of ‘the first line of Gray’s Elegy’ (48–9) as an example), is so difficult to follow that the great majority of its readers and expositors in its 100 years’ history have found little they could say about it. This silence has created an impression that the gist of OD can be got without attending to this obscure chunk of text. I have tried to argue that while this may be true to some extent, the resultant picture is fatally incomplete. It provides no plausible explanation, consistent with the known facts, to why Russell was in need of a new theory of denoting at that point; of what precisely was the difficulty he was grappling with. To try to fill in the gap with problems any theory of denoting confronts, and to which Russell already had solutions at the outset, is to tell a plausible-sounding story, but not the true one. NOTES 1. W. V. O. Quine ‘Russell’s Ontological Development’. I choose Quine not because his view on this matter is singular, but rather because it is so characteristic of writers of his generation. (Another example is A. J. Ayer in his Russell: 53–55.) Quine’s merit is his putting this characteristic view particularly crisply, and also because, coming from his pen, it may have enjoyed more influence. 2. In the passage just quoted Russell confesses to having admitted objects, such as the golden mountain, which subsist but do not exist (i.e., purported referents of what I speak of as ‘empty descriptions’); but Quine implies he had endorsed impossible objects like the round square (referents of contradictory descriptions). Surely the difference is significant. While one may be justified in applying the label ‘Meinongian’ to both, I reserve it, as well as my attention, to the weaker thesis. I am aware of no textual evidence suggesting that Russell ever endorsed the stronger view Quine attributes to him. 3. In a nutshell: this theory maintains that a proposition—a complex entity which is neither linguistic nor mental—expressed by a sentence whose subject is, e.g., ‘the present Queen of England’, has in its subject position a denoting concept/complex (as opposed to the monarch herself, when the subject is ‘Elizabeth II’). The constituents of this complex are the concepts Queen , present, and the object England. Some such complexes have a denotation (which is what using the corresponding phrase results in speaking about); others (like ‘the present Queen of France’) do not. The same holds, mutatis mutandis, of phrases beginning with the words ‘all’, ‘a’, ‘some’, ‘any’, ‘every’. 4. ‘Meinong’s Theory of Complexes and Assumptions’ (in three parts, originally in Mind of April, July, and October 1904). Reprinted in Lackey (1973) 21–76. Another, much shorter review of a volume Untersuchungen zur Gegenstandstheorie und Psychologie consisting of essays by Meinong and his pupils, was published in the same issue of Mind as was OD (see Lackey (1973) 77–93). 5. See Russell (1904:62). The question at stake in this discussion is whether every judgement and presentation needs to have an object. This particular comment (which is not even put forward as conclusive) is thought to support

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Page 99 the view which denies this, which is contrary to Russell’s stand on the question in this paper. As we know from other writings of Russell’s from both before and after the time of this review, he would have argued that the object (of such a presentation or judgement) was the denoting concept the difference between a and b, but that it has no denotation. 6. On this point we have the evidence of Russell’s most elaborate discussion of modal terms ‘Necessity and Possibility’ (1905e) delivered in the same month OD was published. 7. What might have led Hylton to his interpretation is the fact that Russell’s discussion (in EIP) of the distinction between two senses of ‘exist’ (explained shortly) does not mention the notion of being. This, however, is explained by the fact that existence, but not being, is relevant to his reply to MacColl. 8. See note on p. 78 of Russell’s review of ‘Gegenstandstheorie und Psychologie’ (1905b), and his footnote on p. 48 of OD. 9. Exist1 and being are explicitly contrasted on p. 71 and in greater detail on pp. 449–50. Existence2 is discussed on pp. 21 and 93. The tripartite distinction is laid out again very clearly in EIP in a manner which gives no reason to suppose any change in Russell’s view. 10. It might be noted that this is a general statement, by no means confined to mathematical entities, and it expresses the very same position which we found in the earlier quotation from EIP, which Hylton regarded as marking a change in Russell’s position. 11. In the Russellian context, saying that they are logically distinct is tantamount to saying that the propositions expressed by the sentences containing each expression (let us suppose in subject position) differ in kind . While in one an ‘ordinary’ entity (be it an object or a concept) occupies the subject position and is what the proposition is about; in the other we find a ‘special’ kind of entity (with the peculiar logical property of denoting), which is never what that proposition is about. 12. I think it is consistent with Russell’s position to take ‘proper name’ here as including concept names too, so long as they are genuinely simple, i.e., indefinable, as some concepts are bound to be. 13. Thus understood, Russell’s line here is an exact parallel of the one he mentions in the later My Philosophical Development (1959). The crucial difference is that there it was explicitly applied to definite descriptions. In his 1944 ‘My Mental Development’ (written for the volume devoted to him in the ‘Library of Living Philosophers’, edited by Schilpp) Russell described the background to OD in a way which, though ultimately unsatisfactory, is closer to the truth than that offered in My Philosophical Development. In the former he attributes to Meinong an argument of the above form applied to descriptive phrases, saying that it did not satisfy him; while in the later account he attributes this line of argument to his former self. If I am right, then neither of these is correct. In PoM he did apply an analogous argument, but only to proper names . 14. This receives further corroboration from a remark he makes about Waverley’s adventures and those told in 1,001 Nights ( PoM: §444). Despite its inconclusiveness, it would have made no sense for him to make it unless he held that they had being. 15. Such a line was indeed explicitly taken by the early Frege in Dialogue with Pünjer on Existence , in Hermes, Kambartel and Kaulbach (eds), Posthumous Writings, (Oxford: Blackwell, 1979): 53–67. 16. To spell out this link: Since definite descriptions are by definition complex expressions containing concept-words, it is always possible to invent a contradictory phrase, where the absence of a referent is no mere contingency. Taking a phrase’s intelligibility as implying a referent thus leads to

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Page 100 admitting contradictory entities. Proper names, by contrast, are simple symbols bereft of any conceptual content (at least on Russell’s understanding), thus they give no scope for a contradiction to arise. 17. It may be worth noting here that such ‘slotting’ is no mere logical trick. Its force and appeal derive from the plausibility of the epistemic corollary that when using such a name we always have before our minds some description or other, and that when this is not the case, we fail to say or understand anything when using such names. 18. Bearing in mind that the point being made by each of these lists is negative, i.e., to remove a natural assumption that only existents are under consideration, adds to the plausibility of this being the case. 19. Russell’s conception of the relation between the account of the variable and denoting can be seen in Ch. 8 of PoM. Denoting seems to have been intended to be one of the notions used in the account of the variable. 20. The difference arises from the fact that, unlike the referents of the other kinds of denoting concepts, those of ‘the’ phrases are not combinations, but individuals. 21. Strange though this may seem to us today, until he struck upon the theory of descriptions Russell regarded the account of ‘a’, ‘all’, ‘every’, etc., in terms of denoting concepts as more fundamental than their (nowadays standard) account in terms of quantifiers and variables—even though he was well aware of the latter. REFERENCES Ayer, A. J. (1972) Russell, London: Fontana/Collins (Fontana Modern Masters). Hylton, P. (1990) Russell, Idealism, and the Emergence of Analytical Philosophy , Oxford: Clarendon Press. Lackey, D., ed. (1973) Essays in Analysis , London: Allen and Unwin. Marsh, R. C., ed. (1956) Logic and Knowledge , London: Allen and Unwin. Pears, D. F., ed. (1972) Bertrand Russell: A Collection of Critical Essays, Garden City, NY: Doubleday Anchor. Quine, W. V. O. (1966) ‘Russell’s Ontological Development’, in D. F. Pears (1972): 290–344 (originally published 1967). Russell, B. (1903) The Principles of Mathematics, 2nd edn, London: Allen and Unwin, 1937. ——. (1904) ‘Meinong’s Theory of Complexes and Assumptions’, in D. Lackey (1973): 21–76. ——. (1905a) ‘The Existential Import of Propositions’, in D. Lackey (1973): 98–102. ——. (1905b) ‘Review of: A. Meinong, Untersuchungen zur Gegenstandstheorie und Psychologie in D. Lackey (1973): 77–88. ——. (1905c) ‘On Fundamentals’, in A. Urquhart (1994): 360–413. ——. (1905d) ‘On Denoting’, reprinted in R. C. Marsh (1956): 41–56. (Also in D. Lackey (1973): 103– 19.) ——. (1905e) ‘Necessity and Possibility’ in A. Urquhart (1994): 508–20. ——. (1912) The Problems of Philosophy , Oxford: Oxford University Press, 1974. ——. (1944) ‘My Mental Development’ in Schilpp, P.A., ed. (1944): 1–20. ——. (1959) My Philosophical Development, London: Allen and Unwin (Unwin Books edn). Schilpp, P.A. (1944) The Philosophy of Bertrand Russell, Evanston IL: Northwestern University Press. Urquhart A., ed. (1994) The Collected Papers of Bertrand Russell, vol. 4, Foundations of Logic, 1903–05 , London: Routledge.

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Page 101 6 Explaining G. F. Stout’s Reaction to Russell’s ‘On Denoting’ Omar W. Nasim George Frederick Stout was not only one of Russell’s early teachers, but also may have, along with James Ward, directed the young Russell’s attention to thinkers like Meinong and Brentano. As early as 1896, Stout himself was engaging this Austrian realist tradition. He made some significant contributions to it, but most importantly he thereby also helped to introduce many British philosophers to these Austrian developments. As a matter of fact, as I try to show in what follows, Stout was in many ways an English representative of this tradition—with a twist of his own, of course. It must be recalled, though, that Stout was by this time already well recognized in the field of philosophical psychology. Stout revolted against some of the long-standing English traditions in philosophical psychology, such as associationism and psychological atomism. He also rejected the related German traditions of physiological-psychology, and the mechanization of the mind by reduction to natural physical laws. Consequently, he advanced an interesting theory of conation and striving, with an emphasis, like Ward, on attention, and introduced into English psychology and philosophy the tripartite distinction between mental acts, contents, or what he called ‘presentations’ ( Inhalt ), and objects. Edition after edition of his book of 1899, Manual of Psychology , was published and widely read for nearly half a century. It was mainly used as a university textbook in psychology, but it was also an original contribution to the subject. It is no wonder then, that in 1891 Stout took over from Croom Robertson the editorship of Mind, a journal dedicated to both psychology and philosophy. This was ideal, because Stout was a philosopher who believed that psychology must be founded on a secure philosophical basis. The vast majority of his articles reflect this and are primarily dedicated to epistemological matters. Much of his work in these fields is, however, imbued with semantic issues. As Sir T. P. Nunn recollected in 1916: ‘It is probably not rash to suggest that the idea of the relation between symbol and meaning has for years played a dominating part in Professor Stout’s thought. He has used it (if I may say so without impertinence) in a masterly manner and with results of permanent importance’ (168). It was in his capacity as the editor of Mind that Stout was at first quite hesitant in publishing Russell’s seminal ‘On Denoting’. We know of this

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Page 102 incident only through Russell’s brief account of it in My Philosophical Development, where he recalls: This doctrine struck the then editor as so preposterous that he begged me to reconsider it and not to demand its publication as it stood. I, however, was persuaded of its soundness and refused to give way. It was afterwards generally accepted, and came to be thought my most important contribution to logic. (1959:83) This communication, if it was in the form of a letter (and not just Stout’s oral expression to Russell, in person), from Stout to Russell, has not survived. I know of no existent published or unpublished account of this episode from Stout’s point of view. What we do have is a letter from Stout to Russell, from the latter part of 1903, in which Stout details some of his misgivings with Russell’s early theory of denoting concepts. Fortunately, this letter has been published in full by Alasdair Urquhart in the 1994–95 winter edition of Russell. Urquhart contrasts Stout’s letter with Moore’s reaction, as expressed in a letter to Russell from 23 October 1905: I was very interested in your article in Mind, and ended by accepting your main conclusions (if I understand them) though at first I was strongly opposed to one of them. What I should chiefly like explained is this. You say ‘ all the constituents of propositions we apprehend are entities with which we have immediate acquaintance’. Have we, then, immediate acquaintance with the variable? And what sort of entity is it? (167) Moore’s observation in this letter shows that he actually understood more of this theory than he later suggested. Urquhart then contrasts this early reaction of Moore’s to Stout’s ‘rambling and diffuse comments’. ‘Even after several readings,’ Urquhart comments, ‘it is hard to make out what Stout describes as his position ‘(168). This assessment of Stout’s letter is in many ways understandable. It is certainly a difficult letter to read, let alone understand. My aim in this paper is not to suggest that Stout’s letter can be made fully explicable, or even fully relevant to Russell’s two theories of denoting. Nor do I attempt a line-by-line interpretation of this long letter. Rather, what I wish to get across are the ways in which this letter actually does attempt to address issues that Russell’s theories of denoting were also meant to address. This letter is actually one of many that were written in a lengthy correspondence that took place between Russell and Stout in these years.1 What we have in this letter is not an isolated event, but rather part of the elaboration of a more systematic point of view. Not only is a part of this view to be found in some of these letters, but also, and more coherently, in material Stout published on relevant issues between the years 1902 and 1921, when he gave the second of his Gifford Lectures. In some of this published material, Stout explicitly attacks Russell’s theory of descriptions. By examining this array of

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Page 103 material, I attempt to distil at least one possible line of argument that Stout tried to advance in his letter of 1903 against Russell’s early theory of denoting concepts. This also reveals interesting motivations for Stout’s dislike of this early theory of denoting. In particular, Stout’s distaste may be related to his commitment to certain fundamental tenets he shared with the Austrian realists. Once these motivations come to the fore, we are able at least to extend Stout’s early distaste to Russell’s theory of descriptions of 1905, and speculate as to why he thought ‘On Denoting’ needed to be reconsidered. I begin with a brief account of Russell’s early theory of denoting concepts and its place within the context of his realism. I then describe, in some detail, Stout’s position vis-à-vis issues related to denotation. Russell and Denoting The details of Russell’s early theory of denoting, found in his Principles of Mathematics ( PoM), are quite well known. I do not therefore present any detailed account of this theory. What I do present in this section, however, is certain salient features of this early theory of denoting, which I then relate to Stout’s general doctrine. In particular, I aim to show how Russell’s early theory of denoting conflicted with the semantic theories of the Austrian realists, like Meinong and Twardowski. This conflict is made puzzling, as both Coffa and Hylton note, by the fact that Russell was also, in other parts of his PoM quite consciously in line with the fundamental ‘semantic monism’ or the ‘direct realism’ of these Austrian realists. This is especially evident with regard to Russell’s notion of a ‘proposition’. Sentences are linguistic expressions of propositions. The linguistic units of a sentence therefore indicate certain nonlinguistic constituent terms of a proposition. These terms make up a proposition which is nonlinguistic and mind-independent. Propositions, thereby, actually contain the objects they are about. There is no mediatory element between a proposition and what it is about. Rather, in every judgement or assertion we are directly related to that thing we are making an assertion or judgement about. The judgement or assertion does not contain a representational element (such as an ‘idea’) which is somehow related to what the proposition is about. Rather, what the proposition is about is identical with the subject-term of that proposition. This Coffa calls Russell’s ‘thesis of confined aboutness’ (1991:105). This thesis of Russell’s is in harmony with the Austrian realist assumption that, to put it rather simply, no representation can be without an object. Famously, even inconsistent representations (such as ‘a round-square’) must have an object. This fundamental assumption was seen by many of Brentano’s students as a direct repudiation of Bolzano’s anti-Kantian stance that there can be representations without an object. In more Kantian language, Bolzano claimed that knowledge is possible without the blend of concept and intuition. Russell quite explicitly and consciously sided with the Austrian realist tradition. In an oft-quoted passage from PoM, Russell famously sums up quite powerfully this Austrian assumption and its implications:

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Page 104 Being is that which belongs to every conceivable term, to every possible object of thought—in short to everything that can possibly occur in any proposition, true or false, and to all such propositions themselves… ‘ A is not’ must always be either false or meaningless. For if A were nothing, it could not be said not to be; ‘ A is not’ implies that there is a term A whose being is denied, and hence that A is. Thus unless ‘ A is not’ be an empty sound, it must be false—whatever A may be, it certainly is. Numbers, the Homeric gods, relations, chimeras and four-dimensional spaces all have being, for if they were not entities of a kind, we could make no propositions about them. (449) Having said that, Russell’s primary focus in his 1903 book was mathematical knowledge. It was in explaining certain mathematical facts, however, that Russell seemed to find exceptions to the Austrian stance described above. Consider the proposition expressed by: ‘Every natural number is either odd or even.’ This proposition is certainly meaningful and true. As we saw, the thesis of confined aboutness states that what the proposition is about is actually contained in the proposition itself. The problem here for Russell evidently becomes: in what way is an infinitely complex proposition ‘grasped’? Russell’s answer is interesting: we cannot grasp any proposition of infinite complexity (§72). In the words of Hylton, Even in the most extreme and unrestrained phase of [Russell’s] realism, the idea that we grasp infinitely complex propositions was too implausible for Russell to accept. So the issue of generality —how we can, for example, grasp a proposition about all the natural numbers—is one which does not fit neatly into his direct realism. The difficulty which this issue creates for direct realism forces upon Russell some modification of that doctrine. (2003:213) What is this modification? Russell modifies his direct realism by introducing denoting concepts. For Coffa, denoting concepts are not as much a modification of Russell’s semantic monism as they are an abandonment of it for what he calls semantic dualism. That is, Russell abandons his semantic monism, described above, for the view that there are propositions that do not contain the objects which those propositions are about, but rather contain a certain type of a representational element he calls a denoting concept. ‘The [semantic] dualist’, says Coffa, thinks that we must associate two different elements with each piece of grammar: roughly its contribution to what the sentence says and its contribution to what it is about. The latter is in the world; but where the former is, and even whether this question makes any sense at all, are matters on which the dualist would normally hesitate. (1991:79)

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Page 105 Let us briefly look at what this early theory of denoting is. If we cannot grasp an object of infinite complexity, according to Russell, how then can it be a constituent of a proposition which is meaningful? Russell’s answer is that such an object is not a constituent part of a proposition, but that the proposition, nevertheless, is still meaningful because it contains a denoting concept which denotes that object. Thus the object of this sort is not a constituent of the proposition, but is merely denoted, by the denoting concept, which is something we can grasp and know to have that relation to that object. Therefore, propositions expressed by means of denoting concepts are propositions which do not contain what they are about. The denoting relation itself is indefinable and is made into a logical constant. As Russell puts it: But the fact that description is possible—that we are able, by the employment of concepts, to designate a thing which is not a concept—is due to a logical relation between some concepts and some terms, in virtue of which such concepts inherently and logically denote such terms. It is this sense of denoting which is here in question…A concept denotes when, if it occurs in a proposition, the proposition is not about the concept, but about a term connected in a certain peculiar way with the concept. (53) What is essential to note, moreover, is that not only is the representational element, which is introduced in the form of a denoting concept, abhorrent to Russell’s commitments to the assumptions of the Austrian realists, made in the same book , but that Russell goes on to admit that there can be denoting concepts which in fact do not denote anything. And thereby, at least with regard to certain quantificational words, Russell sides with Bolzano and Frege’s contention that representations may be meaningful without directly denoting objects. Finally, I believe both Hylton and Coffa are right in pointing out the intriguing fact that Russell, at least in this period, was not very conscious of this conflict. In this regard, then, one of the things which stands out as captivating in Stout’s letter to Russell, is the fact that Stout does seem to be quite conscious of this conflict in Russell and even attempts to point it out to him. STOUT AND THE AUSTRIAN REALISTS Apart from some glaring eccentricities, Stout’s overall doctrine of judgement abides by the Austrian realist assumptions I mentioned above. Indeed, Stout explicitly saw himself as a part of this tradition. In an article from 1911 entitled, ‘Some Fundamental Points in the Theory of Knowledge’ he begins by saying, ‘The terms “ Akt”, “ Inhalt ”, and “ Gegenstand” are the keywords of a certain theory of knowledge which constitutes, in my opinion, the most important recent development of philosophical thought in Germany’ (1911b: 353). To be sure, he goes on to summarize the main aspects of this ‘German’ development, and concludes:

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Page 106 The general scheme which I have attempted to reproduce in broad outline has for me a special interest, because it is akin to views which I have independently developed in my book on Analytic Psychology , which was published in 1896. I there connect my own position with that of Brentano, accepting his distinction between objects of consciousness and the modes in which consciousness refers to its object, but criticizing his failure to distinguish between ‘ Objekt ’ and ‘ Inhalt ’. (356) In a footnote to this passage he adds, ‘I am not claiming priority, but only independence. Priority of publication belongs, I believe, to Zwardowsky’ ([ sic ] 356, n1). What is interesting about this passage is Stout’s claim that he actually adjusted Brentano’s intentional in-existent doctrine, in the same way that Twardowski did, and for the same types of reasons. And like Twardowski, Brentano’s student, Stout actually made such a critical adjustment of Brentano, not as a refutation of him, but rather as a refinement to a doctrine that Stout was quite sympathetic with. What I do wish to focus on here are certain features of Stout’s doctrine which are relevant in explaining his reaction against denoting concepts. To begin with, Stout is explicitly an adherent of the Austrian realist assumption mentioned above, that no representation may be without an object. This adherence goes all the way back to his early work in psychology, but certainly permeates his later work in epistemology.2 What is even more fundamental in Stout’s overall doctrine, moreover, is the idea that there can be no mediating element between a representation and its object.3 Or, to put it in his terminology, no object of any representation has mere being for thought, but all must also have real being. In a difficult article from 1908 entitled, ‘Immediacy, Mediacy, and Coherence’, Stout starts the discussion off by formulating what he thinks are the typical reasons for positing a representational element, what he there calls ‘content of knowledge’. ‘According to this view’, says Stout, ‘there intervenes between reality and the knower a very peculiar kind of entity called “a content”…Its being is merely being-for-thought’ (302). The usual justification for such content, or mediatory element, says Stout, is that I can imagine a centaur, though no centaurs exist. Now, it seems plain, if we are to admit contents of knowledge as distinguished from the content of reality in cases where the distinction is forced upon us in this fashion, we are logically bound to assume a similar distinction in all cases… Thus, the logical view seems to be that all knowledge is mediated, by representative contents. (305) But for Stout ‘it seems to involve an absurdity to suppose that what I think of has no being except the being thought of’ (1911b: 355). And that, instead, ‘When I believe or disbelieve or suppose that a centaur actually exits, I must think of its actually existing. And what I mean by this is certainly not the fact that I think of it’ (355). He is even more explicit about this when he contrasts his doctrine with that of Bradley: ‘my divergence from Mr. Bradley is most

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Page 107 pronounced and emphatic. My position is, that whatever is thought, in so far as it is thought, is therefore real. His position is, that whatever is thought, in so far as it is thought, is therefore unreal’ (1911a: 346). He goes on to note, that ‘My disagreement with Russell, on the other hand, is, comparatively speaking, one of detail’ (347). As we have seen, this remark is quite apt with regard to the Russell of The Principles who seems to be in harmony with the Austrian realists and Stout on just these sorts of issues. Consequently, Stout believes that the mediatory view, or what amounts to the same, semantic dualism, is a natural outcome of a certain type of explanation of the problem of error and the play of fancy. To account for these latter, as we saw above, the semantic dualist introduces representative content. Stout’s strategy is to undercut this introduction by showing how error and the play of fancy can be accounted for without a mediatory element (342). He does this by introducing the notion of possibility. In articles ranging from 1902 to his Gifford Lectures of 1919 and 1921, what is continuously emphasized about possibilities is that they are not mere contents of thought, but are real constituents of the world. ‘If it is once admitted that logical possibilities enter into the constitution of the known reality’, explains Stout, ‘and are not “contents” having merely a “being for thought”, we can, I believe, show that merely “representative contents” are not required to explain error or the play of fancy’ (342). Without getting into the details of this tricky and at times confusing theory, the basic idea is simply that, like actualities, possibilities are real, and are in this way both opposed to mere appearances. The very nature of actual things, says Stout, is ‘saturated through and through with possibility’ (1908:305). ‘Now, in reference to any logical possibility’, continues Stout, which our thought apprehends, we may take up certain alternative subjective attitudes, called belief, disbelief, doubt, or mere imagination. These subjective attitudes do not alter the nature of the logical possibilities to which they refer. The same logical possibility may be an object of either belief, disbelief, or doubt. I may either treat it as a possibility that is actualized or as a possibility that is not actualized, or I may remain undecided between these alternatives. (305–6) Thus error, claims Stout, ‘first arises when the mind not only thinks of a possibility being fulfilled, but also believes in its being fulfilled’ (1911a: 343). Other than the fact that, from Russell’s perspective, Stout places too much emphasis on the propositional attitude here, Russell also, in a letter not dated, but probably from around the same period as the articles from which these passages quoted above were taken (1908–1911), says: You can’t mean that when I judge ‘Charles I died in his bed’ the object before my mind is ‘the possibility that Charles I died in his bed’. It seems quite obvious that the notion of possibility is not before my mind… My difficulty is that I do not see what possibility can mean in such a use of it.

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Page 108 There seems to me to be nothing which is not actual—a possible which is not actual seems to me strictly nothing. Hence with my view of possibility there would be no objective in the case of error, unless the objective were actual… You seem to say: ‘ a -having-the-relation-R-to-b’ (which I call a Rb) is a definite object, sometimes actual, sometimes merely possible, but subsisting in any case. My view is that unless a has relation R to b, there simply is no such thing as a Rb, either actual or possible.4 In any case, what I have tried to show is that Stout was a conscious adherent of certain fundamental tenets of the Austrian realist school. He held a semantic monism, explicitly rejected a semantic dualism, and believed, against Bolzano and Frege, that no representation can be without an object. He even went as far as to accept, albeit in his own fashion, certain subsistent entities, as a result. It is, then, from this perspective that Stout’s letter attacking Russell’s theory of denoting concepts must be read. STOUT’S LETTER OF 1903 Coffa, in describing the discrepancy between the two Russells, as found in The Principles of Mathematics, sums up by saying: It is easy to underestimate the extent to which this Russellian doctrine [of denoting] conflicts with traditional semantic dogma… It is clear, of course, that Russell’s theory of denoting conflicts with the thesis of confined aboutness… A denoting concept, Russell explained, need in no way resemble what it denotes. (1991:105, my emphasis) Amongst the clutter of ideas in Stout’s letter that make it seem ‘rambling’ and ‘obtuse’ (Urquhart 1994:168), Stout strikingly does not underestimate this conflict in Russell. Stout begins the letter by implying that he actually agrees with Russell’s thesis of confined aboutness and regards it as ‘self-evident’. He writes: It is no admission on my part that immediate cognition does and must occur. I have never dreamt of denying this. It is to me self-evident that a proposition as such is necessarily complex and must contain elements which are not themselves propositions and that these must ultimately be known immediately and not through ‘denoting’ characters. (Urquhart 1994:168) And this is precisely why he believes that he must hold that whatever being or existence belongs to the whole of the denoting characteristic must belong to what it denotes. It is true that when I think of a thread such as would exactly fit the eye of a particular

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Page 109 needle, there may be no such thread actually existing. But the relatedness expressed by ‘exactly fitting’ is not known as actual: it is only known as, in a certain definable sense, possible. (168–69) We have seen above what this sense of possibility is, and what exactly it is meant to achieve. If I may put it simply, Russell’s denoting concepts are precisely those types of representational content which Stout’s theory of possibility is meant to do away with. Furthermore, in accordance with Stout’s adherence to the view that no representation may be without an object, he says, ‘I reject your view that …a denoting characteristic cannot imply the existence of what it denotes’ (168). That is, there are no cases in which a representation can be without an object. As we have seen, Russell explicitly accepts cases, in line with Bolzano and Frege, where a denoting concept may denote nothing at all. Stout also rejects Russell’s view that (here Stout is quoting Russell) ‘in some cases we can prove that something is denoted but not what’ (170); for example, in the proposition expressed by ‘The actual point which is the centre of the material universe at the beginning of the twentieth century is not a constituent of any proposition which we can discover concerning it.’ Here Stout goes as far as to say that: ‘In supposing x to be the actual centre, you must really be thinking of the actual centre and not of anything else instead of it. Otherwise you would be making a different and logically irrelevant supposition’ (171). Again this sort of objection echoes Twardowski’s conclusion against Bolzano: Hence nothing stands in the way of asserting that to every presentation there corresponds an object, whether the object exists or not. The expression ‘objectless presentation’ is such that it contains a contradiction; for, there is no presentation which does not present something as an object. (Twardowski 1977:26) Whatever the merit of these arguments against Russell’s theory of denoting concepts, what should be evident is the fact that Stout did have an overarching perspective, which allowed him to have certain misgivings about denoting concepts. Stout definitely shared many important and fundamental assumptions with Russell and the Austrian realists, but this is precisely why denoting concepts came as such a surprise to Stout’s sensibilities. STOUT AND ‘ON DENOTING’ So how does all this relate to Stout’s reaction to ‘On Denoting’? Again, we have no record of this reaction, except from Russell’s later recollection of it in My Philosophical Development. Taking what I have said above, however, about Stout’s attachment to certain tenets of the Austrian realist tradition, and coupling these with the sparse remarks he does make with regard to definite descriptions in his later works, we might be able to arrive

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Page 110 at a better picture as to why Stout may have been averse to the publication of Russell’s innovative 1905 paper. Ten years later, in a paper of 1915 called ‘Russell’s Theory of Judgement’, Stout makes his first explicit reference to Russell’s ‘On Denoting’. First he makes a brief remark, saying, ‘It is perhaps the most fundamental tenet of his [Russell’s] philosophy that acquaintance with a thing is the indispensable presupposition of knowledge about it. He is, therefore, bound to explain away “knowledge by description”, and he attempts to do so in his article “On Denoting”’ (1915:252). Stout then goes on, later in the text, to briefly formulate his critique of Russell’s 1905 paper. Stout writes: I take knowledge by description to be as ultimate as knowledge by acquaintance… Mr. Russell refuses to regard knowledge by description as ultimate. In his article in Mind (vol. xiv, n.s.) he attempts to give an account of it which shall presuppose nothing but knowledge by acquaintance. His explanation is somewhat intricate; but I need not deal with its intricacies here. It is sufficient to say that I stumble on the very threshold. Mr. Russell, in attempting to account for knowledge by description in terms of what is not knowledge by description, assumes as fundamental ‘the notion of the variable’ and he cannot stir a step without it. If, therefore, the notion of the variable involves anything which is known by description and not by acquaintance, his explanation moves in a vicious circle. (256–57) This criticism is like Moore’s comment quoted at the beginning of this paper. Moore’s comment, however, was delivered to Russell in the very same month that OD was published, while Stout’s criticism is a good ten years off. The question here is whether or not Stout’s criticism quoted above was the reason for his aversion and hesitation in publishing the 1905 ‘On Denoting’? I am inclined to say no. I believe that a more fundamental reason can be given for Stout’s reaction to ‘On Denoting’. Again, keeping in mind what I have said about Stout’s 1903 letter, and the philosophical context into which I placed that letter, we can make sense of a few remarks that Stout makes later in his Gifford Lectures of 1919 and 1921 about Russell’s theory of definite descriptions. There Stout has the following to say about this theory: For in strictness we do not know at all what we are said to ‘know by description’; we only know, at the most, the description of it. We believe that something exists and has a certain character, and that there is nothing else having this character. But the meaning of the word ‘something’ is general. It is applicable in the same sense to many and diverse ‘somethings’…. Thus a proposition expressing a description contains nothing but a complex of interrelated universals. If the proposition is true, then there must be some actually existing particular which the description describes. But we are not acquainted with this particular and consequently we cannot know about it. Consequently we cannot know

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Page 111 that anything real is described by the description… Thus, whether the proposition is true or false, I know only the description and never anything corresponding to it. (1952:63–64) Aside from the inadequacies displayed in Stout’s understanding the nature of descriptions, what is important to notice in this passage is that Stout is alluding to the fact that the theory of descriptions, like Russell’s early theory of denoting, commends representations without an object; or as he puts it elsewhere in the same chapter on Russell: Now I do not see how it can be denied that there is a system of evidently true propositions which are not directly concerned with actual existences. Further, it seems clear that truth cannot be true of nothing. They must express what in some sense has being. We cannot know and yet know nothing… [For Russell] We can know universals and relations of universals where no instances can be given. We know, for example, that ‘All products of two integers, which never have been and never will be thought of by any human being, are ever over 100.’ Yet from the nature of the case we, being human beings, cannot give any instance of such pairs of integers or of their products…we frequently understand the meaning of general names, without having before our minds any single example of what they mean… [But to] think of a universal is to think of all its instances as such . (89–90) Russell’s theory of descriptions, as articulated in his 1905 paper, is a rejection of his earlier theory of denoting concepts. That there can be some mediating factor between a proposition and its meaning is now rejected by Russell. So we have a return to Russell’s semantic monism, something he now shared, once again, with Stout. However, generally speaking, Stout is right in believing that definite descriptions need not refer—this is precisely Russell’s incomplete symbol strategy. They do not have a meaning relation to some denoting concept, nor do they have a meaning relation to the object they seem to be about. It is this aspect, I believe, that Stout finds most disagreeable in Russell’s theory of definite descriptions—that a representation can be without an object. But it is specifically this aspect that Stout also rejected, as we saw in his letter of 1903, in Russell’s early theory of denoting as well. I shall venture to suggest that, from this perspective, Stout had reason to believe that the two theories were closely related, and both were, in similar ways, at fault in suggesting that representations may be without an object. Finally, this fault in both theories, from Stout’s perspective, was indeed surprising, given that Russell seemed also to share certain assumptions with the Austrian realists and Stout himself —assumptions which directly conflicted with these two theories of denoting. My conjecture is, that it might have been due to such reasons, therefore, that Stout may have had misgivings with regard to the publication of Russell’s 1905 article, ‘On Denoting’.

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Page 112 NOTES 1. These letters are dedicated to many issues, sometimes things which have nothing to do with matters relevant here. 2. For example, take a passage from his 1902 article, ‘Error’: ‘Our thought can be true or false only in relation to the object which we mean or intend and we mean or intend that object because we are, from whatever motive, interested in it rather than in other things’ (267-8). 3. This point actually becomes a little confused with Stout’s introduction of the vital notion of ‘presentation’, which is a modification of Twardowski’s content or Inhalt . For more on this please see the forthcoming: Omar W. Nasim, Russell and the Edwardian Philosophers: Constructing the World (Palgrave Macmillan Press, 2008): especially Ch. 2 on Stout. 4. Letter from Russell to Stout entitled: ‘Stout on Truth’; Russell Archives, McMaster University. REFERENCES Coffa, J. A. (1991) The Semantic Tradition from Kant to Carnap, Cambridge: Cambridge University Press. Hylton, P. (2003) ‘The Theory of Descriptions’, in The Cambridge Companion to Bertrand Russell, ed. N. Griffin, Cambridge: Cambridge University Press. Nunn, T. P. (1915–16) ‘Sense-Data and Physical Objects’, in Proceedings of the Aristotelian Society , 16: 156–78. Russell, Bertrand. (1903) The Principles of Mathematics. 2nd edition. New York: Norton, 1938. ——. (1959) My Philosophical Development. London: Allen and Unwin. Stout, G. F. (1902) ‘Error’, in Stout (1930). ——. (1908) ‘Immediacy, Mediacy, and Coherence’, in Stout (1930). ——. (1911a) ‘Real Being and Being for Thought’, in Stout (1930). ——. (1911b) ‘Some Fundamental Points in the Theory of Knowledge’, in Stout (1930). ——. (1915) ‘Russell’s Theory of Judgement’, in Stout (1930). ——. (1930) Studies in Philosophy and Psychology , London: MacMillan and Co., Ltd. ——. (1952) God and Nature: The Second of Two Volumes Based on the Gifford Lectures 1919 and 1921, Cambridge: Cambridge University Press. Twardowski, K. (1977) On the Content and Object of Presentations, trans. R. Grossmann, The Hague: Nijhoff. Urquhart, A. (1994) ‘G. F. Stout and the Theory of Descriptions’, in Russell, n.s. 14: 163–71.

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Page 113 7 Russell on ‘the’ in the Plural David Bostock In the present chapter we shall be concerned with the in the plural: the inhabitants of London, the sons of rich men, and so on. In other words we shall be concerned with classes . —Russell, Introduction to Mathematical Philosophy (181) My aim in this paper is first to trace Russell’s wrestlings with the idea of a class, and to offer some elucidation of his ideas in cases where I suspect that they are not too well understood; and second to say whether we, nowadays, should think of those ideas as still worthy of attention. My history is of a broad-brush kind, and almost everywhere confines attention to works which Russell himself prepared for publication. My elucidations are sometimes quite anachronistic, relying on modern perspectives which Russell himself would find quite unfamiliar. And, naturally, the evaluation is also from a modern perspective. I confine my discussion to what we have now come to call Russell’s simple theory of types, mainly because there is quite enough to say about this so-called ‘simple’ theory, and hence no space to consider its ‘ramified’ elaboration. But I also believe that it was only the simple theory that Russell himself was at all sure of. In the metaphysics which he expounds in his lectures on ‘The Philosophy of Logical Atomism’ (1918), the ideas behind the simple theory are emphasized, but there is almost no hint of the ‘ramifications’ which his official theory also involves. The story divides into five main stages. First there is Russell’s early theory of denoting, as set out in Chapters 4 through 6 of his Principles of Mathematics (1903). But, second, there is also, in the same work, a recognition that there must be something wrong with this theory, at least as it affects classes, and some first attempts at meeting the problem. One must count as a third stage the revised theory of denoting, as set out in the famous article ‘On Denoting’ (1905). This article does not mention ‘the’ in the plural, the notion of a class or anything else that is obviously relevant to my topic. But Russell himself describes it as providing the clue which led him to his final theory,1 so we should not ignore it. I count as the fourth stage the various ideas about classes that he did explicitly explore at around the same time, in particular, as recorded in the article ‘On

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Page 114 Some Difficulties in the Theory of Transfinite Numbers and Order Types’ (1906a). Then, finally, there is the theory that Russell in the end adopted, as in his ‘Mathematical Logic as Based on the Theory of Types’ (1908), his ‘Theory of Logical Types’ (1910b), and again in Principia Mathematica (Whitehead and Russell 1910). THE EARLY THEORY OF DENOTING At the time he was writing The Principles of Mathematics, Russell’s understanding of quantification was very inadequate. This is in a way surprising, for he had been enthusiastic about the powers of modern logic since his meeting with Peano in the summer of 1900, and there is a gap of two and a half years between this meeting and the completion of the Principles . (Its preface is dated December 1902.) But it appears that during all this time he had not seriously reflected upon how the logician’s quantifiers are most usefully employed in some areas of mathematics, and although he had reflected on (what we recognize as) the way that quantifiers work in natural language he had not understood it at all. The early theory of denoting phrases (or denoting concepts) that we find in Chapter 5 of the Principles clearly reveals this. It is a treatment of such words as ‘all’, ‘every’ and ‘any’ which quite fails to address how these different words are used in English to indicate the different scopes of a quantification.2 In what Dau (1986) very fairly calls the ‘official’ version of the theory, Russell claims that such phrases as ‘every man’ and ‘any man’ are indeed denoting phrases, that is, their role is to denote certain objects. These objects are said to be ‘combinations’ of all the men that there are, but combinations which are ‘effected without the use of relations’, and which in these cases are ‘neither one nor many’ (1903: §59). Moreover, since there are contexts in which ‘every man’ and ‘any man’ are not interchangeable, Russell infers that they must each denote different combinations of men, and the combinations denoted by ‘a man’ and ‘some man’ are of course different again. He himself admits that these supposed combinations are ‘very paradoxical objects’ (§62), but apparently he does not see this as a reason for avoiding them. What is relevant to our topic is that Russell treats the phrase ‘all men’ as in most ways similar to ‘every man’ and ‘any man’, that is, as denoting a certain combination of men. But he also distinguishes it, on the ground that ‘all men’ is a plural expression whereas his other ‘denoting phrases’ are grammatically singular, and so he supposes that it denotes a plural object, while the others denote objects that are ‘neither one nor many’. This plural object he identifies with the class of all men, except that he wishes to distinguish between what he calls a ‘class as many’ and a ‘class as one’. The plural phrase ‘all men’ denotes the former, while the singular phrase ‘the class of all men’ denotes the latter. He offers as a further reason for

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Page 115 supposing that there are such plural objects that they are needed to be what numbers are predicated of. For while there are things that are two (or any other number) there is nothing that is two. A singular subject simply is one, and you cannot say that it are any other number. One can fairly object that it was a mistake on Russell’s part to associate the word ‘all’ with these plural objects, and this can in fact be shown from his own examples. Taking a simplified case in which there are just two objects (both men) that are in question, namely Brown and Jones, he gives as an example of the ‘combination’ that is relevant here ‘Brown and Jones are two of Miss Smith’s suitors’, which he then simplifies just to ‘Brown and Jones are two’ (p. 59). This is supposed to be an example of the kind of ‘combination’ of objects that the word ‘all’ introduces, but in fact the sentence ‘all Miss Smith’s suitors are two’ can only be understood in a quite different way (for example, as claiming that each of them is two years old). However one can understand ‘ the suitors of Miss Smith are two’ in much the same sense as ‘Brown and Jones are two’, that is, as making a claim about the number of the objects in question. As Russell later realizes, it is not ‘all’ but ‘the’ in the plural that is better seen as introducing the kind of ‘plural object’ of which numbers can be predicated. This way of expressing such a numerical claim is of course very stilted and unidiomatic English. We are likely to be more sympathetic to Frege’s way of explaining a ‘statement of number’, that is, as ‘making an assertion about a concept’ (1884: p. 59). We construe this as applying the number in the form of a numerical quantifier, as in ‘There are 2 things x such that x is a suitor of Miss Smith’, or more briefly, ‘There are 2 suitors of Miss Smith’. But it is relevant to note that in this sentence the numerical quantifier ‘there are 2…’ is applied to a plural expression, as is Russell’s preferred form ‘…are 2’.3 So I think that we can not unreasonably conclude that there is much in common between Frege’s thought that numbers are applied to concepts and Russell’s thought that they are applied to plural objects . Indeed, Frege himself comes close to identifying a Russellian class-as-many with what he calls a concept, since he offers this criterion: ‘As soon as a word is used with the indefinite article or in the plural without any article, it is a concept-word’ (1884:64). But there is the difference that Russell’s plural phrases do begin with ‘the’, whereas Frege says—but see note 3—that his do not. 4 An important reason, then, for supposing that there are such things as classes ‘as many’ is that they are needed to explain how (cardinal) numbers can have application. But Russell thinks that we also have to be able to consider the same class ‘as one’, for we do have a singular expression for it, namely, ‘the class of so-&-so’s’. It is this singular expression that we use when we make the class the subject of our assertions, for example, when we wish to say that the class is a member of some other class. Here Russell’s first thought is that we must be treating the class ‘as one’, if only because the expression ‘is a member of’ can only be applied to what is

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Page 116 grammatically a singular subject.5 So we find in the Principles this interesting duality in the notion of a class. The ‘class as many’ has much in common with a Fregean concept, whereas the ‘class as one’ clearly corresponds to what Frege would regard as the extension of that concept. Just as Frege assumed that every concept has an extension, so Russell is first-off inclined to think that every class taken ‘as many’ can also be taken ‘as one’. But he does see that the contradiction which he discovered in Frege’s logic makes this assumption problematic. So we turn to this contradiction, and to Russell’s first thoughts about it. THE EARLY THEORY OF TYPES After his meeting with Peano in the summer of 1900 Russell became more and more confident that his proposed reduction of mathematics to logic was going to work. Here is his own description: Those months [that is, July through December 1900] had been an intellectual honeymoon such as I have never experienced before or since. Every day I found myself understanding something I had not understood on the previous day. I thought all difficulties were solved and all problems were at an end. But the honeymoon could not last, and early in the following year intellectual sorrow descended upon me in full measure. (1959:56) Russell discovered what he always called ‘the Contradiction’, and the ‘sorrow’ that then descended upon him was to last for a good many years, at least until he published a solution that satisfied him for the time being, in ‘Mathematical Logic as Based on the Theory of Types’ (1908), and I suspect that in his own unpublished thought it lasted longer still. He made the discovery by considering Cantor’s proof that every class has more subclasses than it has members, and working out how this would apply to the supposed universal class which has everything whatever as a member. Cantor’s ‘diagonal procedure’ then led very quickly to the paradoxical class of all those classes that are not members of themselves. But it was easy to see that the source of the problem was not just with this class in particular, for the argument apparently shows that there must be more classes of objects than there are objects, and hence that classes cannot themselves be objects. In the Principles we have Russell’s first response to this quite unexpected fact. His initial reaction is to draw upon the distinction that he has already made between a class-as-one and a class-as-many. The main idea is that there will be classes-as-many to which no class-as-one corresponds. He frequently insists that a class-as-one (when it exists) must be of the same type as its members, so that if the members are individuals then so too is

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Page 117 the class.6 (Already in the Principles Russell is beginning to use the word ‘individual’ for whatever is of lowest type.) The obvious question that this raises is: when is there such a thing as a class-as-one, as well as a class-as-many? Russell appears to offer two rather different answers. In the first discussion in Chapter 10 he suggests that what is important is the kind of propositional function that defines the class: it must not be what he calls a ‘quadratic’ function. This idea is not very clearly explained, but, in outline, it is that the problematic propositional functions are those that can take as an argument an item which is itself defined in terms of that function (§§103–4). It is clear that this idea is the ancestor of what Russell later came to call ‘the zigzag theory’. However, in the appendix to the Principles which addresses this problem we find the rather different idea that ‘There are more classes than individuals; but predicates are individuals. Consequently not all classes have defining predicates’ (§499).7 There may be a suggestion here—though it is only a suggestion—that a class-as-one will exist only when we can produce some predicate that defines it. Since any natural language can define only countably many classes, this may at first appear to be a useful idea. But, on reflection, it can easily be seen that it will not do by itself, for apparently we can define the paradoxical Russell class which yields a contradiction. Anyway, Russell’s broad approach at this stage is to invoke his distinction between a class-as-many and a class-as-one, to put some restriction on what may be admitted as a class-as-one, and to impose a type theory on classes-as-many. These classes-as-many are regarded as falling into their own type hierarchy, for he now supposes that a class-as-many may itself be a member of a higher-level class-asmany, and does not have to be first exchanged for its associated class-as-one. (As he says, on this conception ‘a class of classes will be many many’s’, §489.)8 I think one can fairly say that his final solution, in (1908), is a strengthening of this basic idea, for it claims that we never need to assume the existence of a class-as-one, and while we do need (a version of) classes-as-many these must be governed by a type theory (as Frege’s concepts also are). But the final type theory is (for good reason) considerably more restrictive than the early version sketched in the Principles . In fact, the early version strongly resembles the ‘cumulative hierarchy of sets’ that is the natural model for ZF set theory. First, its types do form a cumulative hierarchy. Russell initially explains a type as the range of significance of a propositional function (§497), which one might naturally take as implying—as in the later theory—that the hierarchy is ‘strict’ rather than cumulative. But in the Principles he is also inclined to assume that the sum of any two types is itself a type, which clearly allows us to form a cumulative version of this structure.9 Second, the hierarchy in the Principles includes an infinite type, higher than all the finite types, as we also find in ZF. But here there is the difference that Russell seems to envisage only one infinite type, which he thinks of as corresponding to the first infinite

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Page 118 cardinal , whereas in the ZF hierarchy there are many, and they correspond to the infinite ordinal numbers from ω on. Since ω + 1 is not the same number as ω, there is no temptation to think that sets which are of infinite rank in the ZF theory might be members of themselves. But since Russell does think that his classes of infinite type may be members of themselves. His main motive for this is evidently the case of the numbers . His first thought, like Frege’s final thought, was that one could identify the number n with the class of all n-membered classes. But, since numbers can be applied to classes of every type, if this definition of ‘number’ is to be retained it is apparently necessary for there to be an infinite type which contains classes of all types, including classes of that same infinite type itself. Thus Russell admits that within the infinite type may be true (§498, cf. §130n), so that is certainly significant, but apparently in the Principles he does not see that this will immediately resurrect his original paradox at the infinite level. However, the point cannot have escaped him for long, and after the Principles we never do hear of infinite types. It is quite clear that the final theory does not permit them. This early type theory is sketched both for classes (which is fairly straight-forward) and for relations of two or more places (which adds complications of detail, but no new principles). However, Russell does not attempt to extend the theory to propositions, and he ends his discussion by noticing an apparently analogous paradox that threatens to break out over classes of propositions, to which he offers no solution. (The idea is that for each class of propositions there is a proposition which asserts that all members of that class are true. But by Cantor’s theorem there must be more classes of propositions than there are propositions. So this cannot be right.) Accordingly, the final word of the Principles is that more work is needed. THE REVISED THEORY OF DENOTING The article ‘On Denoting’ of 1905 is probably Russell’s best known work. The bulk of the article concerns ‘the’ in the singular (44–56). There is no mention anywhere either of ‘the’ in the plural or of classes. But a couple of pages at the beginning do outline a treatment of Russell’s other ‘denoting phrases’, that is, those beginning with ‘all’ or ‘every’ or ‘some’ or ‘a’ (42–43).10 The discussion is extremely brief. In effect, Russell is here completely withdrawing his earlier account, but he does not explain either what was wrong with it or why the new account is an improvement. Nor does he even give the new account in sufficient detail for one to see how it resolves the old problems. He introduces what we recognize as a universal quantifier as something that says of a propositional function that it is ‘always true’ (that is, true for all values of the relevant variable) and, similarly, an existential quantifier as saying that the function is ‘sometimes true’. He must now recognize that the scopes of these quantifiers can make a difference,

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Page 119 but he says absolutely nothing about it.11 In fact, he mentions the phenomenon of scope only in connection with the definite article ‘the’, where he distinguishes what he calls ‘primary’ and ‘secondary’ occurrence. If he can distinguish scopes in this rather sophisticated case, he can surely do so with the simple quantifiers, but apparently it is not a point that he thinks worth mentioning. I suspect that this is because, since his study of Frege in 1903, the point is now so second-nature to him that he has forgotten that it needs explaining to others.12 In any case, the relevance of this article to my topic does not come in the detail of his new theory, but in the general principles which he thinks of as underlying it. In the Principles he had said ‘grammar, though not our master, will yet be taken as our guide’ (§46). The theory of ‘On Denoting’ is his first step away from this idea. In English grammar the phrases that he calls ‘denoting phrases’ can almost always take the place in a sentence that is occupied by an ordinary proper name. So, taking grammar as his guide, Russell had quite naturally assumed that their function was also the same, that is, to denote some object. He therefore tried to provide some weird and wonderful ‘combinations’ of objects to be their denotations. But his new theory is that, despite what grammar suggests, these phrases do not denote. I wish that he had said that more explicitly. What he does say instead is that these phrases ‘do not have meaning in isolation’, which is a way of saying that they do not function as a proper name does. He now gives a different explanation of how they contribute to the meanings of the sentences that contain them. In the Principles he had taken it to be obvious that ‘every word occurring in a sentence must have some meaning’ (§46), and he had always construed meaning as reference to one or another object. This same doctrine is in play when he argues that what any word means can always be made the logical subject of a sentence, and so qualifies as what he calls ‘a term’ (§49). For example, the predicate ‘human’ means a certain object, namely, humanity, and we can surely talk about humanity. What is happening here is that the adjective ‘human’ is being transformed into a noun ‘humanity’, and English grammar certainly licenses such a transformation. It also allows one to nominalize a verb (for example, ‘killing’ or ‘to kill’), or a sentence (for example, ‘Brutus’s killing of Caesar’) or apparently any part of speech. To mention a simple device which (in the Principles ) Russell himself never mentions, you can apparently transform any expression whatever into a noun-phrase by surrounding it with quotation marks, and perhaps adding a suitable prefix such as ‘the meaning of … ’ It would seem that nounphrases are always available, and that that is a main support for his claim that everything whatever can occur as the logical subject to a proposition. In the appendix to the Principles which discusses Frege’s doctrines, Russell notes Frege’s paradoxical claim that concepts cannot be named, and hence that the expression ‘the concept horse’ cannot refer to a concept. It is hardly surprising that he finds this an intolerable position (§483). He

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Page 120 has himself admitted that what he regards as a plural object cannot strictly speaking be named by a singular name, and that the same applies to what he calls an ‘ambiguous object’, such as is (on one version of his theory)13 denoted by a phrase of the form ‘any so-&-so’ (for example, §58n, §70n, §74). But in the Principles he will go no further than this from the basic thought that every word has a meaning, and that this meaning can always be made the logical subject of a proposition. It is ‘On Denoting’ that liberates him from this presupposition, that allows him to set aside the suggestions of English grammar, and to contemplate much more radical positions. As I have said, ‘On Denoting’ itself is entirely silent on expressions which look as if they refer to classes, but it surely started a train of thought. Perhaps these expressions too ‘do not have meaning in isolation’? INTERIM THEORIES Shortly after ‘On Denoting’ Russell once more addressed the topic of classes. He reports progress in his article ‘On Some Difficulties in the Theory of Transfinite Numbers and Order Types’ (1906a), where he mentions three different theories as worth pursuing, namely: (a) The zigzag theory (b) The theory of limitation of size (c) The no-classes theory The first two of these are theories according to which there are such things as classes, and they are all assumed to be of the same type as one another, so the problem is to say which expressions purporting to mention classes do actually succeed in doing so. The third, as its title shows, is a theory which makes no such assumption; its aim is to avoid all mention of classes altogether. In a note added at the end, after the paper had been read but before it had been printed, Russell adds that he is now becoming convinced that the third option is the best. I take them in order. The Zigzag Theory This approach begins with a careful analysis of those class-descriptions that can be seen to give rise to contradiction. Russell suggests that in all of them there is a kind of ‘zigzagging’ feature. He describes it in this way: we get a contradiction when we suppose that there is a class u such that (i) all the members of u have a certain property φ, and (ii) there is a function f whose value for that class as argument is again an object with the property φ. For then either there will be no such thing as the class of everything which has the property φ, or —if there is such a class—then the function f will have no value for that class as argument (141–42). The idea is that

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Page 121 in the construction of that class there is a kind of ‘zigzag’ between the members of the class and the values of the function f . But, to put the idea in much more general terms, it is this: a class will fail to exist when the predicate which defines it has a certain kind of complexity, and nice simple predicates will always succeed in defining classes. For example, there will be a universal class of all objects, defined by a predicate such as ‘ … is identical with itself’ or ‘ … is either red or not red’. But, unsurprisingly, Russell has to admit that he has not found what seems to him to be a satisfactory way of distinguishing between the simple predicates that do define classes and the ‘zigzaggy’ ones that do not. However, there is a general objection to the idea that we can distinguish the apparent classes that really do exist from the others that do not just by considering the kind of predicates that define them. First, there will surely be infinitely many (‘simple’) class-descriptions that do succeed in defining classes. (For example, start with any object you like and then iterate the prefix ‘the class consisting of … ’ any finite number of times.) Hence, if every class is an individual there will be infinitely many individuals.14 By Cantor’s theorem one then expects there to be uncountably many classes of individuals. But second, there cannot be more than countably many predicates of any kind, whether those that do or those that do not define classes, as Russell himself well knew (1906b: 184–85). So only countably many of the candidates for being classes can have their case determined in this way, that is, by the kind of predicate that purports to define them, and this leaves uncountably many still undecided. Some supplementary criterion is therefore needed, and has yet to be supplied. If we may take up the hint that is perhaps offered in §499 of the Principles , it seems that Russell might be inclined to say that a class exists only if there is some (suitable) predicate that does define it. But then we have only countably many classes, which cannot be enough to satisfy Russell’s ambition of deducing all of classical mathematics. With that I leave the ‘zigzag’ theory. It is sometimes said that this theory has some resemblance to the theory which Quine proposed in his ‘New Foundations for Mathematical Logic’ (1937). I make no comment on that, except to remark—as is now well known—that Quine’s theory would seem to be a very peculiar theory, and one which appears to have no natural model.15 Limitation of Size The ZF set theory that must nowadays be counted as the generally accepted theory can obviously be described as a theory of limitation of size. So it is at first surprising that in ‘On Some Difficulties’ Russell treats this idea so briefly. He says, fairly enough, that the theory is quite naturally suggested by reflection on the Burali-Forti paradox, and he has the idea that a class will be ‘too big’ to exist if it would have as many members as there

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Page 122 are ordinal numbers. Taking on board Zermelo’s axiom of choice, and its consequence that every class can be well ordered, he therefore proposes as the foundation of the theory that a class exists if and only if it can be correlated one-to-one with some proper initial segment of the series of all ordinal numbers. This idea is only slightly different from today’s thought that a class exists if and only if it has some ordinal number as its ‘rank’, to mark the stage in the cumulative hierarchy at which it is first constructed. In each case it is the ordinal numbers that are being invoked to determine what is to count as ‘too big’, and in fact the two suggestions are equivalent in the presence of the axiom of choice. So, since Russell’s proposal in this case is so near to the theory that is generally accepted these days, one asks why he feels able to reject it in little more than a page. I think that there are two things to be said in explanation, though neither of them is actually said in Russell’s own discussion. The only point that he makes himself is that the proposal is not very helpful until we know how far up the series of ordinals it is legitimate to go. It might happen that ω was already illegitimate … or it might happen that ω2 was illegitimate, or ωω or ω1 or any other ordinal having no immediate predecessor. We need further axioms before we can tell where the series begins to be illegitimate.’ (153, my emphasis)16 From today’s perspective one replies that that is exactly what the task is, namely, to provide further axioms. Zermelo began this task by introducing axioms of pairing and union, which provide the finite ordinals, an axiom of infinity which posits the first infinite ordinal, and a power set axiom that then takes us yet further. Fraenkel added to these his axiom of replacement, which certainly ‘legitimized’ ω2, ωω and many more. In more recent times we have become familiar with yet more axioms of the same kind, postulating the existence of hitherto ‘inaccessible’ ordinals. But it would appear that Russell himself never gave any attention to this task of providing suitable existence-axioms, even though he had himself suggested exactly that project. Why so? One reason that I suspect was influential is that he was still pursuing his goal of showing that all mathematics is really just logic. But logic is by tradition supposed to be a completely general subject, making no particular assumptions about the existence of this or that particular kind of thing. As Russell was aware, it cannot altogether avoid all existence-claims. In the third theory sketched in this article it assumes the existence of propositions, and in Russell’s final theory it assumes the existence of propositional functions, but these assumptions are supposed to be of an entirely general nature. However, the various special assumptions of set-existence that are made in the ZF axioms are quite different in style, and in fact, as soon as it became accepted that a good set theory would have to have such

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Page 123 axioms, the idea that set theory counted as a part of ‘logic’ was very generally rejected. Since what Russell wanted was an acceptable logic , it is not altogether surprising that he did not pursue this line of thought. I think that there was probably another reason at work, though again it is not avowed in the article in question. Russell was always aware that the contradiction which affected the naïve view of classes was equally a contradiction for the naïve view of properties and relations, of propositional functions, and even of predicates taken as linguistic expressions. There cannot be such a thing as the property of not being a property of oneself, or the propositional function which yields true propositions just when its arguments are functions that do not apply to themselves, or even the predicate ‘heterological’. Precisely the same contradiction turns up in each case. Now with classes the ‘limitation of size’ approach is in a way attractive, just because we do quite naturally think of classes as ‘constructed out of’ their members, and so the idea that a class cannot exist until a stage ‘after’ all its members exist does have some appeal. But there is no such appeal in the other cases. Properties are not ‘constructed from’ the objects that have them; nor are propositional functions ‘constructed from’ those of their arguments that happen to yield true propositions as values; nor does a linguistic predicate depend for its existence on the items that it happens to be true of. It strikes us as weird to hold that such linguistic predicates as ‘ … is the same as itself’ or ‘ … is either red or not red’ cannot exist, because if they did they would be true of too many things. In these cases the idea of ‘limitation of size’ seems entirely inappropriate. But Russell always wanted some general solution to these vexing paradoxes, so this is again a good reason for him not taking this proposal very seriously. The No-Classes Theory This theory is very briefly described in ‘On Some Difficulties’, but then much more fully explored in the succeeding paper ‘On the Substitutional Theory of Classes and Relations’ (1906b). In effect, it is the only place in which Russell states what we have come to call his simple theory of types, for all his subsequent expositions concern the more complicated ‘ramified’ theory. But the simple theory is presented here with a special and peculiar twist that is not repeated elsewhere. In its usual version the simple theory is also a ‘no-classes’ theory, in which what looks like a reference to a class is paraphrased away in favour of a reference to propositional functions, so that we nowhere assume the existence of such things as classes. This remains Russell’s final view on classes, and it is not altered in any important way in subsequent revisions. But in the usual version the paraphrase does assume the existence of propositional functions, whereas this first version of this theory, that is, the ‘substitutional’ version, also avoids assuming propositional functions. Apparent reference to them is similarly explained

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Page 124 away as ‘really’ a reference to something else. The motivation for this is, no doubt, that Russell’s original paradox applies to the naïve view of propositional functions just as much as to the naïve view of classes. So, if we aim to avoid this paradox by banishing classes altogether, we had better banish propositional functions as well. I consider the simple theory in its usual version in my next section. In this section I discuss only the ‘special twist’ of the early version, that is, its way of eliminating reference to propositional functions. The basic idea is that variables for propositional functions may (with a little ingenuity) be replaced by variables for the propositions that contain them. Let us begin with a simple case, for example, the propositional function expressed by ‘ … is a man’. We are used to representing this by a letter ‘ F ’, and then (in a second-level logic) we treat this letter as a variable which can be bound by quantifiers. But the ‘no-classes’ theory, as Russell first presents it, has no such letter ‘ F ’. Instead, we take a whole proposition, such as ‘Socrates is a man’, and we consider the effect of substituting for the name ‘Socrates’ the names of other individuals. This gives us a range of propositions , each of which says that something is a man, and what we might have wanted to say about the function ‘ … is a man’ can now be said instead about the propositions in this range. So quantifiers over propositional functions are replaced by quantifiers over propositions.17 Thus, let ‘ p’ be a variable ranging over propositions, let ‘ a ’ be a variable ranging over individuals, and let ‘ p/ a ;x’ represent what ‘ p’ becomes when x is substituted for a in p. Then the simple claims that we might have expected to express as:  

are now to be written as:

  In effect, the collection of symbols ‘ p/ a ’ functions as if it were a variable for monadic propositional functions of first level, though clearly it is something that ‘has no meaning in isolation’, for it represents what is expressed in English by ‘the result of replacing a in p by … ’.18 It is not to be thought of as naming either a propositional function or anything else. To obtain in a similar way an expression that functions as a variable for propositional functions of the second level, we may begin by thinking in this way: what is needed is a proposition which contains a function of first level, and then we need to consider all propositions obtained by substituting other functions of first level for that one. Since first-level functions are now represented by incomplete symbols of the form ‘ q/ a ’, we therefore want

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Page 125 to be able to speak of the result of replacing such a symbol by another of the same form, say ‘ r/ b’. But Russell thinks that we cannot without further explanation just write   because the positions here filled by ‘ q/ a ’ and ‘ r/ b’ are supposed to be positions for individuals, and these expressions are not expressions for individuals. But the remedy is simple. All we need to do is introduce a way of simultaneously substituting in a proposition p for two individuals that occur in it, and this is quite a straightforward idea.19 So let us put   for ‘what results from p upon simultaneously replacing a by x and b by y’. Then, recalling that in this system propositions are counted as (a special case of) individuals, we can obtain the desired effect by means of the formula   So long as q and a do occur in p in the context ‘ q/ a ’, this evidently yields what we want. Clearly we could proceed to yet higher levels in the same way, though I shall not do so. It must also be admitted that formulae written in this notation do become unpleasantly complex,20 but that is not a point of any philosophical significance. To sum up: a variable for a monadic propositional function of first level is replaced by the incomplete symbol ‘ p/ a ’; a variable for a monadic propositional function of second level is replaced by the incomplete symbol ‘ p/( q, a )’; and in the same way all other variables of the simple theory of types can be replaced by such incomplete symbols. Hence quantification over such variables can always be represented in this theory simply as quantifications over propositions and the individuals that occur in them. Moreover, since these incomplete symbols are not construed as naming anything, all the restrictions of the simple theory of types on how symbols may significantly be combined are automatically observed in this theory, simply as a matter of what ordinary grammar requires. Russell notes this point explicitly on pp. 177–78.21 As is demonstrated in detail by §4 of Landini (2003), whatever can be said in the ordinary version of the simple theory of types can also be said in this theory, and for the most part whatever cannot be said in the simple theory of types also cannot be said in this theory. But there is an important exception, which we must now consider. The paper ‘On the Substitutional Theory of Classes and Relations’, which I have been citing, was in fact never published, because although Russell had submitted it for publication there was a delay, and by the time that publication was agreed Russell had changed his mind and so withdrew the paper.

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Page 126 It is sometimes suggested (for example, in Lackey 1973:131–32) that the change of mind was at least partly due to Whitehead’s complaint that the notation had become too complex. I doubt whether this complaint can have been very influential, for when it came to practical purposes Russell was quite capable of simplifying the official notation of a theory. (Indeed, it is never quite clear what the official notation of Principia Mathematica is, for the notation that is used in practice is a simplified one, relying everywhere on the device of ‘systematic ambiguity’.) It is surely more important that Russell came to see that quantifying over all propositions at once, without introducing any type-distinctions, leads to trouble. He himself comments, at the end of ‘On the Substitutional Theory’, that the only serious danger with this theory is ‘lest some contradiction should be found to result from the assumption that propositions are entities; but I have not found any such contradiction, and it is very hard to believe that there are no such things as propositions’ (188). As a matter of fact he had already found a contradiction about propositions, which he had published in the final section of the Principles (§500). Perhaps he thought that he now had an answer to that puzzle, though, if so, we do not know what his answer was.22 In any case, he did soon discover another, which very clearly does arise within the substitutional theory as first conceived. Very roughly, it shows how to construct within that theory a version of Russell’s own original paradox concerning classes (or propositional functions). But the details are complicated, and I here pass over them.23 Russell’s response was to propose that propositions be segregated into different types or orders, which is the start of what we now call his ramified theory of types. The basic idea is that a proposition which contains within itself a quantification over propositions must be of a higher order than the propositions that are quantified over within it. Actually, the idea is not put in quite this way at its first occurrence, in his paper ‘On “Insolubilia” and Their Solution by Symbolic Logic’ (1906c). There Russell prefers to restrict the notion of a proposition to those that are quantifier-free, but then to allow what he calls ‘statements’ which do quantify over propositions and over other statements. So offically it is statements and not propositions that are first distinguished into different types or orders. But in a paper written shortly afterwards, ‘Mathematical Logic as Based on the Theory of Types’ (1908), this unexpected approach is dropped, and it is now propositions that are distinguished into various orders, according to the quantifications over propositions that they contain. In each of these papers Russell retains the idea of the substitutional theory, that reference to propositional functions may be replaced by reference to the propositions (obtained by substitution) that are their values. Hence the type and order of a propositional function is inherited from the type and order of the propositions that are its values. But in the second of them, although this approach is endorsed in theory, it is also admitted that in practice it is ‘technically inconvenient’ (77), and Russell goes back to using variables

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Page 127 that represent propositional functions directly. In subsequent writings (in particular, Principia Mathematica ) the old substitutional approach is never mentioned, though one might suspect that it lingers on in the (very questionable) thesis that is so emphasized in Principia , that a propositional function ‘presupposes’ its values. The official theory of Principia is of course the full ramified theory of types, and for reasons of space I cannot discuss that here. I note incidentally that Landini (1996) very plausibly argues that in practice Principia uses only the simple theory, for (a) its function-variables are confined to variables for predicative functions, (b) the axioms of reducibility provide suitable comprehension principles for predicative functions, and (c) the predicative functions do form a simple type-hierarchy. But I do not wish to approach the simple theory by this roundabout route, nor via the substitutional theory, with its awkward reliance on quantification over propositions. Let us think of it in the way that it is usually thought of these days. The quantifiers will range just over individuals and predicates (or propositional functions) of various levels, but not over propositions. The first level of the theory is just the ordinary first-order predicate logic that all of us are now familiar with. The idea is to extend this theory to encompass predicates (or propositional functions) of higher levels. THE SIMPLE THEORY OF TYPES To a first approximation the simple hierarchy of monadic predicates can be thought of as obtained in this way. Begin with a sentence that mentions an individual, for example, Socrates is a man. Drop out the reference to that individual, and substitute a gap in its place, as in … is a man. This is a first-level predicate. Now consider another sentence which contains that same predicate in a different context, for example, where the reference to a particular individual has been replaced by a quantified variable ranging over individuals, as in  

We can now drop out that first-level predicate and leave a gap in its place, as in

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Page 128   These are second-level predicates. Then again we can put a variable ‘ F ’ into the gap that they contain and introduce a quantifier to bind it, as in Once more we can drop out the second-level predicates, leaving a gap in their place, to form

 

  These are third-level predicates. Then again we can introduce a suitable variable to fill these gaps, and bind it with a quantifier, and so on and on indefinitely. But what would be a suitable variable in this case? It helps to start with a particular example of a second-level predicate. One can say of any 2-place relation R that it is transitive by saying   We quite often wish to confine attention to relations that are transitive, and for this and other purposes it is convenient to have an abbreviation for this notion. As a first thought one might suggest just   But this is inadequate for two connected reasons. First, the notation does not make it clear that ‘ R’ here represents a 2-place relation. More importantly, it cannot easily be extended to cases where the relation we wish to talk of is not represented by a single letter. For example, one might wish to say that if R is transitive then so is the relation which holds from x to y if and only if Rxy^Gy, but for this purpose the variables ‘ x’ and ‘ y’ need to be shown explicitly.24 Nor will it do to write simply   For this expression appears to contain ‘ x’ and ‘ y’ as free variables, whereas they are of course bound in both the antecedent and the consequent of the proposition we wish to express. Here are three ways of meeting this problem: ‘ … is transitive’ may be represented by  

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Page 129 Each of these notations is supposed to be just an abbreviation for what we started with, namely,

 

  In practice Church’s notation is the most convenient (for example, for stating rules of substitution), and so it has, in effect, superseded both Frege’s and Russell’s. But there is nothing wrong with Frege’s, and so far as I am aware whatever can be done with Church’s notation can also be done with Frege’s, and vice versa. (We have only to view Church’s formula as breaking into two at the colon, rather than the bracket, to obtain a minor variant on Frege’s formula.) As a matter of fact there is something wrong with Russell’s notation, for in certain cases the formulae that it yields would be ambiguous.25 But this is of minor importance. My point is that the Russellian ‘cap-notation’ is trying to do just what Church’s λnotation does do, and what Frege’s notation also does in a superficially different way. In this example it explicitly exhibits a first-level predicate ‘ R’ as argument to a second-level predicate ‘Trans’. But it is only an abbreviation, and is not to be thought of as making any new assumption about the status of the letter ‘ R’. It is often said that in Principia Mathematica propositional functions occur in two roles, both as predicates and as logical subjects, and that it is the cap-notation that accomplishes this (see, for example, Sainsbury 1979:290; Cocchiarella 1980:98). I cannot deny that Russell’s informal explanations do rather strongly suggest just this, for they frequently treat an expression such as ‘ R ’ as if it were a noun-phrase (such as ‘the relation which holds from any x to any y if and only if Rxy’), which is used to name what ‘ Rxy’ predicates of x and y. But he does this because his explanations are given in English , and in English one inevitably uses a noun-phrase to refer to what one is talking about. (The present example illustrates this very nicely: in English we use the predicate ‘ … is transitive’, which has the syntax of a first-level predicate and so requires a noun-phrase as its subject.) But the language of the theory of types is not English, and it contains no way of turning a predicate-expression (of any level) into a noun-phrase. In particular the cap-notation does not do this, and because it looks as though it does I think that it is better avoided. Frege’s notation is less misleading on this score, because it retains within the symbol for a second-level predicate the indication that the following variables are bound. So it is easier to see that the symbol ‘ Rxy’ is still a symbol for a predicate, and not for an associated nounphrase, both in ‘Transxy( Rxy)’ and in what this abbreviates. The point of this discussion of ‘Trans’ was to seek for a suitable way of representing a second-level predicate. The example was of a particular

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Page 130 second-level predicate, which could be spelt out in full without any abbreviation. But I aim to use it as a guide to the best way of introducing a variable which takes the place of any arbitrary second-level predicate, and is used not to abbreviate a given one but to generalize over them all. As I have said, I think that we are least likely to mislead ourselves if we follow Frege’s method. He introduces a new letter ‘ M ’ which functions in this role, and it will therefore occur in such contexts as   This new variable can then be bound by quantifiers in the usual fashion, and we are ready to proceed to the next level of the hierarchy. But we still treat predicates as predicates; they do not become nouns. Some, such as Quine, will no doubt protest that we are treating predicates as noun-phrases when we use quantifiers that bind predicate-variables. This is again because in English the quantifiers are expressed by such words as ‘every’, and English grammar requires that these words be followed by a noun or noun-phrase.26 But the language of the theory of types is not English, and its quantifiers are not bound by the same restriction. We may nevertheless quite easily understand them. Just as a quantifier over individuals, ‘ x (—x—)’, may be explained as saying that ‘—x—’ comes out true for all ways of interpreting ‘ x’, so equally ‘ F (—F —)’ may be explained as saying that ‘—F —’ comes out true for all ways of interpreting ‘ F ’. In the first case one interprets the letter (on a given domain) by saying what object (in that domain) it is to refer to, and in the second case by saying which objects (in that domain) it is to be true of. But this does not treat a predicate-letter as if it named an object, and in the theory of types there is no way of doing this: a predicate always occurs with the syntax of a predicate, and not that of a name.27 So far I have described only the hierarchy of monadic predicates. The full theory of types, of course, includes dyadic predicates, and more generally, predicates of any polyadicity. This also introduces a complication into what I have described as the level of a predicate, for in the full theory there are also what one naturally calls ‘mixed level’ relations, taking one argument of one level and another of a different level. This certainly complicates things in practice, but no difference of principle is involved, so I here pass over all the details. It is still the case that a predicate of any type can significantly occur only with arguments of the appropriate lower type(s). The rationale for this is completely straightforward, and can be illustrated just from the monadic hierarchy that we began with. At the lowest level are names of individuals. Next come the first-level predicates, which contain gaps where such a name may be slotted in to make a sentence, or a variable which takes the place of those names to make an open sentence. Next come the second-level predicates which contain gaps where a firstlevel predicate may be slotted in. And so on up. But a gap that may be filled by the name of an individual (say, ‘Socrates’) cannot be filled instead by an expression of

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Page 131 any other type, for example, by ‘ … is a man’ or by ‘ x (—x—)’, for the result would simply be ungrammatical, for example,   These are obviously not well-formed sentences, and the same continues to apply as we move further up the hierarchy. We have seen that Russell himself gave just this line of argument in ‘On the Substitutional Theory’ (177– 78) and in ‘On “Insolubilia”’ (201–2). I think that he means to repeat it in §4 of Chapter 2 of the Introduction to Principia Mathematica , which is entitled ‘Why a given function requires arguments of a certain type’.28 My explanation spoke of the ‘gaps’ which expressions for propositional functions contain, whereas in this section Russell speaks of the ‘ambiguity’ that is essential to a function. It would be fair to say that what we each have in mind is that an expression for a function contains a free variable, and so the function cannot occur in a proposition unless either it contains some higher-level function (such as a quantifier) which binds this variable, or the variable is supplanted by a constant of suitable type. In Russell’s terms, the ‘ambiguity’ must be eliminated if a genuine proposition is to result. Moreover, he explicitly says that in is a man is a the ambiguity is not eliminated, evidently because there is here nothing to bind the variable ‘ x’ (48). There are times when he shows quite clearly that his cap-notation is not intended to turn a predicate into a name, grammatically suited to function as a subject-expression to a first-level predicate. In ordinary English there are many ways of nominalizing what starts as a predicate, but Russell’s focus is on mathematics, and in the vocabulary of mathematics there is only one nominalizing technique that is at all widespread, namely, that which prefixes ‘the class of … ’. But although Russell’s theory now admits propositional functions, it is still a ‘no-class’ theory and contains no such nominalizing device. It does introduce a notation which looks as if it refers to classes. Using modern symbols, the definition is that formulae containing class-descriptions   are to be taken as short for the associated formulae29   This definition has some similarities to Russell’s well-known definition of definite descriptions in ‘On Denoting’. In that case, what appeared to be

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Page 132 a reference to a particular individual was replaced by a quantifier ranging over individuals, and in the present case what appears to be a reference to a particular class is replaced by a predicate-quantifier. Perhaps it was this resemblance that led Russell to say that it was ‘On Denoting’ that gave him his clue to the theory of classes. But in truth the ideas are very different. The theory of definite descriptions assumes the existence of individuals, though it ‘re-parses’ some expressions which apparently refer to them. But the superficially similar theory of classes does not in any way assume the existence of classes, as ordinarily conceived. The class-expressions in Principia are treated as incomplete symbols and eliminated by a paraphrase that does assume the existence of propositional functions, but not of the classes that may be viewed as resulting from their nominalization. I add that Russell’s reason for introducing this definition was that he understood his predicate-letters intensionally, but wished to ensure that the class-expressions functioned extensionally. The definition does achieve this result, that is, it allows us to deduce the usual axiom of extensionality30   But this does not create the problems that Frege’s notorious axiom V does, even though it looks exactly the same as his axiom. Problems are avoided just because the expressions ‘{ x:Fx }’, which look as if they refer to classes, are construed by Russell as having the syntax of predicates and not of names. As a matter of personal preference, I would rather construe the predicate-letters extensionally in the first place. In the orthodox first-level logic we assume the correctness of Leibniz’s law   Its correctness is required by what is now the standard way of explaining validity in this logic. A valid formula is one that is true in all domains under all permitted interpretations, and the permitted interpretations simply assign denotations. (That is, a name-letter is interpreted by assigning to it some object of the domain that it refers to, and a predicate-letter by assigning to it some objects which it is true of.) On this account, Leibniz’s law must be taken to be valid. As we all know, there are examples in a natural language when it appears not to be, because in these cases the senses of the expressions involved are making a difference, and not only their denotations. But in order to keep our logic simple we just shrug and say that in these cases the logic fails to apply. I would advocate a similar treatment of logic at the next level, that is, that we only allow as interpretations of the letter ‘ M ’ those that verify the formula31  

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Page 133 On this understanding, Russell’s definition of the usual notation for classes would serve no purpose, and where ordinary mathematics does apparently refer to classes we simply paraphrase this directly as a use of predicates—or, in Russell’s preferred terminology, of propositional functions. Of course, this was not Russell’s own view in the first edition of Principia Mathematica , but he was tempted to it in the second (Whitehead and Russell 1925). This brings me to my final question in this section: what is a propositional function? As we have seen, in earlier days Russell supposed that propositional functions had no existence apart from the propositions that contain them. This is the view of the Principles (§85), and in ‘On the Substitutional Theory’ it becomes a way of avoiding the assumption that they have any kind of existence. Moreover, when, in ‘Mathematical Logic as Based on the Theory of Types’, he finds this theory ‘technically inconvenient’ and reintroduces explicit variables for propositional functions, he still claims that these variables could in principle be eliminated in the same way as before (1908:77). But in Principia there is no longer any talk of how these variables might be avoided, and in fact the earlier approach seems to be entirely revised. For now that he has seen that if propositions are part of the theory then they will have to be distinguished into types, his reaction is to dispense with propositions altogether, since types may just as well be applied to propositional functions directly. So it comes about that in the formal system of Principia there are no variables ranging over propositions,32 and instead we find a new theory claiming that symbols for propositions are now to be viewed as ‘incomplete symbols’, with ‘no meaning in isolation’. This is Russell’s so-called ‘multiple-relation theory of judgement’. It is presented as a theory whereby ‘ x judges that p’ is no longer thought of as stating a relation between x and the proposition that p but instead as stating that a ‘multiple’ relation holds between x and the several constituents of p.33 As I understand it, something like this theory is meant to apply to any case where there appears to be reference to (or quantification over) propositions, and that is no doubt why in this same section that introduces the theory Russell is at pains to elucidate the apparent property of propositions that is of most relevance to logic, namely truth. (But, as in other examples of this theory, the ‘multiple relation’ aspect of his explanation of truth applies only to the case where p is an atomic proposition. The explanation of truth in other cases is designed to accord with the vicious-circle principle, and so falls outside my present topic.) It would therefore appear that we have a complete volte-face . The early view begins with the thought that propositional functions depend for their existence on the propositions that contain them. The propositions exist in their own right, but the functions either do not exist at all or—if they do—have only a derivative existence. In any case, the early view does not count propositional functions as ‘constituents’ of the propositions in which they occur, and we find this claim repeated in Principia

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Page 134 Mathematica (39, 55). But at the same time the later view of Principia does, in its formal system, treat propositional functions as existing in their own right, and makes no use of variables for propositions, while the accompanying metaphysics says that propositions do not really exist after all, and it is only their constituents that do. If we may now identify propositional functions with the universals that are among the constituents of propositions, we apparently have a complete reversal. In the early view propositional functions, if they existed at all, existed only in the propositions that contain them, and not in their own right. But in the later view it would seem that propositional functions (as universals) do exist in their own right, while propositions do not. Instead, apparent reference to propositions must be paraphrased away as ‘really’ a reference to the particulars and universals that are their constituents. This account of a complete reversal depends upon identifying the propositional functions, which were once thought of as ‘abstracted from’ whole propositions, with the universals, which are always regarded as the constituents which propositions are made from. But the identification is hazardous, and it is noticeable that Russell himself says almost nothing about the relations between the two. Certainly, there are times when he asserts that a propositional function which is true of a given individual may be regarded as a property of that individual (see, for example, Russell 1907b: 281; Whitehead and Russell 1910:56–57, 166). There are also times when he uses the word ‘property’ of the universals that he usually calls qualities (for example, 1918:192). But these locutions seldom occur together, and it is quite possible that Russell did not wish us to draw the inference that they suggest. This problem is discussed in Chapter 2 of Linsky (1999), who suggests—as seems to me to be very plausible—that only some propositional functions should be equated with the universals that are constituents of propositions. As he points out (29–30), for the purpose of his ‘principle of acquaintance’ Russell needs only a small number of universals, namely, those that are required in the analysis of the more complex propositional functions that propositions may also contain. So I would suggest that it is only in these few simple cases that propositional functions may be more or less equated with those entities that Russell called universals, while in more complex cases the functions should still be viewed as existing only in the propositions that contain them.34 Hence, if these propositions are now to be construed as nothing ‘over and above’ their constituents, then the same will apply, too, to most propositional functions. For in the general case a propositional function is just like a proposition, except that it contains what Russell calls an ‘ambiguity’, but which we would rather call a free variable, or (after Frege) a ‘gap’. How then should we understand propositions (and propositional functions) in the new context of the ‘multiple relation’ theory of judgement? I think that we may take a hint from what Russell says when he is explaining this theory: ‘Owing to the plurality of the objects of a single judgement,

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Page 135 it follows that what we call a “proposition” (in the sense in which this is distinguished from the phrase expressing it) is not a single entity at all’ (44). To paraphrase this in more down-to-earth terms: we no longer suppose that there are such things as propositions, except insofar as there certainly are sentences which are thought of as expressing them. So it comes about that, for practical purposes, propositions are simply identified with sentences, and hence propositional functions with open sentences. This identification is explicit in works written after Principia (that is, 1918:185, 196; 1919:195), and it seems to me best to read it back into Principia itself. We have Russell’s own support for this reading, for he says in My Philosophical Development (1959): ‘Whitehead and I thought of a propositional function as an expression’ (124). It is no doubt the simplest course. It has seemed to several interpreters that if propositional functions are simply open sentences (in some unspecified language) then when a variable for propositional functions is bound by a quantifier we have to interpret the quantification as substitutional: it speaks simply of what results when the variable is replaced by all, or by some, of the relevant open sentences.35 Russell himself seems to have thought in the same way; at any rate in the much later An Inquiry into Meaning and Truth (1940) he explicitly says: ‘In the language of second-order, variables denote symbols, not what is symbolized’ (192). But there is an immediate objection to this approach, namely, that there cannot (in any learnable language) be more than countably many open sentences, and so this approach must be inadequate for the deduction of the classical theory of real numbers. However, we certainly do not have to adopt this interpretation of the quantifiers. After all, it is usual to say that the schematic letters ‘ a ’, ‘ b’, ‘ c ’ take the place of names without commitment to the idea that the bound variables ‘ x’, ‘ y’, ‘ z ’ that can take their place range only over the objects in the domain that happen to have names. We can similarly say that letters ‘ F ’, ‘ G’ take the place of open sentences without supposing that when they are bound by quantifiers the only interpretations that are relevant are those that we happen to have expressions for. I have already explained how. But it would certainly seem that Russell himself did not think in this way. SOME REFLECTIONS Russell certainly saw that what keeps his (simple) theory of types free from paradoxes is that it provides no way of naming what is first expressed by an expression of a different type. For example, in the lectures on ‘The Philosophy of Logical Atomism’ (1918), when he is endeavouring to explain what it is to understand a predicate, he says: ‘A predicate can never occur except as a predicate. When it seems to occur as a subject the phrase wants amplifying and explaining’ (205; similarly for relations: 206). The needed ‘amplification’ would be one that shows how the original claim could be

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Page 136 rephrased so that the predicate no longer seemed to occur as a subject. In a similar vein he has earlier said that propositions do not name facts, and added: ‘You must not run away with the idea that you can name facts in any other way; you cannot. You cannot name them at all … You can never put the sort of thing that makes a proposition to be true or false in the position of a logical subject’ (188, compare 269–70). In both places he should be understood as speaking of what can be done in the ‘logically perfect’ language which these lectures concern, a language which has the syntax of Principia Mathematica (197–98). In ordinary English you can certainly transform a predicate or a sentence into a noun-phrase, for example, by using such expressions as ‘the property of being wise’ or ‘the fact that Socrates was wise’, and in the Principles Russell had insisted that this must always be possible. But it is true that you cannot do that in the language of Principia Mathematica . Since Russell is writing these lectures not in that language but in English, he is constantly himself doing these things which he claims ‘cannot be done’ (as in the sentence just quoted from 188). But the thought is that it is just because such linguistic constructions are freely available in English that we so often find ourselves led into contradictions (as, for example, with the property of not being a property of itself). He gives just this diagnosis himself in the ‘Philosophy of Logical Atomism’: ‘The trouble that there is arises from our inveterate habit of trying to name what cannot be named’ (267). Naturally, the ‘logically perfect’ language will be one in which such contradictions cannot arise, so it will contain no means of ‘nominalizing’ an expression that is not already a noun.36 The distinction between ordinary English on the one hand, and the language of the theory of types on the other, is relevant to a point which is sometimes raised in objection to the theory, namely, that the theory cannot be stated without infringing itself.37 This is usually understood, in effect, as the point that you cannot state the theory in English while conforming to its own rules. But that is in no way surprising and not in any way a serious objection. The two languages are different languages, conforming to different rules of grammar, and if this were not so one could not sensibly claim that one is better than the other. What is perhaps a more pertinent point is that there is no way of stating, in the language of the theory of types, the rules of that language itself. To put this in different terms: the language does not contain its own semantics. So, if we feel that those semantics need an explicit formulation, we have to ‘ascend’ to a different language (a meta-language) at a higher level. But (a) why should we think that any explicit formulation is required? After all, we all learned to speak English without learning any explicit semantics for it, and I see no reason in principle why the language of the theory of types could not be mastered in the same way. The learner picks up the grammar of the language just by being constantly exposed to it. Wittgenstein in his Tractatus (1921) goes further, claiming that no semantics can be stated, for this is one of the main thoughts behind his dictum: ‘What can be shown, cannot be said’ (4.1212). But (b) I would

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Page 137 rather say that, if an explicit semantics is required, then Russell gave the right response in his introduction to the Tractatus (final paragraph), where he says that metalanguages are surely possible, though of course they must be handled with care, lest the contradictions break out once more. I set this point aside. It is true that the language of the simple theory of types cannot state its own semantics in any straightforward way, but that is not a serious objection. Much more serious is the point that there are so many other things which cannot be said in this language and which we do wish to be able to say. The best known instance, and the one that most affects Russell’s own ambitions, is the problem of how to introduce a suitable vocabulary for speaking of numbers. Russell could not believe (as Frege believed) that numbers may be regarded as objects of the lowest type (that is, as ‘individuals’). Instead, he begins with the idea that a number should be taken to be a class of equinumerous classes, and then with the advent of the ‘no-class’ theory this becomes the idea that talk of numbers should be paraphrased as talk of propositional functions, namely, those (of at least second level) that are true of all monadic functions of the lower level which are true of the same number of things. These are the propositional functions that we call the numerical quantifiers (‘there are 2 … ’, ‘there are 3 … ’ and so on). So what is required is a good theory of the numerical quantifiers, and that is something that the language of the theory of types apparently cannot provide. The main reason is very simple: the numerical quantifiers can be sensibly applied to monadic predicates of every level, but that apparently means that they themselves cannot be assigned to any level, and the theory of types cannot permit this. It was mainly this problem that first led Russell, in the theory which is sketched in the Principles , to include an infinite type. The idea was that classes of this infinite type should be able to have classes of all finite types as members, and perhaps even classes of their own infinite type. The language of Principia Mathematica contains no such type, and a first thought is that it would make no sense for it to do so. For the hierarchy of finite types is a strict hierarchy and not a cumulative one; at no stage in that hierarchy can an expression of one type be meaningfully applied to an expression of any other type than the one immediately below it. I have indicated how simple grammatical considerations apparently require this. With a cumulative hierarchy, such as we are familiar with in ZF set theory, extension to an infinite level seems quite natural. But this is because the ZF theory is a theory of objects (namely, sets) which all belong to one and the same logical type. However, the theory of types is not like this; it is essentially a theory of predicates , not of objects. I have nevertheless proposed (in ‘A study of type-neutrality,’ 1980) something like the addition of an infinite type. The initial thought is this: we do actually apply the same quantifier-symbols, ‘ ’ and ‘ ’, at every level in the hierarchy, and we do not think of them as having different meanings at each level. (The explanation of these quantifiers that I suggested, namely,

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Page 138 that ‘ α (—α—)’ counts as true if ‘—α—’ is true for every permitted interpretation of the variable ‘α’, applies unchanged at every level, whatever the type of the variable ‘α’.) To accommodate this phenomenon, Russell spoke of the ‘systematic ambiguity’ of formulae containing such symbols, but my response is that there is not really any ‘ambiguity’, for these symbols and do in fact mean the same at every level. This is the start towards recognizing that there are also what I call ‘type-neutral’ predicates, which are not restricted in their application to items of just one type, as the official language of the theory of types requires them to be. Supposing that this case is granted for ‘ ’ and ‘ ’, the next question is clearly: how many other such ‘type-neutral’ predicates should we recognize? Here, the first thought is that anything which can be defined just in terms of ‘ ’ and ‘ ’ (and the truth functions) should qualify. So, if we may assume that identity may be defined in these terms (that is, ‘α = β’ for ‘ φ(φα ↔ φβ)’), then the numerical quantifiers will qualify.38 But so also will many other predicates, for example, the predicate ‘Trans’ mentioned earlier, for this can meaningfully be applied to dyadic relations of every level. Russell himself produces the relevant generalization: certain words have ‘systematic ambiguity of type, such as truth , falsehood, function, property, class, relation, cardinal , ordinal, name , definition …. Such words and symbols embrace practically all the ideas with which mathematics and logic are concerned’ (Whitehead and Russell 1910:64–65). To put it in my own words: almost all of logic is concerned with what I call ‘type-neutral’ predicates, so the logic of these special predicates cries out for investigation. I have attempted to make a start on this in ‘A study of type-neutrality’ (1980), and I will not try to summarize those explorations here. I am the first to admit that the details of the theory (or theories) that I proposed there are not exactly straightforward. It is not easy to harmonize some natural thoughts about type-neutrality with the requirement of avoiding contradiction. I think it very likely that others could do a better job of it, but I do think that the idea is worth pursuing. It may reasonably be said that mathematics is adequately served by the ZF set theory (or its descendants, such as NBG or MKM). If one is concentrating on the notion of a set, then the ideas behind the ZF hierarchy can seem quite natural, because we do find it natural to think of sets in terms of the metaphor of construction: sets are (in a way) ‘built from’ their members. But for centuries philosophers have been concerned with other entities, for example, properties, or simply predicates, which no one would think of as ‘built from’ the objects that they happen to be true of. An indication is that we all find it natural to say that one and the same property might (in some other possible world) have applied to other objects than it actually (in this world) does apply to. By contrast, the usual understanding is that the membership of a class determines its identity in all possible situations (so it cannot have different members in different worlds, while remaining the same class).

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Page 139 It seems to me that Russell’s (simple) theory of types is a good start on how to think of such things as properties are supposed to be, but also that it needs to be supplemented by something like my idea of a ‘type-neutral’ predicate if obvious inadequacies are to be avoided. NOTES 1. My Philosophical Development (1959:79); Autobiography (1967:229). 2. This early theory of denoting is not (as I had once suspected) a relic of prePeano thinking, for it appears first in the revised draft of Part I of the Principles that Russell wrote in 1901 (Russell 1993, Paper 2). Since it is only one small part of this theory that is immediately relevant to my present topic, I do not discuss it here, but (contra Dau 1986) I do take it to be obvious that the theory will not do. (The criticisms raised by Geach 1962: Ch. 4 are decisive.) Russell rejects it without discussion in the first three pages of ‘On Denoting’ (1905). 3. The same applies to the form which Frege ends by preferring, namely, ‘the number of … is two’. Again, what fills the gap is a plural expression. (And I note that in this case it may well begin with ‘the’.) 4. I note, as confirming a similarity between Frege’s concepts and Russell’s plural objects, that Boolos (1984) shows how quantification over monadic concepts can be represented in English by plural quantification. 5. We shortly meet a second thought, i.e., in the text to n8. (In daily life we seldom do wish to say that one class is a member of another, but of course Russell is concerned with what is needed in mathematics.) 6. E.g., §104, §135n, §137n, §497. 7. In §48 a ‘predicate’ is in effect defined as a one-place concept, and it is admitted that this is scarcely distinguishable from what Russell calls a ‘class concept’ (cf. also §58). 8. Since a class-as-many is a plural object, and so must take a plural verb, it is not too easy to see how to say that this class-as-many is a member of some other. We might perhaps offer an example such as ‘the men in this room are members of one of the competing football teams’, where the membership relation is expressed by ’ … are members of one of … ’, a phrase which links two plural expressions. 9. Let the two lowest types be V0 (all individuals) and V1 (all classes of individuals). Then the cumulative structure is formed simply by ignoring V1 itself as a type and instead taking the sum of V0 and V1 as the next type. And so on up. 10. Strangely, the phrase ‘any man’ is not mentioned here, but the phrase ‘no man’ is now included. We may note that ‘all’ is now equated with ‘every’, and is no longer thought of as introducing a plural item. 11. In Principles he had argued that ‘some man’ and ‘a man’ must denote different objects, since there are contexts in which they are not interchangeable. Now he simply equates the two, with no further explanation. 12. In §III of ‘Mathematical Logic as Based on the Theory of Types’ (1908) he does give arguments against the old theory and for some features of the new theory, but scopes are still not mentioned. 13. This is the version that Dau (1986) calls the ‘unofficial’ version. 14. In ‘On “Insolubilia”’ (1906c: 202–3) Russell offers a different argument for there being an infinity of individuals. He is assuming there that propositions are individuals and shows how to construct an infinity of different

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Page 140 propositions. (Let a be an individual; let p1 be the proposition ‘ a = a ’; let pn+1 be the proposition ‘ a = pn’.) In ‘The Substitutional Theory’ (1906b) he offers a proof that there are infinitely many relations (181), but this proof relies upon construing relations intensionally. Of course, by the time that we reach Principia , an axiom of infinity can no longer be deduced and has to be simply postulated. 15. For useful surveys of investigations into Quine’s NF, and its descendant ML, see Quine 1963: Ch. 13, and Hatcher 1968: Ch. 7. 16. By ‘illegitimate’ Russell presumably means ‘non-existent’. Compare an earlier statement: ‘At present it is not easy to see where this series [sc. of ordinals] begins to be non-existent, if such a bull may be permitted’ (144). 17. As Russell describes the situation, ‘anything said about a propositional function is to be regarded as a mere abbreviation for a statement about some or all of its values’ (154n)—that is, about some or all of the propositions which one might think of as containing that function. This recalls his statement in the Principles that ‘the φ in φ x is not a separate and distinguishable entity: it lives in the propositions of the form φ x, and cannot survive analysis’ (§85). 18. Perhaps better, ‘the result of replacing a in p by … is true’. Russell’s formulae are deliberately ambiguous between expressions which assert propositions and expressions which name those propositions. Without harm to the system one may easily resolve this ambiguity (as Landini 1998 does) by introducing an explicit symbol, say ‘{ … }’, so understood that ‘{ p}’ names what ‘ p’ asserts. A suitable comprehension axiom then asserts that all propositions can be named in this way. But in this system it is only propositions and the individuals that occur in them that can be named, for these are the only things that are assumed to exist. 19. The formal definition is complex, and so I do not give it. The reason is that if—as is natural—one thinks of a simultaneous substitution as just one substitution followed by another, then what is introduced by the first substitution may affect the second, which is not what is wanted. Russell shows how to avoid this on pp. 173–74. Landini (1998) observes that the complication is not really needed (133). 20. Some fairly simple examples are given in Hylton (1980:21); more complex examples may be found in Landini (1998: Chs. 4–7, passim) and (2003: §§3–4). 21. He also repeats it in ‘On “Insolubilia”’: 201–2. 22. The puzzle in its original version concerns classes of propositions. Clearly it can be rephrased in terms of propositional functions which take propositions as arguments, and then rephrased once more in the terminology of the substitutional theory, replacing reference to these propositional functions by references to all the propositions which result from a given proposition by substituting for some proposition that occurs in it. 23. Full details are given in Landini (1998:201–6). He dubs this contradiction ‘the p0/ a 0 paradox’. 24. Principia would be tempted to avoid this by adopting the circumlocution: xy( Sxy↔ Rxy Gy) → (Trans ( R) → Trans ( S)) 25. For a simple example, consider and explicitly as second-level predicates. Then the same formula is rendered in these three ways by our three notations: Frege: x y( Rxy) Church: (λ x: (λ y: Rxy)) Russell: ( ( R )). Clearly the Russellian version is ambiguous, for it cannot show whether the initial ‘ ’ governs the capped ‘ x’ or the capped ‘ y’. (In the formal development of Principia the cap-notation is very seldom used , since the device of

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Page 141 systematic ambiguity allows one to omit it. Cf. ‘We have found it convenient and possible … to keep explicit use of symbols of the type ‘φ ’ … almost entirely out of this work’ (19).) 26. There are exceptions. In such words as ‘everywhere’, ‘anyhow’, ‘sometimes’ the quantifier is followed not by a noun but by an adverb. 27. I should make it clear that this account of the meaning of ‘ F ’ is mine, and not Russell’s. I come later to Russell’s own account. 28. I regard this section as applying to the simple theory of types. Of course Russell elsewhere invokes the vicious-circle principle to justify his type-restrictions, and that is the appropriate procedure for the ramified theory. But in this section Russell means by ‘type’ just what I mean by ‘level’. 29. In the Principia version the variable ‘ G’ is here restricted to range only over ‘predicative’ functions of x. This of course is a complication required only by the ramified theory of types, so I here ignore it. (A full explanation is given in L. Linsky 1987:30–33.) 30. The deduction assumes that identity is defined for predicate-letters, e.g., by F = G for M ( MxFx ↔ MxGx). 31. Hence an interpretation of the letter ‘ M ’ will simply specify which interpretations of ‘ F ’ it is to be true of. 32. The sole exception is proposition *14.3, and the accompanying comment makes it clear that it is an exception. 33. The ‘multiple relation’ theory of judgement appears first in ‘On the Nature of Truth’ (1907a), but merely as a suggestion which Russell does not affirm. It is affirmed in ‘On the Nature of Truth and Falsehood’ (1910a) and in Principia (1910: Introduction, Ch. 2, §2, repeating what was evidently a draft of this introduction, namely, ‘The Theory of Logical Types’, 1910b: 223–25). The theory reappears in Ch. 12 of The Problems of Philosophy (1912), and was to have played an important role in the unpublished Theory of Knowledge manuscript of 1913. Apparently, Wittgenstein’s criticisms of the theory of judgement were a main cause of why Russell abandoned that work. But he continued to think that the ‘multiple relation’ theory was at least on the right lines, since he proposes it once more (though tentatively) in lecture IV of ‘The Philosophy of Logical Atomism’ (1918:225–26). 34. Linsky suggests that all of Russell’s so-called ‘predicative’ functions will correspond to universals (1999:104–9). But since predicative functions may still have some internal complexity, I regard this suggestion as too generous. 35. E.g., Sainsbury (1979: Ch. 8, §3); Linsky (1999:15–20). 36. It is claimed by Cocchiarella (1980) that these claims about what one cannot say are due to the influence of Wittgenstein, and therefore should not be read back into Principia , which was composed before Russell met Wittgenstein (109–11). However, I think myself that very many of the views that Russell generously credits to Wittgenstein were views that he had already reached himself, or were implicit in what he had already thought, before they ever met. And this particular view, that nominalizing leads to contradictions, was one which he himself had canvassed way back in the Principles of Mathematics. He surely did not need to learn it from anyone else. 37. The objection was raised both by Gödel and by Max Black in their contributions to Schilpp (1944). It was pressed again by Fitch (1952:225) and by the Kneales (1962:670). There is a discussion in Copi (1971:71–75), and a recognition that the objection is of no importance in Landini (1996: §2). 38. I had had this thought, in the middle 1960s, before I was informed (by Arthur Prior) that Borkowski (1958) had had it before me. But I certainly learnt something from reflecting on what Borkowski had to say.

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Page 142 REFERENCES Boolos, G. (1984) ‘To be is to be a value of a variable, or to be some values of some variables’, Journal of Philosophy 81: 430–49. Borkowski, L. (1958) ‘Reduction of arithmetic to logic based on the theory of types without the axiom of infinity and the typical ambiguity of arithmetical constants’, Studia Logica 8: 283–95. Bostock, D. (1980) ‘A study of type-neutrality’, Journal of Philosophical Logic 9: 211–96 and 363–414. Cocchiarella, N. (1980) ‘The Development of the Theory of Logical Types and the Notion of a Logical Subject in Russell’s Early Philosophy’, Synthese 45: 71–115. Copi, I. M. (1972) The Theory of Logical Types, London: Routledge and Kegan Paul. Dau, P. (1986) ‘Russell’s First Theory of Denoting and Quantification’, Notre Dame Journal of Formal Logic 27: 133–66. Fitch, F. B. (1952) Symbolic Logic, New York: Ronald. Frege, G. (1884) Die Grundlagen der Arithmetik , Breslau: Koebner. Translated by J. L. Austin as The Foundations of Arithmetic , Oxford: Blackwell, 1953. Geach, P. T. (1962) Reference and Generality , Ithaca, NY: Cornell University Press. Hatcher, W. S. (1968) Foundations of Mathematics, Philadelphia: W. B. Saunders. Hylton, P. (1980) ‘Russell’s Substitutional Theory’, Synthese 45: 1–31. ——. (1990) Russell, Idealism, and the Emergence of Analytic Philosophy , Oxford: Clarendon Press. Kneale, W. and M. (1962) The Development of Logic , Oxford: Clarendon Press. Lackey, D., ed. (1973) Essays in Analysis , London: George Allen and Unwin. Landini, G. (1996) ‘Will the real Principia Mathematica please stand up?’, in R. Monk and A. Palmer (eds), Bertrand Russell and the Origins of Analytical Philosophy , Bristol: Thoemmes Press: 287–330. ——. (1998) Russell’s Hidden Substitutional Theory , Oxford: Oxford University Press. ——. (2003) ‘Russell’s Substitutional Theory’, in N. Griffin (ed.), The Cambridge Companion to Bertrand Russell, Cambridge: Cambridge University Press: 241–85. Linsky, B. (1999) Russell’s Metaphysical Logic , Stanford, CA: CSLI Publications. Linsky, L. (1987) ‘Russell’s “No-Classes” Theory of Classes’, in J. J. Thomson (ed.), On Being and Saying, Cambridge, MA: MIT Press: 21–39. Marsh, R. C., ed. (1956) Logic and Knowledge , London: George Allen and Unwin. Quine, W. V. O. (1937) ‘New Foundations for Mathematical Logic’, American Mathematical Monthly 44: 70–80. ——. (1951) Mathematical Logic , 2nd edn, Cambridge, MA: Harvard University Press. ——. (1963) Set Theory and its Logic , Cambridge, MA: Harvard University Press. Russell, B. (1903) Principles of Mathematics, 2nd edn, London: George Allen and Unwin, 1937. ——. (1905) ‘On Denoting’, Mind 14: 479–93. Reprinted in Marsh (1956) and in Lackey (1973). ——. (1906a) ‘On Some Difficulties in the Theory of Transfinite Numbers and Order Types’, Proceedings of the London Mathematical Society 2: 29–53. Reprinted in Lackey (1973).

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Page 143 ——. (1906b) ‘On the Substitutional Theory of Classes and Relations’, printed for the first time in Lackey (1973). ——. (1906c), ‘On “Insolubilia” and Their Solution in Symbolic Logic’, published in French in the Revue de Métaphysique et de Morale 14: 627–50. English translation in Lackey (1973). ——. (1907a) ‘On the Nature of Truth’, Proceedings of the Aristotelian Society 7: 28–49. ——. (1907b) ‘The Regressive Method of Discovering the Premises of Mathematics’, first printed in Lackey (1973): 272–83. ——. (1908) ‘Mathematical Logic as Based on the Theory of Types’, American Journal of Mathematics 30: 222–62. Reprinted in Marsh (1956). ——. (1910a) Philosophical Essays, London: Longmans Green, 2nd edn, London: George Allen and Unwin, 1966. ——. (1910b) ‘La théorie des types logiques’, Revue de Métaphysique et de Morale 18: 263–301. English translation in Lackey (1973). ——. (1912) The Problems of Philosophy , London: Williams and Norgate. ——. (1918) ‘The Philosophy of Logical Atomism’, Monist 28: 495–527 and 29: 33–63, 190–222, 344– 80. Reprinted in Marsh (1956). ——. (1919) Introduction to Mathematical Philosophy , London: George Allen and Unwin. ——. (1922) Introduction to Tractatus Logico-Philosophicus , in Wittgenstein (1921). ——. (1940) An Inquiry into Meaning and Truth , London: George Allen and Unwin. ——. (1959) My Philosophical Development, London: George Allen and Unwin. ——. (1967) Autobiography , London: George Allen and Unwin. ——. (1993) The Collected Papers of Bertrand Russell, vol. 3, Towards the “Principles of Mathematics”, 1900–02 , ed. G. H. Moore, London: Routledge. Sainsbury, R. M. (1979) Russell, London: Routledge and Kegan Paul. Schilpp, P. A., ed. (1944) The Philosophy of Bertrand Russell, Evanston and Chicago: Northwestern University Press. Whitehead, A. N., and Russell, B. (1910) Principia Mathematica , vol. 1, London: Cambridge University Press. ——. (1925) Principia Mathematica , 2nd edn, London: Cambridge University Press. Wittgenstein, L. (1921) Tractatus Logico-Philosophicus , 2nd translation by D. F. Pears and B. F. McGuinness, London: Routledge and Kegan Paul, 1961.

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Page 144 8 Psychological Content and Indeterminacy with Respect to Being Two Notes on the Russell-Meinong Debate Johann Christian Marek PRELIMINARIES There have been different stages in the Russell-Meinong debate,1 and the conference at which this paper was presented provided some evidence that the dispute is still going on. I present here a rather detailed note on a philosophical-psychological point —Russell’s denial of psychological contents—which concerns both Bertrand Russell and Alexius Meinong, and a shorter note on a logical-ontological point — Meinong’s principle of the indifference of the pure object to being—which may be more significant to Meinong interpreters. The debate was opened in 1899 by Russell’s review of Meinong’s ‘Ueber die Bedeutung des Weber’schen Gesetzes’, and in 1903 Russell quite often refers to Meinong in The Principles of Mathematics. The most intensive and lively stage of the discussion was constituted by Russell’s reviews (1904, 1905b, 1906, 1907) and letters2 and his essay (1905a), and by Meinong’s reaction to them (1904a, 1907) between the years 1904 and 1907. After 1907, until Meinong’s death in 1920, you can find references on both sides (Meinong 1910, 1915, 1917; Russell 1914, 1918–19, 1919). Meinong mentioned Russell’s criticisms and comments relatively often, and he reacted to them mostly in a defensive way. He nearly always referred to the texts that Russell had written about him or which were relevant for his work. Meinong never studied Russell’s work for its own sake; he did not show much interest beyond Russell’s commentaries. On the other hand, Russell was using and quoting Meinong’s views quite often, although he was becoming more and more critical until finally Russell often referred to Meinong as an example of a philosophy (especially philosophy of logic and also philosophy of psychology) which has to be refuted. The main reason why Meinong did not study Russell’s work in more detail was an external one. Meinong suffered from an inherited semi-blindness, a handicap that was a hindrance already in his early life and deteriorated to almost complete blindness in the course of his life. People, his wife, for example, had to read philosophical texts to him. So it was rather awkward for him to get acquaintance with larger works in English (see Dölling 2001:55–56).

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Page 145 Russell’s later, mostly critical comments on Meinong (in 1914, 1918–19, 1919) were not noticed by Meinong, and other comments (in 1921 and in 1959, for example) could not be noticed by the nonexistent Meinong anymore. Later stages of the debate were the work of commentators, friends and foes of both sides. John Findlay’s book on Meinong—presented in 1933 as a doctoral thesis in Graz and evaluated by Ernst Mally as supervisor3—is still a valuable source. Gilbert Ryle’s comments are well known,4 as well as William Kneale’s dictum ‘With the horrors of Meinong’s jungle fresh in our minds, we cannot accept such language until we are convinced that it is harmless.’5 In the late fifties Roderick M. Chisholm started writing contributions to Franz Brentano’s descriptive psychology and the notion of intentionality, and to Meinong’s theory of objects. Chisholm’s interest was stirred up by George E. Moore’s discussion of Brentano and by Russell’s criticism of both Brentano and Meinong, especially by Russell’s arguments in The Analysis of Mind (Chisholm 1986:10; 1997:8). In his ‘Self-Profile’, from 1986, Chisholm writes: I was especially impressed by what Brentano had written about consciousness and intentionality; it seemed to me to be much more profound philosophically than what was to be found in what British and American philosophers were saying about the philosophy of mind. And I was also intrigued by Meinong and had the feeling that Russell had not succeeded, as many thought he had, in demolishing the theory of objects. (10) TWO MAIN THEMES IN RUSSELL’S CRITICISM OF MEINONG, AND THE ROLE OF ‘ON DENOTING’ A good number of people superficially acquainted with the Russell-Meinong relationship are confined to Russell’s short critical remarks in ‘On Denoting’. Taken in isolation these remarks give the impression that Russell’s reception of Meinong consisted solely in the exposition of obvious inconsistencies in Meinong’s theory of objects. Indeed, Russell explicitly accuses Meinong five times of not obeying the law of contradiction.6 If one reads some of the short commentaries on Russell’s relation to Meinong, including Russell’s own comments, that negative impression remains. One gets the impression that Russell mentioned Meinong only in order to reject his theory as bizarre and untenable, because such a theory appears ‘to result from a certain logical naiveté, which compels us, from poverty of available hypotheses, to do violence to instincts which deserve respect’ (Russell 1913: Part 2, Chapter 1:108), and because in such a theory ‘there is a failure of that feeling for reality, which ought to be preserved even in the most abstract studies’ (Russell 1919: Chapter 16:169). Russell

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Page 146 changed his former objections of breaking the law of contradiction mainly to reproaches of lacking a (robust) sense of reality.7 The negative impression one may get from comments like that has often led to an oversimplified and wrong picture of the Russell-Meinong relationship. In point of fact, Russell took Meinong’s philosophy very seriously and studied many of Meinong’s writings carefully (more than one thousand pages). During several years Russell was very sympathetic to Meinong’s positions,8 both in philosophy of logic and in philosophy of mind. One should keep in mind that—besides the differences—there are quite a lot of affinities between both thinkers: • Meinong was not a trained and qualified mathematician like Russell, but he knew traditional logic since he had attended Franz Brentano’s logic courses in 1875 and in 1877 in Vienna9 and had co-operated with Alois Höfler in writing a textbook in logic (1890). Meinong, in contrast to his pupil Mally, did not deal with the logical reform that had been accomplished by Peano and Frege, whereas Russell saw a kind of enlightenment to be derived from Peano (see Russell 1959: Chapter 6:66). • In contrast to Russell, Meinong was a studied historian, a trained historian of philosophy and a psychologist too (though he was more concerned with descriptive than with experimental psychology). Russell—as he himself said in his review (1904:350)—was not himself a psychologist, but he later became more and more interested in psychology and theory of knowledge. • Meinong’s conception of his theory of objects came close to Russell’s view of philosophy of logic (and mathematics) in Russell’s The Principles of Mathematics (1903), where Russell dealt with a lot of metaphysical problems (space, matter, motion, causality, part and whole, continuum). In 1904, Russell wrote in a letter to Meinong: ‘I find myself in almost complete accord with the general point of view and the problems which are dealt with are ones which seem to me very important. I myself have been accustomed to use the name “Logic” for that which you call “Theory of Objects”, and the reasons you cite against this use on p. 20ff appear to me hardly decisive.’10 Indeed, Meinong used the term ‘logic’ in a different way, namely for technology to get a better, more effective technique of thinking and reasoning; logic was supposed to pertain to practical philosophy.11 • Russell appreciated Meinong’s empirical attitude when he said ‘there is an empirical manner of investigating, which should be applied in every subject-matter’ (1904:205), and Meinong characterized his own method also in this vein. Later Meinong said that his philosophy is a philosophy from below , a working method that follows the precepts of a kind of bottom-up thinking. Similar to the empirical sciences, which start from experience as given data, the theory of objects as a

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Page 147 paradigmatic a priori science starts with the pre-given things, which are subsistent [ bestehend ] or even outside of being [ außerseiend], as data.12 Russell’s dictum ‘grammar, though not our master, will yet be taken as our guide’ (1903: Chapter 4: §46:42) has a counterpart in Meinong (1904a: §10:513 [113]), where it is written ‘that the general theory of objects has to learn from grammar just as the specialized theory of objects can and must learn from mathematics’.13 In Meinong’s Nachlass you can find the remark that ‘the investigation starts best on the linguistic material’.14 Because of this ‘the answer to the question what the common man thinks of this or that situation or of this or that word is an indispensable presupposition of all the rest’.15 There are two main and fundamental criticisms that Russell raised against Meinong, and it is worth noting that Russell himself was at first an adherent of the views he later criticized. 1. The one main criticism is concerned with Meinong’s acknowledgement of nonentities (beingless objects), or better, with Meinong’s theory of objects and the related concept of a kind of intentionality or semantics which requires nonentities as objects. 2. The other is concerned with Meinong’s (descriptive) psychology, especially the thesis that consciousness has to be conceived as a relation to objects with the aid of mental content. In ‘On Denoting’ there is explicit criticism against Meinong’s conception of entities or, rather, nonentities. Russell thinks he can cure Meinong’s inconsistencies radically by his theory of denoting. The problems involved stem from the view ‘that if a word means something, there must be some thing that it means. The theory of descriptions which I [Russell] arrived at in 1905 showed that this was a mistake and swept away a host of otherwise insoluble problems’ (1959: Chapter 5:63). In ‘On Denoting’ Russell introduced another theory that was important for him, namely, the distinction between (knowledge by) acquaintance and knowledge by description. The distinction between acquaintance and knowledge about is the distinction between the things we have presentations of, and the things we only reach by means of denoting phrases … In perception we have acquaintance with the objects of perception, and in thought we have acquaintance with objects of a more logical character; but we do not necessarily have acquaintance with the objects denoted by phrases composed of words with whose meanings we are acquainted. (1905a: 479–80) Thus in every proposition that we can apprehend … all the constituents are really entities with which we have immediate acquaintance. (492)

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Page 148 Logical analysis shows which constituents are only apparent ones and can be eliminated for that reason. It is worth noting that the notion of acquaintance plays a rather important part in Russell’s later criticism of Meinong’s philosophy of mind. As we will see, yet another reason for rejecting Meinong lies dormant in Russell’s 1905 article. MEINONG’S THEORY OF MENTAL CONTENT Russell’s Initial Agreement with Meinong’s Account In his 1904 reviews, Russell did not criticize Meinong’s division of a mental experience into act, content and object,16 rather he showed agreement with this distinction. Later on, in The Analysis of Mind (1921), Russell thought he had to abandon Brentano’s and Meinong’s central views of knowledge and of mental experience. Russell severely opposed that tripartite distinction, and finally he completely abandoned mentality intentionalistically understood. Conceding that until very lately he had believed in Brentano’s view of mental directedness to objects, Russell said he could not believe anymore ‘that mental phenomena have essential reference to objects’ (1921: Lecture I: 15). In My Philosophical Development (1959: Chapter 12:134) he ascribed to Brentano the view that in sensation there are three elements, act, content and object—a view he had originally accepted, Russell said. It is controversial whether Brentano had really divided the elements of a sensation into act, content, and object, as Russell declared, and it is also controversial whether or in what sense Brentano’s thesis that all mental acts have something as object can be interpreted in the way Meinong did, to wit, via a relational theory of objects of thought. In any case, Meinong held those views later criticized and dismissed by Russell. In contrast to his argumentation against nonexistent objects in ‘On Denoting’, Russell did not try to prove that Meinong held a false, contradictory point of view. Instead, he came to think that the distinction between content and object is needless and that Meinong had not adequately proved that mental acts and contents were existing things. In his interpretation and criticism of Meinong’s conception of a psychological (mental) content, Russell did not mention Twardowski’s work On the Content and Object of Presentations (1894). This has some advantages because Twardowski’s account led several interpreters astray in interpreting Meinong’s psychological content, as we will see. Introduction of Mental Contents à la Meinong Certainly it makes a difference, (1) whether a person is happy that it is raining, or whether the person is only assuming that it is raining, [different modes, acts]; (2) whether a person is happy that it is raining (about

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Page 149 the rain), or whether the person is happy that the sun is shining (about the sunshine), [different contents or objects]. We can make out distinct mental facts, but are the aforementioned differences genuinely mental? Meinong thought that the difference between the act-aspects is a genuinely mental difference, and he thought that different objects constitute different mental events (experiences) although this difference is not genuinely mental. Thinking of different objects is only correlated with a genuinely mental difference because there is a correlation between the object and something in the experience that Meinong calls ‘psychological content’. If you have two different presentations [ Vorstellungen ], one of red and another of green, for example, the difference between the objects is founded on a genuinely mental difference, namely, the difference between the psychological red-content and the psychological green-content. The presentations are presentations of two different objects, red and green, via the correlated different psychological contents. Meinong explicitly introduced the distinction between the (psychological or mental) content and the object of presentations in his treatise ‘On Objects of Higher Order and Their Relationship to Internal Perception’ (1899). There, he conceded that one could find a great deal of interesting and useful information in Twardowski’s study from 1894, but—as Meinong emphasized—concerning ‘the whole difficult and important problem of objects’ and not exactly in relation to the difference between content and object (1899: §2:381 [141]). Twardowski’s book sharpened Meinong’s view on nonexistent and impossible objects. It is true that Twardowski’s work can be seen as the occasion, or perhaps as the catalyst, for Meinong to begin to think more deeply about the content-object distinction, and indeed Meinong took over some of Twardowski’s arguments, even though in slightly modified versions. However, Meinong never thought that Twardowski’s distinction and his conception of the content of a presentation could be understood as a precise conceptual clarification that should be adopted unquestioningly. After 1894, Meinong took psychological contents, that is, the contents of presentations, of judgements and so on, as something purely mental and concrete. Therefore, such contents are always something real. Twardowski, however, says that the content is a mental picture, but he also identifies the mental content with the meaning of a name and with Bolzano’s objective presentation (idea), that is, the presentation as such [ Vorstellung an sich ]. For that reason Twardowski takes the content—in contrast to the (real) act—as something that always lacks reality. Meinong, however, became more and more aware of the purely mental nature of the psychological content. He realized that the mental content was not something abstract or conceptual in the sense of something inten s ional (with an ‘s’), that it was not some sort of a meaning at all. Meinong’s Argumentation in Favour of the Content-Theory Like Twardowski, Meinong demonstrated that psychological contents of mental acts have to be acknowledged by appealing to different arguments.17

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Page 150 1. A first argument shows that when the presentation of an object exists, the content also exists, although the object may not exist. The presentations (a) of a golden mountain, (b) of the difference between red and green, or (c) of a round square are such cases. The presentations concerned always exist, but their objects do not: there is no such thing as the golden mountain (= a). Differences do not exist, they may only subsist (= b), and things like round squares cannot exist (= c). 2. The second argument asserts that a presentation can be different to its object. The presentation can be about past or future objects, whereas the presentation itself occurs at the present moment. The object may be physical but the presentation as such is wholly mental, and with it its respective content. The object may be coloured or cold or heavy, but the content cannot be of this kind. 3. In a further argument Meinong shows that we know from experience that we present different objects. Since it cannot be that completely similar presentations are about different objects, the variation of objects must be correlated with a variation of the presenting experiences. This argumentation is summarized in ‘On Objects of Higher Order’: On the other hand, however, presentations—as far as they are presentations of different objects— cannot be completely similar to each other: In whatever way the relation between the presentation and its object is to be conceived, the difference between the objects must somehow come down to a difference between the presentations in question. Now that in which presentations of different objects differ from each other, irrespective of their agreement in act, is that which claims the designation ‘content of presentation’: this exists, is therefore real and present, is also psychical of course, even when the object presented, so to speak, by means of it, may be non-existent, non-real, non-present, nonpsychical. (1899: §2:384 [143]) The content is something immanent but it is usually not an immanent object in the sense that it is the object of the presentation and exists also inside the presentation. The mental content becomes such an immanent object only if it is the object of a so-called self-presentation, that is, in a reflexive experience in which the content presents itself, so to speak (compare Marek 2001, 2003). Both the existing real things, which are not mental, and the subsisting ideal things cannot literally exist in the mind, and neither do things like the golden mountain or the round square, because they do not exist at all. Although Meinong admits nonexistent objects, he claims that existing in a presentation (something like Brentano’s phenomenal, intentional inexistence of an object) is not existence at all; it is at most ‘pseudoexistence’ (Meinong 1899: §2:383 [142]; 1906: §10:422–25). What, in

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Page 151 fact, does exist in the case of the presentation of the golden mountain, for example, is the whole presentation of the golden mountain, which includes the act-aspect and the content-aspect as its parts (see Meinong 1899: §2:382–84 [141–43]). Mental Contents as Qualia that Can Be Introspected In §11 of ‘Über die Erfahrungsgrundlagen unseres Wissens’ (1906) Meinong alludes to the experiential character of the content. To have a content is, as it were, to feel in a certain way. The content is an inherent particular quality, a kind of quale . We feel different when different things are presented to us.18 Nevertheless, Meinong concedes that the postulation of mental contents is mainly theoretically inferred. He would also concede that we do not grasp mental contents in inner perception sufficiently well. The main reason for this deficiency lies in the fact that our everyday life is oriented towards objects in the external world; it is usually ‘turned outwards, not inwards’. As our vocabulary is object-related, we do not have specific words for the contents. That we use words for contents in a derived manner at best (‘the sensation with a red-content’, for instance) obscures our capacity to apprehend mental contents directly. (See Meinong 1899: §2:385 [143]; 1906: §11:426–28; 1915: §33:252.) Meinong seems to accept that the specific qualitative peculiarities of the whole experience depend on different kinds of mental aspects. The qualitative peculiarity of an experience is founded on at least two aspects—the act and the content. The Ideal Relation between Contents and Their Objects: Adequacy Meinong calls the relation of a content to its corresponding object ‘adequacy relation’ (see Meinong 1902: §§29–30; 1910: §§43–44), and he takes it to be an ideal relation. Ideal relations in contrast to real relations subsist necessarily between the terms of the relation. If the one colour, say red, is different from the other, say green, then they must be different. If you compare colours located somewhere, the relation between a colour spot and its location is called real because the colour, say red, could be located elsewhere, or another colour could be in the place of the red colour spot. Ideal relations, however, attach once and for all and with necessity to their terms. (See Meinong 1902: §30:127–29; 1910: §44:266–68; 1899: §7:398–99.) Meinong just postulates the adequacy relation and offers only negative determinations of it. He stresses the point that adequacy is not a relationship of sameness or of similarity. Since it is an ideal relation, real relations—for example, pictorial or even causal relationships—are excluded. A positive hint is given by a kind of metaphorical use of the word ‘fitting’; the

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Page 152 mental content and its object must be fitted to each other (Meinong 1902: §29:124–27; 1910: §43). If you assume that there is an ideal correspondence between the content and its object, the question still arises ‘What makes it the case that the experience is directed to its corresponding object?’ Meinong answers this question in a resigned tone: ‘As to how it happens that the relation of adequacy between content and object obtains in a case where there is such great similarity and in another case where there is such great dissimilarity, I admit I can give no answer at present’ (Meinong 1910: §43:265 [191]).19 As Meinong denies the ‘real’ character of the adequacy relation he falls outside of what is nowadays called naturalism in philosophy. This ‘ideal’ bond between the presentations and their objects allows Meinong to state that there is a categorical distance between the immanent mental content and its usually nonimmanent object on the one hand and, nevertheless, a kind of logical closeness between them on the other hand. This joint claim serves as a supporting argument against the reproach of psychologism. Psychologism (in its negative sense) is the ‘inappropriate use of psychological method’ in logic and theory of knowledge, Meinong says (1904a: §8:504–6 [95–97]). It mainly consists in mistaking an object for an immanent mental experience that really or supposedly apprehends the object. That happens if one does not sufficiently distinguish between content and object of an inner experience or if one fails to distinguish them at all (Meinong 1907: §26). What is often called ‘content’, especially ‘conceptual content’, is not a Meinongian psychological content. Meinong distinguishes between psychological (=mental) and logical (= conceptual) content in his later work. The mental content is not something abstract or conceptual in the sense of something intensional; it is not something like a meaning. However, the connection to meaning and intension is guaranteed by the above-mentioned ideal relation of adequacy, which Meinong postulates. Perhaps this is a reason why quite a lot of Meinong interpreters seem to bring the Meinongian psychological content too close to the sphere of intensions.20 But this mistake confuses psychological content with its object (and with its logical content), and, therefore, is nothing else than psychologism. RUSSELL’S ARGUMENTATION AGAINST THE ACCEPTANCE OF MENTAL CONTENTS IN HIS THEORY OF KNOWLEDGE Russell’s most interesting argumentation against Meinong’s psychological contents can be found in his Theory of Knowledge (1913: Part 1, Chapter 3:33–44). This text was published in The Monist under the title ‘Analysis of Experience’ (1914:24:435–53). Russell wrote this criticism in a phase when he still accepted a kind of intentionality-thesis: mental facts are defined as facts involving acquaintance or some relations like judging, desiring, and so on, which presuppose acquaintance (1913:37, 45). Russell maintains that

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Page 153 acquaintance is a dual (two-place) cognitive relation between a subject and an object (37, 45). When an object is in my present experience, then I am acquainted with it; it is not necessary for me to reflect upon my experience, or to observe that the object has the property of belonging to my experience, in order to be acquainted with it, but on the contrary, the object itself is known to me without the need of any reflection on my part as to its properties or relations. (39) That the subject is acquainted with an object is shown by using a proper name that applies directly to the object and does not in any way describe the object to which it applies. The word ‘this’, for example, is a proper name applied to the object to which the subject is attending, although ‘it would be an error to suppose that “this” means “the object which I am now attending”’ (40). The dual relation of acquaintance is an external relation, not an internal one. An internal relation between two terms is constituted by the intrinsic properties of the two related terms or of the whole which they compose, whereas a relation interpreted as external is not grounded in the natures of the related terms (1959:12, 54–56). Russell holds that the fact that the subject is acquainted with different things does not involve an immanent qualitative difference in the subject. To this point I suggest the following analogy: Think about the ceremony of eating a fondue; you need a spit, a fork for skewering pieces of food—pieces of meat, of cheese, of vegetables, for example. Although the skewer stays the same, the skeweringrelation is different according to the different pieces of food spiked on the skewer. The analogy is the following: Our mind is the skewer, acquaintance is the skewering-relation, and the skewered things are the objects of (simple) thoughts. In his counter-argumentation Russell offers no proof that there are in fact no mental contents or that the notion of mental contents is inconsistent. Rather, he shows that his view about acquaintance combined with his doctrine of external relations gives no good reasons for the supposition that there are such things as mental contents. Mental contents become superfluous. Let us consider the argumentation in more detail by going through Meinong’s arguments and Russell’s counter-arguments point for point. Argument (1) The Case of a Presentation of Nonexistent Objects ‘Dieser [Inhalt der Vorstellung] existiert …, mag der sozusagen mit seiner Hilfe vorgestellte Gegenstand auch nicht-existierend … sein.’ [This [content of a presentation] exists …, even when the object presented, so to speak, by means of it, may be non-existent.] (Meinong 1899:384 [143]; compare Russell 1913:42.)

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Subject Object → A presentation is directed to a nonentity as object I have a presentation of the round square Meinong’s view: (i) There is a nonexistent object which is the object of a presentation that exists. (ii) This existing presentation has as its part an existent mental content (iia) which is ideally correlated to the nonentity, and (iib) this correlation is responsible for (explains) the directedness to nonexistents. Russell’s view: There are no objects which do not exist; the presentations in question are not directed to nonentities. The round square and the golden mountain, for example, are not objects at all. Sentences that are supposed to be about them have to be rephrased by his theory of definite descriptions. ‘The instances of non-existent objects quoted by Meinong are largely disposed of by the theory of incomplete symbols’ (1913:42). Argument (2) The Case of a Presentation of an Object that is Qualitatively Different to its Presentation ‘[D]ieser [Inhalt der Vorstellung] … ist also real und gegenwärtig, natürlich auch psychisch, mag der sozusagen mit seiner Hilfe vorgestellte Gegenstand … nicht-real, nicht-gegenwärtig, nicht-psychisch sein.’ [This [content of a presentation] … is therefore real and present, is also psychical of course, even when the object presented, so to speak, by means of it, may be … non-real, non-present, and nonpsychical.] (Meinong 1899:384 [143]; compare Russell 1913:42.) Subject Object → A presentation is directed an object that is different (concerning time and quality) to the to whole mental act I have a presentation of hot coffee I have a presentation of tomorrow’s heat I have a (memory-) of yesterday’s eaten cake presentation Meinong’s view: (i) The object of the presentation has determinations that the whole presentation or its parts do not have (hot, not-hot; present, future, and past, respectively). (ii) The whole presentation has as its part the mental content which (iia) is ideally correlated to the differently determined object, and (iib) this correlation is responsible for (explains) the directedness to it. Russell’s view: In cases of existent objects the mental relation (of the presentation to the mind) is either the relation of acquaintance, which is external, and no intermediary content is necessary, or the things are not

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Page 155 presented, although they may be known by description. Future things, for example, are like that. Remembering, on the other hand, consists of memory-presentations. Memory-presentations are complexes of which one constituent is present while the other is past. Russell thinks it ‘is not clear that such a complex has any definite position in the time-series: the fact that the remembering subject is in the present is no sufficient reason for regarding the whole complex as present. And similar remarks apply to the case of presentations whose objects are not in time at all’ (1913:42). Argument (3) The Case of Presentations with Different Objects ‘Andererseits aber können Vorstellungen, sofern sie Vorstellungen verschiedener Gegenstände sind, untereinander nicht völlig gleich sein: wie immer die Relation der Vorstellung zu ihrem Gegenstande aufzufassen sein mag, die Verschiedenheit der Gegenstände muß irgendwie auf Verschiedenheit der betreffenden Vorstellungen zurückgehen.’ [On the other hand, however, presentations—as far as they are presentations of different objects—cannot be completely similar to each other: In whatever way the relation between the presentation and its object is to be conceived, the difference of the objects must somehow come down to a difference between the presentations in question.] (Meinong 1899:384 [143]; compare Russell 1913:42) Subject Object A, Object B → The presentations are directed to different objects: red and green, respectively My presentations of red and green, respectively Meinong’s view: (i) There are objects of presentations different from each other (red and green, for example) which are the objects of different existent presentations. (ii) The presentation of red and the presentation of green have as their part existent mental contents which (iia) are ideally correlated to the respective objects, and (iib) these correlations are supposed to be responsible for (explain) the respective directedness to the different objects. Russell’s view: The difference of the objects alone explains the difference of the acquaintance relations: But in fact the difference of object supplies all the difference required…from the fact that the complex ‘my awareness of A’ is different from the complex ‘my awareness of B ’, it does not follow that when I am aware of A I have some intrinsic quality which I do not have when I am aware of B but not of A. There is therefore no reason for assuming a difference in the subject corresponding to the difference between two presented objects. (1913:43)

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Page 156 Although it seems obvious that the subject’s mind is in different states when it has a presentation of one thing and when it has a presentation of another, Russell thinks it is superfluous to adopt an internal theory of the mental relation: it is not necessary to assume that intrinsic differences in the subject’s presentations must correspond to differences in the presented objects . The cognitive relation is primarily acquaintance (or can be grounded in acquaintance), which is an external relation. According to Meinong, the difference among mental acts which consists in the fact that the acts have different objects is not a genuinely mental difference, but it involves a genuinely mental difference, because there has to be a difference in the corresponding mental contents. It is hard to say what Russell thinks: there are cases of acquaintance (of different things), and as acquaintance is something mental, there are different mental events. But there is no corresponding internal mental difference in the acts. Russell just denies that wherever there are different objects, there must also be some qualitative difference, that is, a difference of mental contents. The last argument Russell put forward against Meinong’s mental contents is the difficulty of discovering contents introspectively (1913:43–44). Russell, rather like Moore, argues that he is quite unable to discover any such contents by introspection.21 On the other hand, Meinong—as we have seen—thinks introspection can show us that contents have a qualitative, experiential character. Since Meinong’s arguments are not satisfactory and since such introspective evidence is lacking, Russell therefore concludes that there is no reason to admit mental contents (1913:44). SOME FURTHER COMMENTS If you think that the complete mental experience consists of two genuinely mental, that is, qualitative, parts, namely, the act and the content, the question arises: ‘How to combine the experiential qualities, especially the different qualia that are contents?’ An experience which contains a red-content and a round-content as well is not a presentation of something red and round yet. In your explanation of the perception of something red and round you may refer to something like spatial coincidence of the redquale with the round-quale. Contents of presentations like the red-content, however, are not qualia with an extension like sensual qualities. Meinong seems to have thought of complexes of contents,22 and he also agrees that to every object which your mind is directed to—also to complex objects—there is a correspondent psychological content. Meinong does not present an account of complexes of contents as he does not present an account for understanding the mysterious adequacy-relation either .

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Page 157 Russell’s denial of introspective evidence for the existence of mental contents is just the negation of Meinong’s appeal to the inner experience of psychological contents. Actually, there is some introspective evidence, the feeling of understanding, for example, which comes close to a feeling of fitting or to the way a meaningful word feels. We can see that Meinong’s interpretation of mental content as a special way of feeling [ zu Mute sein ] is similar to William James’ view that ‘[e]ach word, in such a sentence, is felt, not only as a word, but as having a meaning’ (James 1890: Volume 1, Chapter 9:265). In the same chapter James states, ‘We ought to say a feeling of and , a feeling of if, a feeling of but , and a feeling of by, quite as readily as we say a feeling of blue or a feeling of cold’ (245–46). Ludwig Wittgenstein was also fascinated by this subject matter, but he was sceptical about the thesis that there are experiences of meaning or the feelings of words. That Wittgenstein’s discussion of this topic seems to be prompted by James is shown by the following remarks in Wittgenstein’s Remarks on the Philosophy of Psychology , vol. 2. 264. James might perhaps say: ‘I read each word with the feeling appropriate to it. “But” with the butfeeling’, and so on.—And even if that is true—what does it really signify? What is the grammar of the concept ‘but-feeling’?—It certainly isn’t a feeling just because I call it ‘a feeling’. 265. How strange, that something has happened while I was speaking and yet I cannot say what!—The best thing would be to say it was an illusion, and nothing really happened; and now I investigate the usefulness of the utterance. (1980:51) According to Russell, when we think of universals we are acquainted with them (at least when we are not thinking of them by means of descriptions like the colour blue as the colour of my friend’s eyes). How can we explain that we are thinking of the colour blue and not of green in such an immediate way? Think of the fondue fork. In this case we can give a natural, causal account of the difference between the skewered pieces whereas the fork stays the same. If the mind does not change internally, as Russell says, there must be an external reason that our mind has impaled the blue universal and not the green one. But how is this possible? What kind of external circumstance is responsible that the person is attending to the universal blue and not to green at the moment? I cannot see a natural, causal relation that would provide a sufficient solution. Universals by themselves cannot causally contribute to the specific thoughts; they are not causally effective like pieces of cheese. Is here, in Russell’s account, also a kind of mysterious relation of adequacy at work?

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Page 158 A NOTE ON THE PRINCIPLE OF THE INDIFFERENCE OF THE PURE OBJECT TO BEING Meinong thinks that not only existing things but also all kinds of nonentities—among them even impossible objects, like the round square, or paradoxical objects—find their place in his theory of objects. Hence, in his article ‘The Theory of Objects’ (1904a: §3:490 [83]) Meinong makes the seemingly paradoxical statement ‘There are objects of which it is true that there are no such objects’. In order to give a consistent account, he introduces two closely related principles about the relation between the being of objects and the so-being of objects. The one is the ‘principle of the independence of so-being from being’ [Prinzip der Unabhängigkeit des Soseins vom Sein], the other is the ‘principle of the indifference of the pure object to being’ [Satz vom Außersein des reinen Gegenstandes] (1904a: §§3–4: 489–94 [81–86]).23 The independence principle states that ‘the so-being of an object is not affected by its non-being’ [dass das Sosein eines Gegenstandes durch dessen Nichtsein sozusagen nicht mitbetroffen ist] (1904a: §3:489 [82]), that is to say, an object’s having properties is independent of its being. ‘That which is not in any way external to the object, but constitutes its proper essence, consists in its so-being, which is attaching to the object whether the object has being or not’ [daß dasjenige, was dem Gegenstande in keiner Weise äußerlich ist, vielmehr sein eigentliches Wesen ausmacht, in seinem Sosein besteht, das dem Gegenstande anhaftet, mag er sein oder nicht sein] (§4:494 [86]). The indifference principle says: ‘The object is by nature indifferent to being, although in any case one of the object’s two objectives of being, its being or its non-being, subsists [= is the case]’ [der Gegenstand ist von Natur außerseiend, obwohl von seinen beiden Seinsobjektiven, seinem Sein und seinem Nichtsein, jedenfalls eines besteht] (§4:494 [86]).24 This principle is supposed to be a more accurate formulation of the claim that ‘the pure object stands “beyond being and non-being”’ [der reine Gegenstand stehe ‘jenseits von Sein und Nichtsein’] (§4:494 [86]). This catchphrase means that neither being nor nonbeing belongs to the make-up of an object’s nature, but it does not say that an object is beyond being and nonbeing in the sense that it has neither being nor nonbeing—therefore, the second clause that one of its (the object’s) objectives of being, its being or its nonbeing, subsists. Although the nonbeing of an object may be involved, guaranteed by the object’s nature (so-being)—in the case of the round square, for example—the nonbeing does not belong to its nature, is not a part of its nature. In other words: Being is not part of an object’s nature, but nevertheless any object either is or is not. It is worth noting that commentators25 are mainly concerned with the first part of the principle and not with the second one; that is, they

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Page 159 mainly refer to the claim Findlay formulated with these words, ‘[w]hether an object is or not, makes no difference to what the object is’ (Findlay 1933:49). The second part says that one of an object’s objectives of being, its being or its nonbeing, subsists, or in Findlay’s words, ‘the law of excluded middle lays it down that every object necessarily stands in a fact of being or in a fact of non-being’ (49). In contrast to this, Meinong says in Über Möglichkeit und Wahrscheinlichkeit (1915: §25:179–80), that some objects are not determined with respect to being at all. As already mentioned above, the nature of some objects, namely, inconsistently determined objects like the biangle, the triangle with four sides or the noncircular circle exclude being, they cannot, and therefore, do not have being. But pure objects like the triangle as such are neither subsistent nor nonsubsistent; they have neither being nor nonbeing. Doesn’t this claim contradict the second clause of the indifference principle? Meinong suggests the following solution (1915: §25). First, he introduces in more detail the notion of incompletely determined objects, called ‘incomplete objects’ for short. Pure things like the triangle as such are incomplete objects. The triangle as such has three angles (constitutive property), it has three sides (consecutive property; it is somehow included in the object’s constitutive properties), but it is neither green nor nongreen, scalene nor nonscalene (equilateral), equiangular nor nonequiangular, and so on. Denying that such an object i is F does not imply affirming that i is not F , because the denial that i is F may also be correct when i is not determined with respect to F .26 Incomplete objects allow infringing the law of excluded middle (and impossible objects the law of noncontradiction) only concerning the inner or internal negation and not the outer, external negation. With respect to external negation , which may be interpreted as sentence negation, broadened, widened negation [ erweiterte Negation]27, Meinong acknowledges the validity of the following two laws:   With respect to internal negation —that is, predicate negation, predicate complementation [ unerweiterte Negation], Meinong admits that the following principles are true, and so neither the law of noncontradiction nor the law of excluded middle are valid.  

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Page 160 With respect to an incomplete object i, the triangle as such, for instance, it is not the case that it is either scalene or nonscalene (equilateral):   In Über Möglichkeit und Wahrscheinlichkeit (1915: §25, 179) Meinong also says that everything which has being is completely determined, but he stresses the point that not every completely determined object has being. Some of them do not have being, or even cannot have being because they are overdetermined, they have a certain property and also its complement. Nevertheless, if an object is completely determined it either has being or nonbeing; there is no completely determined object which has neither being nor nonbeing. ‘Every object that is completely determined with respect to so-being is also determined with respect to being.’28 What about the case of incompletely determined objects? In the case of incomplete objects Meinong also thinks that some of them cannot have being because of their conflicting determinations (the ‘biangle’, the noncircular circle, for example). For such a thing i it is true that   and   as well (where ‘ B !’ is an abbreviation for Meinong’s ‘has being’). Cases like that of the triangle as such, however, show that stating   would be a real contradiction, a contradiction with respect to external negation, and   would be a violation of the external version of the law of excluded middle (where ‘ t ’ is an abbreviation for the triangle as such). Meinong, for that reason, would agree that the triangle as such does not have being when the negation is taken in its external sense. Hence it is true that   That is why the incomplete object triangle as such does not violate the law of excluded middle in its external interpretation of the negation—and no counterexample to the second part of the indifference principle is given.

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Page 161 Nevertheless, another problem arises. In the case of internal negation (predicate negation) the law of excluded middle does not hold for such objects as the triangle as such. It is true that   and it is also true that you cannot infer from this   which would be a violation of the ‘external’ version of the law of excluded middle. Meinong writes: Whoever asserts ‘it is not, or it does not hold, that a is [has being]’ is not allowed to infer from this ‘ a is not’, except if it can be presupposed that a is determined with respect to being. If it is not the case that a is, then two possibilities can be taken into consideration: either a is not, or a is not at all determined with respect to being. (Meinong 1915:180)29 We can sum up: a is determined with respect to being [ seinsbestimmt] → [¬(B ! a ) → (~B !) a ]; a is not determined with respect to being → ¬[¬(B ! a ) → (~B !) a ]; ¬(B ! a ) → [(~B !) a a is not determined with respect to being]. All complete objects have either being or nonbeing, and all incomplete objects do not have being. Therefore, the law of excluded middle in the external version is assured. But incomplete objects either have nonbeing (impossible objects at least), or are not determined with respect to being. However, a new question arises from this: ‘What does the negative predicate “is not determined with respect to being” mean?’—Neither being, ‘ B !’, nor nonbeing, ‘~ B !’, of an object o is meant by it, but it implies that it is not the case that the object o has being: ‘¬( B ! o)’. This ‘being not determined (indeterminacy) with respect to being’ [ Seinsunbestimmtheit] seems to be a new puzzling kind of indifference to being (outside-being [ Außersein]) or, in other words, a new kind of standing beyond being and nonbeing [ jenseits von Sein und Nicht-Sein zu stehen ]. It is worth noticing that the indeterminacy with respect to being must not be mixed up with the outside-being, because every object has outside-being but only some of them are not determined with respect to being. The place where indeterminacy with respect to being is at home shows in the following Meinongian table of categories:

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NOTES 1. Papers on the Russell-Meinong debate are inter alia : Griffin 1985–86; Reicher 2005; Simons 1992; Smith 1985, 2005; Voltolini 2001. 2. Kindinger 1965:150–53. Translations of the three Russell letters to Meinong in Smith 1985:347–50. 3. In his referee report, dated 15 December 1933, Ernst Mally wrote on p. 9: ‘auch seine Kritik scheint mir durchaus richtig, nur manchesmal zu duldsam zu sein’ [also his criticism seems to be quite correct to me, although sometimes too indulgent]. Mally’s referee report on Findlay’s dissertation thesis can be found in Ernst Mally’s Nachlass in the university library in Graz. Mally’s referee report will be published in the yearly periodical Meinong Studies . 4. Especially ‘that Gegenstandstheorie itself is dead, buried and not going to be resurrected’, in Ryle 1972:7. 5. Kneale (1949): 32. On p. 12 you can find the phrase ‘But after a period of wandering in Meinong’s jungle of subsistence’ and as its footnote ‘The jungle is described in Meinong’s book, Über Annahmen.’ 6. On p. 483: ‘the chief objection is that such objects, admittedly, are apt to infringe the law of contradiction’; p. 483: ‘The above breach of the law of contradiction is avoided by Frege’s theory’; p. 484: ‘The former course

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Page 163 may be taken, as by Meinong, by admitting objects which do not subsist, and denying that they obey the law of contradiction; this, however, is to be avoided if possible’; p. 485: ‘Hence it would appear, it must always be self-contradictory to deny the being of anything; but we have seen, in connection with Meinong, that to admit being also sometimes leads to contradictions’; p. 491: ‘This [MacColl’s remark regarding individuals as of two sorts, real and unreal] is essentially Meinong’s theory, which we have seen reason to reject because it conflicts with the law of contradiction.’ 7. Russell 1919: Ch. 16:169–70; Russell 1918–19, Lecture 4, Sec. 2:223. Here you can also read: ‘I think Meinong is rather deficient in just that instinct for reality’. 8. Besides criticism, later Russell also expressed some kind of appreciation of Meinong when he said in My Philosophical Development (1959: Ch. 7:84): ‘Meinong, for whose work I had had a great respect, had failed to note this difference.’ The unnoticed difference Russell alluded to is the distinction between names and descriptions. Meinong did not realize ‘that a name cannot occur significantly in a proposition unless there is something that it names, whereas a description is not subject to this limitation’. Also, in his short autobiography (1944:13), Russell starts his criticism with a word of recognition (‘Meinong, whose work interested me’), but he ends very decisively: ‘Meinong inferred that there is a golden mountain, which is golden and a mountain, but does not exist. He even thought that the existent golden mountain is existent, but does not exist. This did not satisfy me, and the desire to avoid Meinong’s unduly populous realm of being led me to the theory of descriptions.’ Nonetheless, Russell’s critical remarks themselves show that Meinong exerted significant influence on him. 9. See Meinong’s complete shorthand notes of two logic lectures of Brentano in Meinong-Nachlass der Universitätsbibliothek Graz, Karton I/c: ‘Alte und neue Logik’ (Sommer-Semester 1875); ‘Logik’ (SommerSemester 1877). 10. Russell wrote the letter in perfect German. Original in Kindinger 1965:150–1. English translation of the whole letter is in Smith 1985:347–8. See also Simons 1992:173. 11. Meinong 1904a: §7, 501 [93]: ‘it is only with great difficulty that the notion of logic can be separated from that of a technology [ Kunstlehre] devoted to the advancement of our intellectual powers. Consequently, logic always remains a practical discipline .’ Similarly in Meinong 1907: §20:322– 23. 12. Meinong 1917: §11:387 [92]: ‘Die Gegenstandstheorie ist ohne Zweifel eine apriorische, um nicht zu sagen die apriorische Wissenschaft, und auch Bestand und Außersein der Gegenstände ist der Natur dieser Gegenstände, also a priori zu entnehmen. Dennoch geht dieses Seinswissen auf ein direktes Erfassen dieser Gegenstände als auf eine Art Quasi-Empirie zurück, die es auch der Gegenstandstheorie gar wohl gestattet, gleich den empirischen Wissenschaften den Weg von unten nach oben zu nehmen.’ [The theory of objects is, without doubt, an a priori science, if not, indeed, the a priori science. Subsistence and indifference to being [= outside-being] of objects can be known a priori from the nature of the objects in question. Nevertheless, this knowledge of being can be traced back to a direct apprehension of these objects, as a sort of quasi-experience by means of which the theory of objects is in a position to take a path from below upwards, just as the empirical sciences do.] See also Meinong 1921, Sec. 2.F: 42: ‘Der Fechner sche Gedanke der Ästhetik von unten gestattet eben eine sinngemäße Erweiterung zu dem der Philosophie von unten und eine solche begreift zwanglos selbst die Gegenstandstheorie in sich, soweit diese von dem als bestehend oder selbst außerseiend Gegebenen ebenso ausgehen kann wie eine empirische Wissenschaft von dem der Erfahrung Gegebenen.’

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Page 164 [Fechner’s notion of the ‘aesthetics from below’ allows an analogous amplification to the ‘philosophy from below’. Such a philosophy involves also the theory of objects without restraint insofar as this theory is able to proceed from the given, taken as subsistent or even outside being as an empirical science proceeds from the experiential given.] 13. ‘[D]ie allgemeine Gegenstandstheorie habe von der Grammatik in ähnlicher Weise zu lernen, wie die spezielle Gegenstandstheorie von der Mathematik lernen kann und soll.’ See also Meinong 1907: Sec. 5, §19:109–10. 14. ‘Die Untersuchung beginnt am besten am Sprachmaterial.’ Meinong-Nachlass der Universitätsbibliothek Graz, Karton IV/b ‘Kolleg über Erkenntnistheorie’ (Winter-Semester 1985/96), Kapitel I, Blatt 1. I owe this and the next quotation to Manotta 2005:65. 15. See Meinong-Nachlass der Universitätsbibliothek Graz, Karton XI/e, ‘Elemente der Erkenntnistheorie’ (Winter-Semester 1890/91), Erster allgemeiner Teil. Erstes Kapitel, Blatt 5: ‘ist jedesmal dann die Beantwortung der Frage, was der gemeine Mann bei dieser Sachlage, bei diesem Wort eigentlich denkt, unerlässliche Voraussetzung alles Übrigen’. 16. ‘In psychical matters, at any rate in the case of presentations and judgments, it is necessary, Meinong points out, to distinguish three elements, the act, the content, and the object. All presentations have in common the act of presentation, but the presentations of different objects differ in respect of their contents. It is necessary sharply to distinguish content and object: the content of a presentation exists when the presentation exists, but the object need not exist—it may be self-contradictory, it may be something which happens not to be a fact, such as a golden mountain, it may be essentially incapable of existence, as for instance equality, it may be physical, not psychical, or it may be something which did exist or will exist, but does not exist at present’ (1904:207). 17. Russell mentioned most of these arguments in detail in 1904:207 (see n16 above), and in 1913: Part 1, Ch. 3:41–42 (= 1914: Part 3). 18. Meinong 1906, §11:427: ‘Das qualitativ Eigenartige, das wir erleben, indem wir Rot sehen oder an Rot denken, gehört also, das ist im Grunde ganz selbst verständlich, nicht dem Gegenstande, sondern dem Inhalte an. Und daß uns anders zu Mute ist, wenn wir einmal Rot, einmal Grün sehen, das liegt wieder nicht am Gegenstande, sondern am Inhalte.’ [Therefore, the qualitative peculiarity we experience in seeing red or thinking of red, that really as a matter of course, belongs to the content not to the object. And that we feel different when we see red at a time and sometimes green at a time is not because of the object but because of the content.] 19. Great similarity, namely identity, between content and object is given in the case of the selfpresentation of the content, and great dissimilarity in the case where the object is something nonmental, something physical or ideal. 20. Grossmann (1974), for example, when he says on p. 55 that Meinong’s ‘contents are the ideas and concepts of the tradition’. 21. Moore just denies that wherever there are different objects, there must also be some qualitative difference, i.e., a difference of contents. He doubts, for example, that there is any internal difference between seeing a red colour and seeing a blue one. Against the statement that there are mental contents, Moore only argues that he is quite unable, by introspection, to discover any such contents. Moore 1909–10:55; Moore 1910:403–4; Marek 2001:271–72. 22. In 1899: §5:390 [146], Meinong very incidentally hints at the idea that complexes and relations can not only be applied to objects but also to contents. In later works Meinong also introduces contents of judgements and assumptions

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Page 165 and of other mental experiences and activities such as feelings and desires. The content of a judgement has as objectual counterpart its objective (a kind of state of affairs), the content of a feeling is correlated with a dignitative , and the content of a desire with a desiderative as its correspondent object. All those objects are complex, objects of higher order. See Meinong 1910: §59; Meinong 1917: §7 and §11. 23. The independence principle was first formulated by Ernst Mally in the year 1903. An alternative, more literal translation of Satz vom Außersein des reinen Gegenstandes would be ‘principle of the outside-being of the pure object’. 24. If o is an object, the being of o ( that o is) is one of o’s objectives of being. Objectives in Meinong terms are the objects of thoughts (of judgements and assumptions); they are something like states of affairs or propositions. 25. Findlay 1933 and 1963; Lambert 1983; Jacquette 1996, for example. 26. Meinong 1915: §25:178: ‘Wer bestreitet, so darf man sagen, daß A B sei, braucht darum noch nicht zu behaupten, daß A nicht B sei, falls er nicht etwa das im Auge hat, was oben als die erweiterte Negation bezeichnet worden ist; denn er hat auch dann schon recht, wenn A nur nicht B -bestimmt ist.’ [Whoever denies—you may say—that A is B , does not need to assert that A is not B , unless he keeps an eye on that which was called ‘widened negation’ above; because he is already right, when A is only not determined with respect to B .] 27. Meinong 1915: §25:174. If it is not the case that x is F , then still two different cases can take place: Either x is not F , or x is not determined with respect to F . The external negation [ erweiterte Negation] embraces these both cases, whereas the internal negation [ unerweiterte Negation] includes only the case that x is not F . 28. The entire quotation in German: ‘Daß alles Seiende, genauer also alles Existierende oder Bestehende, vollständig soseinsbestimmt ist, haben wir gesehen; kann man nun auch umgekehrt behaupten, daß alle Gegenstände mit vollständig bestimmtem Sosein existieren oder bestehen? Das wäre sicher falsch: nichts ist leichter als sich Gegenstände auszudenken, die nicht existieren oder selbst, da ihnen ein innerer Widerstreit anhaftet, auch nicht bestehen, ohne daß darum irgend eine ihrer Bestimmungen als offen gelassen in Anspruch genommen werden müßte. Soviel aber wird man behaupten dürfen, daß es keinen vollständig bestimmten Gegenstand gibt oder geben kann, der nicht entweder existiert oder nicht existiert, entweder besteht oder nicht besteht, kurz entweder ist oder nicht ist: jeder vollständig soseinsbestimmte Gegenstand ist auch seinsbestimmt.’ 29. ‘Wer also behauptet: “es ist nicht, oder es gilt nicht, daß A ist” darf darum noch nicht behaupten “A ist nicht”, außer sofern vorausgesetzt werden darf, dass A seinsbestimmt ist. Ist also nicht, daß A ist, dann kommen zwei Möglichkeiten in Betracht: entweder A ist nicht oder A ist gar nicht seinsbestimmt.’ REFERENCES All references to Meinong’s work, as a rule, follow the Alexius Meinong Gesamtausgabe (1968–78). Throughout this article most of the consulted translations of Meinong’s work have been modified when necessary. The page numbers of the translations are given within square brackets. The German word ‘ Vorstellung’ is rendered as ‘presentation’, its corresponding verb ‘ vorstellen’ as ‘present’. In English works on Meinong you can find as alternative translations of ‘ Vorstellung’ the expressions ‘idea’ (for instance, sometimes in Findlay and Grossmann) and ‘representation’ (for instance, in Heanue).

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Page 166 Albertazzi, L., Jacquette, D. and Poli, R., eds. (2001) The School of Alexius Meinong, Aldershot: Ashgate. Chisholm, R. M. (1986) ‘Self-Profile’, in R. J. Bogdan (ed.), Roderick M. Chisholm , Dordrecht: Reidel: 3– 77. ——. (1997) ‘My Philosophical Development’, in L. E. Hahn (ed.), The Philosophy of Roderick M. Chisholm , Chicago/La Salle, IL: Open Court. (The Library of Living Philosophers, vol. 25: 3–41.) Dölling, E. (2001) ‘Alexius Meinong’s Life and Work’, in L. Albertazzi, D. Jacquette and R. Poli (2001): 49–76. Findlay, J. N. (1933) Meinong’s Theory of Objects, London: Oxford University Press, 1933. 2nd, enlarged edn, Meinong’s Theory of Objects and Values , Oxford: Clarendon Press, 1963. Griffin, N. (1985–86) ‘Russell’s Critique of Meinong’s Theory of Objects’, in Haller (1985–86): 375–401. Grossmann, R. (1974) Meinong, London/Boston: Routledge and Kegan Paul. Haller, R., ed. (1985–86) Non-Existence and Predication, Amsterdam/Atlanta, GA: Rodopi (= Grazer Philosophische Studien , vol. 25/26). Höfler, A. (unter Mitwirkung von Alexius Meinong [in collaboration with A. Meinong]) (1890) Philosophische Propädeutik. I. Theil: Logik , Wien: F. Tempsky. Jacquette, D. (1996) Meinongian Logic. The Semantics of Existence and Nonexistence, Berlin/New York: Walter de Gruyter. James, W. (1890) The Principles of Psychology , 2 vols., New York: Henry Holt. Kindinger, R., ed. (1965) Philosophenbriefe. Aus der wissenschaftlichen Korrespondenz von Alexius Meinong, Graz: Akademische Druck- u. Verlagsanstalt. Kneale, W. (1949) Probability and Induction, 2nd, corrected impression, Oxford: Clarendon Press, 1952. Lambert, K. (1983) Meinong and the Principle of Independence , Cambridge: Cambridge University Press. Linsky, B. and Imaguire, G., eds. (2005) On Denoting: 1905–2005, München: Philosophia. Manotta, M. (2005) ‘Sprache, Wahrheit und Rechtfertigung. Alexius Meinongs frühe Schaffensperioden zur Erkenntnislehre’, Meinong Studien/Meinong Studies 1: 63–93. Marek, J. C. (2001) ‘Meinong on Psychological Content’, in L. Albertazzi, D. Jacquette and R. Poli (2001): 261–86. ——. (2003) ‘On Self-Presentation’, in C. Kanzian, J. Quitterer, E. Runggaldier (eds), Persons. An Interdisciplinary Approach. Proceedings of the 25th International Wittgenstein Symposium , Wien: öbv & hpt: 163–73. Meinong, A. (1896) ‘Über die Bedeutung des Weber’schen Gesetzes. Beiträge zur Psychologie des Vergleichens und Messens’, Zeitschrift für Psychologie und Physiologie der Sinnesorgane 11: 81–133, 230–85, 353–404. Separate edn, Hamburg/ Leipzig: L. Voss, 1896. Reprinted in Meinong (1968–78), vol. 2:215–376. ——. (1899) ‘Über Gegenstände höherer Ordnung und deren Verhältnis zur inneren Wahrnehmung’, Zeitschrift für Psychologie und Physiologie der Sinnesorgane , 21: 182–272. Reprinted in Meinong (1968– 78), vol. 2: 377–480. Translated as ‘On Objects of Higher Order and Their Relationship to Internal Perception’ by M. Schubert Kalsi (1978): 137–208. ——. (1902) Ueber Annahmen, Leipzig: J. A. Barth. Erg.-Bd. II of Zeitschrift für Psychologie und Physiologie der Sinnesorgane . Partially reprinted in Meinong (1968–78), vol. 4. See also Meinong (1910). ——. (1904a) ‘Über Gegenstandstheorie’ in Meinong (1904b): 1–51. Reprinted in Meinong (1968–78), vol. 2: 481–535. Translated as ‘The Theory of Objects’ in R. M. Chisholm (ed.), Realism and the Background of Phenomenology , Glencoe, IL: Free Press, 1960; reprint: Atascadero, CA: Ridgeview, 1981:76–117.

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Page 167 ——., ed. (1904b) Untersuchungen zur Gegenstandstheorie und Psychologie , Leipzig: J. A. Barth. ——. (1906) ‘Über die Erfahrungsgrundlagen unseres Wissens’, in Abhandlungen zur Didaktik und Philosophie der Naturwissenschaften, Band I, Heft 6, Berlin: J. Springer. Reprinted in Meinong (1968– 78), vol. 5: 367–481. ——. (1907) Über die Stellung der Gegenstandstheorie im System der Wissenschaften , Leipzig: R. Voigtländer. Reprinted in Meinong (1968–78), vol. 5: 197–365. ——. (1910) Über Annahmen, 2nd edn, Leipzig: J. A. Barth, 1910. 2nd rev. edn of Meinong (1902). Reprinted in Meinong (1968–78), vol. 4: xv–xxv and 1–384. Translated with an introduction by J. Heanue as On Assumptions, Berkeley/Los Angeles/London: University of California Press, 1983. ——. (1915) Über Möglichkeit und Wahrscheinlichkeit. Beiträge zur Gegenstandstheorie und Erkenntnistheorie , Leipzig: J. A. Barth. Reprinted as vol. 6 of Meinong (1968–78). ——. (1917) ‘Über emotionale Präsentation’, in Sitzungsberichte der Kais. Akademie der Wissenschaften in Wien. Philosophisch-historische Klasse , Band 183, Abhandlung 2, Wien: Hölder. Reprinted in Meinong (1968–78), vol. 3: 283–467. Translated with an introduction by M. Schubert Kalsi as On Emotional Presentation, Evanston: Northwestern University Press, 1972. ——. (1921) ‘A. Meinong (Selbstdarstellung)’ in R. Schmidt (ed.), Die deutsche Philosophie der Gegenwart in Selbstdarstellungen, vol. 1, Leipzig: F. Meiner: 91–150. Reprinted in Meinong (1968–78), vol. 7:1–62. ——. (1968–78) Alexius Meinong Gesamtausgabe , ed. R. Haller, R. Kindinger in collaboration with R. M. Chisholm, 7 vols., Graz: Akademische Druck- u. Verlagsanstalt. See also Meinong (1978). ——. (1978) Alexius Meinong Ergänzungsband zur Gesamtausgabe. Kolleghefte und Fragmente. Schriften aus dem Nachlaß , ed. R. Fabian and R. Haller, Graz: Akademische Druck- u. Verlagsanstalt. Suppl. vol. of Meinong (1968–78). Moore, G. E. (1909–10) ‘The Subject-Matter of Psychology’, Proceedings of the Aristotelian Society , 10: 36–62. ——. (1910) ‘[Critical Notice of August Messer’s] Empfindung und Denken (1908)’, Mind, n.s. 19: 395– 409. Reicher, M. (2005) ‘Russell, Meinong, and the Problem of Existent Nonexistents’, in B. Linsky and G. Imaguire (2005): 167–93. Routley, R. [= R. Sylvan] (1980) Exploring Meinong’s Jungle and Beyond. An Investigation of Noneism and the Theory of Items , Canberra: Research School of Social Sciences, Australian National University. Russell, B. (1899) Review of A. Meinong, Ueber die Bedeutung des Weber’schen Gesetzes, Mind, n.s. 8: 251–56. Reprinted in Russell, Philosophical Papers, 1896–99 , London/New York: Routledge, 1993 (= The Collected Papers of Bertrand Russell, vol. 2): 147–52. ——. (1903) The Principles of Mathematics, Cambridge: Cambridge University Press. Reprint with an introduction by J. G. Slater, London: Routledge, 1992. ——. (1904) ‘Meinong’s Theory of Complexes and Assumptions’, Mind, n.s. 13: 204–19, 336–54, 509– 24. Review of Meinong (1899) and (1902). Reprinted in Russell (1973): 21–76 and in Russell (1994): 431–74. ——. (1905a) ‘On Denoting’, Mind, n.s. 14: 479–93. Reprinted in Russell (1956): 39–56; (1973): 103– 19; and (1994): 414–27. ——. (1905b) Review of Meinong and Others, Untersuchungen zur Gegenstandstheorie und Psychologie , Mind, n.s. 14: 530–38. Reprinted in Russell (1973): 77–88 and in Russell (1994): 595–604. ——. (1906) Review of A. Meinong’s Ueber die Erfahrungsgrundlagen unseres Wissens, Mind, n.s. 15: 412–15.

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Page 168 ——. (1907) Review of A. Meinong’s Ueber die Stellung der Gegenstandstheorie im System der Wissenschaften , Mind, n.s. 16: 436–39. Reprinted in Russell (1973): 89–93. ——. (1913) Theory of Knowledge. The 1913 Manuscript, London/Boston/Sydney: George Allen and Unwin, 1984 (= The Collected Papers of Bertrand Russell, vol. 7). See also Russell (1914). ——. (1914) ‘On the Nature of Acquaintance’, [Part 1] ‘Preliminary Description of Experience’, The Monist 24: 1–16 (reprinted in Russell (1956) and as Part 1, Ch. 1 of Russell (1913)); [Part] ‘II. Neutral Monism’, The Monist 24: 161–87 (reprinted in Russell (1956) and as Part 1, Ch. 2 of (1913)); [Part] ‘III. Analysis of Experience’, The Monist 24: 435–53 (reprinted in Russell (1956) and as Part 1, Ch. 3 of (1913)). ——. (1918–19) ‘The Philosophy of Logical Atomism’, The Monist 28 (1918): 495–527; The Monist 29 (1919): 33–63, 190–222, 345–80. Reprinted in Russell (1956): 175–281. ——. (1919) Introduction to Mathematical Philosophy , London: George Allen and Unwin; New York: Macmillan Company. Reprint with an introduction by J. G. Slater, London/New York: Routledge, 1993. ——. (1921) The Analysis of Mind, London: George Allen and Unwin; New York: Macmillan Company. ——. (1944) ‘My Mental Development’, in P. A. Schilpp (ed.), The Philosophy of Bertrand Russell, 3rd edn, New York/Evanston/London: Harper and Row, 1963: 3–20. ——. (1956) Logic and Knowledge: Essays, 1901–1950, ed. R. C. Marsh, London: George Allen and Unwin; New York: Macmillan Company. It contains as chapters Russell (1905a): 39–56; (1914): 127–74; and (1918–19): 175–281. ——. (1959) My Philosophical Development, London: George Allen and Unwin; New York: Simon & Schuster. ——. (1973) Essays in Analysis , ed. D. Lackey, London: George Allen and Unwin. It contains inter alia : Russell (1904): 21–76; (1905a): 103–19; (1905b): 77–88; (1907): 89–93. ——. (1994) Foundations of Logic. 1903–05 , London/New York: Routledge (= The Collected Papers of Bertrand Russell, vol. 4). It contains inter alia Russell (1904): 431–74; (1905a): 414–27; (1905b): 596– 604. Ryle, G. (1972) ‘Intentionality-Theory and the Nature of Thinking’, in R. Haller (ed.), Jenseits von Sein und Nichtsein. Beiträge zur Meinong-Forschung, Graz: Akademische Druck- u. Verlagsanstalt, 7–14. Schubert Kalsi, M. (1978) Alexius Meinong on Objects of Higher Order and Husserl’s Phenomenology , Dordrecht: Kluwer. Simons, P. (1992) ‘On What There Isn’t: The Meinong Russell Dispute’, in P. Simons, Philosophy and Logic in Central Europe from Bolzano to Tarski. Selected Essays, Dordrecht: Kluwer: 159–191. Smith, J. F. (1985) ‘The Russell-Meinong Debate’, Philosophy and Phenomenological Research , 45: 305– 50. ——. (2005) ‘Russell’s “On Denoting”, the Laws of Logic, and the Refutation of Meinong’, in B. Linsky and G. Imaguire (2005): 137–66. Twardowski, K. (1894) Zur Lehre vom Inhalt und Gegenstand der Vorstellungen. Eine psychologische Untersuchung , Wien: Hölder. Reprinted with an introduction by R. Haller, München/Wien: Philosophia, 1982. Translated with an introduction by R. Grossmann: On the Content and Object of Presentations. A Psychological Investigation , The Hague: Nijhoff, 1977. Voltolini, A. (2001) ‘What is Alive and What is Dead in Russell’s Critique of Meinong’ in L. Albertazzi, D. Jacquette and R. Poli (2001): 489–516. Wittgenstein, L. (1980) Remarks on the Philosophy of Psychology , vol. 2, Oxford: Blackwell.

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Page 169 9 Meditations on Meinong’s Golden Mountain Dale Jacquette REFERENCE, PREDICATION AND EXISTENCE When Bertrand Russell published ‘On Denoting’ in 1905, he crossed a denotational semantic Rubicon. He changed course dramatically in that year from his previously qualified sympathy for some parts of Alexius Meinong’s object theory to undisguised hostility. In discovering Meinong’s writings during the course of his research into the relation of logic to ontology, Russell seems to have felt a strong attraction for certain aspects of Meinong’s semantics, and appreciated in particular what he praises as Meinong’s scientific methodology. Meinong’s willingness to treat imperceivable objects, such as those ostensibly designated in mathematics as nonexistents to which reference and true predications of properties would remain possible at first struck a resonant chord with Russell in his quest for a way to attach the formalisms of his new mathematical logic to an ontically austere and in other ways scientifically respectable semantics and metaphysics. Russell’s moderate admiration for certain aspects of Meinong’s object theory was nevertheless short-lived. It came to an abrupt and irrevocable end with the analysis of definite descriptions in Russell’s justly celebrated essay now entering its second century of philosophical appreciation, critical discussion and dispute. Meinong regards beingless objects as referentially and predicationally precisely on a par with spatiotemporally existent entities. To acknowledge that the round square is round and square and that the golden mountain is golden and a mountain, despite the fact that no such things exist, makes these beingless objects the intended referents of our thoughts and speech acts, just as when we think of an existent object like Mount Everest or the Taj Mahal. Russell is intrigued but at no point fully convinced by Meinong’s semantic largesse. It is an historically interesting question with important philosophical implications to understand why Russell did not develop his interest in Meinong’s work by adapting his own form of Meinongian Gegenstandstheorie as part of his system-building, but turned more decidedly towards a theory of denoting limited exclusively to existent objects. Part of the answer seems to be that Russell in his own thinking about the meaning

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Page 170 of symbolic logical expressions and relatively well-behaved sentences in colloquial language was never able to separate the pure semantics of reference from the applied ontology of intended objects, as Meinong demands from the beginning of his published writings. Whether as a gut-level conflict of pretheoretical or preanalytic intuitions, a fundamental difference of philosophical temperament or worldview, the surprising and revealing fact is that Russell in all his commentary on Meinong and reviews of his writings never once correctly formulates Meinong’s independence of Sosein (sobeing, comparable to Fregean sense or Sinn ) from Sein (being) thesis. He repeatedly attributes to Meinong a view that he evidently himself regards as incontestable, but that as it happens is precisely what Meinong emphatically denies—maintaining that not only spatio-temporally nonexistent, but even beingless nonexistent and nonsubsistent objects can be referred to in thought, denoted in language, and enter semantically into true constitutive property predications. The fact that Russell nowhere offers a recognizable exposition of the central thesis of Meinong’s object theory supports the criticism that Russell never fully understood Meinong’s doctrine of the independence of Sosein from Sein or the Außersein (extraontology) of the pure object. For Meinong, the insight that we can think and talk about the golden mountain, even though no golden mountain actually exists, by virtue of its being an intended object, is the heart and soul of object theory. It is implied in his estimation by the mind-independent thought-transcendent reformulation of his teacher Franz Brentano’s thesis that all thought is intentional, built into the foundation of all Meinong’s reflections on meaning and metaphysics. In his 1874 Psychologie vom empirischen Standpunkt , Brentano argues that characteristically every presentation ( Vorstellung), judgement ( Urteil ), and emotion ( Gefühl)—and, Meinong would later add as a fourth category, assumption ( Annahme)—is always about something or intends an object. Meinong adopts Brentano’s starting place and develops the implication that in that case when we think or express thoughts about such objects as the golden mountain and the round square we actually refer to these beingless intended or merely semantic objects, and that they truly have the properties of being golden and a mountain in the case of the golden mountain, and of being round and square in the case of the round square, even though the golden mountain does not happen to exist and the round square cannot possibly exist. He generalizes the lessons of free assumption when he concludes that the meanings of thoughts and their expressions in every instance should be explicated by a semantics that is ontically neutral. Whether or not an intended object of thought or language actually exists is thereby made a distinct, independent and secondary question; one, moreover, that cannot even intelligibly arise unless we have already established the meaning of such a thought or its expression in action, typically in art or language. Russell in his early encounter with object theory likes the idea that if Meinong is right, then mathematical objects would not need to exist in order to

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Page 171 be the genuine referents and true predication subjects of mathematical theorems. What he does not immediately realize is that for Meinong there are also intended objects included in the object theory semantic domain that are altogether beingless in the sense that they are neither spatio-temporally existent nor subsistent abstract Platonic entities. He casts about for some sense of the word ‘being’ by which to allow intended objects like the golden mountain and round square to ‘be’ even though they do not exist, so that we can say that the golden mountain is the object of a certain thought and that the round square is round and is square. Meinong, although he never engaged Russell directly on this issue, is well-positioned to reply that he denies ‘being’ in any ontic sense of the golden mountain and round square. The use of cognates and conjugations of ‘being’ in saying that the golden mountain and round square are thought of and that they are, respectively, golden and a mountain and round and square, according to object theory, are not ontically loaded, in the sense of the ‘is’ of being, but are equivocal expressions of the ‘is’ of predication, where true predication in turn is logically independent of the predication subject’s ontic status. This fundamental underlying principle of Meinong’s theory of meaning and reference is never acknowledged or adequately expressed in Russell’s critical appraisals of Meinong’s philosophy. When we read Russell’s reviews of Meinong’s work through 1905 and 1907, and his correspondence with Meinong in the previous year of 1904, it is clear that Russell largely approves of what he takes to be Meinong’s empirical methodology. He is impressed also with what he takes to be the broad ontic sweep of a Gegenstandstheorie or general theory of objects such as Meinong envisioned. However, Russell could never countenance, perhaps, as we have suggested, because he never entirely understood, Meinong’s concept of an extraontology of semantic objects available for intentional acts independently of their ontic status. He returns again and again to the idea that anything we can think or talk about must have being (or ‘Being’) in some sense. Reading Russell as sympathetically as possible on these topics easily leaves us more confused than enlightened. We document some of the major difficulties in understanding what Russell means by ‘being’ or ‘Being’ in his criticisms of Meinong and his struggles to join semantics to ontology in a project to which Frege is preferred as ultimately contributing a significantly different approach. Whether or not Russell was right to raise the criticisms and draw the inferences he does in rejecting Meinong’s außerseiende semantic domain takes us from intellectual history to philosophically more interesting questions. Russell for a variety of reasons begins after 1905 to move increasingly toward an extensionalist theory of meaning that has greater affinity with the distinctively extensionalist aspect of Frege’s philosophy. Naturally, it is possible to find presentiments of Russell’s extensionalism from the outset of his career. The very fact that Russell does not properly interpret Meinong’s thesis of the independence of so-being from being, but tries to attribute being in an attenuated sense to all intended objects, after

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Page 172 which he despairs of making sense of Meinong’s object theory, is already an indication of Russell’s deeprooted commitment to some form of extensionalism. Under Wittgenstein’s influence in the following decade, Russell is persuaded to adopt an even more radically extensionalist semantics and ontology, reflected in the second edition of Principia Mathematica . Wittgenstein in the early period culminating in the Tractatus Logico-Philosophicus hopes to comprehend all genuine propositions by means of an extensionality thesis through which truth functional operations are applied to elementary space-timecolour forms of completely analysed descriptions. Russell seems to have been impressed again by the beauty of a comprehensive recursion for all propositions of a logic and gravitated progressively towards the extensionalist outlook in philosophical logic that inspired Wittgenstein’s application of the general form of proposition in the Tractatus . Qualifications are needed. There are several related aspects of semantic intensionality. Russell is an intensionalist prior to 1903 in Principles of Mathematics, by virtue of accepting a version of Frege’s concept of sense, in the form of what Russell calls ‘denoting concepts’, applied only to definite descriptions. In ‘On Denoting’, two years later, Russell rejects the category of Fregean senses or denoting concepts even for definite descriptions. Russell remains an intensionalist in other respects as well, even after the publication of ‘On Denoting’, through the publication of the first edition of Principia Mathematica in 1910, 1912 and 1913, until the second edition in 1925. Russell’s propositional functions in the first edition of Principia Mathematica are intensional in yet another sense of the word, in that the propositions that serve as values for coextensive functions can nevertheless be distinct, according to more fine-grained identity conditions for propositions. Frege, for his part, is an intensionalist in that his distinction between sense ( Sinn ) and reference ( Bedeutung ) admits properties as the senses of proper names in a very general way that includes any singular referring expression. The senses of names in turn are related compositionally to the senses of sentences that combine proper names, where the reference of a proper name (or sentence) is determined by the name’s (or sentence’s) sense. Frege, unlike Meinong, is nevertheless not an intensionalist in his referential semantics, in that Frege permits reference only to existent objects. We shall accordingly distinguish between intensional and extensional referential semantics, using explicit terminology to keep separate other intensional aspects of semantics. In this regard, although Frege is an intensionalist in many aspects of his theory of meaning, and Russell increasingly less so from 1903 to 1905, and especially after 1925, both Frege generally and Russell after 1905, in contrast with Meinong, are radically extensional in the specifically referential aspect of their respective philosophical semantics. Russell by nature or in spirit is more Fregean than he could ever be Meinongian in his referential semantics, even and especially if he were first to correctly grasp Meinong’s independence and Außersein theses.

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Page 174 constitutive properties. The objects in the intensionalist domain, regardless of their ontic status, are potentially referents and true predication subjects of thought and language. Frege is supposed to be the great grandfather of analytic referential extensionalism. With due qualifications, this attribution (or allegation) is true enough. Analytic philosophers are not always sufficiently patient with or interested in historical questions. They like the history even of their own subject to be simple and progressive, with clean-lined origins and passing down of intellectual mantles like the oversimplified cumulative histories of science that Thomas Kuhn decries in The Structure of Scientific Revolutions . To whatever extent we may share the sense that the history of analytic philosophy overlooks important figures like Frege’s own teacher Hermann Lotze and Bernard Bolzano, among others, it still makes sense to accord Frege an important place in the analytic turn in philosophy that looks back especially to Russell, Wittgenstein, and G. E. Moore in the early part of the twentieth century. Frege’s theory of reference together with his account of truth conditions for thoughts or propositions ( Gedanken) is purely referentially extensional in the abstract. If Frege is right, then we can only refer to existent things in a semantic domain that is limited exclusively to extant entities, whether spatio-temporal or abstract. Frege’s analysis of reference nevertheless has a foundational intensional element. In his 1892 essay ‘Über Sinn und Bedeutung’, Frege gives an important place to intension by arguing that sense determines reference. In a crucial footnote to the essay, one of the few places where Frege deigns to comment on the sense of a proper name, Frege indicates that the sense of a proper name is the complete abstract set of abstract properties that logically are true at most of one individual existent entity, the entity possessing all and only the properties in the property set that exhausts the proper name’s sense. Frege comments briefly on the sense of the proper name ‘Aristotle’ and on the possibility that different thinkers might have different opinions about the sense of the name. As he suggests, we can consider the sense of the proper name ‘Aristotle’ to include among indefinitely many other properties, the property of being the student of Plato and the teacher of Alexander the Great. The reference of the name ‘Aristotle’ is then that extant entity, if there is one, that happens to have the properties collected together as the sense of this proper name. If there is no such existent entity, as in the case of the Fregean proper name, ‘The golden mountain’, that possesses the properties of being golden and a mountain, then, contrary to Meinong’s intensionalism, the name does not refer. This is Fregean intensionalism, and intensionalists who want to align themselves with the analytic tradition should make the most of it. It must nevertheless be said that Frege himself does not seem to be particularly interested in the senses of terms or sentences as much as he is in their references. He is much more generally concerned with the reference and the truth-values of propositions, especially in mathematics, both of which in his semantic philosophy are otherwise treated purely extensionally.

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Page 175 Meinong, on the contrary, is much more intensionalist in the characteristically ‘Meinongian’ part of his referential semantics. He also has an extensionalist referential component in his work, in the sense that he recognizes that some intended objects have being as existent or subsistent entities, and that in such cases ordinary extensionalist predication and truth conditions apply, just as they are supposed more universally to do in Frege. Where Meinong breaks away from extensionalism is in that aspect of his object theory according to which any and every combination of constitutive properties in what Frege would call the Sinn associated with a proper name determines indifferently an existent subsistent, or beingless object of reference, whose predication and truth conditions are precisely the same as those of existent objects, independently of the object’s ontic status. Frege’s intensionalism, like Meinong’s extensionalism, is so limited and qualified in this regard that it is appropriate as a matter of emphasis, as many commentators have habitually done, to speak of Frege’s theory of referential meaning without further qualification as (primarily) extensionalist in contrast with Meinong’s (primarily) intensionalist semantics. The situation is much the same when we speak for convenience with due caveats of René Descartes’s philosophy as rationalist, without losing sight of the fact that he finds an important place in his system for reliance on the deliverances of empirical science, and of David Hume’s philosophy as empiricist, although like G. W. Leibniz he distinguishes between rational relations of ideas and matters of fact, and connects ideas together conceptually much like a rationalist, provided that the ideas themselves originate in immediate sense impressions. With due consideration to these nuances, we shall follow that practice here also in setting forth an admittedly oversimplified scheme of categories by which to plot the main lines of Russell’s semantic-metaphysical inquiry, one particularly important culminating moment of which is represented by ‘On Denoting’. We know that Russell, while never in any meaningful sense a Meinongian, rather precipitously repudiated any form of intensionalist referential Meinongian object theory, in favour of a more purely Fregean theory of reference and predication. However, we do not know exactly why. These are tantalizing suggestions, but we lack a compelling rationale for Russell’s change of heart. The answer, as we shall see, is not to be found in ‘On Denoting’. Nor does it unequivocally appear in the preceding 1903 edition of The Principles of Mathematics, nor in subsequent discussions of definite descriptions in the two editions of Principia Mathematica . These writings do not provide a background explanation, but only express Russell’s mounting disaffection for Meinong’s apparent ontic munificence in philosophical semantics. Russell’s later work, An Introduction to Mathematical Philosophy , in particular, so seriously misunderstands Meinong that the best we can conclude is that Russell, working from memory in prison at the time, had not restudied Meinong’s theory recently enough or with sufficient care to have a clear sense of what he was rejecting. We know from Russell’s

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Page 176 own list of books read while serving a sentence for protesting Great Britain’s involvement in World War I that at the time he did not consult any of Meinong’s works (Russell 1986). The only conjecture concerning Russell’s disaffection for Meinongian object theory that these writings support is that, given what Russell took Meinong to be saying, he found it absurd to agree that it is possible for such intended objects as the golden mountain and round square to have even so much as an attenuated sense of ‘logical being’ merely because we can ostensibly think and communicate about them. The theory of definite descriptions Russell presents in ‘On Denoting’ codifies but goes no distance in trying to justify his realization that the theory of meaning and the logic of denotation requires an extensionalist commitment to the existence of whatever entities can be referred to in order to stand as the subjects of true constitutive property predications.1 RUSSELL’S (MIS-)INTERPRETATION OF MEINONG Let us imagine that Russell had only an imperfect understanding of Meinong’s Gegenstandstheorie at first, that he was attracted to certain features of it that resonated positively with some of his own ideas. He must have done so to the extent that in 1904, unless he was merely being polite, he was still able to write to Meinong: I have read [your “Über Gegenstandstheorie”] … with great interest. I find myself in almost complete agreement with the general viewpoint and the problems dealt with seem to me very important. I myself have been accustomed to use the name “Logic” for that which you call “Theory of Objects”’.2 In Part I of his three-part expository essay, in Mind, volume 13, 1904, Russell was similarly moved to write, cautiously, but overall approvingly, as follows: That every presentation and every belief must have an object other than itself and, except in certain cases where mental existents happen to be concerned, extra-mental … and that the object of a thought, even when this object does not exist, has a Being which is in no way dependent upon its being an object of thought: all these are theses which, though generally rejected, can nevertheless be supported by arguments which deserve at least a refutation. Except Frege, I know of no writer on the theory of knowledge who comes as near to this position as Meinong. In what follows, I shall have the double purpose of expounding his opinions and of advocating my own; the points of agreement are so numerous and important that the two aims can be easily combined. (1904:204)3

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Page 177 True, Russell foists the confusing being-predication thesis onto Meinong. He misinterprets Meinong as attributing Being even to objects that Meinong expressly says neither exist nor subsist, that are beingless and lack being ( Sein) in any sense of the word. Nor should we downplay the fact that in this passage Russell only says that no one except Frege comes as close as Meinong to the view of every object of thought as a ‘Being’. One can of course come very close to a philosophical position without actually embracing it. Still, it is strange in that case to regard Meinong as coming anywhere within howitzer shot of a view he repeatedly and emphatically denies. All this is indisputable. Let it pass for the moment, in order to relish Russell’s declaration in 1904 that he has much in common with Meinong, and that Frege comes at least almost as near to the assertions in Meinong that Russell claims can be supported by arguments that minimally deserve an effort at refutation and replacement by a preferred alternative. Frege and Meinong are at least momentarily considered as on a par, spaced apart as they are on Russell’s balance beam as he contemplates whether and how to tip the scales. While he is no doubt keenly aware of the differences between them, Russell is prepared to evaluate the advantages and disadvantages of each, and to appreciate their commonalities as revealing something useful for his own purposes in understanding the relations between logic, semantics and ontology. One year later, in reviewing Meinong’s edited collection of papers from the Graz school, the Untersuchungen zur Gegenstandstheorie und Psychologie , Russell writes even more appreciatively: The philosophy set forth in [the first three and eighth essays] is a development of that contained in Meinong’s [ Über ] Annahmen, and its value appears to me to be very great. Its originality consists mainly in the banishment of the psychologism which has been universal in English philosophy from the beginning and in German philosophy since Kant, and in the recognition that philosophy cannot concern itself exclusively with things that exist. (1905b: 530)4 The significance of this limited endorsement of Meinong’s object theory is that it appears in the very same volume of Mind, Volume 14, 1905, as ‘On Denoting’. Allowing for the time lag that frequently occurs for book reviews versus essays, along with the usual publishing contingencies, we still have the basis for an historical enigma. We are left wondering how, why, and exactly when in or around 1905 Russell could have so suddenly and so radically changed his once qualifiedly good opinion of Meinong’s Gegenstandstheorie in favour of Frege’s Begriffsschrift, that in the celebrated 1905 essay he finds it necessary to distance himself permanently from Meinong’s theory of reference and predication. Suppose, therefore, that as Russell became more familiar with what he took to be the ontology of Meinong’s semantics he began to see deeper issues dividing himself from Meinong more clearly, and proceeded to

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Page 178 discount Meinong’s intensionalist concept of meaning. Russell, with his model of philosophy as the continuation of natural science by other means, was never averse to discharging a hypothesis and revisiting his assumptions if he thought they had led him astray. If this is what happened in the reversal of opinion he underwent with respect to Meinong’s object theory, as in some sense seems likely, perhaps even obvious, then we may at last have the makings for a plausible story concerning Russell’s estrangement from what had first been his cautious admiration for Meinong’s object theory. The awakening to the limitations of Meinong’s theory of nonexistent objects as Russell began to turn toward a more radically extensionalist referential semantics and ontology, to recognize and develop the extensionalist side of his philosophical persona, eventually to be mirrored also in his reconceptions of mathematical logic, can be dated to the publication of ‘On Denoting’, where he finally and for the first time unequivocally renounces Meinong’s object theory. What is needed in order to understand Russell’s rejection of Meinong in ‘On Denoting’ are three things. First, a critical examination of Russell’s ostensible reason for replacing Meinong’s intensionalist object theory of reference and predication with a Fregean extensionalist theory of reference. Russell over a period of years successively purges a more purely extensional reference theory of Frege’s concept of sense, taking the final step in this particular direction in 1905. Second, a general critique of the alternative extensionalist referential theory that Russell proposes to substitute for Meinong’s, including an examination of Russell’s concept of being (Being) and the distinction between being and existence. Finally, third, a fully developed counter-Russellian Meinongian object theory of definite descriptions to stand against Russell’s, to demonstrate its advantages over Russell’s analysis, and to satisfy ourselves that Russell’s theory of definite descriptions does not by itself constitute a conclusive refutation of Meinongianism in lieu of an adequate counterpart Meinongian logic of definite descriptions. What follows is a criticism of Russell and an exposition of a nonstandard intensionalist Meinongian analysis of definite descriptions. It is in effect a Meinongian reply to ‘On Denoting’ that Meinong himself never ventured. Its purpose is to undermine and reverse the dialectical opposition between Russell and Meinong as it has most often been understood by logicians in the extensionalist analytic tradition. Russell’s theory of definite descriptions, not least because of confusions over the Gray’s Elegy passages, has often been misunderstood, but has nevertheless exerted a profound anti-Meinongian influence on the subsequent course of analytic philosophy, in the years since ‘On Denoting’, after its first period of obscurity, deservedly became required reading. Analytic philosophers, and I speak as a member of that tribe, are often only too grateful if they can spare themselves the burden of mastering yet another semantic theory or ontology, or, for that matter, epistemology. What they choose to study they pursue with such intensity that if they believe there are good knockdown

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Page 179 reasons for discounting an entire way of thinking, they may sometimes take advantage of the freedom, say, not to study Meinong. Why, moreover, should they not discount the lifework of Alexius Meinong? Meinong was the student of Brentano, who in turn was branded psychologistic by his own student Edmund Husserl, after Husserl was criticized as psychologistic by Frege in a caustic review of Husserl’s 1891 Philosophie der Arithmetik: Psychologische und logische Untersuchungen . Did Russell not prove that Meinong’s theory was entangled in contradictions? That there was supposed to ‘be’ (?!) an existent present King of France, even though no present King of France exists? Is it not absurd from the outset to say that we can refer to the golden mountain when in fact there is no such thing, or to suppose that we can truly predicate the property of being golden or a mountain of the golden mountain when no golden mountain exists to sustain these predications? Meinong should always remain an important figure for mainstream extensionalist analytic philosophy precisely because he challenges just these basic assumptions. No, he proclaims, if we are to begin with the empirical data of thought and its meaningful expression, then we must acknowledge that we frequently think about and predicate properties of things that do not actually or even possibly exist. These are the intended objects of our thoughts, which we sometimes express also in language, in myth, fiction, hypothetical assumption, intentional direction toward a state of affairs as the projected outcome of an action or sequence of actions, in the plastic arts and in recreational flights of fantasy. The sections concerning Meinong in ‘On Denoting’ suggest that Russell thought of Meinong’s approach even then as a potentially viable alternative to what turns out to be his preferred (purified) Fregean solution (lacking Frege’s category of sense or Russell’s prior and narrowly limited commitment to denoting concepts as intermediaries between denoting expressions and their denotations) to the problem of understanding reference. Russell describes Meinongian object theory merely as disadvantageous when compared with Frege’s distinction between sense and reference, in view of its extensionalist commitment to the existence of all denoted entities. He nevertheless believes that Meinong’s theory entails a difficulty for which he cannot see any satisfactory solution. This single consideration, of great significance in Russell’s eyes, is enough to tip the scales away from Meinong and permanently thereafter toward an extreme form of referential extensionalism that finally outdoes Frege, let alone Meinong.5 It is an extraordinary historical moment at precisely this juncture in 1905 that was to shape the direction of analytic philosophy forever. What remains an unsettled mystery on such an interpretation is how in the first place Russell could ever have taken Meinong’s theory as seriously as he seems to have done. Russell stakes his rejection of Meinong’s object theory on the belief that it implies contradictions, that it violates the law of (non-) contradiction. We can readily imagine that only a problem of this logical magnitude could conceivably have driven Russell away from a theory to which he

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Page 180 had otherwise been attracted and which he describes in ‘On Denoting’ as one among a range of choices for thinking about the problems of meaning and reference that in other ways stands as a competitor to Frege’s. Here is Russell’s first mention of and first formulation of his objection to Meinong in the essay: The evidence for the above theory is derived from the difficulties which seem unavoidable if we regard denoting phrases as standing for genuine constituents of the propositions in whose verbal expressions they occur. Of the possible theories which admit such constituents the simplest is that of Meinong. This theory regards any grammatically correct denoting phrase as standing for an object . Thus ‘the present King of France’, ‘the round square’, etc., are supposed to be genuine objects. It is admitted that such objects do not subsist , but nevertheless they are supposed to be objects. This is in itself a difficult view; but the chief objection is that such objects, admittedly, are apt to infringe the law of contradiction. (1905a: 482–83) On the face of things, if it could be substantiated, this seems to be such a damaging complaint that it is hard to see how Russell could offer Meinong’s object theory the least serious attention, let alone to describe it as ‘possible’. Perhaps all that Russell means is that it is possible for Meinong to have put forward a theory that in content by virtue of its contradictory implications is logically impossible. He continues: It is contended, for example, that the existent present King of France exists, and also that he does not exist; that the round square is round, and also not round; etc. But this is intolerable; and if any theory can be found to avoid this result, it is surely to be preferred. The above breach of the law of contradiction is avoided by Frege’s theory. He distinguishes, in a denoting phrase, two elements, which we may call the meaning and the denotation . (483) In this single paragraph Frege’s stock skyrockets while Meinong’s tanks. Logical contradiction is generally to be avoided, unless Russell is to be faulted for not anticipating paraconsistency. For that reason, Russell surprisingly seems to minimize the importance of having discovered such a glaring logical inconsistency in Meinong’s object theory. Now he adds: Thus we must either provide a denotation in cases in which it is at first sight absent, or we must abandon the view that the denotation is what is concerned in propositions which contain denoting phrases. The latter is the course that I advocate. The former course may be taken, as by Meinong, by admitting objects which do not subsist, and denying that they obey the law of contradiction; this, however, is to be avoided if

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Page 181 possible. Another way of taking the same course (so far as our present alternative is concerned) is adopted by Frege, who provides by definition some purely conventional denotation for cases in which otherwise there would be none. (484) Again, Russell contrasts the virtues of Frege with the vices of Meinong. He appears to understate the difficulties to which Meinongian object theory is heir when he says merely that failure to obey the law of contradiction is to be avoided ‘if possible’. It will not do to say that Russell is unwilling to let go of Meinong entirely until he has substituted his own reductive analysis of definite descriptions in terms of quantification theory and identity, unless we are willing to interpret Russell as being much more of a Meinongian prior to the discovery of these ‘contradictions’ than most supporters or critics of Russell or Meinong are generally prepared to grant. If in fact Meinong’s theory runs into contradictions, then I think Meinong himself as a good empiricist in theory construction should join in the chorus chanting that we have no choice but to abandon object theory and cast about for yet another alternative. We can turn to Frege’s or some other theory, but we could not in that case continue seriously to consider Meinong’s. Russell almost makes it seem as though, other things being equal, we ought to prefer a theory that preserves logical consistency, perhaps on aesthetic grounds; whereas surely, especially in the days before paraconsistent or dialethic logic, the problem should be considered as damning. This, remarkably, is not what Russell says. Possibly the most charitable reconstruction of Russell’s remarks on Meinong in ‘On Denoting’ signal Russell’s admission of the possibility that there may yet be a way of saving object theory from logical inconsistency. Russell is nevertheless so enamoured of the analysis of definite descriptions in the emerging new predicate calculus that he is about to reveal in the essay that he is prepared to leapfrog over Meinong’s object theory in almost any way he can, even if it means embracing Platonism in an extensionalist referential framework, as he ultimately follows Frege in doing. As I understand Russell’s project in ‘On Denoting’, he addresses three specific semantic-ontological puzzles, introducing a formal logical solution in the reduction of all Fregean proper names to definite descriptions, and cashing out their meaning in terms of logical constants such as the existential quantifier and identity sign. He does so in part, as the puzzles he chooses to address make clear, in order to rescue semantic theory and metaphysics from the contradictions of Meinong’s object theory, and in the process secures the referential semantic and ontological foundations of mathematical logic in a Fregean domain of exclusively existent entities. It is in his 1912 defence of an abstract order of Platonic entities, ‘The World of Universals’ in The Problems of Philosophy (1912a), and in his essay of the same year ‘On the Relations of Universals and Particulars’, in Proceedings of the Aristotelian Society (1912b), that Russell commits his ontology to existent abstract universals as the ultimate constituents of

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Page 182 Fregean Sinne. When this component of Russell’s programme is hammered into place, he is able to reduce all proper names to definite descriptions, and the predications of all definite descriptions to universals as objects of knowledge by acquaintance rather than description. Russell must identify a nondescriptive foundation for descriptions, in order to avoid an infinite regress. The universals are general objects of acquaintance, designated, as Russell proposes already in his 1910 essay, ‘Knowledge by Description and Knowledge by Acquaintance’, in the linguistically simplest terms as ‘this’ and ‘that’, within a thinker’s experience. Why this development of Russell’s theory of meaning should not also be seen as objectionably psychologistic, to which even Frege despite his Platonism would presumably have taken the greatest exception, is yet another mystery in Russell’s analysis of definite descriptions as a defining moment in the early textbook history of analytic philosophy. Meinong has long been criticized for mishandling Russell’s criticism according to which object theory is supposed to entail that the existent present King of France (in other versions, the existent golden mountain or existent round square) both exists and does not exist. Richard Routley (Sylvan), myself and others, have argued that Meinong should instead have enforced his distinction between two very different types of properties.6 J. N. Findlay translates Meinong’s adaptation of Ernst Mally’s terminology for konstitutorische und ausserkonstitutorische Bestimmungen as the relevant difference between nuclear and extranuclear properties.7 Nuclear properties are those, like being red or round, golden and a mountain or mountainous, that are freely assumable as belonging to an intended object’s Sosein or so-being, while extranuclear properties such as being existent, nonexistent, possible, impossible, complete, incomplete, and so on, are not freely assumable and do not belong to an object’s Sosein. By appealing to the distinction between nuclear and extranuclear properties, it would have been possible and arguably preferable for Meinong to have maintained in response to Russell’s objection that the existent present King of France simply does not exist because no extranuclear property or its complement like existence or nonexistence is freely assumable in characterizing or offering identity conditions for an intended object. The right answer would then be that object theory is perfectly logically consistent, that there is no threat to the requirement of noncontradiction, and hence no basis in Russell’s criticism for giving up entirely on Meinong’s semantics and choosing Frege’s instead. Contrary to Russell’s unsupported assertion, Meinong nowhere allows that the present King of France (golden mountain, round square) exists and also does not exist. He simply holds, as any reasonable and sufficiently knowledgeable person would, that the present King of France does not exist. If Frege’s Begriffsschrift combined with his later sense-reference distinction is accepted, restricting denotation exclusively to existent objects, then a different kind of argument would need to be made offering other reasons than the fact that Meinong was so thoroughly confused as to

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Page 183 have advanced a theory according to which the same intended objects are supposed both to exist and not exist.8 What Meinong actually proposes as a solution to Russell’s problem, as opposed to what he could and probably should have said, still does not land him in the sort of contradiction that would warrant fleeing from his version of intensionalism to a more purely extensionalist theory of meaning. If we had any reason for being attracted to Meinong’s intensionalism in the first place, as Russell within limits acknowledges, then the problem of the existent golden mountain or existent round square or present King of France does not topple object theory by exposing anything more than a superficial inconsistency for which a defensible solution exists, rather than a genuine deep and intractable contradiction. Meinong, for better or worse, distinguishes between a literally diluted or watered-down ( depotenzierte ) nuclear sense of existence, lacking the modal moment ( das Modalmoment ) and full-blooded extranuclear existence in full possession of the modal moment. If there is a sense to be made out between what actually exists and what is merely said as a characterizing property of an object that is falsely supposed to exist, as Meinong seems to intend, then there is no need to regard Meinong’s object theory as logically inconsistent. Such an application might be found in the distinction between Macbeth’s two daggers in Shakespeare’s play, the one with which he and Lady Macbeth slay King Duncan, and the one that Macbeth later hallucinates as floating before him. Neither of the daggers actually exists, but one of them within the play is supposed to exist, and has the property of existence attributed to it, while the other even within the play and as far as the play is concerned is supposed not to exist.9 The existent present King of France, as Meinong replies to Russell, is supposed to be existent even though he does not exist. The distinction is not nonsensical, even if it is not the best answer to Russell’s objection. Nevertheless, it has at least some intuitive basis, and there is no explicit contradiction in the conjunction if a syntactical distinction is observed in concluding that the existent King of France is existent-sans-modal-moment even if he does not exist, or is not existent-cum-modal-moment. Russell seems to throw up his arms in frustration or disgust at Meinong’s reply. There is, after all, despite the formula’s apparent infelicities, something to be said for distinguishing between the ontic status of London as opposed to Dr. Watson in the Sherlock Holmes stories, between Napoleon and Pierre Bezuhov in Tolstoy’s War and Peace , and in general between things that actually exist and those that are merely said to exist in characterizing an intended object by free assumption. Suppose that a twelvekarat golden mountain actually does exist. Then we would still want to be able to distinguish it from a fictional eighteen-karat golden mountain by speaking alternatively of the existent golden mountain and the nonexistent golden mountain. Meinong nowhere says nor is he anywhere committed to the proposition that the existent present King of France both exists and does

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Page 184 not exist univocally in the same extranuclear sense of the word. If Russell rejects Meinong’s object theory of denotation on grounds of logical inconsistency, it can only be because he does not properly understand or appreciate the force of Meinong’s distinction between nuclear and extranuclear properties (Findlay 1963:106–10). The fact that Russell relies, albeit with some hesitation and qualification, on the inconsistency objection to Meinong’s object theory, encourages the impression that there might be some further implicit reason for his defection from Meinongian intensionalism to Fregean referential extensionalism. If these indications are symptomatic of something deeper at work in Russell’s reversal of interest, then the original problem persists concerning Russell’s turn from Meinong to Frege. We can formulate the issue in this way. Did Russell really believe that Meinong’s theory was hopelessly embroiled in outright logical contradiction to the extent that there was no choice but to adopt a version of Frege’s extensionalist thesis limiting reference to existent objects? Or did he have more fundamental reasons for preferring a purified Fregean approach, as a result of which he was satisfied to dismiss Meinong’s theory by insinuating that it might be logically inconsistent? The enigma of Russell’s dramatic rejection of Meinong is perpetuated by his proliferation of mixed signals. He does not really seem to believe that there are knockdown grounds for regarding Meinong’s object theory as contradictory. To the extent that he attributes contradictions to Meinong, he does not seem to believe that the contradictions to which the account is subject are necessarily decisive. He merely states that it might be better to choose another theory in light of the apparent inconsistencies in Meinong’s theory. Moreover, Meinong’s reply to Russell’s problem of the existent present King of France and existent golden mountain or existent round square, by which he claims to have identified contradictory implications in Meinong’s object theory, is by no means absurd. It answers a need for a useful distinction in intensionalist semantic analysis. Meinong has an even stronger, intuitively more acceptable solution in reserve, holding firm on the categorical difference between nuclear and extranuclear properties, by means of which Russell’s problem can be avoided entirely without logical inconsistency.10 RUSSELL’S CONCEPT OF BEING We should take note of apparent conflicts in Russell’s understanding of the concept of being. We find Russell, for example, again in his 1904 letter to Meinong, writing: I have always believed until now that every object must be in some sense, and I find it difficult to recognize nonexistent objects. In a case such as the golden mountain or round square one must distinguish

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Page 185 between sense and reference (in accordance with Frege’s distinction). The sense is an object and has being, whereas the reference on the other hand is not an object. (Farrell Smith 1985:348) Russell does not mention, as Frege does, that the (conventional) sense of a nondenoting term is only an indirect object, and that the term has no proper denotation as such. The position is at least ostensibly at odds with what Russell maintains in The Principles of Mathematics, where he states that even nonexistent objects must have being (‘Being’). It is complicated to sort out these terminological differences, but the task is indispensable to understanding Russell’s rejection of Meinong’s object theory in ‘On Denoting’ and Introduction to Mathematical Philosophy . In the Principles , Russell writes: It should be observed that A and B need not exist, but must, like anything that can be mentioned, have Being. The distinction of Being and existence is important, and is well illustrated by the process of counting. What can be counted must be something, and must certainly be , though it need by no means be possessed of the further privilege of existence. Thus what we demand of the terms of our collection is merely that each should be an entity. (1938:71) Here it is interesting that Russell should maintain that whatever can be mentioned or counted, regardless of whether it exists or is nonexistent, must be an entity. For the Oxford English Dictionary defines an ‘entity’ as: ‘noun (pl. entities) a thing with distinct and independent existence.—origin French entité , from Latin ens “being”‘. This is yet another example of the way in which Russell’s terminology is out of sync with ordinary language. Russell is clear in any case in distinguishing between Being and existence, and seems to be saying something remotely Meinongian by allowing that anything that we can think of, mention, or count, even if it does not exist, must nevertheless have some kind of appropriate semantic status, which he chooses, however misleadingly, to speak of as Being. Later in the text, Russell adds (mildly) to the confusion when he refrains from capitalizing ‘Being’, and writes it instead simply as ‘being’: Being is that which belongs to every conceivable term, to every possible object of thought—in short to everything that can possibly occur in any proposition, true or false, and to all such propositions themselves. Being belongs to whatever can be counted. If A be any term that can be counted as one, it is plain that A is something, and therefore that A is … Numbers, the homeric [ sic ] gods, relations, chimeras, and four-dimensional spaces all have being, for if they were not entities of a kind, we could make no propositions about them. Thus being is a general attribute of everything, and to mention anything is to show that it is. (449)

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Page 186 Continuing, Russell again contrasts being with existence, while persisting in speaking of ostensible objects with Being (being) but lacking existence as entities: Existence , on the contrary, is the prerogative of some only amongst beings. To exist is to have a specific relation to existence—a relation, by the way, which existence itself does not have. This shows, incidentally, the weakness of the existential theory of judgment—the theory, that is, that every proposition is concerned with something that exists. For if this theory were true, it would still be true that existence itself is an entity, and it must be admitted that existence does not exist. Thus the consideration of existence itself leads to non-existential propositions, and so contradicts the theory. The theory seems, in fact, to have arisen from neglect of the distinction between existence and being. Yet this distinction is essential, if we are ever to deny the existence of anything. For what does not exist must be something, or it would be meaningless to deny its existence; and hence we need the concept of being, as that which belongs even to the non-existent. (449–50)11 Aside from the inconsistent capitalization of ‘being’ in these passages, taken collectively, and the strange use of both the words ‘being’ and ‘entity’, Russell’s motivation for distinguishing between being and existence is explicable as a variation of the problem that Socrates raises in Plato’s dialogues the Sophist and Parmenides.12 Where an apparent contradiction threatens, in the judgement that something must be in order to have the property of not existing, there a distinction of some sort must be drawn. Russell and Meinong recognize the problem, but their solutions rely on markedly different distinctions with markedly different semantic and metaphysical presuppositions and implications. The question of the extent to which Russell properly understands Meinong can be approached in one way by asking whether, and if so to what degree or in what way, Russell’s use of similar terminology maps onto Meinong’s. In making the attempt we soon discover that we cannot directly correlate Russell’s distinction between being and existence with Meinong’s distinction between Sein and Existenz , or between Bestand and Existenz , or between Außersein and Existenz . The category of being for Russell includes existence, but not conversely. This is true of Meinong’s distinction between Sein and Existenz , but Meinong would staunchly deny that chimeras and the Homeric gods have being in the sense of Sein. Bestand and Existenz for Meinong, on the other hand, are mutually exclusive. There is an interpretation of Meinong’s concept of the Außersein (extra-being or extraontology) that matches up somewhat with Russell’s distinction between being and existence. Meinong wants to say that every object, which Russell further constrains as every conceivable object, belongs to a domain, membership in which does not depend on its ontic status. This sounds much

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Page 187 like what Russell must mean by attributing being even to chimeras and the Homeric gods, which Meinong and Russell would presumably agree do not exist. Russell’s choice of terminology is not particularly conventional, and Meinong’s usage seems more in accord with ordinary linguistic practice in regarding existence as a mode of being, translating directly from the German. For it must strike even philosophically sophisticated readers accustomed to stipulative technical terminologies as flatly false to say that chimeras and the Homeric gods have being, or, for that matter, to insist on a distinction between being and existence. If Russell can swallow the conclusion that chimeras or the Homeric gods have being or that they are, why then does he choke on Meinong’s later assertion that the existent golden mountain is existent even though it does not exist? The contrast Russell seems to have in mind also does not obviously recapitulate Meinong’s scholastic distinction, undoubtedly imbibed through his study with Brentano, between existence and subsistence. If we imagine that by ‘existence’ Russell refers to existence in Meinong’s sense, but by ‘Being’ or ‘being’ he means subsistence in Meinong’s adoption of the medieval terminology for an abstract aspatio-temporal mode of being, then we might try to say that the term ‘Homeric gods’ has being, even in the ordinary sense, and that it is a term that would denote if only the Homeric gods happened to exist. We could quibble in that case about the appropriateness of the term ‘being’ as anything that can be counted, on the grounds that we will be speaking of the being of intended objects that are neither spatio-temporal nor abstract entities. If the Homeric gods do not exist, however, then we must wonder what exactly we are supposed to be counting when we go through the roster of Zeus, Apollo, Hera, and so on, as 1, 2, 3, and so on? At most, it would seem that in that case we are counting nothing more than our concepts or ideas of gods, which no Meinongian or radical referential extensionalist need deny exist, let alone denying that such concepts or ideas have being, even in the ordinary sense. How, on the other hand, can we possibly be counting gods in that case, on the assumption that there are no Homeric gods to be counted? Do the gods have being, then, in the sense that counterfactually they would be denoted if only they existed? That suggestion too does not seem to be fully thought through. For then we could say the same about the round square, the elliptical triangle, and the like, all of which can be counted as concepts or ideas, as Russell seems to allow, but are not even the possibly existent denotations of possibly Fregean or Russellian denoting terms or phrases. Exactly how Russell’s distinction is supposed to fit together with his rejection of Frege’s distinction between sense ( Sinn ) and reference or denotation ( Bedeutung ) and the existence requirement in the analysis of definite descriptions in ‘On Denoting’ raises further interpretational problems. Russell holds that in ‘The F is G’, an F exists, which for Russell implies that in the sentence F is denoted . Where an F does not exist, Frege claims that ‘the F ’ has sense but no reference or denotation. Russell denies this,

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Page 188 but maintains that the F must have being, without which we would not even be able intelligibly to think or say of it that it does not exist. The Gray’s Elegy section of the essay is further intended to argue away the need for Fregean senses from an adequate theory of denotation. None of this should come as any surprise to readers of Russell’s 1905 essay. What is not often noticed is that Russell’s theory implies that being and existence alike cannot be among the constitutive properties of things. If they were, then it follows immediately that the (nonexistent) present King of France would have at least the property of nonexistence. Russell’s notation does not attribute existence to things as a property represented by a predicate, but by means of the existential quantifier. Nonexistence is equally not a property by these conditions, but represented instead by the propositional negation of an existential quantification. Such a proposal is fine for existence and nonexistence, but what about Russell’s concept of being? Can it be a property of things? Clearly it cannot, because Russell in the Principles acknowledges that chimeras and the Homeric gods have Being, whereas the corresponding terms, ‘chimeras’, ‘Homeric gods’, or names putatively designating individual chimeras or Homeric gods, ‘Zeus’, say, possess sense but lack any direct reference or semantic denotation. Following Frege, as he indicates in his 1904 letter to Meinong, the most that Russell can allow is that such terms have only indirect reference, which is their conventional sense. If no such objects are denoted by these terms, then there are no such objects to stand as the bearers of any properties. The extent to which Russell’s categories might be confused comes into sharper focus when we ask what it could possibly mean in that case to say that nonexistent objects have being. How can nonexistents in Russell’s logic and semantic theory have anything at all? How can they even be said to be , if nonexistents generally cannot be the objects of any true predications? If, on the other hand, nonexistent objects for Russell can at least have and perhaps only have the property of being, then what is the logical basis for distinguishing between this one and only exceptional kind of property, where ordinary properties like being in 1905 a present King of France are such that nonexistent objects logically cannot possess them? Unlike existence, Russell makes no provision for being as a special kind of quantifier, which would exempt attributions of being from standard predicate-object constructions within his symbolic logic. Perhaps he would say that there is no need to do so, since no object fails to ‘have’ being. In that event, however, we are left with even more unsettled questions about how Russell understands the logic of being. If we introduce a new quantifier, B, we can try to say on Russell’s behalf, for example, that B xKx ^ ¬ xKx . This will not do, however, because the distinct nonoverlapping quantifier scopes do not guarantee that we are even ostensibly talking about the same object (or conventional sense associated with the corresponding term) in the two conjuncts. We can try instead to write: B x( Kx ^ ¬ yKy ^x = y). In this case, however, it seems that we are attributing a further relational

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Page 189 property, that of being identical to something (not an object) with Being, to an ostensibly nonexistent object. Nonexistent objects in Russell’s logic are nevertheless not supposed to have any properties, because, to speak intuitively from within this extensionalist perspective, they are not there to possess them. The same problem does not arise for Russell’s analysis of definite descriptions, because in G ι xFx ↔ x( Fx ^ y( Fy ↔ x = y)^Gx), we never need to consider the x = y clause when the entire proposition is rendered false by the fact that ¬ xFx . Thus, whether or not Russell’s Being is interpreted as a predicate or quantifier, there seems to be no way for him to avoid the true predication of some kind of property to nonexistent objects. Since Russell does not provide philosophical justification for special logical principles for the discriminatory true attribution of the property of being or of having being as opposed to the property of being in 1905 a present King of France, we are left with the problem of reconciling his conclusion that even nonexistent objects ‘have’ being, and that nonexistent objects cannot have any other kinds of properties. What is lacking is a solid basis in logic and metaphysics for allowing such a conspicuous exception for Russell’s concept of being. Meinong arguably handles these issues more naturally by allowing only that all thoughts are directed toward objects, not all of which have being ( Sein) either in the sense of existence or subsistence. We are left as a result wondering exactly what Russell means by ‘being’ (‘Being’) in saying that the golden mountain ‘has’ being. It clearly does not mean that the golden mountain exists, or even subsists in the manner of abstract entities, according to the Scholastic distinction Meinong inherits from Brentano. Nor can it mean that the golden mountain is a nonexistent object as Meinong holds, as something capable of being denoted to stand as the subject of true predications of properties. What, however, is it supposed to mean in more positive terms, especially in view of the fact that its logic cannot involve predication or special quantification? We assume that it cannot mean being an object of thought or language, because Russell denies that terms ostensibly referring to nonexistent objects have any reference or denotation, but only an indirect object that is the corresponding term’s conventional sense. If there is no denoted object, not even a Meinongian nonexistent one ostensibly referred to by a pseudo-name such as ‘Zeus’ or to the pseudo-definite-description ‘the golden mountain’ or ‘the present (1905) King of France’, on the other hand, then why does Russell insist that the ostensible objects in these cases nevertheless have being? What in that case is supposed to have being and what is it for something that can bear no (other) properties to have being? If Russell hopes to avoid a Meinongian object theory by substituting for it his own synthesis of the being-existence thesis and Fregean extensional reference-or-denotation, and if the concept of being on which he relies cannot be adequately clarified and reconciled even by invoking Frege’s sense-reference distinction, then he has not finally advanced a satisfactory alternative to Meinong’s object theory.

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Page 190 BASE CAMP ON THE SLOPES OF MEINONG’S GOLDEN MOUNTAIN What, then, of the choices presented by Russell’s synthesis of the being-existence distinction and Frege’s sense-reference or denotation distinction? Let us return to the problem of understanding ostensible references to the golden mountain. Meinong is certainly not the first philosopher to speak of a golden mountain. The idea that we can refer to a nonexistent object and truly predicate constitutive properties of a golden mountain as a result also could not have originated with him. He merely formulates the semantic principles by which thoughts about and ostensible references in language to a golden mountain could be seen as part of a larger intensionalist theory, inspired by Brentano’s psychognosy or descriptive empirical phenomenological psychology. If Meinong did not pick up the idea of a golden mountain from the ambient literary culture of his time, he may have learned of it from his studies of Hume’s philosophy. Brentano, Meinong’s dissertation supervisor at the University of Vienna, directed Meinong in light of his historical training to Hume for background in the classical British empiricists, resulting in Meinong’s first publications, the Hume-Studien I and II (1877, 1882). Hume in turn may have adopted the concept from Berkeley, who speaks of a golden mountain in connection with the modal distinction between possible and actual existence. In Three Dialogues Between Hylas and Philonous (1734), Second Dialogue, Berkeley writes: Hyl: Upon the whole, I am content to own the existence of matter is highly improbable; but the direct and absolute impossibility of it does not appear to me. Phil: But granting Matter to be possible, yet, upon that account merely, it can have no more claim to existence than a golden mountain, or a centaur. Hyl: I acknowledge it; but still you do not deny it is possible; and that which is possible, for aught you know, may actually exist. (1949–58: Vol. 2, 224) Hume, in An Enquiry Concerning Human Understanding , describes a cut-and-paste method by which the imagination constructs such composite ideas as that of a golden mountain, in terms reminiscent of those similarly applied by Descartes in Meditations on First Philosophy (1985: Volume 1, Meditation 3), when discussing the principle that the origin of any of our ideas must have at least as much formal reality as the idea has objective reality. Hume argues in the first Enquiry , Section 2, ‘Of the Origin of Ideas’: But though our thought seems to possess this unbounded liberty, we shall find, upon a nearer examination, that it is really confined within very narrow limits, and that all this creative power of the mind amounts

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Page 191 to no more than the faculty of compounding, transposing, augmenting, or diminishing the materials afforded us by the senses and experience. When we think of a golden mountain, we only join two consistent ideas, gold, and mountain, with which we were formerly acquainted. A virtuous horse we can conceive because, from our own feeling, we can conceive virtue; and this we may unite to the figure and shape of a horse, which is an animal familiar to us. In short, all the materials of thinking are derived either from our outward or inward sentiment: the mixture and composition of these belongs alone to the mind and will. Or, to express myself in philosophical language, all our ideas or more feeble perceptions are copies of our impressions or more lively ones. (1975: §13:19) What could be a more attractive focus of desire and motivation for action in a myth or fantasy than the idea of an enormous chunk of gold? And if a massive chunk, then why not one with the dimensions of an entire mountain, a pure mineral deposit of the malleable substance of sufficient size that you can hike and ski and build a chateau on it? The fable of the golden mountain as such has become a stock part of many cultures. Grimm’s fairy tales, for example, contain a typical such yarn about ‘The King of the Golden Mountain’ (1812). In the story, a merchant promises his son to a dwarf in exchange for riches; the son through ingenuity and luck escapes this fate and travels to an enchanted castle where he rescues a maiden and becomes King of the Golden Mountain.13 Despite the differences between Russell and Meinong that emerged especially after the publication of ‘On Denoting’, there are remarkable affinities that a cautious critic should not overlook. Russell, like Frege before him, is committed to a principle of logic and set theory that is also very much at the heart of Meinong’s object theory. The principle in Frege and Russell is that there exists a set for every logically consistent description of its putative membership by reference to any specification of qualities or relations. It is only by means of such a comprehension principle that Russell’s paradox can arise, and it lies at the foundation of Frege’s thesis that intension determines extension, or, equivalently, that sense determines reference. The same principle has interestingly different ontic consequences in an intensionalist as opposed to extensionalist framework. It offers a common basis for insight into extensionalist criticisms of intensionalism, in generic terms, between Fregeanism and Meinongianism, and into intensionalist criticisms of extensionalism that reveal the limitations of possible extensionalist objections to Meinong’s object theory. The Russell vs. Meinong debate is a specific instance of a more general dispute between referential extensionalism (Frege, Russell) and intensionalism (Meinong). What is the distinction, and how should it be characterized? An extensionalist theory of meaning typically assumes three things: (1) the existent objects that constitute a semantic domain are logically

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Page 192 predetermined. (2) All genuinely designating or denoting terms refer only to these objects. (3) The truth of propositions or declarative sentences in which properties are predicated of objects can be interpreted as the inclusion of an existent object in the extension of the predicate. The extension of a predicate in turn consists of all and only the existent objects possessing the property represented by the predicate, and is otherwise interpreted as false. Intensionalism, by contrast, as in the semantics underwriting Meinong’s object theory, begins with combinations of properties (an object’s Sosein) and defines existent or nonexistent objects as corresponding to unique property combinations, regardless of their ontic status (independent of and indifferent to Sein). A proposition or categorical declarative sentence in intensionalist semantics is interpreted as true when the property predicated of an object is included in the object’s property combination, and otherwise as false.14 The essential differences between extensionalist and intensionalist semantics are summarized in the following table: Extensionalism: Predetermined Semantic Starting Place:  Domain Consisting of All and Only Existent Objects Names and Other Designating Terms Refer Only to Existent Objects in the Domain Truth of Propositions (Declarative Sentences):  Object included in extension of all existent objects  possessing the property represented by the predicate—  proposition is TRUE; otherwise, proposition is FALSE Intensionalism: Predetermined Semantic Starting Place:  Individually Logically Possible Properties Names and Other Designating Terms Refer to Any Object Regardless of its Ontic Status  Associated with Any Combination of Logically Possible Properties Truth of Propositions (Declarative Sentences):  Object included in semantic domain of all (existent or nonexistent) objects  possessing the property represented by the predicate—  proposition is TRUE; otherwise, proposition is FALSE. The golden mountain, an incomplete nonexistent object in Meinongian object theory semantics, is truly golden and a mountain, according to Meinong, even though no such object happens to exist; the round square, an impossible object, is both round and square, even though no such object can possibly exist (see Meinong 1904). The propositions in question are true in a Meinongian intensionalist semantics because the nonexistent objects in question are included in the (ontically neutral) semantic domains, respectively, of all existent or nonexistent golden things and of all existent or nonexistent mountains, and of all existent or nonexistent round objects and of all existent or nonexistent square objects. Russell’s commitment after 1905

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Page 193 to an extensionalist referential Fregean semantics purged of Frege’s concept of sense or Russell’s own prior acceptance of denoting concepts, obliges him on the contrary to conclude that the proposition that the golden mountain is golden, despite sporting the superficial appearance of tautology, is false, on the grounds that no golden mountain exists. The purified Fregean extensionalist understanding of the referential semantics of names and definite descriptions appearing within sentential contexts is heralded in ‘On Denoting’ (1905a: especially 483–85).15 MEINONGIAN INTENSIONALIST LOGIC OF DEFINITE DESCRIPTIONS In Meinongian object theory, the interpretation of definite descriptions is more complex than in Russell’s extensionalist referential account. The sentence ‘The present King of France is bald’ is neither true nor false, simply because there is no adequate source of information about the nonexistent present King of France to determine whether or not the object in question has or does not have the property of being bald. In explaining his theory of definite descriptions, Russell takes as his most important and memorable example the proposition, ‘The present King of France is bald’ (483).16 The choice of this case is significant, because there is no present King of France, or, as Meinongians are wont to say, the present King of France is a nonexistent object. Russell’s three-part decomposition of the definite description, as is well known, involves: (i) an existence assertion; (ii) a uniqueness assertion; (iii) the predication of a property to the unique existent as identified in (i) and (ii) (481–84). Thus, if the proposition that the present King of France ( K ) is bald ( B ) is symbolized as B ( ιxKx), where the inverted iota ( ι) represents the definite descriptor ‘the’ within the usual extensional quantificational apparatus and extensional interpretation of identity, then Russell’s analysis states:   The intended interpretation of this formula requires an extensional quantificational semantics, by which, among other things, the ‘existential’ quantifier ‘ ’ has real ontic or existential import, implying in this application that ‘there exists an x such that … ’. The first clause of the Russellian analysis entails that a unique object must exist in order to have properties truly predicated of it in a definite description context. Since Russell regards names as incomplete symbols to be replaced upon reductive analysis by definite descriptions, the account has the effect of doing away entirely with reference to and true predication of properties to all but existent entities. On such an analysis, the above sentence turns out to be false. The existence condition is unsatisfied where there exists no present King of France, rendering the entire

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Page 194 existentially quantified conjunction false. The same treatment automatically interprets as false predications such as, ‘The golden mountain is golden’ and ‘The round square is round and square’, that, in Meinongian semantics by contrast, and many persons innocent of and untutored in extensionalist logic and referential semantics, relying only on their pretheoretical linguistic intuitions, would understand, as true.17 For this reason, classical definite description theory cannot be incorporated into an object theory logic without revision. If Russell’s theory of definite descriptions is correct, then there is no prospect for a Meinongian semantics of reference and true predication of properties to named or definitely described nonexistent objects. If, however, Russell’s theory is not correct, and if Meinongian logic is to be developed as an alternative to Russellian extensional logic, Meinongian systems must also be fitted with formalisms for analysing definite description in ordinary language.18 Meinong’s independence thesis can now be more precisely defined by means of a Sosein function, which takes any object as argument into the complete set of the object’s properties:   By instantiating the golden mountain as an intended object in the object theory domain, the Sosein function equivalence implies:   On the assumption that the antecedent that S( ιmx( golden-mountain ( x))) = {goldenness, mountainhood } is analytically true, it follows, as we should expect in Meinongian semantics, that the golden mountain is golden and a mountain (mountainous). The case can be compared with the similar but also relevantly different situation in which a Meinongian semantics might be used to interpret the definite description, ‘The father of Zeus is the god of time’, or, ‘The son of Chronos is the god of time’. Here we happen to have sufficient knowledge from the background of an explicit mythological tradition to determine that in Meinongian semantics the nonexistent object in question in the first instance truly has, and in the second instance truly does not have, the property predicated of it. With respect to the case of the present King of France, without further explanation, we have no such basis for evaluation. Meinong classifies nonexistent objects that are indeterminate for certain kinds of predications as incomplete objects ( unvollständige Gegenstände ). It is natural to suppose that the truth-value for those predications for which such objects are indeterminate or incomplete is most naturally represented in a three-valued or gap-valued semantics as neither true nor false, but undetermined in truth-value.19

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Page 195 Whereas Russell’s theory of definite descriptions regards all predications of definitely described nonexistent objects as false by virtue of failing to satisfy the first, existence, condition, a Meinongian theory by contrast more discriminately evaluates some definite description predications of properties to nonexistent objects as true, others as false, and others arguably as neither true nor false. ‘The present King of France is a king’ is true; ‘The present King of France is a commoner’ is false (although ‘The present commoner King of France is a commoner’, like ‘The round square is round and square’, is true). ‘The present King of France is bald’ is not just epistemically, but more fundamentally ontically or semantically, undetermined in truth value, because the present King of France is a predicationally incomplete object. From a Meinongian object theory perspective, Russell’s analysis may therefore be said to have formulated only a specialized extensional theory of definite description or extensional fragment of the complete theory of definite description, with limited application to descriptors for existent entities. An object theory logic should provide an unambiguous way of expressing the limitations of Russell’s theory, and of supplementing the extensionalist account with descriptors for nonexistent Meinongian objects. To characterize the choices between Russellian and Meinongian definite description theories from the perspective of a semantically more encompassing Meinongian framework, it is best to begin by reinterpreting the ‘existential’ quantifier. This quantifier is standardly extensionally understood as implying real existence, so that to write ‘( x) Fx ’ is to say that there really exists an object with property F . For Meinongian purposes, the quantifier is most naturally understood as ontically neutral, indicating only that a logic’s semantic domain consisting of existent and nonexistent objects in a combined ontology and extraontology contains an existent or nonexistent object with the property truly predicated of it. The use of the quantifier ‘ ’ in a predicate expression on this account does not entail that an object falling within its range actually exists, but only that an existent or nonexistent object with the specified property has the property or properties truly predicated of it.20 The analysis of definite descriptions is made fully general with respect to the entire Meinongian semantic domain or ontology and extraontology of existent and nonexistent objects by rejecting Russell’s existence condition. In its place, the ‘existential’ quantifier non-ontically reinterpreted continues to serve the purpose of indicating an object’s domain membership, although domain membership is no longer restricted to the range of existent objects only, but includes potential reference to existent and nonexistent Meinongian objects in a combined Meinongian ontology and extraontology. This makes it possible to subsume Russell’s theory as a proper part of the complete object theory analysis. The existence condition in Russell’s analysis is no longer effected simply by the existential quantifier, but is now expressed instead as before by the existence ‘ E!’ predicate.

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Page 196 The analyses are generalized to allow for multiple predications to definitely described objects. Russell’s theory for definite descriptor ‘ ιr’, with application to existent objects only, in this notation states (1≤ i≤n): This is evidently a special case of the broader, semantically more comprehensive version of definite description required for Meinongian object theory logic, interpreting the Meinongian definite descriptor, ‘ ιm ’, in this way:

 

  In (DDM), commitment to the real existence of definitely described objects for true predications of properties in (DDR) drops out. The existential quantifier remains, but now has the effect only of indicating domain membership in a combined ontology and extraontology of existent and nonexistent objects, any of which can potentially have properties truly predicated of them. The existence predicate ‘ E!’ used to express the Russellian existence requirement disappears from the Meinongian counterpart definition, though an ontically neutral domain membership condition expressed by the ontically neutral quantifier ‘ ’ remains in its place, and the uniqueness and predication conditions are preserved as in Russell’s three-part analysis. Meinongian (DDM) is thus more general than Russellian (DDR). The true predication of a property to a Russellian definitely described existent object implies the true predication of that same property to the same Meinongian definitely described existent object, since all Russellian definitely described existent objects are also Meinongian objects, but not conversely. The Meinongian theory additionally allows true predications of properties to definitely described nonexistent objects, which Russell’s theory does not countenance, and hence is broader in scope. To see informally that the inclusion holds, let ‘ F ( ιmx( Fx ))’ represent the sentence ‘The m golden mountain is golden’. This is obviously true in Meinongian logic, though ‘The r golden mountain is golden’ in Russellian or Fregean extensionalist logic is false. The relation between (DDR) and (DDM) is established in this way as inclusion or enclosure. Every consequence available in Russellian definite description theory with limited application to existent objects only is also a consequence of Meinongian definite description theory. There are nevertheless implications for true predications of properties to definitely described nonexistent objects that hold in Meinongian but not in Russellian definite description theory.21

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Page 197 AT THE SUMMIT: MEINONGIAN CRITIQUE OF RUSSELLIAN DEFINITE DESCRIPTION Russell’s theory of descriptions has been so influential in the widespread analytic disapprobation of Meinong’s object theory that it may be worthwhile to conclude by considering an argument against Russell in support of Meinongian description theory. Consider the proposition, ‘The golden mountain is mythological’. Intuitively, the proposition is true. On Russell’s analysis in the previously introduced notation the proposition reads:

  The interpretation is unsound, because it converts a true into a false proposition. The biconditional fails and the equivalence is rendered false because the existence conjunct does not hold. Defenders of Russell’s theory will not hesitate to point out that there is something special about the predicate ‘mythological’ on which the counterexample turns. For the golden mountain to be mythological is for it to be nonexistent (and described in a myth or to have the words ‘the golden mountain’ or their equivalents inscribed in the writings of storytellers). If, for convenience, we ignore the second component concerning linguistic ascent or inscriptional reference, then, contrary to our prior more general objection to extensionalism partnered with Quinean semantic ascent, to say that the golden mountain is mythological is just to say that the golden mountain does not exist. The first step towards a correct analysis of the proposition in the above context might now be:   The equivalence is true, since both constituent propositions are true (assuming for simplicity sake that the golden mountain does not exist, and that nonexistence exhausts the extranuclear property of being mythological). When Russellian analysis is applied to the definite description in the right-hand side of the biconditional, however, the equivalence is counterintuitively made false, and with it the original proposition that the golden mountain is mythological. Thus, we have: Russell’s analysis suffers from the fatal defect of requiring that an intuitively true proposition about the mythology of the golden mountain be reduced in meaning to the false proposition that a mythological golden mountain exists. It further converts the contingent truth that the golden

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Page 198 mountain is mythological (an empirical question to be settled by explorers, scientists, historians, and literary scholars), to the logical inconsistency or necessary falsehood that a golden mountain both exists and does not exist. Armed with Russell’s theory of descriptions, an investigator need only logically analyse sentences about the nonexistent creatures of myth ostensibly designated by definite descriptions in order to determine a priori that all such objects are logically impossible. This is too strong a conclusion, and indicates that something in Russell’s analysis is fundamentally amiss.22 What is worse, if suitable precautions against standard inference rules are not taken, the reduction permits (by detachment from the truth that the golden mountain is mythological) deduction of the logical inconsistency that there is something that exists and does not exist, ( x)( E! x ^ ¬E! x). This introduces semantic chaos of a much greater magnitude than anything envisioned in Meinong’s position that there are nonexistent impossible objects whose Soseine contain both a nuclear property and its complement. Meinong’s theory, despite Russell’s unsubstantiated allegations in ‘On Denoting’, does not generate formal contradiction, provided that the independence thesis is restricted to nuclear predications, and a correspondingly rigid distinction between sentence negation and predicate complementation is observed. Russell’s reduction on the imagined interpretation in contrast involves the contradictory extranuclear proposition that if the golden mountain is mythological, then a golden mountain exists and it is not the case that a golden mountain exists. The problem arises absurdly and gratuitously, then, not only as Russell imagines for the existent golden mountain, but even for Hume’s and Berkeley’s and the Brothers Grimm’s golden mountain considered only as such, without the illadvised super-addition of the extranuclear existence predicate. Russell’s description theory runs up against the dilemma that it must either interpret intuitively true propositions like ‘The golden mountain is mythological’ as false, or else misconstrue certain contingently true or false propositions as logically necessarily false. The problem lies in the extensionalist demand that definite description entails existence, reflected in the first conjunct of Russell’s analysis. The difficulty is avoided in ontically neutral Meinongian description theory, in which no existence requirement is made. Meinongian intensionalist description theory is preferable in this regard to the Russellian extensionalist account, wherewith Russell’s historically important analysis is rendered philosophically inconclusive as a criticism of Meinong’s object theory.23 NOTES 1. See Janet Farrell Smith (1985). Nicholas Griffin, in his essay, ‘Russell’s “Horrible Travesty” of Meinong’ (1977), tries to defend Russell on his interpretation of Meinong, and in particular with respect to whether or not Russell falsely attributes the being-predication thesis to Meinong. Griffin makes

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Page 199 some valuable points, but overall I find his effort to rehabilitate the accuracy of Russell’s Meinong scholarship ineffective. Griffin shows, what need not be denied, that Russell sometimes interprets Meinong correctly on the relation of existence and subsistence to being, and on Meinong’s postulation of a realm of objects that are neither existent nor subsistent. The difficulty is rather in the damage done by other passages in which Russell flagrantly misrepresents Meinong’s ontic categories, in some places supposing that all Meinongian objects must have being, in other places equating Meinong’s notion of subsistence with being, and confusing Meinong’s ontic neutrality in reference and predication theory, as in the phenomenology of presentation, judgement, emotion, and assumption, with the thesis that intended objects must after all subsist or have being in order to stand as reference and predication subjects. Indeed, close examination of some of the passages Griffin quotes in Russell’s defence reveals further mistakes in Russell’s reading of Meinong. The fact that Russell sometimes gets Meinong right does not adequately mitigate the problems created by the overall inconsistencies in his exposition of Meinong’s object theory. Griffin acknowledges that there are also passages in which Russell misinterprets Meinong on these issues, and these unfortunately have been disproportionately influential in shaping later philosophical opinion about the merits of Meinong’s object theory. 2. Russell, letter to Meinong of 15 December 1904; translation in J. Farrell Smith (1985:347). Russell’s cordial words in this first letter are somewhat mitigated by his formulaic repetition of similar remarks in later letters. Thus, in his later letters to Meinong, after the 1905 publication of ‘On Denoting’, Russell’s letter of 5 June 1906 includes the statement: ‘I am also of the opinion that the differences between us are entirely unimportant. In general I find myself to have almost exactly the same viewpoint as you’ (348). The letter of 5 February 1907 offers the same gesture on a different topic: ‘I have carefully read what you have written on the concept of necessity and I believe the difference of opinion between us is not so great as it appears at first sight’ (349). 3. Russell also writes: ‘Before entering upon details, I wish to emphasise the admirable method of Meinong’s researches, which, in a brief epitome, it is quite impossible to preserve. Although empiricism as a philosophy does not appear to be tenable, there is an empirical manner of investigating, which should be applied in every subject-matter. This is possessed in a very perfect form by the works we are considering … Whatever may ultimately prove to be the value of Meinong’s particular contentions, the value of his method is undoubtedly very great; and on this account if on no other, he deserves careful study’ (205). 4. See Russell 1905b: ‘Presentations, judgments and assumptions, Meinong points out, always have objects ; and these objects are independent of the states of mind in which they are apprehended. This independence has been obscured hitherto by the “prejudice in favour of the existent” ( des Wirklichen), which has led people to suppose that, when a thought has a nonexistent object, there is really no object distinct from the thought. But this is an error: existents are only an infinitesimal part of the objects of knowledge. This is illustrated by mathematics, which never deals with anything to which existence is essential, and deals in the main with objects which cannot exist, such as numbers. Now we do not need first to study the knowledge of objects before we study the objects themselves; hence the study of objects is essentially independent of both psychology and theory of knowledge. It may be objected that the study of objects must be coextensive with all knowledge; but we may consider separately the more general properties and kinds of

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Page 200 objects, and this is an essential part of philosophy. It is this that Meinong calls Gegenstandstheorie ’ (530–31). 5. A valuable discussion of these topics is found in Gideon Makin (2001). 6. See Routley (1981:496); Jacquette (1986:423–38); Jacquette (1996:80–91). Meinong’s concept of the modal moment and watering-down extranuclear properties to nuclear versions is presented in Meinong (1969–78: Vol. 6, 266). Also J. N. Findlay (1995:103–4). 7. Meinong (176–77). J. N. Findlay (176). See Jacquette (2001). 8. Meinong’s solution to Russell’s problem of the existent golden mountain is presented in Meinong (Vol. 5, 278–82). 9. I consider a version of this problem in Jacquette (1989). See also Jacquette (1996:256–64). 10. See Routley (1981): ‘logically important though the modal moment is, the [nuclear-extranuclear] property distinction alone, properly applied, is enough to meet all objections to theories of objects based on illegitimate appeals to the Characterization Postulate [Routley’s version of Meinong’s thesis of the Independence of Sosein (so-being) from Sein (being)]. The Meinong whose theory includes an unrestricted Characterization Postulate is accordingly, like Meinong the super-platonist, a mythological Meinong’ (496). 11. In ‘On Denoting’, Russell seems to assimilate Meinong’s Außersein with his own concept of being; he writes: ‘Hence, it would appear, it must always be self-contradictory to deny the being of anything; but we have seen, in connexion with Meinong, that to admit being also sometimes leads to contradictions’ (485). Russell’s argument here and in the Principles of Mathematics recalls Socrates discussion with the Eleatic Stranger in Plato’s dialogue the Sophist . See the following note. 12. Plato, Sophist, 236d–64b; Parmenides 160b–e. Parmenides’ fragments are collected in Ancilla to the Pre-Socratic Philosophers: A Complete Translation of the Fragments in Diels, Fragmente der Vorsokratiker , edited and translated by Kathleen Freeman (Cambridge: Harvard University Press, 1957): 41–51. See Francis Jeffry Pelletier, Parmenides, Plato and the Semantics of Not-Being (Chicago: University of Chicago Press, 1990). 13. Wilhelm K. Grimm, Jacob L. C. Grimm, Wilhelm C. Grimm, The Annotated Brothers Grimm, translated and edited by M. Tatar (New York: W. W. Norton and Company, Inc., 2004). 14. I discuss these alternative approaches to semantics and metaphysics in depth in Jacquette (2002: especially 158–81). 15. Marie E. Reicher has recently tried to breathe new life into Russell’s objection by arguing that Russell’s problem needs to be seriously addressed by defenders of a Meinongian object theory. In ‘Russell, Meinong, and the Problem of Existent Nonexistents’ (2005), Reicher concludes: ‘If one likes pointed formulations, perhaps one might wish to put it this way: Russell might not have succeeded in defeating object theory tout court , but he succeeded in defeating Meinongian object theory’ (191). A key assumption in Reicher’s effort to resuscitate Russell’s existent present King of France problem nevertheless seems false, and to my knowledge falsely attributed to Meinong in any of his formulations of object theory. Reicher maintains that Meinong is committed to what she calls ‘ The description principle ’: ‘If we use a particular description in order to “pick out” a nonexistent object, the object has all those properties that are mentioned in the description’ (171). On the strength of this principle she offers (171) a four-step argument to show that the same reasoning involving the ‘description principle’ (together with other principles in my opinion less controversially attributed to Meinong) that supports the inclusion of a present King of France in a Meinongian extraontological semantic

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Page 201 domain must also be extended to an existent present King of France that we can agree does not exist. My objection to Reicher is that the description principle as she characterizes it is too strong, subject to counterexamples that depend on considerations that in other ways are independent of Meinong’s object theory, and that Meinong himself—for good reasons, I would say—nowhere explicitly accepts Reicher’s ‘description principle’ as she formulates it (although he does accept a similar principle). The version of the principle that I prefer in this context states, adapting Reicher’s formulation: ‘If we use a particular description in order to “pick out” a nonexistent object, then the object has all the properties that are essential to picking it out (distinguishing it from all other objects).’ Is the mention of ‘existent’ in the ‘existent present King of France’ essential to picking out the Meinongian object of reference? The answer rather depends on exactly what object we believe ourselves to be picking out. We should avoid unnecessarily opening the door to all properties that are merely ‘mentioned’ in a description that picks out a nonexistent object, although that assumption is obviously required for Russell’s objection and Reicher’s discussion. Here is an analogy borrowed from Saul A. Kripke’s discussion of reference in nonMeinongian terms in his lectures on Naming and Necessity (1980). Suppose that I speak of the man with the martini across the room who in fact has Perrier and no alcohol in his glass. In this case, I think it is most natural to say that I refer to the man across the room and I falsely attribute to him the property of holding a martini. I would not be inclined to say, as Reicher and Russell apparently believe Meinong is obligated to do, that I am referring in that situation to another (nonexistent) object that truly has the properties of being a man, being across from me in the room I occupy, and is holding a martini. The same is true of a thought described as being ostensibly about the existent present King of France. If I use this definite description, then I refer to the present King of France, and I falsely attribute to that (nonexistent) object (in 1905, the then or still present King of France) the property of being existent. 16. ‘But now consider “the King of France is bald”. By parity of form [with “the King of England is bald”], this also ought to be about the denotation of the phrase “the King of France”. But this phrase, though it has a meaning, provided “the King of England” has a meaning, has certainly no denotation, at least in no obvious sense. Hence one would suppose that “the King of France is bald” ought to be nonsense; but it is not nonsense, since it is plainly false’ (483–84). 17. Findlay: ‘Meinong also holds that there are many true statements that we can make about [nonexistent objects]. Though it is not a fact that the golden mountain or the round square exists, he thinks it is unquestionably a fact that the golden mountain is golden and mountainous, and that the round square is both round and square’ (1963:43). 18. The need for a non-Russellian nonextensional theory of definite descriptions in a complete formalization of Meinong’s object theory is obvious from the fact that so many of the intended objects that belong to the Meinongian semantic domain or ontology and extraontology of existent and nonexistent objects are designated by definite descriptors. These notably include, among indeterminately many others, the golden mountain and the round square. 19. An argument to this effect is given by Terrence Parsons (1974:571). 20. That the ‘existential’ quantifier has no existential or ontic import in Meinongian semantics is also affirmed by Parsons (1980:69–70) and by Routley (1981:174). A useful discussion of related topics appears in Fine (1982). See also Fine (1984). 21. See Jacquette (1994) and (1996:140–47).

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Page 202 22. This is obviously true if Russell’s Principia Mathematica proposition (*14.02) is invoked in this connection to analyse being mythological (transposed in the present notation) as: ( x( Fx ^ ( y)( Fy ↔ y ≠ x)). For then logically contingent statements of this or that object being mythological will all turn out to be logically impossible by virtue of entailing the outright contradiction of existing while at the same time failing to be identical to any existent entity. Note that we cannot simply apply *14.02 to the righthand side of (3), which admittedly is not even well-formed in Principia Mathematica , because of differences in Russell’s interpretation of both the existence E! property and the existential quantifier. The right-hand side of (3) is accordingly an appropriately modified version of the kind of analysis Russell himself would be prepared to give. It is ‘Russellian’ only in the sense that it conforms to the main lines of Russell’s analysis of definite descriptions in its commitment to referential extensionalism, in sharp contrast with Meinong’s referential intensionalism. A similar criticism of Russell’s theory of definite descriptions is sketched in Jacquette (1991). 23. I am grateful to participants at the conference on ‘Russell vs. Meinong: 100 Years After “On Denoting”‘, McMaster University, 14–18 May 2005, especially Peter Simons, Paul Weingartner, and Nicholas Griffin. I thank the Netherlands Institute for Advanced Study in the Humanities and Social Sciences (NIAS), Royal Netherlands Academy for the Arts and Sciences (KNAW), for supporting this among related research projects during my Resident Research Fellowship at the Institute in 2005–06. REFERENCES Berkeley, G. (1949–58) Three Dialogues Between Hylas and Philonous , The Works of George Berkeley, Bishop of Cloyne , 9 vols., A. A. Luce and T. E. Jessup (eds), London: Thomas Nelson and Sons. Descartes, R. (1985) Meditations on First Philosophy , The Philosophical Writings of Descartes, trans. and ed. by J. Cottingham, R. Stoothoff and D. Murdoch, Cambridge: Cambridge University Press. Farrell Smith, J. (1985) ‘The Russell-Meinong Debate’, Philosophy and Phenomenological Research 45: 305–50. Findlay, J. N. (1963) Meinong’s Theory of Objects and Values , ed. with an introduction by D. Jacquette, Oxford: Oxford University Press; Aldershot: Ashgate Publishing, 1995 (Gregg Revivals), all references to this edition. Fine, K. (1982) ‘The Problem of Non-Existents’, Topoi 1: 97–140. ——. (1984) ‘Critical Review of Parsons’ Non-Existent Objects, Philosophical Studies 45: 95–142. Griffin, N. (1977) ‘Russell’s “Horrible Travesty” of Meinong’, Russell: The Journal of the Bertrand Russell Archives 97: 39–51. Hume, D. (1975) An Enquiry Concerning Human Understanding , in Enquiries Concerning Human Understanding and Concerning the Principles of Morals, reprinted from the 1777 edition with introduction and analytical index by L. A. Selby-Bigge, 3rd edn, with text revised and notes by P. H. Nidditch, Oxford: The Clarendon Press. Jacquette, D. (1986) ‘Meinong’s Doctrine of the Modal Moment’, Grazer Philosophische Studien 25–6: 423–38. ——. (1989) ‘Intentional Semantics and the Logic of Fiction’, The British Journal of Aesthetics 29: 168– 76. ——. (1991) ‘Definite Descriptions’, in Handbook of Metaphysics and Ontology , H. Burkhardt and B. Smith (eds), Munich/Vienna: Philosophia Verlag: 201–2.

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Page 203 ——. (1994) ‘A Meinongian Theory of Definite Description’, Axiomathes 5: 345–59. ——. (1996) Meinongian Logic: The Semantics of Existence and Nonexistence, Berlin/New York: Walter de Gruyter. ——. (2001) ‘ Außersein of the Pure Object’, The School of Alexius Meinong, L. Albertazzi, D. Jacquette and R. Poli (eds), Aldershot: Ashgate Publishing: 373–96. ——. (2002) Ontology , Chesham: Acumen Publishing. Kripke, S. A. (1980) Naming and Necessity , Cambridge: Harvard University Press. Makin, G. (2001) The Metaphysicians of Meaning: Russell and Frege on Sense and Denotation , London: Routledge. Meinong, A. (1877) ‘Hume-Studien I, Zur Geschichte und Kritik des modernen Nominalismus’, Akademie der Wissenschaften 87: 185–260. ——. (1882) ‘Hume-Studien II, Zur Relationstheorie’, Akademie der Wissenschaften 101: 608–59. ——. (1904) ‘Über Gegenstandstheorie’, in Meinong (ed.), Untersuchungen zur Gegenstandstheorie und Psychologie , Leipzig: Verlag von Johann Ambrosius Barth: 481–530. ——. (1907) Über die Stellung der Gegenstandstheorie im System der Wissenschaften , Gesamtausgabe , Leipzig: R. Voigtländer. ——. (1969–78) Über Möglichkeit und Wahrscheinlichkeit: Beiträge zur Gegenstandstheorie und Erkenntnistheorie , in Alexius Meinong Gesamtausgabe , eds R. Haller and R. Kindinger in collaboration with R. M. Chisholm, 8 vols., Graz: Akademische Druck- u. Verlagsanstalt. Parsons, T. (1974) ‘A Prolegomenon to Meinongian Semantics’, The Journal of Philosophy 71: 561–80. ——. (1980) Nonexistent Objects, New Haven: Yale University Press. Reicher, M. E. (2005) ‘Russell, Meinong, and the Problem of Existent Nonexistents’, in B. Linsky and G. Imaguire (eds), On Denoting: 1905–2005, Munich: Philosophia Verlag. Routley, R. (1981) Exploring Meinong’s Jungle and Beyond , interim edn, Canberra: Australian National University. Russell, B. (1904) ‘Meinong’s Theory of Complexes and Assumptions (I)’, Mind 13: 204–19. ——. (1905a) ‘On Denoting’, Mind 14: 479–93. ——. (1905b) ‘Critical Notice of Meinong Untersuchungen zur Gegenstandstheorie und Psychologie ’, Mind 14: 530–8. ——. (1910) ‘Knowledge by Acquaintance and Knowledge by Description’, Proceedings of the Aristotelian Society 11: 108–28. Reprinted in Russell, Mysticism and Logic , London: Allen and Unwin, 1963: 152–67. ——. (1912a) ‘The World of Universals’, The Problems of Philosophy , London: Williams and Norgate: Ch. 9: 91–100. ——. (1912b) ‘On the Relations of Universals and Particulars’, in Proceedings of the Aristotelian Society 12: 1–24. Reprinted in Russell, Logic and Knowledge , London: Allen and Unwin, 1956: 105–24. ——. (1938) The Principles of Mathematics, 2nd edn (first published 1903), New York: W.W. Norton and Company, Inc. ——. (1986) The Philosophy of Logical Atomism and Other Essays 1914–1919 , ed. J. G. Slater, The Collected Papers of Bertrand Russell, London: George Allen and Unwin. The McMaster University edn, vol. 8, appendix 3, ‘Philosophical Books Read in Prison’, 1918: 326–28.

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Page 204 10 Rethinking Item Theory Nicholas Griffin NAÏVE ITEM THEORY What I shall call naïve item theory is based upon two unrestricted principles of great power and some intuitive appeal. The first is Meinong’s principle of freedom of assumption: that we can assume whatever we like; that is, we can think of, speak about, consider, investigate, or imagine anything we like, without any restrictions whatsoever.1 Freedom of assumption should be understood as giving us a stock of items about which to make assumptions. The claim is that whatever assumption we make, there is an item about which it is made. It will be well to establish some terminology here. Traditionally philosophers have spoken of ‘determining’ an object in thought, but I shall follow Routley in talking of ‘characterizing’ an item2 and the paradigm for this will be linguistic rather than psychological. Typically, therefore, we set about characterizing an item by describing it. Meinong’s freedom of assumption principle may thus be stated: (UFA) However we characterize an item, there is an item thus characterized; or, covering the paradigm linguistic cases only: (UFAL) For every description, there is an item it describes; or, in a more metaphysical mode, which parallels Parsons’ (1980) approach to introducing items: (UFAP) For every set of properties, there is an item characterized by those properties.3 Given the enormous expressive powers of natural language and the vast range of thought, Meinong’s original freedom of assumption principle seems, on the face of it, very reasonable. Freedom of assumption gives item theory its notable richness and makes it, as a semantic theory, superior to classical semantics, where so much discourse has to be reformulated (often in unsatisfactory ways) to make it fit within the imposed ontological constraints. (UFAL) and (UFAP) reflect item theory’s links to a particularly

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Page 205 direct and attractively simple semantics which Sylvan called ‘face-value semantics’ (1995). On a fully face-value semantics, for each well-formed predicate expression there is a property it expresses, and for each well-formed referential expression there is an item (or items) it refers to.4 As an initial position, face-value semantics has serious attractions, especially for the semantic representation of natural language, and it links directly to item theory. However, item theory neither entails nor is entailed by face-value semantics. The latter, in any case, is in need of qualification, a topic which will not be pursued here.5 The second crucial principle of item theory is what Routley (1980:46) called the characterization postulate,6 which in its naïve, unrestricted form can be stated: (UCPP) An item has all those properties which characterize it, or, to switch from material to formal mode and offer a less metaphysical version: (UCP) If a is an item characterized by φ, ‘φ(a )’ is true.7 The characterization postulate also has a good deal of prima facie plausibility. Barring pathological limit cases,8 all items have some properties, and we need item theory to tell us which ones. (UCP) tells us they have those properties which characterize them. This is not unreasonable: if we think of the golden mountain we think of an item which is golden and a mountain; that is, an item which has the properties of being golden and of being a mountain. For if it is an item, then it has some properties; and if it has any properties then presumably it has those which comprise its character, the properties of being golden and of being a mountain. Indeed, if the item we thought of lacked these properties then, surely, it was not the golden mountain of which we thought (Meinong 1910:61). So freedom of assumption provides us with our stock of items, and the characterization postulate provides us with truths about them. Therein lies the main problem of naïve item theory, for, as can be shown, not all of what the characterization postulate delivers is true. THREE BASIC PROBLEMS There are three types of problem case for naïve item theory, three types of counter-example to unlimited freedom of assumption and unrestricted characterization. In each case the derivation is straight-forward but, in the best-known examples, not quite immediate. I shall refer to the three types of cases as consistency, status, and relational counter-examples respectively, and give but a single example of each.

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Page 206 A. Consistency counter-examples. By freedom of assumption, we can talk about the round square; by the characterization postulate, the round square will be round and square. But since being square entails being not round, the round square will be both round and not round. Thus the theory entails inconsistencies. B. Status counter-examples. If freedom of assumption is unrestricted, then, in addition to talking about the golden mountain, we can talk about the existing golden mountain; by the characterization postulate, while the golden mountain is golden and mountainous, the existing golden mountain is golden, mountainous and exists. But no golden mountain exists. Thus the theory entails status claims about items at variance with known facts. C. Relational counter-examples. By freedom of assumption, we can think about the man who was married to Joan of Arc (let’s call him ‘Gilles’). By unrestricted characterization, Gilles was married to Joan of Arc. Since marriage is a symmetrical relation, it follows that Joan of Arc was married to Gilles and, thus, that Joan of Arc was married. But Joan of Arc was never married. Thus the theory entails claims about existing items at variance with known facts. These are, in fact, all the main objections to item theory. We owe the first two to Russell (1905:418; 1905b: 598–99; 1907:92–93) and, so far as I know, we owe the third to John Woods (1974:42ff, 135ff). The third problem is, moreover, by far the most difficult, and is discussed extensively by Parsons and Sylvan.9 It is perhaps surprising that Russell did not think of it, given his heavy interest in relations. I suspect, though I have no hard evidence, that he may have thought that relations were still so problematic that the objection would be taken to be an objection to relations, or at least to allowing them to constitute part of the character of an item, rather than to nonexistent items per se. Although I give only a single example of each kind of counter-example, it is easy to see how to generate further examples at least in the consistency and relational cases. Extending the status class is less straight-forward, since it depends upon what counts as a status characteristic. Existence is not the only one. All modal characteristics are status features in the required sense (for example, ‘actual’, ‘possible’, ‘contingent’, and so on), and there are many others (for example, ‘valid’, ‘consistent’, ‘simple’, ‘unique’, ‘true’, ‘known’). Each one can be used to characterize an item which will, via (UCP), constitute a counter-example to naïve item theory: for example, ‘the possible round square’, ‘the unique prime between 1 and 10’, ‘the known counter-example to Goldbach’s Conjecture’. Although there are any number of proposed solutions to these problems, they remain, I think, still extremely nasty problems. None of the proposed solutions is, in my opinion, quite satisfactory.

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Page 207 MAKING THE PROBLEMS IMMEDIATE As already noted, the derivation of each of these examples is straight-forward but not immediate. The examples so far considered do not, strictly, arise just from the two postulates of item theory, all of them depend upon additional principles which have not been stated, principles which seem perhaps too obvious to need stating. In the case of the first example, we need principles which enable us to infer that the round square is not round from the claim that it is square. In the third example, we need a principle which allows us to infer ‘Joan was married to Gilles’ from ‘Gilles was married to Joan’ and one which allows us to infer ‘Joan was married’ from ‘Joan was married to Gilles’. In the second example, the need for additional principles may seem less obvious, but, in fact, even there we need a principle which allows us to convert the adjective ‘existing’ into the verb ‘exists’. These supplementary principles have been the target of some attempts to solve the three problems. Routley (1980:268–69), for example, tries to solve the third problem by a distinction between entire and reduced relations: for reduced relations, the additional principles needed to generate the counterexample fail. Meinong himself, in replying to Russell, attempted to solve the second problem by distinguishing between ‘existent’ and ‘exists’. He allowed the conversion of ‘existing’ to ‘existent’, but not to ‘exists’, so that, while it would be true to say of the existing golden mountain that it is existent, it would not follow that it exists.10 Curiously, I don’t know of any attempt to solve the first problem by rejecting the principle which allows us to infer ‘ x is not round’ from ‘ x is square’. This is odd, because the principle to which one is most likely to appeal to licence such inferences, namely, (Ux)( x is square → x is not round), should fail when the quantifier is ontologically neutral and ranges over impossibilia such as the round square.11 But, whatever particular grounds may be urged against this or that supplementary principle, attacking the supplementary principles is no way to deal with the counter-examples, for, thanks to the huge power of freedom of assumption, we are at liberty to change each of the examples in a way that entirely eliminates the need for any supplementary principles. Thus: (a') instead of taking ‘the round square’ as our example, we could, by unlimited freedom of assumption, take ‘the round item which is not round’; (b') instead of ‘the existing golden mountain’, we could take ‘the golden mountain which exists’; and (c') instead of ‘the man who was married to Joan of Arc’, we could take ‘the item such that Joan of Arc was married’ (that is, ‘( ιx)(Joan is married)’).12

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Page 208 In each case, the characterization principle alone now delivers the same counter-example we had before. In short, the supplementary principles used in the derivation of the counter-examples are essentially irrelevant to the problem, and, where they are appealed to, they are pretty much innocent by-standers as far as generating the problem is concerned. The clash, then, is a straight conflict between assumption and characterization—everything else is irrelevant. Let us turn to some proposed solutions. THE CONSISTENCY COUNTER-EXAMPLES The consistency counter-examples seem to me to be in a different category to the others because, in the end, I don’t think that they are counter-examples at all, but simply consequences of the theory. For those who like their theories consistent this is bound to be problematic. Item theory, in my book, does yield contradictions, that is: for some statements, both the statement and its negation are entailed by the theory. But since these statements are all about contradictory items, like the round square, I don’t regard this as a fault of the theory. Contradictory items are just that—contradictory. And it is rather to the credit of the theory that it produces the contradictions that make them so.13 Most Meinongians, however, have a strong desire to preserve the law of noncontradiction. They have sought to consistentize the theory in the face of the consistency counter-examples by means of a distinction between sentential and predicate negation. When it is asserted that the round square is not round, it is claimed that the negation is that of the predicate, not of the sentence. The round square has, in addition to the property of being round, the ‘opposite’ property of being nonround. The law of noncontradiction does not hold for predicate negation: in general, impossibilia have both a property and its ‘opposite’. This does not imply either that some sentence is both true and false, or that a sentence and its negation are both true. The law of noncontradiction does hold for sentential negation. In Meinong’s view, the sentential negation in ‘~φ a ’ is taken to assert the lack of the property φ. The round square does not both have and lack the property of roundness; it has the property of roundness and it also has the property of nonroundness. Despite the fact that Routley does not in the end insist on a consistent form of item theory, he spends a good deal of time in Exploring Meinong’s Jungle and Beyond on elaborating such a proposal.14 There seem to me two types of difficulty with this proposal. The first is that the theory still owes us an account of the distinction between predicate and sentence negation. Admittedly, the distinction between lacking a property and having the opposite property does seem intuitively plausible. After all, doesn’t Russell’s theory of descriptions rely upon a similar distinction between cases in which the negation occurs within the scope of the description and cases in which the description occurs within the scope

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Page 209 of the negation? It is often suggested that Meinong has merely created a comparable and equally necessary distinction—between narrow and wide negation—for his own theory. There is some merit in this point, but it is slight. For Russell’s theory has but one type of negation—sentential negation—and the scope distinction depends entirely on where the negation operator occurs in a compound sentence. In Meinong’s theory there are two fundamentally different types of negation, and neither can be explained in terms of the other. If we take sentential negation to be well understood, the problem is to define predicate negation in some way that doesn’t collapse back into sentential negation. We need to know, for each property, what the ‘opposite’ property is. A natural suggestion is to assign both an extension and an antiextension to each predicate: the antiextension of the predicate ‘φ’ is the extension of the negated predicate ‘nonφ’. Note, however, that we are defining these extensions on the full domain of items, so we cannot insist that the extension and the antiextension are either exhaustive or even disjoint: the round square will fall into both the extension and the antiextension of ‘round’ and the present King of France will fall into neither the extension nor the antiextension of ‘bald’. How, then, are we to constrain the choice of the antiextension? Routley (1980:193) imposes only one condition, namely, that double negation is satisfied, that is, the antiextension of the antiextension is identical to the original extension. But this, pretty obviously, does not give a unique semantic definition of predicate negation. Any number of antiextensions will be consistent with this condition.15 It remains quite unclear how we are to select one of them as the extension of the negated property. One wants, of course, φ and non-φ to be in some sense incompatible. There are, however, some difficult general problems in defining incompatible properties in item theory. Let ‘φ ψ’ read ‘φ is incompatible with ψ’. It seems natural to try to cash this out in extensional terms, as implying that no item can have both properties, that is, as   where ‘~’ is sentential negation. But this, evidently, will not do with the neutral quantifier ranging unrestrictedly over all items. On naïve item theory ( ιx)(φx & ψ x) will be a legitimate instantiation for the variable. On (Ia) there will be no incompatible properties. On the other hand, if we formulate our account using existential quantifiers—readily defined in item theory by ( x) Ax =df(Px)(E!x & Ax), where ‘E!’ is the predicate ‘exists’—we get an account that is too weak:   Here the notion of property incompatibility depends upon the vagaries of what exists. If, as seems likely, nothing is both bright pink and an asteroid,

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Page 210 it will follow that being bright pink and being an asteroid are incompatible properties. This is not the distinction we want. The right suggestion seems to be that φ and ψ are incompatible if it is not possible that there exists an item which has both; that is:   or using Routley’s possibilia quantifier ‘(Σ x)’, read: ‘for some possible x … ’ (Routley 1980:80):   This would seem to work well, except that item theorists typically want the notion of incompatible properties to allow us to distinguish possibilia from impossibilia: the ability to do this in a natural way is often taken to be one of the advantages of item theory. We wanted to say that an item was possible if it has no incompatible properties; impossible if two or more of its properties were incompatible.16 (Ic) makes our notion of incompatible properties depend upon a prior notion of a possible item. This we don’t have—at least so far as I can see—in advance of an account of property incompatibility. Moreover, to identify one property as incompatible with another does not necessarily identify it as the property-negation of the other. The property of being a bachelor is incompatible with the property of being nonmale and with the property of being married, but neither of these properties should be identified with the property of being a nonbachelor. The latter is surely more appropriately identified as the property of being either a nonmale or married, which suggests that the negation of a property φ could be identified as the disjunction of all the properties incompatible with φ. Parsons (1980:19–20, 105–6) offers a different approach, identifying the property negation of φ as the property that all existing items have if and only if they don’t have φ.17 Here, a ’s not having the property φ should not be identified with ‘φ(a )’ being false, for we need to allow the possibility that many predications will be nonsignificant, and that many others (though significant) may lack truthvalues by reason of vagueness, or quantum indeterminacy or whatever. Parsons’ proposal nonetheless identifies several properties that one might have expected a Meinongian to want to keep distinct: the property negation of ‘human’ and ‘featherless biped’, for example, are one-and-the-same. Damage here might be reduced by modalizing the definition—but not eliminated, for a case can be made for distinguishing even necessarily co-extensive properties.18 I should point out that the difficulty of properly specifying predicate negation does not extend to other forms of nonclassical negation, even forms for which both the law of excluded middle and the law of no contradiction fail. The argument is not at all akin to those objections which

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Page 211 used to be raised against the intelligibility of nonclassical connectives (cf. Copeland 1979, for example). Perfectly good accounts of such nonstandard negations can be given, and not merely as formal semantic tricks—as, for example, Restall (1999) ably shows. The problem is a much more limited one of characterizing negation as a function from properties to properties in a way that is not parasitic upon sentential negation and when standard devices, such as set-complementation and the like, cannot be used because of the failure of LEM and LNC. Nor do I claim to have shown that no account of the required negation could be given. But if one is possible, I desire that it be produced—to the best of my knowledge, no one has so far done so.19 The second objection to this type of solution to the consistency counter-examples is that it fails. That is, even if we can make the distinction between predicate and sentential negation, we still do not achieve a consistent theory without restricting assumption, or characterization, or both. If there is a genuine distinction between predicate and sentential negation, then we have two distinct characteristics, both of which can be used to characterize distinct items. If the (ordinary) round square is merely round and nonround, then, by freedom of assumption, we can consider what might be called the strongly round square, that is the round square which is round and (sententially) not round, the round square which (if we follow Meinong) both has and lacks roundness. As regards the consistency counter-examples, it seems to me altogether preferable to give up the attempt to consistentize the theory; to admit, that is, that there are items a such that both ‘φa ’ and ‘~φ a ’ are true. Such items are all impossible, of course. But if a is impossible then ‘φa & ~φa ’ is exactly what we’d expect, for some φ. After all, if we are thinking about an impossible object, it should come as no surprise to find that it is inconsistent. This seems to me the correct reply to the objection that item theory leads straight to inconsistency: some items are straight inconsistent.20 Freedom of assumption demands no less.21 (It follows, of course, that one needs a paraconsistent carrier logic for item theory, otherwise the theory will collapse into triviality.) Unfortunately, we cannot entirely leave the consistency counter-examples in quite this convenient way. There are, from the point of view of consistency, worse items than even the strongly round square. Consider, for example, ( ιx)( x ≠ x). Such an item will, of course, be impossible, but applying (UCP) to it yields, not a violation of the law of noncontradiction (at least, not without further principles), but of the law of identity. Should item theorists give up that as well? Not if they have any sense. For the problem is readily generalizable. Let L be any logical principle, then freedom of assumption gives us the item ( ιx)~L. If we follow my prescription for the round square here, item theory will be left without a logic at all.22 The policy advocated here, of accepting the inconsistencies generated by (UCP) for items characterized by inconsistent ‘ordinary’ properties (such as

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Page 212 ‘round’ and ‘nonround’) will not do for items, the inconsistency of which arises from unusual properties like these (for example, the property of violating a principle of logic). Though the distinction between the two kinds of properties is hardly clear, the latter seem in some way similar to status properties, another inexactly defined class of properties which might, as a result, be enlarged to admit them. At all events, bearing this in mind, I turn to the status counter-examples. THE STATUS COUNTER-EXAMPLES There is a very wide consensus that the way to handle the status counterexamples is by making a fundamental distinction in item theory between status properties and others. Such a distinction in object theory originates in Ernst Mally’s distinction between Sein (being) properties and Sosein (being so) properties and was embodied in his famous independence thesis: that Sosein is independent of Sein (an item’s having properties does not depend upon its having being) (Mally 1904:126).23 It is underwritten by a long philosophical tradition, stretching back well before object theory, that asserts that Sein characteristics are not genuine properties at all, or at least not normal ones. Not all status properties are, strictly speaking, Sein properties: for example, ‘simple’ is clearly a status feature, but has nothing to do with being. In later writings Meinong (1915:176–77) distinguished between ‘ konstitutorische ’ (‘constitutive’) and ‘ ausserkonstitutorische ’ (‘non-constitutive’) properties, for which Findlay introduced the English terms ‘nuclear’ and ‘extra-nuclear’ (Findlay 1933:176), which were adopted by Parsons (1978; 1980:23–24). Routley used ‘characterizing’ and ‘non-characterizing’ (and sometimes ‘assumptible’ and ‘non-assumptible’) for essentially the same distinction (1980:46–47). In what follows I continue to use ‘characteristic’ and ‘characterizing’ to cover both nuclear and extra-nuclear properties (thereby departing from Sylvan’s terminology, in favour of Meinong’s and Parson’s). Now there is plainly something dead right about the distinction between nuclear and extra-nuclear properties. It gains plausibility from the philosophical tradition which separated existence from other properties. Moreover, there is a good deal of agreement as to which properties are extra-nuclear, which, in itself, suggests the distinction is in some sense a natural or intuitive one. There is not agreement, however, on how extra-nuclear properties are to be defined: examples are generally listed and the reader is then expected to be able to think of others. I’m inclined to think that all extra-nuclear properties are higher-order; but not all higher-order properties are extra-nuclear, for example, the property of falling under the concept ‘red’ would seem to be nuclear, since the property of being red is. There is certainly need for more work on the distinction, but it won’t get done here.

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Page 213 Even with the distinction between nuclear and extra-nuclear properties, however, the status counterexamples can still only be eliminated by restricting either freedom of assumption or characterization to exclude extra-nuclear properties. In fact, it is almost invariably characterization which is restricted. Freedom of assumption remains unrestricted, so that extra-nuclear properties can be used to characterize items. As a result, the golden mountain and the existing golden mountain are two different items. The characterization postulate, on the other hand, is applied to nuclear properties only: (RCP) An item has all the nuclear properties used to characterize it. Using (RCP), it follows that the golden mountain and the existing golden mountain (barring further characterization) have the same properties. They do, however, have different characteristics. It follows, then, that individuation of items is by characteristics rather than by properties.24 Individuation by characteristics rather than by properties is not intrinsically implausible, but it may seem as if, on this theory, we have two modes of predication: what one might call ‘mere characterization’, which is supplied by freedom of assumption; and, as it were, genuine property-attributing predication, which (in the case of nonexistent items) is supplied by the restricted characterization postulate. Mally, when he turned away from Meinong’s version of object theory, proposed an alternative which makes use of just such a distinction between two types of predication: a property, he said, may ‘determine’ an object and an object may ‘satisfy’ a property, but the one relation is not the converse of the other (Mally 1912:76). More recently the proposal has been revived and elaborated by Zalta (1983),25 who draws the distinction as one between encoding a property and exemplifying it. On this theory the golden mountain encodes the properties of being golden, and being a mountain, but it does not exemplify either of these properties. Nonetheless, it is a genuine object, an element of the domain on which the theory is interpreted and over which its variables range. Identity principles are different for existents and nonexistents: existents are identical if they exemplify the same properties, nonexistents, if they encode the same properties (Zalta 1983:33). While existent items only exemplify properties and never encode them, nonexistents both encode and exemplify properties (33). For example, the golden mountain exemplifies the property of being thought about by Meinong and the property of encoding the properties of being golden and being a mountain. It also exemplifies ‘many “negative” properties’ (McMichael and Zalta 1979:312, n5), including presumably the property of being nonexistent. Generally, one expects that nonexistent items will exemplify appropriate status properties on Zalta’s account, whether or not these are properties encoded by the item, and whether or not they are negative properties. Thus one assumes that the nonexistent golden mountain

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Page 214 both encodes and exemplifies the property of nonexistence, and that it will exemplify (but not encode) the property of being possible. There would, of course, be little to be gained from distinguishing two types of predication, if that distinction turned out after all to be parasitic upon a distinction between different types of property. Although Zalta (1983:34) adopts the axiom OBJ (Px)(A! x & ( F )( xF ≡φ)), where φ is any wff where x is not free (‘A! x’ reads ‘ x is an abstract object’ (i.e. x does not exist) and ‘ xF ’ reads ‘ x encodes F ’) which seems to guarantee freedom of assumption—as McMichael and Zalta (1979:307) put it, the axiom asserts that ‘[f]or every expressible set of properties, there is a Meinongian object which includes [i.e. encodes] just those properties’—the appearance is misleading. For, suppose we characterize an item as ‘the nonexistent item which exemplifies F ’, that is, ‘( ιx)(A! x & Fx )’, where ‘ F ’ is some ‘ordinary’ property like being golden. As Zalta (1983:47) notes, such a description ‘would fail to denote’, that is, there would be no object, existent or nonexistent, corresponding to the description since, in the description, the relation between x and F is one of exemplification rather than encoding. This is a plain limitation on freedom of assumption, though it creates no immediate conflict with OBJ, because ‘ Fx ’ is not of the same form as the left hand side of the equivalence in OBJ. Nor does it conflict with the informal statement of the axiom, for ‘ xF ’ and ‘ Fx ’ do not involve different properties. Nonetheless, since a nonexistent object may exemplify the property of being encoded by F , one wonders why it should not be possible for a nonexistent object to encode the property of being exemplified by F . In fact, Zalta leaves us no way to express this. The item which exemplifies the property of being encoded by F may be denoted by the description ‘( ι x)(A! x & (λ yyF ) x)’, but the item which encodes the property of being exemplified by F cannot be expressed by the description ‘( ι x)(A! x & x(λ yFy ))’, for by Zalta’s principles of λ-identity (Zalta 1983:30), λxFx = F , so the description reduces to ‘( ι x)(A! x & xF )’. By contrast, no parallel λ-identity principle seems to be offered for λxxF , which is surely odd, because in ‘(λ yyF ) x’, x would seem to exemplify the very same property that it encodes in ‘ x(λ yFy )’, namely, F . Zalta is thus able to treat the two descriptions differently, albeit essentially by fiat. The two central notions of Zalta’s theory, the two styles of predication themselves, exemplification and encoding, are not themselves expressible in the theory; if they were, we would be able, in the absence of principles expressly intended to bar the possibility, to encode the property of being exemplified by F . In other words, OBJ ensures that there is an item which encodes every expressible set of properties, only by limiting the sets of properties which are expressible. An alternative route is to supply two kinds of predicate instead of two types of predication. This, in fact, was the route taken by Meinong when

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Page 215 first confronted by Russell’s status counter-examples. Meinong, notoriously, drew a distinction between ‘existent’ and ‘exists’: claiming that the existing golden mountain genuinely has the property of being existent but nonetheless does not exist (Meinong 1907:17 [ GA 5:223]). The existing golden mountain has what Meinong called ‘watered-down’ ( depotenzierte ) existence, existence which lacked the ‘modal moment’ (Meinong 1915:282). This approach has commended itself to Parsons, who doesn’t countenance talk about the modal moment (1980:44), but does admit that every extra-nuclear property has a watered-down companion which is nuclear (68).26 The chief motivation for this is to try to restore some of what has been lost by restricting the characterization postulate. We can restore some of the theory’s lost power by assigning a surrogate, watered-down, nuclear property to nonexistent items characterized by extra-nuclear properties. Characterization remains restricted, however. Nonexistents do not necessarily have the extra-nuclear properties that characterize them—but this is all to the good. Assumption remains free—so that we can characterize nonexistent items by means of full-strength, extra-nuclear properties. But the restricted characterization postulate then endows these items only with the watered-down, nuclear version of the predicate. Alternatively, one may restrict freedom of assumption by rejecting the possibility of characterizing an item by means of full-strength extra-nuclear properties.27 On this line, it is held that we cannot characterize an item as ‘the golden mountain with full-strength existence’, but that this does not matter much, since we can characterize an item as ‘the golden mountain with watered-down existence’. The problems with this approach are rather like the problems with the attempt to deal with the consistency counter-examples by a distinction between sentential and predicate negation. Indeed, one could think of predicate negation as a watered-down version of sentential negation. In the first place, counter-examples are not entirely eliminated, unless the distinction is accompanied by a restriction on the characterization postulate or on freedom of assumption. The restriction is mitigated, though not eliminated, by the availability of watered-down surrogates, just as, in the consistency cases, the restriction is mitigated by the availability of predicate negation. Restricting (UCP) leads to obscurities, since we have an item (the full-strength existing golden mountain) which is characterized by a property (full-strength existence) which it doesn’t have. This is not made much clearer by saying that it does have a different but very similar property—namely, watered-down existence. The second policy—that of restricting freedom of assumption—is clearer, but seems to refute itself. When we say we can’t characterize an item as the golden mountain with full-strength existence, we seem to have done just that. A second problem is that the relation between the full-strength and the watered-down version of a property is left unexplained.28 No one, including

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Page 216 Parsons, has been able to make much sense of Meinong’s doctrine of the modal moment. But it is hard to see how the notion of watering-down can be clear when that of the modal moment is not, since the modal moment is just what a property loses when it gets watered-down. Modalizing (adding the modal moment) and watering-down are simply inverse operations: one should be intelligible if the other is. On the other hand, the restrictions on characterization are reasonable. As Routley puts it (1980:256): ‘assumption cannot determine ontology’, nor other forms of status either. (UCP) must in any case be rejected, if only because of the ‘nonstandard’ properties considered at the end of the last section, λx~L, and the like. Moreover, (UCP) refutes itself: consider ( ι x)(~UCP). Unrestricted freedom of assumption is retained, and the problem of explaining the watering-down feature might be regarded as a topic for further investigation. Nonetheless, one might be able to live with such a theory, or, indeed, with the simpler versions which avoid the modal moment and watering down but use (RCP), were it not for the relational counter-examples. THE RELATIONAL COUNTER-EXAMPLES The relational counter-examples are by far the worst problems the theory faces. The distinction between nuclear and extra-nuclear properties and the restriction of the characterization postulate in respect of the latter does have some plausibility. There seems no such plausibility in restricting either assumption or characterization to exclude relational properties. As Routley notes (1980:268), excluding relations from the characterization postulate would be ‘crippling’. Plainly, we often do characterize nonexistent items by means of their relations. Moreover, what item have we thus characterized but one which does have the relation in question? Who is Anna Karenina’s husband but the man who is married to Anna Karenina? What, then, of Joan of Arc’s husband? The usual solution to the relational problems is to make special distinctions among relations. Routley distinguishes between ‘entire’ and ‘reduced’ relations (1980:268–69, 577–90). Entire relations have the full range of entailments normally associated with them (for example, symmetry, transitivity, active-topassive transformation, transitive to intransitive verb transformations, and so on). Reduced relations do not. When nonexistent items are characterized by their relations to existent items, the characterization postulate will ascribe to the nonentity only a reduced relation. In dealing with counter-example (c), it is the active-passive transformation that bears the brunt of Routley’s criticism. Spelling out (c) in more detail, we have (1) Gilles married Joan of Arc (by (UCP)) (2) Joan of Arc was married to Gilles (by active-passive transformation) (3) Joan of Arc was married (by transitive-intransitive transformation)

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Page 217 Routley rightly claims that blocking the inference from (2) to (3) is implausible,29 and therefore concentrates on blocking that from (1) to (2). But this, to my mind, is equally implausible. On Routley’s theory, Gilles has the property of being married to Joan of Arc, but the relation holds only in the reduced sense. And from the fact that Gilles is married (in the reduced sense) to Joan of Arc, it does not follow that Joan of Arc is married to Gilles, nor that Joan of Arc is married. Only if Gilles and Joan were (so to speak) entirely married, would these inferences hold. Again, from the fact that Sherlock Holmes is characterized by Conan Doyle as living in London, it follows that Holmes does live in London (but only in the reduced sense). We are not permitted to infer that London numbers Sherlock Holmes among its inhabitants, as we would if the ‘lived in’ relation were an entire one. Evidently one could extend this type of treatment to the other two classes of counter-examples. One could hold that the round square was square only in a reduced sense which did not entail that it was not round;30 or that the existent golden mountain was existent in a reduced sense which did not imply that it existed. Indeed, it is tempting to regard reduced relations as something akin to watered-down properties. Routley claims that the active-passive transformation is not supplied by traditional or classical logic and thus ‘central logical principles are not being upset’ if it is rejected in some cases (1980:267–8).31 Traditional logic, of course, supplies no relational principles at all, but in classical logic the case is different. For every relation R there is its converse , such that   This is the principle that has to be rejected for reduced relations and it is central to the logic of relations. Nor is the active-pasive transformation alone in question. By freedom of assumption we could characterize Gilles thus:   (UCP) then gives us (2) directly. One nasty consequence of Sylvan’s approach is that it makes the logical behaviour of relations dependent upon the ontological status of the items they relate—and in more complex ways than we have so far let on. Tensed existence does not seem to involve these problems. If Richard Burton was the husband of Elizabeth Taylor, then it follows that Taylor was married to Burton—the fact that Burton no longer exists is, in this case, beside the point. Yet elsewhere Routley excoriates the classical gerrymander which treats ‘exists’ as a tenseless verb in order to permit classical objectural quantification over past existents (1980:361–64). Moreover, relations between two nonexistents seem to be entire— Anna Karenina was married to Alexei Karenin and this implies that Alexei was married. But there are

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Page 218 complications: Anna Karenina’s lesbian lover may have loved Anna Karenina, but this must be a reduced love, since Anna was not loved by a lesbian.33 Moreover, there seem to be degrees of reduction. The ‘lived in’ relation between Holmes and London is reduced enough to prevent us from inferring that London included Holmes among its inhabitants, but not so reduced as to prevent our inferring that Holmes had a London residence or that, since London is in England and ‘in’ is transitive, he lived in England. On yet other occasions it seems that the relations require a full set of properties. Suppose that I characterize the number n = ( ι x) ( x > 7 & x < 5). It is not clear that I can do this unless ‘>’ and ‘<’ are transitive, asymmetric and irreflexive, for without these properties it is difficult to believe that they are the relations of ‘greater than’ and ‘less than’ that I have in mind in characterizing n. In short, the logical behaviour of reduced relations seems to be pretty chaotic. In this respect, Parsons’ proposal for plugging up relations is preferable (1980:26–27, 59–60, 75–77). For a two-place relation R we can make one-place properties by ‘plugging up’ either of R’s argument places. Parsons uses ‘ x[ Ry]’ to symbolize ‘ x has the property which results from plugging up R’s second place by y’ and ‘[ xR] y’ to symbolize ‘ y has the property which results from plugging up R’s first place by x’. Normally, it would be assumed that   Parsons solves the problems of relational characterization by holding that (A) fails for nonexistents. Thus, Gilles has the one-place property of being married to Joan of Arc; but Joan does not have the one-place property of being married to Gilles. This is less messy than Routley’s doctrine of reduced relations. Nonetheless, it seems equally ad hoc. It offers us no explanation as to why assumption (A) should fail. Nor does it explain in what sense Gilles might have the genuinely relational property of being married to Joan of Arc, when she does not return the compliment. One can easily understand that existents cannot be married to nonexistents, but it is hard to square this with the claim that nonexistents can nonetheless be married to existents. What sort of a relationship could marriage then be? (A question often asked, I fear, but rarely in the sense in which I propose it here.) Nor does the theory handle all our relational problems, for suppose that we characterize Gilles, not as the husband of Joan of Arc, but thus:   If Parsons seeks to block this on the grounds that x as it occurs in ‘[ x was married to]’ is not a genuine constituent of the expression and thus not available for binding by the descriptor, one then wonders in what sense

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Page 219 ‘[Gilles was married to]’ is genuinely a plugged up relation, or even a complex property. Finally, Parson’s doctrine of plugged up relations does not seem to give a full account of relational properties involving nonexistents. For example, it gives no warrant for the following inference: (c) Sherlock Holmes is smarter than J. Edgar Hoover J. Edgar Hoover is dumber than Sherlock Holmes which seems to me to be valid—indeed, sound. Parsons (1980:168–70) suggests that comparatives must be extra-nuclear, but this seems doubtful. A good deal of characterization of nonexistents depends upon comparatives—starting with Anselm’s ‘that than which nothing greater can be conceived’. It would, I think be a serious loss to the coverage provided by item theory, if items could have comparative properties only in some watered-down sense. The treatment of fiction (where comparative characterization is fairly common) would be especially compromised: Holmes would no longer be smarter than Lestrade, Vronsky would not be more alluring than Alexei Karenin. Finally, neither Routley’s nor Parsons’ theory will save unrestricted relational characterization. If we accept Routley’s distinction between entire and reduced relations, then freedom of assumption will allow us to use entire relations in characterizing nonexistents. We can characterize Gilles as the man who is entirely married to Joan of Arc, whose marriage to Joan of Arc entails that she is married to him. Evidently entire relations cannot fall within the scope of the characterization postulate. Similarly for Parson’s theory, as we’ve seen in connection with (G′). THE GENERAL DIFFICULTY Our problems arise in a quite general way. The realm of assumption is wild—and it ought to be. People make the most hare-brained and outlandish assumptions. Freedom of assumption recognizes this fact and writes it into the foundation of item theory. It is this that gives item theory its richness and makes it superior to classical semantics in handling the wealth and diversity (and sheer perversity) of language and thought. Moreover, people’s assumptions are every bit as hare-brained and outlandish as they seem to be. If they believe they are haunted by the ghost of Joan of Arc’s husband, that is exactly whom they believe they are haunted by. It is not a watered-down ghost, and it is not a watered-down husband. It is, in the victim’s supposition, the very ghost of he to whom Joan of Arc was married. The troubles with item theory all occur when the wild realm of assumption has to be integrated into the actual world. Traditional item theory

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Page 220 transfers all the items generated by assumption to the actual world, albeit as nonexistent items. Moreover, by the unrestricted characterization postulate, they take with them all their assumed properties. As a result the actual world contains huge numbers of nonexistent items—which is fine. It also contains massive inconsistencies among its nonexistent items—which is also fine. The real difficulties arise when the incorporation of such nonexistent items into the actual world yields truthclaims which are at variance with facts about the actual world. At this point traditional item theory seeks to resolve the problem by stripping certain nonexistent items of some of their properties and by watering down others. The devices required are complex, awkward, ad hoc, and not always clearly successful. The proposal I want to suggest reverses the traditional item-theoretic line on the relation between the realm of assumption and the actual world. Instead of using the (UCP) as a bridge between the realm of assumption and the actual world, a principle which creates truths in the actual world on the basis of what is assumed, I want to confine (UCP) to the realm of assumption. Instead of a bridge between assumption and actuality, I propose a fire-wall. In my proposal, the realm of assumption remains absolutely free and, so far I can see, naïve item theory holds there without qualification. Talk about ‘ the realm of assumption’, however, is misleading, since there is not a single realm into which all the items of assumption fit. There are a vast multitude of fragmentary realms, which I shall call ‘contexts of supposition’. In one context of supposition or another are all the nonexistent items we have been considering, and they all have, within their contexts of supposition, all the properties they are assumed to have, that is, the properties by which they are characterized. But from the fact that they have these properties in their context of supposition, it doesn’t follow that they have them in the actual world. Nonetheless, there are statements about nonexistent items which remain true in the actual world—such as, for example, that they don’t exist. This, then, is the broad outline of the theory I would like to propose—some further details, by no means enough to constitute a full theory, follow in the next section. SOME HINTS TOWARDS A SOLUTION It hardly goes beyond the commonplace to point out that reference depends upon context; nor, of course, that truth-value depends upon reference. Whether ‘Dulles was head of the CIA’ is true depends upon whether I’m talking of Allen (for whom it is) or of John Foster (for whom it is not). Which Dulles one is talking about is typically made clear by the context in which one speaks. What I want to suggest is that there are certain contexts (which I shall call ‘contexts of supposition’) in which naïve item theory is exactly right. One can suppose whatever one likes and within the context of supposition what one supposes is pretty generally (though not

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Page 221 invariably) correct. There are many, many contexts of supposition—many even for the same item—and they differ from the actual world, sometimes in extreme ways. Because assumption is free, there will be no general principles applying to all contexts of supposition, for, whatever such principle we might suggest, it will be possible, by unlimited freedom of assumption, to choose a context of supposition in which the principle fails. Most contexts of supposition will have a logical structure of some kind, maybe even an elaborate one, but there will be no logical structure, however minimal, that is common to all, and there may be some contexts of supposition entirely devoid of logical principles of any kind (contexts where all inferences fail). But the lawless vagaries that are permitted in the context of supposition do not transfer to the actual world. The status and relational problems in item theory with which we’ve been concerned all arose because the characterization postulate transformed the wildness of free assumption into what was supposed to be actual fact. The error, on the present theory, was that of failing to keep contexts of supposition (where, literally, anything may go) distinct from the actual world. On the present theory, the existing golden mountain really does exist, but only in its context of supposition. Status problems only arise if, from the fact that it exists in its context of supposition, we can infer that it exists in the actual world as well. It is tempting to deny that there are any valid inferences from truths in the context of supposition to truths in the actual world. The actual world is what it is, and none of our suppositions will affect it in the slightest. But this, as we shall see, is too sweeping. Our suppositions do affect the actual world, but more subtly, not by transforming themselves directly into actual world truths. I hope some examples will make things plain. It seems intuitively right to say that, in the context of supposition provided by the Conan Doyle stories, Sherlock Holmes was a detective who lived in London; that these are truths about him; that the predicates used to articulate them express ordinary properties which attach to the items in the ordinary way; and that the sentences which result have their ordinary entailments and other implications (including nondeductive ones). In particular, in the context of supposition provided by the stories, not only does Holmes live in London, but London numbers Holmes among its inhabitants. The reader, in order to follow the stories, is constantly required to heed the ordinariness of the claims made in them and to draw appropriate deductive and nondeductive inferences from them. Moreover, within the context of supposition, London is the actual historical London, a capital city with many inhabitants and buildings and a good deal of poverty and squalor. Again, the reader is forced to suppose this in order to follow the stories. The reader will be constantly surprised if they do not think that London comes to the story equipped with most of its usual features. We are not dealing here with London II on some alternative

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Page 222 earth in a science fiction novel, and the reader does well to be apprised of this fact at the outset. In the Holmes stories London is what is often called an imported or immigrant object: one that, in this case, has been imported from the actual world.34 Of course, while London has, in this context of supposition, a great many of the properties it has in the actual world, it does not have all of them. For example, in the actual world London has the property of not counting Sherlock Holmes among its inhabitants (though it does have the property of being the city in which Conan Doyle supposed that Sherlock Holmes resided). Again, suppose Conan Doyle had written a story in which Dr. Moriarty blows up Buckingham Palace: then it would be true in the context of supposition that Buckingham Palace was blown up, but this would not be true in the actual world.35 Typically, if an item x is imported to context c from the actual world, a, or from another context c*, then it brings with it most of the properties it has in a or in c*. Thus, if c is the context of the Holmes stories, then London has in c most of the properties that it has in a. But Holmes himself has been incorporated into other stories which are not part of the Conan Doyle Holmes canon. If c* is the context provided by such a story, then Holmes has in c* most of the properties he has in c. In fact, we can say roughly that imported objects may be assumed to bring all their properties with them to their new context, except those which are denied, explicitly or by implication, in the new context. There are some qualifications needed here which make an exact general statement somewhat messy. For example, the fact that the new context asserts ~φa is not always grounds for stripping an imported object a of the property φ which it has in its original context, for the context of supposition into which the object is imported may be an inconsistent context which allows the object to both have and lack the property. Another problem is that claims made in consistent contexts of supposition may nonetheless be inconsistent (for example, in stories through author-error). In such cases an explicit denial in the story of some claim may not warrant the assignment of false to the claim in the story—say-so semantics has its limits. It will give some perspective on my position to contrast it briefly with the theory of fiction put forward by John Woods in his The Logic of Fiction (1974). For Woods, both fictional and real items have historyconstitutive properties—the difference is that history-constitutive properties of fictional items depend upon the say-so of the creator of the item in question, whereas those of real items depend upon the facts of the actual world. Similarly, both fictional and real items have fictionalized properties, which depend upon the author’s say-so—in the case of fictionalization about fictional items the author in question is not the original creator of the fictional item in question. Suppose that there is a Conan Doyle story in which Holmes has tea with Gladstone. Then the following hold:

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Page 224 objects, like fictional objects, have their contexts of supposition, but notably impoverished ones which supply (at least in the purest cases) only those properties included in the description which refers to the item. I shall call these ‘isolated contexts’. When Meinong talks of the golden mountain he is supposing an item which has only the properties of being golden and of being a mountain. This is as far as the mere example itself will take you, the isolated context of supposition will supply no more. Since such examples are typically conjured up by logicians, it is more common to suppose that they satisfy also some logical principles—for example, that they also have the properties which follow from the properties mentioned in their descriptions—but, as Meinong noticed, one doesn’t have to do this. One can, after all, suppose whatever one likes. By mentioning the example one creates a context of supposition for it, inviting your audience to consider a situation in which something is both a mountain and golden; if one has something further in mind, one can go on to elaborate, but there is no requirement for further elaboration. As an isolated object, the husband of Joan of Arc has few properties, but in the isolated context to which he is native he is married to Joan of Arc and, within the same context, Joan is married to him. In that context Joan is an imported object and takes with her (barring explicit supposition to the contrary) most of the properties she has in the actual world where she is native. But none of these truths which hold in the isolated context of Joan’s husband transfer to other contexts—and in particular not to the actual world, where Joan remains (quite rightly) unmarried. Her husband is not among the constituents of the actual world, since items cannot be imported into the actual world. Nonetheless, items which don’t exist in the actual world can be spoken about there and we need to consider how, with respect to the actual world, to assign truth-values to sentences about them. It certainly won’t do to assign them the value true in the actual world, for that will give us back all the problems we’ve been trying to deal with. We could assign them false, as on the Russell plan, but that will also lead to problems of consistency, for, given that an object may occur in a variety of different contexts of supposition and acquire in each of them properties which conflict, it cannot consistently retain all these properties when considered with respect to the actual world and thus the sentences ascribing these properties to it cannot all consistently be assigned false with respect to the actual world. My intuition would be that these sentences lack a truth-value in the actual world. At this point it will seem as if I’ve abandoned everything that Meinongians hold dear, and I will certainly admit that it is a reversal of my previous views on the topic. For example, in the actual world, I want to claim, that: (4) Sherlock Holmes is a detective,

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Page 225 is neither true nor false, because Holmes is not in the actual world.39 We could have a complete list of actual world detectives and Holmes would not be among them. Actual objects migrate to fictional contexts, but fictional objects do not migrate to the actual world (even as nonexistent objects). Nonetheless, referring expressions still refer to them even when used in the context of the actual world. And sentences using these referential devices have to be semantically interpreted in the real world. On the theory I’m suggesting such referential devices when used in the context of the actual world, are not referring to nonexistent objects in the actual world, but to objects in the context of supposition (which often exist with respect to that context). But now it seems as if my theory, in avoiding the counter-examples to item theory, has opened itself to all the old problems of classical semantics, the very problems that led people to develop item theory in the first place. In particular, it may be argued there are many truths in the actual world about nonexistents which any adequate semantics must recognize as truths. Consider the following example: (5) Conan Doyle wrote about something A tenable semantics should assign true in the actual world to (5). There is little difficulty here, for although we very often use existential quantifiers, we still have ontologically neutral quantifiers available. These, like other referential devices, reach back into contexts of supposition. The various contexts of supposition, moreover, provide us with a full set of items over which they range. So the fact that what Doyle wrote about doesn’t exist in the actual world is no basis for denying that he wrote about something. There is, in fact, no real problem in assigning true to (5), which ascribes an intentional property to Conan Doyle, who after all exists. But if (5) is true then (6) Conan Doyle wrote about Sherlock Holmes ought to be true also. For what did Conan Doyle write about, if not Sherlock Holmes? Again, there is no real problem with (6), for names (and descriptions, too) are genuinely referential devices, even when the items they refer to do not exist. Obviously our referential devices must be able to reach into different contexts of supposition and refer to the items there—otherwise we would not be able to make the suppositions. So (6) is simply a substitution instance of (5). Moreover, since I don’t adopt either Sylvan’s distinction between full and reduced relations or Parson’s method of plugging up relations, it follows from (6) that (7) Sherlock Holmes was written about by Conan Doyle

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Page 226 is also true in the actual world. Intuitively this seems correct: (7) is surely true. However, (7) ascribes an intentional property to a nonexistent object. Is this a problem? Again, the answer is ‘No’. My theory does not deny that nonexistent items have any properties in the actual world, or, more exactly (since nonexistent items are not strictly in the actual world), it does not deny that some sentences ascribing properties to nonexistent items, in particular, sentences ascribing intentional and status properties, may be true in the actual world. It denies only that sentences ascribing ordinary extensional properties to them may be true in the actual world. By allowing sentences ascribing intentional properties to nonexistents to be true in the actual world, the theory has all the advantages of traditional item theory in handling intentional discourse. It also, of course, differs thereby from classical semantics which is forced to reparse statements like (6) and (7)—typically in implausible ways. Nonetheless, there are still further problems to be faced. For if (6) is true, (8) Conan Doyle thought of a detective, ought to be true as well. For what is Sherlock Holmes, if not a detective? But I have already denied that (4) Sherlock Holmes is a detective has a truth-value in the actual world. How can we infer (8) from (6) unless (4) is true? The key to the solution lies in the fact that although (4) lacks a truth-value in the actual world, it is true in the context of supposition in which Holmes is a native. It is this which permits the inference to go through. Evidently, not any old context of supposition will do here: it must be a context in which Holmes is a native item. Let us imagine a context of supposition in which Holmes is an import, say a story, not in the Conan Doyle canon, in which Holmes, instead of becoming a detective, turns to crime and becomes a more cunning criminal than Moriarty. Then the inference from (6) to (9) Conan Doyle thought of a more cunning criminal than Moriarty fails, even though (10) Holmes is a more cunning criminal than Moriarty is true in some context of supposition, for (10) is not true in the right context of supposition, the context in which Holmes is native. It seems clear that (11) The round square is impossible

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Page 227 can be handled along the lines already suggested. Traditional item theory holds that (11) is true because the round square has incompatible properties. In the present theory this is suspect because in the actual world (12) The round square is round and square and (13) The round square is round and not round are neither true nor false. Nonetheless, in the isolated context of supposition in which the round square is a native, both (12) and (13) are true. Thus, in the appropriate context of supposition the round square has incompatible properties, and this ensures that in the actual world it has the property of being impossible—or, more exactly, (11) is true when evaluated with respect to the actual world. By the same token, the golden mountain is possible in the actual world, because in the appropriate context of supposition it has compatible properties. Finally, the theory provides an elegant solution to the problem of comparative judgements which cross different contexts, for example, the judgement that Homes is smarter than J. Edgar Hoover. Such judgements have proven troublesome, because Hoover is not a constituent of the Conan Doyle stories and Holmes is not a constituent of the actual world, so that, confined to the contexts in which each is native, there are no truths about the intelligence of the other in either context. It seems, however, that in making such a judgement one creates a new context of supposition, in which both Holmes and Hoover are imports. Like all imports they bring with them the properties they have in the contexts in which they are native, including the property of being intelligent (or not). A truth-value can then be assigned in the new context where the comparison is made, on the usual basis of evidence drawn from the contexts in which the items are native. Item theorists may roll their eyes in horror at my actual world, stripped of nonexistent items. But I would claim that keeping nonexistent items out of the actual world does very little damage—they are all there in their contexts of supposition, which is where they belong. If this is what Meinong excoriated as ‘a prejudice in favour of the actual’, then I would reply that it is exactly with regard to the actual world that a prejudice in favour of the actual is appropriate.40 NOTES 1. See, e.g., Meinong 1904a: 92 ( GA 2:500); 1910:246–48, 252 ( GA 4:346–48, 354); 1915:282; 1917:24–25 ( GA 3:28).

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Page 228 2. Routley and Routley 1973:228; Routley 1980:45. In 1995:62, now writing as Richard Sylvan, he used ‘specifying’ instead. This suggests something rather too rigorous for what I have in mind: an item may be described as ‘a thing to make you shudder and make you laugh’, as Henry James does in a ghost story (Cox 1997:67), but to say it is thereby specified is to miss the point. Characterization, by contrast, may be appropriately casual. I shall also speak of the ‘characteristics’ of an item (i.e., those features which characterize it) and (less frequently) of its ‘character’ (i.e., the set of all its characteristics). 3. These ways of formulating the principle are linked to Meinong’s original formulation through the intentionality thesis which he took over from Brentano, namely, that all mental acts have an object. Which object they have is determined by the content of the mental act, i.e., by the way the object is characterized. 4. I keep the familiar term ‘refer’, which was anathema to Sylvan, who regarded it as ontologically loaded. The drawback to his preferred alternative, ‘about’, is that it has no natural verb or noun forms. Needless to say, I use ‘refer’ and its cognates without any ontological connotations. 5. Face-value semantics is sometimes attributed to the pre-’On Denoting’ Russell on the basis of his remarks in 1903:42, an interpretation I reject (cf. Griffin 1996, 2005b). 6. In Routley and Routley 1973, it is called the assumption postulate. 7. It might be questioned whether this is really one of Meinong’s principles, since (to my knowledge) he nowhere states it in its full generality. Nonetheless, he does appeal to it implicitly in his treatment of examples, cf. Meinong 1904a: 82 ( GA 2:490). 8. For example, the item characterized by the null set of properties, which has the property of lacking all properties (as well as the property of being thus characterized and numerous other properties as well, especially negative ones). Some type-theoretic stratification of properties may prove helpful here, though less conventional strategies may be preferable and, in the end, necessary. 9. I have Richard Sylvan’s copy of Woods’ 1974 and he’s written ‘MAJOR PROBLEM’ in the margin alongside Woods’ statement of the problem (Woods 1974:42). In fact, Woods reveals that Sylvan got the problem from him even earlier—it appeared in Woods 1969. Woods recalls Sylvan telling him in 1971 ‘I think you have NO IDEA how serious a problem this is!’ (Peacock and Irvine 2005:105). 10. Meinong 1907:17 ( GA 5:223); 1910:104–5 ( GA 4:141–42); 1915:282. Russell replied that he could not see the difference between the two (1907:93). 11. ‘Ux’ is Routley’s ontologically neutral universal quantifier. Its mate, the particular quantifier ‘P x’, is defined in the usual way: (Px) A =df ~(U x)~A. 12. Such an item is usually called her husband, but if we take Routley’s distinction between entire and reduced properties seriously, the relevant item will be Joan’s entire husband (not her reduced one). 13. This was essentially Meinong’s first reaction, when confronted with Russell’s original argument. He argued that the law of noncontradiction did not apply to impossibilia. Cf. Meinong 1907:16, 62 ( GA 5:222, 268); 1915:278. 14. Rather surprisingly, almost the whole of his book is devoted to elaborating consistent forms of item theory; dialethic forms of the theory are treated, albeit favourably, only in Ch. 1, §23, and in parts of Ch. 5. The distinction between predicate and sentence negation is also to be found in Meinong, who distinguishes between a not-so-being ( Nichtsosein), expressed by a negated predicate, and the notbeing-of-a-so-being ( Nichtsein eines Soseins),

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Page 229 expressed by a negated predicational sentence (1915:171–74). See also Jespersen’s distinction between special (predicate) and nexal (sentence) negation (Jespersen 1924:329–30). 15. Suppose we define the extension and antiextension of a predicate φ upon a well-ordered domain {a 1, a 2 … an>}. Let the extension of φ be the set S. Then the antiextension of φ, i.e., the extension of non-φ, S–, could be defined thus: For each ai, if ai S then aj S– just in case either aj = ai+1 and i is odd, or aj = ai-1 and i is even, or aj = ai and either i = 1 or i = n. Double negation will thus return us to S. However, the double negation condition is also met if we define S– as follows: For each ai, if ai S then aj S– just in case either aj = ai+1 and i is even, or aj = a i-1 and i is odd, or aj = ai and i = 1 or i = n. 16. See, e.g., Mally 1904:127. 17. This holds only for what he calls ‘nuclear properties’; see ‘The Status Counter-Examples’. 18. See also Jorgensen 2004 for further problems with Parsons’ definition, which, however, he prefers to Routley’s. 19. I’m grateful for many long discussions with Carolyn Swanson, who convinced me that Meinong’s style of predicate negation had problems that I hadn’t seen. 20. For a charming example of how such a result is necessary for an adequate theory of fiction see Priest (1997). 21. To adopt this solution does not necessarily prevent one from making a distinction between sentential and predicate negation—if one can be made out. But such a distinction, whatever plausibility it has or lacks, will not help with the consistency counter-examples. 22. As Greg Restall pointed out to me, the problem can be generalized further: For any claim P of any kind whatsoever, freedom of assumption delivers ( ιx) P (and of course ( ιx)~P, as well), so (UCP) renders the theory trivial. 23. Meinong incorporated the independence thesis into his theory of objects early on: Meinong 1904a: 82 ( GA 2:489–90). Mally subsequently rejected the principle (cf. Mally 1912). 24. Otherwise, freedom of assumption would be restricted as well: attempts to characterize an object as the existing golden mountain would succeed only in referring to the golden mountain. 25. See also McMichael and Zalta (1979) where the theory is presented with a somewhat different terminology and notation. Rapaport (1978) has a similar theory. In the more restrictive field of fictional objects, Woods makes an analogous distinction between history-constitutive predications and fictionalizations (Woods 1974:42ff), a position criticized in Griffin (2005a). 26. Most modern versions of item theory (e.g., Routley 1980:496; Jacquette 1985) prefer to dispense with both notions and deal with the status counterexamples by adopting (RCP). This certainly results in a simpler, more elegant form of the theory, as Jacquette argues in some detail. 27. This is evidently Meinong’s preferred solution, cf. 1915:283. 28. Findlay’s exposition (1933: Ch. 4) is clearer than Meinong’s (1915: Ch. 37), but neither does a good job of justifying the notion. 29. From an item-theoretic point of view, rejecting the transition from (2) to (3) calls into question Gilles’ status as an object. 30. Routley suggests this parallel (1980:268). 31. One doubts that he took this point very seriously: preserving classical or traditional logic was rarely of much concern to him. 32. Marriage being a symmetrical relation, it is identical to its converse. Similar problems, however, arise with asymmetrical and nonsymmetrical relations.

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Page 230 33. Woods (1974:27) would deny that Anna Karenina’s lesbian lover is even a nonexistent item, since there is (as yet) no work of fiction to bring her into nonexistence, so to speak. Woods makes an important distinction between fictional items and what he calls ‘nonesuches’, which are not items at all (cf. 1974: Ch. 2). 34. I think Parsons introduced the ‘immigrant/native’ terminology (Parsons 1980:51–52). On the whole in dealing with an object that is an immigrant to the context of supposition, I prefer the term ‘imported’, since the supposer does the importing. The object does not move of its own accord. 35. There is no contradiction here, even though Buckingham Palace is the same object in both contexts, since truth-value assignments are always relative to a context and V(qu(φa ),s) = T and V(qu(φa ),a) = F are consistent assignments (‘s’ is here the context of supposition; ‘a’ is the actual world). The situation is similar to that which is familiar from worlds semantics, though contexts are not worlds: they are typically much less complete and much more disorderly. (Cf. Sylvan 1997:176–77, where, however, the talk is about ‘set-ups’ rather than contexts. The model here of course, is Routley and Meyer’s setup semantics for relevant logic. Cf. Routley and Routley 1972, Routley and Meyer 1972a, 1972b, 1973.) Worlds, on the other hand, may be contexts. In particular, the actual world often is the context of supposition, especially for fact-stating (or putatively fact-stating) discourse; for such discourse, the actual world is typically the default context. 36. I’m not suggesting this is an outcome Woods would embrace, but, without it, it seems clear that his fictionalized Gladstone will acquire all manner of inconsistent fictionalized properties and this, in turn, will make it difficult to preserve intuitively valid inferences about him in any particular fictionalization. 37. This last is essential in any case in order to make consistent truth-value ascriptions to sentences containing indexicals or ambiguous proper names, for example. 38. My main reason for wanting to admit nonesuches as nonexistent items is the need to preserve inference rules such as particularization (quantifier introduction). It seems to me that we ought to be able to infer from ‘The present King of France is bald’ to ‘Some item is bald’. Preserving the inferential role of such singular terms is of more than marginal concern. There is no reason that I can see that would distinguish the greatest prime from the round square as a nonesuch. Yet obviously there are mathematically important inferences to be made about the greatest prime—not least the inference to its impossibility. 39. Why then does it seem so natural (and also quite right) to say ‘Sherlock Holmes is a detective’? I think the answer is just cultural familiarity. Conan Doyle’s stories are so well-known (if only by reputation) that it is easy for us to access (or switch to) the context of supposition of the stories with no more prompting than the use of Holmes’ name. A less familiar fictional detective’s name does not elicit the same response, because, without further clues, we are less easily able to access the context of supposition. But obviously, when the context precludes the Conan Doyle stories, as when someone asks for the name of a private detective to consult about their affairs, proffering Holmes’ name would be distinctly unhelpful: when the context is the actual world, ‘Holmes is a detective’ no longer seems obviously right. 40. I’m grateful to Rhonda Anderson, Carolyn Swanson and Charissa Varma for many long discussions of item theory during the initial preparation of this paper. Different versions were read at the Australasian Association of Logic conference at Macquarie University in July 1997 (a conference dedicated to the memory of Richard Sylvan); at the Mistakes of Reason conference in honour of John Woods at the University of Lethbridge in April 2002; at the Russell vs.

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Page 231 Meinong conference to celebrate the centenary of ‘On Denoting’ at McMaster University in May 2005; at the Fourth Principia International Symposium at Florianopolis, Brazil, in August 2005; and to the philosophy department at McMaster University. I am grateful to participants on all these occasions for their comments. Needless to say, my most fundamental debts are to Richard Sylvan, though sadly I was never able to discuss the paper with him. REFERENCES GA : Alexius Meinong, Gesamtausgabe , ed. R. Haller and R. Kindinger, 8 vols., Graz: Akademische Druckund Verlagsanstalt, 1969–78. Chisholm, R., ed. (1960) Realism and the Background of Phenomenology , Glencoe, IL: The Free Press. Copeland, B. J. (1979) ‘On When a Semantics is not a Semantics: Some Reasons for Disliking the Routley-Meyer Semantics for Relevant Logic’, Journal of Philosophical Logic 8: 399–413. Cox, M. (1997) Twelve Victorian Ghost Stories, Oxford: Oxford University Press. Findlay, J. N. (1933) Meinong’s Theory of Objects and Values , 2nd edn, Oxford: Clarendon 1963. Gabbay, D. M. and Wansing, H., eds. (1999) What is Negation?, Dordrecht: Kluwer. Griffin, N. (1996) ‘Denoting Concepts in The Principles of Mathematics’, in R. Monk and A. Palmer (eds), Bertrand Russell and the Origins of Analytical Philosophy , Bristol: Thoemmes: 23–64. ——. (2005a) ‘Through the Woods to Meinong’s Jungle’, in A. Irvine and K. Peacock (eds), Mistakes of Reason: Essays in Honour of John Woods, Toronto: University of Toronto Press. ——. (2005b) ‘Russell’s Early Semantics’, paper presented to the British Society for the History of Philosophy, St. Catherine’s College, Oxford. Jacquette, D. (1985) ‘Meinong’s Doctrine of the Modal Moment’, Grazer Philosophische Studien 25/26: 423–38. Jespersen, O. (1924) The Philosophy of Grammar, London: Allen and Unwin, 1963. Jorgensen, A. K. (2004) ‘Types of Negation in Logical Reconstructions of Meinong’, Grazer Philosophische Studien 67: 21–36. Mally, E. (1904) ‘Zur Gegenstandstheorie des Messens’ in Meinong (1904b): 121–262. ——. (1912) Gegenstandstheoretische Grundlagen der Logik und Logistik , Leipzig: Barth. McMichael, A. and Zalta, E. (1979) ‘An Alternative Theory of Nonexistent Objects’, Journal of Philosophical Logic 9: 297–313. Meinong, A. (1904a) ‘The Theory of Objects’, trans. I. Levi, D. B. Terrell and R. M. Chisholm, in Chisholm (1960): 76–117. ——., ed. (1904b) Untersuchungen zur Gegenstandstheorie und Psychologie , Leipzig: Barth. ——. (1907) Über die Stellung im System der Wissenschaften , Leipzig: Voigtländer. ——. (1910) On Assumptions, 2nd edn (1st edn 1902), trans. J. Heanue, Berkeley: University of California Press, 1983. ——. (1915) Über Möglichkeit und Wahrscheinlichkeit, Leipzig: Barth = GA 6. ——. (1917) On Emotional Presentation, trans. M. Schubert Kalsi, Evanston: Northwestern University Press, 1972. Parsons, T. (1978) ‘Nuclear and Extranuclear Properties, Meinong and Leibniz’, Noûs 12: 137–51.

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Page 232 ——. (1980) Nonexistent Objects, New Haven: Yale University Press. Peacock, K. A. and Irvine, A. D., eds. (2005) Mistakes of Reason. Essays in Honour of John Woods, Toronto: University of Toronto Press. Priest, G. (1997) ‘Sylvan’s Box: A Short Story and Ten Morals’, Notre Dame Journal of Formal Logic 38: 573–82. Rapaport, W. (1978) ‘Meinongian Theories and a Russellian Paradox’, Noûs 12: 153–80. Restall, G. (1999) ‘Negation in Relevant Logics. (How I Stopped Worrying and Learned to Love the Routley Star)’, in Gabbay and Wansing (1999): 53–76. Routley, R. (1980) Exploring Meinong’s Jungle and Beyond , Canberra: Research School of Social Sciences, Australian National University. Routley, R. and Meyer, R. K. (1972a) ‘The Semantics of Entailment, II’, Journal of Philosophical Logic 1: 53–73. ——. (1972b) ‘The Semantics of Entailment, III’, Journal of Philosophical Logic 1: 192–208. ——. (1973) ‘The Semantics of Entailment, I’, in H. Leblanc (ed.), Truth, Syntax and Modality, Amsterdam: North Holland: 199–243. Routley, R. and Routley, V. (1972) ‘Semantics of First-Degree Entailment’, Noûs 6: 335–58. ——. (1973) ‘Rehabilitating Meinong’s Theory of Objects’, Revue internationale de philosophie , 27: 224– 54. Russell, B. (1903) The Principles of Mathematics, 2nd edn, London: Allen and Unwin, 1964. ——. (1905a) ‘On Denoting’ in Russell (1994): 415–27. ——. (1905b) Review of Meinong (1904b), in Russell (1994): 596–604. ——. (1907) Review of Meinong (1907), in Essays in Analysis , ed. D. Lackey, London: Allen and Unwin, 1973: 89–93. ——. (1994) The Collected Papers of Bertrand Russell, vol. 4, Foundations of Logic, 1903–05 , ed. A. Urquhart, London: Routledge. Sylvan, R. (1995) ‘Re-Exploring Item Theory. Object Theory Liberalized, Pluralized and Simplified but Comprehensivized’, Grazer Philosophische Studien 50: 47–85. ——. (1997) Transcendental Metaphysics. From Radical to Deep Pluralism , Cambridge: The White Horse Press. Woods, J. (1969) ‘Fictionality, and the Logic of Relations’, Southern Journal of Philosophy 7: 51–63. ——. (1974) The Logic of Fiction, The Hague: Mouton. Zalta, E. N. (1983) Abstract Objects. An Introduction to Axiomatic Metaphysics , Dordrecht: Kluwer.

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Page 233 11 Contra Meinong Peter Loptson Some philosophers have historical interests in Alexius Meinong and his theory of objects. Others think that some version or other of his theory is actually true. My focus in this paper is on the latter view. Before turning to the motivations to Meinongianism, however, and whether they justify that theory, it may be useful to situate the fundamental topic of Being and Non-Being within the broad framework in which Meinong, and his great opponent, Russell, were working (and which still operates to a degree now). There are two distinct and incompatible pictures of the Being/Non-Being divide, both of which figure prominently in late nineteenth and early twentieth-century philosophy. According to one, there is an unbridgeable gulf, a chasm or abyss, between Being and Non-Being. Something either is, or it isn’t. A question that is very much secondary, for this conception, is what may turn out to characterize the things that there are, with one party (they may be called the nominalists) drawn to the idea that all of the things that there are are spatio-temporal particulars (and, possibly, complexes—events, states of affairs, facts—involving them), and another party holding that some things that there are are nonspatial (perhaps including mental things and/or abstract things). The second of these parties may choose to use the term ‘existence’ just to stand for spatio-temporal things, and the term ‘subsistence’ to stand for abstract things (and mental things, on some views); but this is merely terminological, or taxonomical, and some prefer simply to identify a single condition, called being, existing, being real or subsisting, and noting that there are some quite basic kinds the things this condition applies to. The second position in the fundamental divide resuscitates a version of the old Platonic doctrine of degrees of being. (And in fact the basic contrast itself can plausibly be seen as anchored in an elemental semantical division between those who think being admits of degrees, and those for whom this idea is unintelligible.) This position has the idea that a fullest degree of being attaches to spatio-temporal items. Then a paler, lesser degree of being—still real being, but (somehow) ‘less’ so—attaches to ideal and abstract things (including mathematical objects, concepts and propositions). Then, for some (not all) on this wing, there is a third, particularly

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Page 234 ‘pale’ category of being, possessed by anything able to be thought of. (For some who take this ‘bolder course’, the specially ‘pale’ items are limited to possibles, for others they include also impossibles.) The historical Meinong, as I read him (I appreciate that others have differing interpretations), actually, inconsistently, vacillated between both these fundamental camps (within his long article ‘The Theory of Objects’ [1904]). Most fundamentally, and in the first instance, he belongs to the first one; and sees as his bold and exciting insight, that the objects his theory affirms (apart from the ones with existence, and subsistence—the two taxa of being) don’t need to have, and don’t have, any sort of being at all. They have properties, but not ( any kind of) being, and—this again is what he thinks is his important breakthrough—we see, through this fact, that having properties just is altogether independent of being. But then Meinong goes on to, in effect, retract this idea, with the doctrine of what he calls Aussersein , the theory of a kind of being that is beyond (the usual sorts of) being. Either Aussersein is an ontic category of some kind, or it is nothing. As an ontic category, it is a ‘third degree’ of being. The Meinong intended in the present paper is chiefly the Meinong who doesn’t affirm Aussersein , though the objections to come will also militate against the one who does. I think that those who are drawn to embrace some version of Meinong’s theory of objects are usually so drawn with one or other of three motivating, or persuading, rationales. One involves an idea that natural language is well-anchored, that is, semantically determinate, clear, and that it enjoys a primacy over philosophical attempts to revise or regiment it, or even establish something linguistic that would be parallel or alternative to it, and that natural language straightforwardly and not finally disputably affirms Meinongian sentences—Sosein-affirming sentences, specifically, property ascriptions to unreal things. We might think of other kinds of cases or contexts where natural language data seems readily to give rise to outcomes of high philosophical theory. We may observe that the tomato on the table is red and that the fire truck that just went by the house is red , and infer that the tomato on the table and the fire truck that just went by the house have something in common , indeed, that there exists—must exist—a certain something or other, which will, in turn, need to be of a certain ontological type or kind, which can qualify as what these objects have in common, namely, the property of being red . The first route to Meinong holds, in a comparable manner, that there are claims we rather straightforwardly and unproblematically make, which will imply that some things have properties, even though, in the cases concerned, these things aren’t real . Although I am—perhaps a bit tendentiously—assigning those moved in this way to adopt Meinongian convictions a set of strong, firm intuitions about certain natural language sentences, namely, that they are clearly and straightforwardly true, and clearly and straightforwardly imply Meinong’s theory (or something close to it), in complete fairness it should be noted—

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Page 235 allowed—that someone might become a Meinongian, under this broad motivating aegis, where they simply held that Meinong was the best bet, or option, among several competing and conflicting ones. This more semantically diffuse or nuanced path might hold that the natural language data is apparently conflicting, hence that the theorist prompted to theory by that data must make choices, and (perhaps) Meinongianism is then seen as the least objectionable of the choices. At any rate, the fundamental idea remains the same: that things we regularly hold true point to the theory of objects. A second motivating path to a Meinongian stance, philosophically, stems from an idea that there is in actual fact no single semantical or logical anchor, that logics and semantical structures are multiple and are devised, or constructed, rather than discovered, and a Meinongian structure or model (perhaps more than one) is doable; nothing falls apart when models with domains that include unreal things are put together, and something interesting and coherent results—as much as one will or can get from any semantical framework or logic. Finally, what I think is the third road to Meinong has important similarities with the first two, explicitly rejecting anchored metaphysicality, as the second one implicitly does (at least for logic ), and affirming that, since no sentences are true in an ontologically substantive— reality-disclosing—sense, Meinongian sentences are among the disparate array of linguistic phenomena, neither better nor worse than others, and able to plant themselves as workably and effectively as might be desired for a well-behaved segment of language. Strictly speaking, this third route will not lead to the historical Meinong, since he affirmed the cogency of metaphysics. The third route, in its most modest version, takes the view that many semantically well-behaved sentences, even whole segments of natural language, simply do not have ontological or metaphysical import, even where they may have grammatically subject-predicate form, and that among these ‘extra-ontological’ sentences are many that assign properties to unreal things. In a full-blown, not modest, version this stance denies that any sentences are genuinely ontological or metaphysical, and takes it as unproblematic, accordingly, that perfectly adequate sentences say, for example, that Sherlock Holmes was a Victorian detective given to wearing deerstalker caps. The second of the three indicated routes to Meinong is a formalist one, chiefly attracting logicians; the first has appeal for friends of ordinary language, some of whom (though certainly not all) are quite antiformalist; the third is more likely to draw neopragmatists, who think that quite a lot of what we say, possibly, in fact, all of it, does not purport to capture reality. All three of these motivating stances can be phrased nonlinguistically—as Meinong himself put his theory, and perhaps might still prefer that his supposed insights be rendered. Each of the three rationales can also be represented by, or paired with, a conception of logic, more precisely, of the logical space within which logic itself is to be found. The first corresponds to the idea that, at least as we would think of it now, classical logic as it

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Page 236 stands, conceived as embodying the whole of the broad structure of truth-assertion and valid inference, is mistaken at least in its claimed comprehensiveness, and inadequate, needing correction and revision, and capable of receiving it (that is, rather than being rejected outright), in Meinongian as well as other directions. The true logic will have a classical proper part, or a proper part that is a modified version of classical logic; and also a Meinongian part, corresponding formally to such ideas as that if Holmes is a detective then some things are detectives and Holmes has some properties (even though, of course, Holmes is unreal, a fictional creation of Conan Doyle). The second framework might be said to correspond to the philosophy of logic of Carnap, where logics are developed, and may be ‘adopted’, for heuristic reasons or reasons of formal interest; some of these logics will be classical, or partly classical, and others Meinongian (and others altogether nonstandard in still other ways). The third framework, or perspective, may share with the first a commitment to there being a—complex—logic that gets things right; but denies the intelligibility (or possibly just the even minimal utility) of classical logic, the ‘true’, or most adequate, logic being a free logic, a logic without existence presuppositions or content. (For the second framework, free logics are just some among the varied, interesting denizens of the house of logic.) Meinong himself, it will be clear, is closest to the first of these frameworks. For him metaphysics is a genuine science, even if its object (that is, its Objekt ) is only a proper part of the still more comprehensive science of objects ( Gegenstanden ). For Meinong also existence has metaphysical content. (In fact, for him, existence requires spatio-temporal content. The more comprehensive genus, of which existence is a species, is Sein, or Being—also sometimes identified as Wirklichkeit, or Reality. Things with Sein, or Wirklichkeit, but lacking Existenz , or Existence, have Bestand , or Subsistence. Meinong is indeed one of those philosophers of whom Quine famously complained, ‘who have united in ruining the good old word “exist ”’(1963:3).) At any rate, Meinong’s interests, and commitments, are not those of a Carnapian formalism; nor, for all his imaginative, for his opponents extravagant, interest in the supposed world beyond Being, and its truths, does Meinong share Wittgensteinian limitations of the intelligibly thinkable and sayable to structures and patterns delineable in ‘our’ forms of life (even if, for some of those Wittgensteinians and neopragmatists, our forms of life include such appropriately assertible items as that Santa Claus is bearded, Superman can fly but isn’t female, and inferences they and their like may warrant). In the present paper, I ignore the second and third of the motivating roads to Meinong, and confine myself to the rationale which is in fact, I think, closest historically to Meinong’s own position, and the theory to which it led him—the Gegenstandstheorie , which Russell, after apparently accepting it in The Principles of Mathematics, in 1903, rejected and sought to refute, in his correspondence with Meinong and in ‘On Denoting’, in 1905.

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Page 237 I want now to state two assumptions, both of which I believe are highly plausible, and which I know that many other philosophers share. Among those philosophers are Bertrand Russell and (I think) Alexius Meinong. The first assumption is that every genuine and unambiguous statement or proposition is equivalent to a statement or proposition which is perspicuous, that is, which represents, or constitutes, a precise or determinate content in (so-called) logical space. This is meant to be an assumption about sentences of natural languages, though it is intended to apply also to sentences of ideal or artificial languages which have been constructed to be languages adequate for science (or for a scientific philosophy). This assumption may be thought to be quite anodyne, hardly worth saying; perhaps on the grounds that it will be analytically true, given that attention has been restricted to unambiguous statements and propositions. On the other hand, it might be regarded as covertly affirming the central tenet of Russell’s logical atomism, according to which all and only true statements/propositions are equivalent to representational symbolic contents which are isomorphic with discrete determinate facts of the world. That thesis is anything but anodyne. In fact, I take the central logical atomist tenet to imply but not be implied by the perspicuity assumption, which is meant to affirm that there is always something definite, and with an in-principle intelligible structure, said, or meant, by unambiguous statements or propositionexpressing sentences of natural and scientific language. The differences between the two might be seen further by noting that logical atomism requires either a correspondence or a deflationary theory of truth, while the perspicuity assumption would also be compatible with a coherence theory. The second assumption I am making is that at least some true perspicuous statements or propositions are ontological or existential or metaphysical in character. They say or imply that something exists or is real. According to this assumption there are existential/ontological facts, independent of ways that observing or representing minds may screen, filter, interpret or regiment linguistic or other data. This assumption is certainly made by both Russell and Meinong, and also, I think, by most other philosophers. It is denied, however, by some pragmatist or neopragmatist philosophers, as well as by logical positivists and some Wittgensteinian and ordinary language philosophers; at least this appears to be the case. Russell—and Quine—make the stronger assumption that all perspicuous discourse is ontological or metaphysical in the sense I mean to identify. They articulate and affirm what Quine called the principle of ontological commitment. Worked through, it is equivalent to Russell’s denial of the Meinongian principle of the independence of Sosein from Sein. Accordingly, it would be question-begging, in a paper meant to argue for the superiority of a Russellian stance to that of Meinong, to assume global or comprehensive ontological commitment, or the principle that Sosein entails Sein (that is, that having properties entails being). However, the principle that at least

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Page 238 some perspicuous discourse is existence-implying, or metaphysical, is common to both Russell and Meinong. The central issue dividing Russell and Meinong is precisely whether there is ever Sosein-ohne-Sein ( Sosein without Sein—property-having without being). The case for Russell, and against Meinong, is multifaceted. There are what we may think of as passive, or negative, arguments, and also active, or positive ones. The former include Occamist—Occam’s razor —arguments that there is simply no need to postulate a Meinongian body of designated propositions which embody the Sosein without Sein idea; that all putative such propositions can be handled, treated, in ways wholly consonant with the Russell Sosein-entails-Sein principle. The active, or positive, arguments include Russell’s own, that the Gegenstandstheorie actually implies formal contradictions, that it will require existent round squares that must, and can’t, exist. Another Russellian argument, its ground more diffuse than the latter, stems from the idea that the really truth-expressing propositions— the ones genuinely, and strictly, corresponding to what is actually so—may well not—in plenty of actual cases don’t—closely resemble sentences of ordinary speech. The latter frequently turn out to be the flotsam and jetsam of vulgar discourse, by no means to be expected to express anything perspicuously, and certainly not to be looked to as affording a foundation, or a body of exemplary cases, of serious theory . So, according to this line of thought, even if some speakers may be found who will affirm sentences appearing to assign properties to Holmes, and so on, this is appearance not reality, that is, these sentences won’t be genuine Soseinsobjektiven. I offer on this occasion a case for Russell, and against Meinong, that is less formal, and less theoretically deep, than either of the latter Russellian arguments. It will embody something of the impulse of the first of the kinds of objections to Meinong just indicated—that there is no good reason to be a Meinongian—with something of the spirit of the second—that there are costs that the theory of objects incurs that make it unpalatable if not formally dismissable. The case I offer is also, unlike Russell’s own, a fundamentally empirical one. The ideas I develop in setting it out may possibly correspond to concepts and distinctions in the huge speech act theory literature, or elsewhere, which I haven’t managed to learn about. If so, I welcome being pointed to places in that literature where these or similar notions appear. I suppose that, in the real world, belief attitudes are not limited to believing-true, believing-false and being undecided about. We also, in many cases, kind of believe something, or believe that there is something right about something, or that it is more or less true, without necessarily straightforwardly believing that it , as it stands, is true. I want to say that we may endorse some propositions (or proposition-like items) in both the kind-of-believe, and the believe-true situations. Against that background: quite often, when we speak (or, for that matter, write), we say one thing, but

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Page 239 there is something else, not obviously or trivially synonymous or equivalent (and in at least some cases definitely neither synonymous or equivalent), that we could have said instead, and which, had we done so, we would have recognized or endorsed as more or less saying what it was that we did say. In some such cases, we wouldn’t have thought of that alternative, on that occasion. If someone else says it, we may well think (and say), that puts it better (more clearly, more eloquently, more succinctly, more appropriately, and so on) than I did—or puts it worse; or puts it about the same—but, in any case, that was an alternative, that would have served, and that I would endorse as more or less conveying the information, or covering the approximate ground, that I did. In others of these cases, the speaker, aware of alternatives, has deliberately chosen one of them as preferred, on the occasion. Sometimes such a process of choice may seem more or less random; it was not that one of these alternatives was judged best; rather, any of them (or some proper subset of them, with more than one member) would have done, and one doesn’t, maybe couldn’t, see a difference, that would matter, for opting for one, but given that one wanted to say a certain something, and this was one of the available options for doing it (apparently as good as any other), this was the one utilized. This is of course compatible with there having been, possibly in all such cases, causes, which might or might not be known (or knowable) to the speaker, and indeed might or might not be explanatorily acceptable to the speaker, of why the actually utilized sentence or expression was the one opted for. I want particularly to focus on cases of the kind I am describing where the members of the option set of expressions that would serve to (more or less) say what the speaker said, and which the speaker does or would endorse as doing so, are not literally synonymous with or, at least straightforwardly, strictly equivalent to each other; and, indeed, members of option sets which may (in actual fact) differ in truthvalue from each other. I want to allow cases where it might be arguable that a given pair of such expressions may be, at some semantical or metaphysical depth level, necessarily co-extensive. But generally, an option set, for present purposes, is to be a set of expressions which seem obviously or overtly different, and nonequivalent, ways of having said (more or less) the same thing, to an adequate or appropriate degree, or with one saying better what was said, on the occasion and in the setting in which something was said, and which the speaker would be prepared to endorse as doing so. So, speaker S says (quotation marks are to be taken as Quinean corner quotation) ‘ e ’; but would recognize not-obviously-equivalent ‘ e 1’, ‘ e 2’, … ‘ en’ as also being able to serve as, do duty for, what S was saying when ‘ e ’ was said. One very straightforward kind of case of the sort of phenomenon intended will be where ‘ e ’ involves a reference to an object S is observing and the referential expression is a proper name or definite description; S’s option set in this case will presumably include an ‘ ei’ where the name/description is replaced with a suitable pronoun, the act of utterance perhaps also involving an appropriate gesture. Here is another

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Page 240 example. A small (imaginary) Ontario city, Middlebury, has an annual athlete of the year award. I am talking with Fred. I remember that Bob is seen out jogging every morning, looks mighty fit, won a Middlebury race, and is a friend of the mayor’s. I say, ‘Bob ought to be a contender for Middlebury athlete of the year.’ Fred reminds me that Bob won the Toronto marathon a few months earlier. I knew this, but had briefly forgotten it. ‘The man who won the Toronto marathon ought to be a contender for Middlebury athlete of the year’ will be in my option set, along with what I had said, and it will be a case of what I will call a trumping member of an option set, for the speaker. Along with other properties to be explained presently, a trumping member of an option set will often be a reason for someone’s viewing it as trumping. As noted as well, some of e 1, … en may, in some circumstances, differ in truthvalue. Some cases of this kind will be posed by the sorts of cases raised by Donnellan, with his notion of referential uses of definite descriptions. Presumably a speaker might, having the appropriate false beliefs, be prepared to endorse each of e 1 through en as saying, or serving to say, more or less, what the speaker actually did say, but one or more of the set actually be false. There will also be cases where a speaker might hesitate, or be unsure, as to whether a given sentence is indeed a member of an option set for the speaker on a particular occasion. It also seems clear, as was suggested above, that a speaker might, in many actual situations, be prepared to assert that some members of what we are calling an option set expresses, more aptly, or accurately, what the speaker said or meant to say. (The speaker need not think a case of a more apt or accurate, and a less apt or accurate, pair of members of an option set, to be one such that the first is true and the second false, though they may think this.) Where members of an option set would be judged by the speaker more apt or accurate than others, we may say that a sentence of the former subset of the option set trumps , or would trump , less apt members. The speaker may of course have actually uttered a sentence such that no other sentence in his or her option set would trump it. Or—and this is the sort of case I particularly wish to focus on—there is a sentence, which someone might draw to the attention of the speaker, which the speaker would acknowledge to be a member of the speaker’s option set on a given occasion, and acknowledge also that it trumps the speaker’s actual utterance. Where this happens, we may say that a trumping sentence is the sentence of fundamental or primary commitment of the speaker who has committed himself or herself to the option set (or who would do so), and the speaker, in this case, withdraws or would withdraw, endorsement of or commitment to any trumped member of the subset. The speaker might say, or think, in such circumstances, Yes, that captures the idea better, or, anyway, is at least a little more accurate, strictly or literally speaking, than (at any rate) these alternatives. It will be clear that these notions of option set, and trumping, are approximate-boundaried ones—a speaker might , in some cases, hesitate, be unsure, or change his or her mind as to whether a

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Page 241 pair of sentences did , for that speaker, say more or less or approximately the same thing, in the intended sense; it will be clear also that it is the speaker who is normally to be taken to be authoritative in the matter. The idea I have been developing for real world contexts of belief attitudes, propositions or statements which may be endorsed as more or less or approximately true, but then surrendered or found less satisfactory than alternatives which will (typically) be nonequivalent and may differ in truth-value (the originally provisionally endorsed proposition or statement false, the ‘better’ successor which ‘trumps’ it true), finds an analogue on the plane of philosophical theory. Interestingly, this analogue plays a central role in the philosophy of Russell. The concept of displacement ‘identity’ (or so-called identity) was developed in 1960s discussions of materialism in the philosophy of mind. The position which came to be called eliminative materialism argued that so-called ‘mental states’ were really in fact brain states. Comparisons were made with other instances in the history of common sense belief, and science, where observed phenomena were conceptualized in ways that were at best approximately true, and in fact, strictly speaking, false and inadequate. (So-called ‘witches’, for example—who, had they really been witches, would have to have had supernatural powers—were actually (identical to) solitary herbgathering women living in the woods and perhaps practising a pre-Christian nature religion.) The eliminative materialists regarded ‘folk psychology’ (the belief that there are beliefs, desires and so on) as a long-standing mistaken body of theory, which does refer, or purport to refer, to real phenomena, though inaccurately. Folk psychology is (for eliminative materialists) ‘kind of’ true, or has genuine parts of reality correctly targeted, but is ‘trumped’ by the more accurate theoretical structures and models of neurophysiology. Historically, the first reasonably clear case of a philosophical eliminativist—philosophical theorist offering ‘analyses’ of phenomena captured not-quite-accurately by previous philosophy, and common sense, is perhaps Hume. Be that as it may, a central and active methodological goal and practice of Russell’s philosophy, at more or less all stages, and for abstract as well as empirical phenomena, is precisely a programmatic eliminativism along just these kinds of lines. Now to Meinong sentences , as alleged to obtain or occur, and to be affirmed and endorsed, in natural language. I note first that sentences—or states of affairs—in which apparent singular referring expressions for, or apparent singular reference to, unreal things, but where the apparent reference is within psychological or other intentional contexts, will not be reckoned as Meinongian sentences here; although a psychological or intentional case that implied (or was argued to imply) a statement asserting that an unreal object had some property would be a case where the statement implied was Meinongian. Thus, Bill is painting a picture of Leda and the swan is not a Meinongian sentence, nor is Mary believes that Artemis is a huntress, or Ponce de Leon sought the fountain of youth. In addition, sentences, or states of affairs that identify unreal things as unreal will not

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Page 242 count as Meinongian sentences. Thus, Hamlet is George’s favourite literary character, and Holmes was Conan Doyle’s best-known fictional creation are not Meinongian sentences. The latter category may seem slightly more problematic than the former in this regard. That is, some Meinongians—though not Meinong himself, on our evidence—might want to construe Holmes as an object , having, in addition to the properties of being a detective, and English, the property of being fictional. The treatment of ascriptions of being—hence, also, of non-being (what Meinong will have called Nichtseinsobjektiven )—is itself a topic of complexity in philosophical semantics, and metaphysics. It will suffice for present purposes to say that it is entirely in the spirit of Meinong, as well as Russell, to differentiate radically Soseinsobjektiven—property-and-relation-ascribing propositions—from Seinsobjektiven (including Nichtseinsobjektiven ). Meinong and Russell agree about the radical differentiation; what they disagree about is what the relations are between the categories of item so differentiated. Standard examples of bona fide Meinong sentences are, then: (1) Holmes is a detective. (2) Superman can fly. (3) The most powerful of the Greek gods fathered Apollo. Meinongians, at least of the first type we identified at the beginning, and likely Meinong himself, would identify each of (1)–(3) as expressing true Soseinsobjektiven—property-ascribing propositions—asserting something of an object , which, as it happens, doesn’t exist. Further, they hold that (1)–(3) are or would be affirmed regularly, widely, and unproblematically, by speakers of natural language, perhaps by all of them with knowledge of the relevant object and innocence of philosophical semanticists’ theories. The latter sentence is of course a factual claim about what appropriate linguistic anthropological investigation would disclose. I now make a comparable factual claim, which I hold empirical investigation would substantiate. The claim is that for each natural language speaker of the theory-innocent sort just referred to, who affirms any of (1)–(3) or any comparable Meinongian sentence, and who realizes that the apparent subject of the sentence is fictional, there will be an option set, that will include a sentence of the type (4) The stories represent that Holmes is a detective. Alternatives might be: (4′) Holmes is supposed to be a detective, as he figures in the Conan Doyle stories. Many other, similar, sentences may be devised; and comparable variants for each of (2) and (3), and for every Meinongian sentence putatively about

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Page 243 Holmes or the king of the Greek gods, will also readily be imaginable, and constructible. The further claim I make is that for every natural language speaker, S, with an option set including (1) and (4)—or suitably comparable variants—(4) will trump (1). Generalizing, and schematizing, the factual claim is that for every Meinongian sentence ‘ p’, in which an unreal object of fiction or other cultural activities is purportedly characterized as having or lacking some property, and which a speaker asserts, there will be an option set sentence ‘it is story-represented that p’ (or a suitable variant) which will, for that speaker, trump ‘ p’. At the same time, the factual claim will assert in addition, no parallel actuality-qualifying assertions are to be met with, posing a comparable trumping phenomenon, with regard to real-world statements. ‘Paris is in France in the actual world’ does not trump ‘Paris is in France’. The latter suffices; it is at something like the end of the perspicuity road (so to speak). There is indeed a ‘prejudice in favour of the actual’ in ordinary (and for that matter, theoretical) thought and speech. The kind of ‘treatment’ defended here in respect of fictional objects is, it will be noted, similar to accounts offered in the literature, by such philosophers as Stuart Brock (2002), Charles Crittenden (1991), Richard Purtill (1973), and Leonard Linsky (1967). What is (very modestly) novel in my account is the set of claims of empirical linguistic anthropology that I have made, and the ‘option set’ and ‘trumping’ ideas. The advantages of the latter are that they will not require (as other treatments do) that Meinongian sentences are actually elliptical for explicitly context-disclosing or context-affirming sentences. Rather, the idea is that the typical speaker, presented with an appropriate context-affirming sentence, will invariably prefer the latter as saying better , at any rate, as saying more literally accurately (in the sense of approximate saying-the-same-thing equivalence identified here), what the Meinongian sentence has said. It may be noted that my empirical claims are about more or less theory-innocent natural language speakers who assert or would be prepared to endorse Meinongian sentences. There may also of course be among the general population natural Russellians, people innocent of theory who, knowing them unreal, would never assert that Holmes is a detective or Hamlet a prince. I actually think that there are lots of natural Russellians. At any rate, whatever their numbers, the option set and trumping ideas will be unnecessary in their cases for adding to the empirical case against Meinongian intuition. So: the natural Meinongians (if there are any) kind-of-believe Meinongian sentences, or in some cases may actually believe them true. The natural Russellians believe Meinongian sentences to be false (or that they fail to be true). For both, the appropriately corresponding story-representational sentence will trump the Meinongian sentence. These claims have of course been made just for Meinongian sentences which are embedded in stories , story fragments or other imaginative activities (including dreams), conscious (or unconscious) devisings of individuals

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Page 244 or cultures. While this is clearly evident for the typical objects with which Meinong begins, and which motivate, for him and his followers to the present day, the Meinongian theory of objects, some Meinongian objects, it is held, are bereft of story or contextual setting. Indeed, for Meinong himself, and most of his followers, a Meinongian object may be constituted by any individualized clustering of properties. The purple eighty-kilogram five-footed elephant presently sitting on G. W. Bush might be such an object. What one notes in advocacies of (what I will call) story-bereft Meinongian objects is that the sole Sosein (property-aggregate) claimed as plausibly assigned them consists in properties alleged to be analytically implied by the defining conception of the object (so-called ‘nuclear’ properties of the object). So, for this Meinongian view, the proposition expressed by ‘The purple eighty-kilogram fivefooted elephant presently sitting on G. W. Bush is an elephant’ will be an allegedly true Soseinsobjektiv generated by the Meinongian object indicated, and all other (allegedly) true Soseinsobjektiven will be comparable. Now, completely independent of Meinongian sentences, of either the story-embedded or the story-bereft kind, we may note a class of sentences of type ‘The F is G’, where there does really exist a unique F object, and where G is analytically contained in F . ‘The present king of Sweden is a king’ will be a good example of this class. Is the just-quoted sentence analytically true? For those who may be disposed to affirm that it is, it may be observed that there will be an option set sentence for someone who may assert the sentence about Sweden’s sovereign, namely, ‘If the present king of Sweden exists, then the present king of Sweden is a king’, which—I claim—will trump the original, for any such speaker. If this is right, then the alleged analyticity of the class of sentences under review will provide no motivating rationale for Meinongianism. Those not disposed to view ‘The present king of Sweden is a king’ as analytic will decline to do so precisely because there might not have been such an individual as King Carl XVI Gustaf, and Sweden might presently have been a republic. Some more empirical claims. I actually think that natural language speakers innocent of Meinong, Russell and their theoretical preoccupations would be quite mystified by story-bereft Meinongian objects. They wouldn’t know what to make of them, and certainly wouldn’t rush forward to register the appropriate Meinongian semantical intuitions. For the story-bereft objects, I claim, the natural theorybereft speaker would welcome Russell’s theory of descriptions, as regimenting, in a helpful way, sentences in which they might figure, including the allegedly analytic Soseinsobjektiven involving them. Companion to such welcoming would be a cheerful acceptance of the Russellian treatment of the Swedish kinds of cases just discussed. Story-embedded Meinongian objects pose more complexity, as the argument of this paper acknowledges. Russell’s theory of descriptions will handle the story-bereft objects directly and

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Page 245 straightforwardly, and the trumping procedure will, less directly, handle the story-embedded objects. It will be clear that, if the foregoing series of arguments is cogent, the alleged natural language ground and support for Meinongianism will be undercut. It will be untrue that the natural mind, or semantical or (wide-sense) ontological intuitions encapsulated in natural language, have a Meinongian component or impulse. For the trumping category of sentences in the relevant option sets do not imply Meinong’s principle of the independence of Sosein from Sein. That it may be represented in a story that something is the case, or that the details of some cultural or symbolic artifact involve supposing, regarding or depicting something as being so no more imply that principle than do facts of our dreams, or works of art, or their contents, imply this. There may still be claimed to be difficulties posed by some of the natural language semantic data, which none of the foregoing account of story-embedded and story-bereft alleged items, and the option set and trumping ideas, will in a satisfactorily clear way address. Perhaps the most difficult cases are posed by (alleged) comparisons between real and unreal objects. Imagine that Sam reads and admires War and Peace , in which the historical Napoleon and the fictional Pierre are characters. Sam, it might be claimed, likes Pierre better than Napoleon, and thinks that the latter is far less morally impressive than the former. What is the would-be Russellian to make of such a fact as that? Sam knows that Napoleon was real, and Pierre not; maybe he has done some historical investigation, and thinks that Tolstoy has represented the real Napoleon fairly accurately, certainly on the moral side of things. Sam’s belief is about the real Napoleon, whom Sam is conceiving of both as the character in Tolstoy and as the real person. And Sam thinks that Pierre was morally superior to that individual. (Pierre, if you’ve read the novel, you will agree is indeed a loveable and admirable character in the story.) If I’m right about my empirical linguistic anthropological claims, then Sam will agree that a member of her option set will be (some factual equivalent of) ‘It is represented in War and Peace that there is an individual Pierre, that there is Napoleon, and that Pierre is more morally impressive than Napoleon.’ And Sam will endorse the latter sentence, agree both that it trumps how she might have expressed her view and that she holds that view. Sam can add that the real historical personage Napoleon appears as a character in the novel, depicted as Tolstoy depicts him. Still another case, discussed in the literature, is posed by ‘Holmes is more famous than any existing detective’ (and comparable cases). Here I will want to make further use of the idea of approximate factual equivalence utilized earlier. The just-quoted sentence is equivalent in at least this sense to ‘People think more about Sherlock Holmes than they do about existing detectives, and they have storyderived conceptions of Holmes that are more extensive than conceptions they have of existing detectives.’

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Page 246 There are still other difficult cases. Consider someone, say, George, who is extremely fearful. Among the things he fears are spiders and serial killers; but he also fears ghosts and fire-breathing dragons. It may be that his deepest fears include these last two, and what most terrifies him of all is a particular firebreathing dragon about which he has nightmares. Of George it may seem correct to say, Some of the things he most fears don’t exist , and, indeed, The thing he most fears doesn’t exist . Both of these sentences, if true, pose challenges for standard classical logic, since with quantification interpreted objectually, they will turn out to be self-contradictory. In both cases, I argue (though I agree that the results are a bit convoluted), we can produce perspicuous ‘equivalents’, along the lines previously indicated, that won’t have this result. I think that compound treatments along these lines should in general be successful in pre-empting putative cases for Meinongian objects. I would supplement them with the idea that the anti-Meinongian (Russellian or otherwise) can and should make ample use of helpful abstract entities, specifically with properties and relations and concepts (regarded either Platonistically or psychologically, as may suit), and with the abstracta known as ways . There is the way that Robert walks, the way (or ways) that Picasso paints pictures and so on. There are also ways things (processes, events, individual characters) are represented in artistic or other imaginative artifacts. All such ways can be (I think correctly) asserted to be real, without implying the reality of individuals which may figure in the ‘way’ when it is a representational ‘way’. The way that Romeo is represented as longing for the absent Juliet is a really existing thing, which might be (sometimes, surely, is) really exemplified in an existing human being. Some ways are, it seems, self-contradictory or impossible. There is the way a round square would be, if there were one. ( That way would consist in being both round and square.) Ways are, presumably, items that very closely resemble properties. At any rate, they too will be helpful arrows for the antiMeinongian quiver. It will be clear that the foregoing is both an informal and an incomplete treatment of the fundamental Meinongian theme. In addition to having made only modest engagement with the immense secondary literature on ‘objects of thought’, some of that theme’s key topics remain unaddressed here, in particular, the need to give an adequate account of the semantics of (apparent) proper names which never, at any time, denote. The latter need is specially acute if we find persuasive the Kripkean rigid designation and causal transmission treatment of proper names that do denote. The general line defended in this paper is that fictional contexts are parasitic on non-fictional, real-world ones. This would suggest, I think, that fictional names should be treated somewhat as implied by Carnap’s individual concepts, adapted in turn by Quine’s ‘pegasizing’ sorts of predicates. But this does require careful and more detailed exploration.

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Page 247 REFERENCES Brock, S. (2002) ‘Fictionalism about Fictional Characters’, Noûs 36.1: 1–21. Chisholm, R., ed. (1960) Realism and the Background of Phenomenology , Glencoe, IL: The Free Press. Crittenden, C. (1991) Unreality: the Metaphysics of Fictional Objects, Ithaca, NY: Cornell University Press. Linsky, L. (1967) Referring, London: Routledge and Kegan Paul. Meinong, A. (1904) ‘The Theory of Objects’, trans. I. Levi, D. B. Terrell and R. M. Chisholm, in Chisholm (1960): 76–117. Purtill, R. (1973) ‘Meinongian Deontic Logic’, Philosophical Forum 4: 585–92. Quine, W. V. O. (1963) ‘On What There Is’, in From a Logical Point of View , New York: Harper Torchbooks.

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Page 248 12 Who is Afraid of Imaginary Objects? Gabriele Contessa There are more things in the heaven and earth Horatio, than are dreamt of, in your philosophy —William Shakespeare, Hamlet , Act I, Scene V THE PROBLEM WITH IMAGINARY OBJECTS People often use expressions such as ‘Sherlock Holmes’ and ‘Pegasus’, which appear to refer to imaginary objects, and make assertions about them such as: (1) Sherlock Holmes smokes a pipe and (2) Sherlock Holmes was created by Arthur Conan Doyle in the late nineteenth century. In what follows, I call internal those sentences that, like (1), talk of imaginary objects as if they were concrete actual objects and external those sentences that, like (2), talk of imaginary objects as fictional characters, mythological creatures and so on (whatever these entities might be). I call object-fictional those internal sentences that occur in a work of fiction and metafictional those sentences, whether internal or external, that occur outside of a work of fiction and are about that work of fiction. Thus, (1) is an object-fictional sentence if it occurs in one of Arthur Conan Doyle’s stories but it is a metafictional sentence if it occurs in the context of the discussion of Conan Doyle’s works. Prima facie, speakers’ reference to imaginary objects would seem to be incompatible with a widely accepted philosophical principle. One of the first formulations of this principle in western philosophy can be found in Plato’s Sophist (237B–E). In this paper, however, I refer to a much more recent formulation of the principle, which has been put forward by John Searle (1969), who calls it the Axiom of Existence. In Searle’s formulation, the Axiom of Existence states: ‘Whatever is referred to must exist’ (77). The problem is that, if we take ‘existence’ to designate the mode of being that is proper of actual concrete objects such as flesh-and-bone people,

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Page 249 animals and material objects, then imaginary objects, like Sherlock Holmes and Pegasus, do not exist and therefore, according to the Axiom of Existence, it is not possible to refer to them. Those who accept the Axiom of Existence have two options. They can either maintain that reference to imaginary objects is only apparent or that imaginary objects exist after all. In what follows, I call eliminativist any account according to which imaginary objects do not exist and reference to imaginary objects can be explained away as merely apparent. To show that apparent reference to imaginary objects is not genuine philosophers have usually relied on one of three main strategies. In ‘Eliminativist Approaches’, I briefly outline each of them and argue that they all fail to be fully descriptively adequate. In ‘Hospitable Approaches’, I consider the option of admitting that imaginary objects exist and that reference to them is genuine reference. I call any account that maintains that imaginary objects in some sense exist hospitable. Different hospitable accounts however disagree as to the nature of imaginary objects. According to possibilist accounts , imaginary objects are possible concrete objects, while, according to abstractist accounts , they are actual abstract objects. I argue that neither option is fully satisfactory. I then outline a hospitable account, the dualist account , which, as I argue, combines the advantages of the versions of the possibilist account and the abstractist account without sharing their respective disadvantages. According to the dualist account, imaginary objects have an intrinsically dual nature and they cannot be entirely reduced to either abstract objects or imaginary objects. An imaginary object is an abstract object that stands for a possible object. Before starting the examination of the various accounts to imaginary objects, it is important to note that this paper is meant to be a piece of descriptive and not prescriptive metaphysics, to use Peter Strawson’s distinction (1959). That is, its aim is to make philosophical sense of the practice of talking and thinking about imaginary objects and of the intuitions that underlie this practice. It is not meant to modify or censor this practice and intuitions but to uncover their implicit presuppositions. ELIMINATIVIST APPROACHES The Predicate Account The first eliminativist strategy I examine, the predicate account , attempts to paraphrase the sentences in which apparently referential expressions occur into synonymous sentences containing no such expressions. Bertrand Russell (1905) and Willard van Orman Quine (1948) are probably the most prominent advocates of the paraphrase programme. In its most ambitious version, the paraphrase is supposed to show the ‘logical form’

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Page 250 of the sentence (like in Russell 1905). According to a more modest version, the paraphrase simply proves that reference to imaginary objects could be avoided without changing the meaning of the sentence. The paraphrase would show that reference to imaginary objects is ultimately dispensable and does not commit us to the existence of these objects. The general idea that underlies the paraphrase programme is that (1) is synonymous with (3) There exists one and only one x such that x is Sherlock Holmes and x smokes a pipe. In the notation of first order logic, (3) has the form x(( Px) ^ ( y( Py → x = y)) ^ Q x), where ‘ Px’ is interpreted as ‘ x is Sherlock Holmes’ and ‘ Qx ’ as ‘ x smokes a pipe’. Thus, (3) does not contain any referring expression. It only asserts the existence (and the uniqueness) of an entity that has the property of being Sherlock Holmes and states that that entity also has the property of being a pipe smoker . If one concedes that the expression ‘Sherlock Holmes’ as it occurs in (3) is not a name but it is only part of a strange-looking predicate, the first step of the programme seems thus successfully completed: (3) does not contain any expression referring to nonexistent entities. However, one might wonder whether any genuine metaphysical advantage is gained from this move. Advocates of the predicate account propose to interpret sentences containing expressions that apparently refer to objects that do not exist as sentences that contain empty predicates. If, on the one hand, the advocates of the predicate account embrace an intensional view of predicates as expressions referring to properties, then they exclude nonexistent entities from their ontology only at the price of admitting uninstantiated properties in it. This is a price that many would not be willing to accept. First, most philosophers who are realist about properties would not be willing to include noninstantiated properties in their ontology (Loux 2002). Second, an ontology that contains noninstantiated properties is not necessarily more austere than an ontology that contains nonexistent objects. If, on the other hand, they embrace a strictly extensional view of predicates, such that two predicates are the same if they have the same extension, then they have to accept that the predicates ‘ x is Sherlock Holmes’, ‘ x is Dr. Watson’, ‘ x is Pegasus’ and, say, ‘ x is the highest prime number’ are, in fact, the same predicate, for they both have as their extension the empty set. Both options seem unsatisfactory. The second step, however, is probably even more problematic. If (3) is to be a paraphrase of any internal sentence such as (1), then (1) and (3) must be synonymous and synonymous sentences necessarily have the same truth-value. But it is far from obvious that (1) and (3) have the same truthvalue. On Russell’s early account, (3) is plainly false. No actual concrete object satisfies the predicate ‘ x is Sherlock Holmes’. However, knowledgeable speakers

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Page 251 unconcerned by philosophical issues would agree that (1) is ‘ in some sense ’ true and its negation false. For example, if a student writes on a true-or-false literature test that (1) is true, her answer is right, if she writes that (1) is false, her answer is wrong. Any descriptively adequate account of the semantics of fictional sentences should be able to account for the fact that some internal sentences such as (1) are ‘ in some sense ’ true and others, such as (4) Sherlock Holmes is an astronaut, are ‘ in some sense ’ false. I call these two phenomena, respectively, the qualified truth and the qualified falsity of internal sentences . Even if one was ready to deny that internal sentences such as (1) and (4) can be true or false in any sense or even have a truth-value, however, it does not seem possible to deny that external sentences, such as (2), are unqualifiedly true. That is, they are true according to historical facts and not just true relatively to some work of fiction. One day an historian of literature might claim that (2) is actually false: Sherlock Holmes was created by someone other than Conan Doyle and Conan Doyle only stole her idea. To support this claim, she would need factual evidence. I call this phenomenon the unqualified truth of external sentences . The predicate account cannot account for the unqualified truth of external sentences. In fact, according to it, external sentences like (2) would appear to be no less false than internal sentences like (1). The predicate account thus is not descriptively adequate (and, to be fair to its advocates, it is not even intended to be so). Speakers who utter sentences like (1) or (2) do not, thereby, implicate that the entities to which they are referring exist as concrete actual objects. In the attempt to avoid any form of ontological commitment to imaginary objects, advocates of the paraphrase programme systematically misconstrue the meaning of the sentences in which expressions referring to imaginary objects occur, and systematically misinterpret what the speakers mean to say when they utter those sentences. It is worth noting here that similar problems are also faced by those accounts, like Peter Strawson’s (see 1950), according to which statements that contain nonreferring expressions, such as (1) and (4), are neither true nor false or those who, like the late Russell (1957), maintain that statements of these sort are untrue rather than simply false. None of these accounts can account for the intuition that, whereas (1) and (4) may both be literally false, (1) is in some nonliteral sense true. The Pretence Account Consider now a second eliminativist account: the pretence account . The pretence account, which in some version or other has been advocated by the

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Page 252 likes of Kendall Walton (1973, 1990), and Gareth Evans (1982), is based on the idea that reference to imaginary objects is not genuine but only pretended and that, therefore, it is not in breach of the Axiom of Existence.1 According to the pretence account, the sentences that occur in a work of fiction belong to a special mode of discourse: fictional discourse, which is to be carefully distinguished from ordinary factual discourse. In writing or uttering an object-fictional sentence in which expressions that appear to refer to imaginary objects occur, the author of a work of fiction pretends that she is referring to actual objects and that she is providing the audience with true information about the objects. The author also intends the audience to participate in the pretence by pretending that the author is referring to something rather than nothing and that what she says about that something is true (cf. Currie 1991: Chapter 1). Advocates of the pretence account usually note that fictional discourse is a form of make-believe similar to children playing with blobs of mud pretending that they are pies (Walton 1973) or to someone shadowboxing pretending that he is fighting imaginary opponents (Evans 1982). The pretence is, to a certain extent, also carried over in internal metafictional sentences. When a speaker utters an internal sentence such as (1) outside of the context of a work of fiction, both the speaker and its audience pretend that ‘Sherlock Holmes’ refers to a real person. Unlike object-fictional sentences, however, internal metafictional sentences are not necessarily pretended to be true. An internal metafictional sentence is pretended to be true only if it is implied by object-fictional sentences in the relevant work of fiction, so that none would pretend a sentence such as (4) to be true. The pretence account faces various problems. Here, I consider only one, which is that the pretence account does not seem able to account for the unqualified truth of external sentences such as (2). There seems to be a perfectly legitimate sense, although maybe not an entirely literal one, in which Conan Doyle ‘created’ Sherlock Holmes. When uttering (2), a speaker and their audience do not seem to be pretending that ‘Sherlock Holmes’ refers to any concrete actual object nor do they pretend that Arthur Conan Doyle created that object. Rather, the speaker seems to be providing her audience with genuine information about the author of the fictional character that is identified by the name ‘Sherlock Holmes’. Testimony to this is the fact that, even if we are able to pretend that, say, Anna Karenina was created by Conan Doyle, we do not seem able to pretend that Holmes was created by Conan Doyle because we actually believe that Holmes was created by Conan Doyle, for it would seem that one can pretend that p is true only if one does not believe that p is true. The Mention Account This leads us to consider a third strategy to paraphrase away reference to imaginary objects, which I call here the mention account . According

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Page 253 to the mention account, when someone is apparently using an expression that refers to an imaginary object they are actually only mentioning that expression.2 According to this account, (1) would be shorthand for (5) Someone wrote a story containing ‘Sherlock Holmes smokes a pipe’ (or containing sentences implying this).3 If (1) was actually only shorthand for (5), then the use of the expression ‘Sherlock Holmes’ in (1) would be ultimately dispensable. The mention account however cannot account for either external sentences or object-fictional sentences. Consider external sentences first. According to the schema suggested above, (2) would be shorthand for (6) Someone wrote a story containing ‘Sherlock Holmes was created by Arthur Conan Doyle in the late nineteenth century’ (or containing sentences implying this). Clearly, (2) is not shorthand for (6). An advocate of the mention account could probably claim that, even if that particular schema does not work in external contexts, it is still possible to claim that external sentences are shorthand for sentences in which the expression ‘Sherlock Holmes’ is only mentioned. If the advocates of the mention account want their claims to be taken seriously, however, they should propose a set of paraphrase schemas that are meant to deal with all external sentences, including ‘Sherlock Holmes is my favourite character in English literature’ or ‘Sherlock Holmes uses abductive reasoning more frequently than Hercules Poirot’. Until then it is not possible to seriously assess their claim that all external sentences are shorthand for sentences in which expressions which refer to imaginary objects are only mentioned. Moreover, the suggested paraphrase schema does not seem to work with object-fictional sentences either. If (1) occurred in one of Conan Doyle’s stories, it cannot be interpreted as shorthand for (5). In fact, in his stories, Conan Doyle is not reporting the content of someone else’s stories to his readers. Advocates of the mention account could probably concede that, when it occurs in the context of objectfictional sentences, the expression ‘Sherlock Holmes’ is used and not mentioned. Nevertheless, they could claim, the expression is not used referentially or, even if it is used referentially, it does not refer to anything. The problem with such a possible reply would be that, in object-fictional sentences, ‘Sherlock Holmes’ seems to be used referentially and seems to refer to a certain character in the novel and not to others. By writing a sentence like (1) in one of his stories, Conan Doyle meant to tell us that the character to which he refers to as ‘Sherlock Holmes’ and not any other of the characters in the novel smokes a pipe. Thus, not only does ‘Sherlock Holmes’ seem to be used referentially in object-fictional sentences, but also

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Page 254 it seems to be used to refer to a certain object and not others. The practices of writing and reading works of fiction (in which there is more than one character) presupposes that different expressions can be used to refer to different characters. If ‘Sherlock Holmes’ and ‘Professor Moriarty’ failed to refer to different objects, we would not be able to distinguish between ‘Sherlock Holmes smokes a pipe’ and ‘Professor Moriarty smokes a pipe’. HOSPITABLE APPROACHES As they stand, none of the main attempts to show that reference to imaginary objects is not genuine seems to be descriptively adequate and some of the problems that these accounts have encountered could be taken as evidence that reference to imaginary objects is, after all, genuine. Those who adopt a hospitable approach, are willing to grant that whatever is referred to must exist. From this assumption, however, they reach the opposite conclusions: since it seems possible to genuinely refer to imaginary objects, imaginary objects must exist. Since they are not concrete actual objects, they must have a different ontological status. The agreement among advocates of hospitable approaches, however, does not go much further than this. Hospitable accounts can be roughly grouped into two broad families: possibilist and abstractist accounts. Even if both possibilist accounts and abstractist accounts maintain that imaginary objects exist, possibilists and abstractists have rather different ideas as to what they are. Possibilist Accounts The main idea behind possibilist accounts is that imaginary objects, though not actual, exist and, as such, they can be referred to. Among the various possible variations on the possibilist theme, I consider only two here, which I call the combinatorial account and the possible world account . The combinatorial account is inspired by Alexius Meinong’s theory of objects and Terence Parsons’ neo-Meinongian account of nonexistent objects (Parsons 1980).4 To illustrate the combinatorial account, suppose that one could write a list of all actual objects and next to each of them the set of the properties5 the object instantiates. Once we run out of actual objects on the first column, however, we can still continue the list of sets of properties by writing all sets of properties that are not coinstantiated by any actual object. For example, since no actual mountain is made of gold, the properties goldness and mountainhood are not members of the set of properties of any actual object. According to the combinatorial account, to each set of properties that are not coinstantiated by any actual object corresponds one and only one possible object. So, we can continue our list by adding one possible but

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Page 255 not actual object for each set of properties that are not coinstantiated by any actual object. It is among these objects that, according to the combinatorial account, the referent of ‘Sherlock Holmes’ can be found. Since no actual object instantiates the properties of, say, being a detective and living at 221B Baker Street , according to the combinatorial account, there is a possible object that instantiates those properties. So, ‘Sherlock Holmes’ refers to a nonactual object whose set of properties includes the property of being a detective and living in 221B Baker Street . On this account, (1) is true because being a pipe smoker is among the properties of that object and (4) is false because being an astronaut is not. The combinatorial account is riddled with problems. I consider only a few here.6 The first is that of identifying the object to which ‘Sherlock Holmes’ refers within the multitude of merely possible objects. The advocate of the combinational account would probably suggest that it is possible to make a list of all the properties attributed to Sherlock Holmes by his author and then find the object on the list that has those properties. This suggestion however is not satisfactory. Suppose that the set H includes all the properties that Conan Doyle attributes to Holmes in his works. Many objects on our list will have H as a subset of the set of their properties. Some of them have a mole on the left shoulder, while others do not. Some are allergic to dust and others are not. Which one of them is Sherlock Holmes? The description of Sherlock Holmes that can be gathered from Conan Doyle’s works does not single out any one of them as the unique referent of ‘Sherlock Holmes’. The advocate of the combinatorial principle, however, could stipulate that ‘Sherlock Holmes’ refers to the object that has all and only the properties attributed to it by his author.7 So, ‘Sherlock Holmes’ refers to the object on our list that has H as its set of properties. This suggestion, however, generates even more problems. Consider two here. First of all, we would tend to think that, say, Sherlock Holmes has a mother even if Conan Doyle never mentioned that. Second, if we are to explain that Sherlock Holmes is not an astronaut by pointing out that being an astronaut is not included among the properties in H, the fact that having a mole on the left shoulder is not included in H either would seem to force us to conclude that Sherlock Holmes does not have a mole on the left shoulder, which is unwarranted given that it is perfectly compatible with Doyle stories that he has one. Another problem is that possibilist accounts cannot account for the truth of external sentences. (2) does not seem to be true because ‘Sherlock Holmes’ refers to a possible object among whose set of properties, alongside that of being a detective and that of being a pipe smoker , includes that of having been created by Conan Doyle. This last property of Sherlock Holmes just does not seem to be on the same level as the other two. If ‘Sherlock Holmes’ referred to the possible but not-actual object that coinstantiated all and only the properties attributed to Sherlock Holmes by Conan Doyle,

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Page 256 then he would not instantiate the property of being created by Conan Doyle because this property is not a property that was ever attributed to it by Conan Doyle—it is an actual property of Sherlock Holmes. To put it more vividly, if someone fitting Conan Doyle’s description of Sherlock Holmes had existed, he would be a brilliant detective who smokes a pipe and lives in Baker Street, but he would not have been created by Conan Doyle. An even more serious problem is that, as Saul Kripke (1980) has convincingly argued, there is simply no real or counterfactual situation in which some real person or other could have been Sherlock Holmes. It is not sufficient for something to fit the description of Sherlock Holmes in order for it to be Sherlock Holmes (in fact, it is not even necessary). Even if, unbeknownst to Conan Doyle and the rest of us, there was someone who actually had all the properties attributed to Holmes in Conan Doyle’s works, including being called ‘Sherlock Holmes’, ‘Sherlock Holmes’ in (1) would still not refer to that person. Therefore, having all the properties which are attributed to Sherlock Holmes is not sufficient to be the referent of ‘Sherlock Holmes’ in (1). If the combinatorial account is afflicted by many problems, the other version of the possibilist account that I consider here, the possible world account inspired by David Lewis’s account of truth in fiction (1978), does not fare much better—and for similar reasons. According to the possible world account, there is a possible world in which Conan Doyle’s stories are literally true. In fact, since there is more than one way in which Conan Doyle’s stories could be true of a world (as there is much that those stories leave unspecified), Conan Doyle’s stories do not identify one but many possible worlds. Now, in each of these worlds, there is a brilliant detective whom the inhabitants of that world refer to as ‘Sherlock Holmes’, who smokes a pipe and who lives in Baker Street. According to the possible world account, ‘Sherlock Holmes’ in the actual world refers to the person who is referred to as ‘Sherlock Holmes’ in one of these fictional worlds. The possible world account is afflicted by problems that are very similar to those that characterized the combinatorial account. The first is that there are a number of different worlds that are compatible with Conan Doyle’s stories and in each of those worlds there is a brilliant detective whose name is ‘Sherlock Holmes’. In some of these worlds, Sherlock Holmes has a mole on his left shoulder, in others not. In some of those worlds, unbeknownst to Dr. Watson, he is an astronaut, in others, not. If we were to take seriously the claim that ‘Sherlock Holmes’ actually refers to one of the Sherlock Holmes that inhabit these possible worlds, the advocate of the modal account should be able to determine which one. However, since the description of Sherlock Holmes in Conan Doyle’s stories is incomplete, none of these identifications seems to be more warranted than any other. Moreover, unless one manages to rule out worlds in which Sherlock Holmes, unbeknownst to the narrator of

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Page 257 the stories, Dr. Watson, participates to a secret space programme, the modal account cannot rule out that (4) is after all true. Another problem is that the possible world accounts cannot account for the truth of external sentences. It does not seem possible to maintain that (2) is true because ‘Sherlock Holmes’ refers to a possible object among whose properties is that of having been created by Conan Doyle. In fact, on most accounts of the nature of possible worlds, it would seem that, if ‘Sherlock Holmes’ in (2) refers to the inhabitant of a possible world, he has not been created by Conan Doyle but exists independently of him. An even more serious problem is the one raised by Kripke. It is not sufficient to have all the properties which are attributed to Sherlock Holmes in order to be the referent of ‘Sherlock Holmes’ in (1). Abstractist Accounts According to abstractist accounts, insofar as the expression ‘Sherlock Holmes’ refers at all, it refers to an abstract entity: a character in a series of works of fiction. Thus, even if Sherlock Holmes is not an actual person and does not actually smoke a pipe, he (or it?) exists. It is one of the best-known characters of detective fiction, who was created by Arthur Conan Doyle and appeared for the first time in the 1887 novel A Study in Scarlet. Accordingly, we should distinguish two uses of the expression ‘Sherlock Holmes’. The first is the objectfictional use. This is the use that Conan Doyle makes of the name within the context of a work of fiction. In this use, the name, which appears to refer to an extraordinary detective in Victorian London, simply fails to refer to anything. The second use is the metafictional use. This is the use that Conan Doyle and his readers make when talking about the leading character in many of Conan Doyle’s works. In this use, the name ‘Sherlock Holmes’ refers to an abstract object (a fictional character) that is part of another abstract artefact (a novel or a short story). The abstract account succeeds where all of the other accounts I have examined so far fail: it manages to explain reference to imaginary objects in external contexts such as (2). In that sentence, the expression ‘Sherlock Holmes’ refers to an actual abstract entity and attributes to that entity a genuine (abstract) property, that of having been created by Arthur Conan Doyle. However, the standard abstract account does not seem equally successful in dealing with those cases in which expressions appear to be referring to imaginary objects that occur in an internal context outside of a work of fiction such as (1) and (4). In fact, the expression ‘Sherlock Holmes’ fails to refer to anything and the whole sentence is either false or fails to have any truth-value. Whereas Conan Doyle could not possibly misdescribe Holmes within the context of the stories he wrote, however, there seems to a sense in which someone would be misdescribing Holmes if she uttered (4). Note that she would not be misdescribing him because he is actually an abstract entity

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Page 258 and abstract entities cannot be astronauts, but because, as I have already noted, there seems to be a sense in which it seems to be true that Sherlock Holmes is a detective. To avoid this problem, various strategies have been proposed. I consider two here. The first, which has been proposed by van Inwagen (1977), claims that sentences such as (1) should be paraphrased as: (7) There exists a place in a work of fiction where the property being a pipe smoker is ascribed to Sherlock Holmes. In other words, when an expression referring to an imaginary object appears in an internal context, the sentence can be paraphrased as saying that a ternary relation, ascription, holds between an abstract object, a property and a passage in a work of fiction. Van Inwagen’s account faces two main problems. The first is that there seem to be properties that are not attributed to imaginary objects in any passage of a work of fiction but that nonetheless seem to be, in some sense, true of the object. Suppose that somewhere in Conan Doyle’s stories one can find the sentence: (8) Sherlock Holmes lives in 221b Baker Street. Suppose also that the following sentence is nowhere to be found in those stories: (9) Sherlock Holmes lives closer to Regent’s Park than to Hyde Park. Given the topography of Victorian London, (8) implies (9). However, whereas the schema underlying (7) can be used to account for our intuition that (8) is in some sense true, it cannot be used to account for our intuition that (9) is in some sense true as well. In fact, we have assumed that nowhere in Conan Doyle’s stories Holmes is ascribed the property of living closer to Regent’s Park than to Hyde Park. In general, fictional characters seem to have more properties than the ones which are attributed to them in the fictional works of which they are part. Literary critics and readers sometimes engage in passionate discussions about whether Hamlet is clinically depressed or whether or not Holmes is a misogynist, even if these properties are not attributed to them by their authors. These opinions are only partly based on the properties which these characters are explicitly ascribed in the works of fiction of which they are part. They are also based on the readers’ background assumptions about what other properties these characters would have, if they actually had the properties they are ascribed. To the extent to which inferences such as the one from (8) to (9) are legitimate (and I think that, to some extent, they are), the qualified truth of (9) is to be explained as much as that of (8).

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Page 259 A second problem is that, according to van Inwagen’s account, the expression ‘Sherlock Holmes’ does not refer to anything when it occurs within a work of fiction. As Nathan Salmon (1998) noted, strictly speaking, nothing can be attributed the property of being a pipe smoker by the occurrence of (1) in the context of Conan Doyle’s stories. Since in the sentences that occur in those stories, the expression ‘Sherlock Holmes’ fails to refer to anything and, a fortiori, it does not refer to the abstract entity Sherlock Holmes. The second version of the abstractist account that I consider here is the one outlined by Salmon (1998). On Salmon’s account, ‘Sherlock Holmes’ refers to the same object, an abstract entity, in both objectfictional and metafictional sentences. Since obviously abstract entities do not smoke, (1) is false. Nevertheless, Conan Doyle and his readers pretend that it is true by pretending that the abstract object to which we refer as ‘Sherlock Holmes’ smokes a pipe. It is important to note that this version of the abstract account differs from the pretence account in one crucial detail. According to the former, the speaker is genuinely referring to something (an abstract object), while according to the latter the speaker is only pretending to refer to something while referring to nothing. Salmon’s account has the advantage of avoiding some of the problems of the other abstractist accounts by eliminating the asymmetry in the analysis of object-fictional and metafictional sentences that characterizes other abstractist accounts. According to this version, the expression ‘Sherlock Holmes’ refers to the same abstract object in both its object-fictional and metafictional uses. But, whenever the expression occurs in external sentences, the speaker pretends that that object is a person. Against Salmon’s account, Sarah Sawyer (2002) has argued that it is not clear what the pretence involved in it amounts to. Sawyer claims that if this pretence amounts to pretending that ‘Sherlock Holmes’ refers to a real man rather than an abstract object, then the abstract object to which the expression actually refers becomes explanatorily redundant and the account incurs in (some of) the problems that afflicted the pretence account. If, on the other hand, the pretence amounts to pretending that an abstract entity is a real person, according to Sawyer, it is not clear how or even whether we can do so. Whereas it is clear how one can pretend to be on a sunny beach when one is not, claims Sawyer, it is not clear how one can pretend that the number two is a man who plays croquet (at least, if we consider the number two to be an abstract entity). And, since Sherlock Holmes is an abstract object, the kind of pretence involved in Salmon’s account seems more similar to the second case of pretence than to the first case. Sawyer’s dilemma does not seem particularly serious. If the first interpretation of Salmon’s account was correct, the abstract object would definitely not be explanatorily redundant. In fact, it would be the object to which ‘Sherlock Holmes’ actually refers both in external and internal sentences (even if, when it occurs in internal sentences, we pretend it refers to something else). If the second interpretation was correct (as I tend to

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Page 260 believe), it is not clear where the difficulty of pretending that the number two is a man who plays croquet exactly lies. The difficulty noted by Sawyer may arise from the fact that the entity referred to as ‘Sherlock Holmes’ cannot be a person in any possible world. Sawyer would be suggesting that it is at least doubtful whether one can pretend that something that is metaphysically impossible is the case. Since pretending that p seems to require pretending that ‘ p’ is true, the difficulty noted by Sawyer would probably stem from the fact that it is not clear whether one can pretend that p, if p is metaphysically impossible. In fact, in the case of a logical impossibility, it seems outright impossible to pretend that, say, a hula-hoop is both round and not round. However, the same does not seem to apply to the case of metaphysical impossibility. People seem to be able to pretend that what is metaphysically impossible is the case. For example, even if no dog could have been a horse in any metaphysically possible world, children sometimes pretend that their dog is a horse. However, Salmon’s account is not immune from problems. For example, the account seems to imply that any referring expression that occurs in an object-fictional sentence and does not refer to any concrete actual object refers to an abstract object. Thus, whereas ‘London’ and ‘Scotland Yard’ in Conan Doyle’s stories refer, respectively, to the city of London and to its police headquarters, ‘Sherlock Holmes’ brother’ and ‘Sherlock Holmes’ violin’ refer to two abstract objects. Of the first one, we pretend that it is the brother of the abstract object to whom ‘Sherlock Holmes’ refers (even if abstract objects do not have brothers); of the second, we pretend that it is the violin which belongs to the abstract object to whom ‘Sherlock Holmes’ refers (even if abstract objects do not own violins). Now, suppose that the following sentence occurs in one of Conan Doyle’s stories: (10) Sherlock Holmes shook his head. If ‘his’ in (10) means ‘Sherlock Holmes’s’ as it would seem, then, according to Salmon’s account, ‘his head’ in (10) must refer to an abstract object, for Sherlock Holmes is an abstract entity and, as such, has no head.8 More precisely, ‘his head’ must refer to an abstract object that we pretend to be the head of the abstract object ‘Sherlock Holmes’ refers to. If this was the case, however, Salmon’s account would have some bizarre consequences. For one thing, Salmon would have to admit that Sherlock Holmes and Sherlock Holmes’ head are two distinct abstract objects and that, in writing his stories, Conan Doyle created two distinct abstract artifacts: Sherlock Holmes and Sherlock Holmes’ head. An advocate of Salmon’s account might reply that this analysis misrepresents their view. According to Salmon’s account, we pretend that Sherlock Holmes is a person and, in so doing, we pretend it has a head. Thus, in (10), ‘his head’ refers to the head that we pretend Sherlock Holmes has. In other

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Page 261 words, we refer to his ‘pretended’ head. However, either Sherlock Holmes’ ‘pretended’ head exists or does not. If it does not exist, then the advocate of Salmon’s account could not refer to it without being in breach of the Axiom of Existence. If it is a real object, it is either an abstract object like Sherlock Holmes or it is a different kind of object. If it is an abstract object, then the view gives rise to the bizarre consequences I have mentioned above. If it is some other kind of real object, the advocates of Salmon’s account still owe us an account of what kind of object the head of a fictional character is. The Dualist Account Both the view that imaginary objects are possible concrete objects and the view that they are actual abstract objects seem to capture some of our intuitions about imaginary objects. However, neither of them seems to be entirely satisfactory. It is interesting to note that the two views seem to some extent complementary—one view seems to be successful where the other fails and vice versa. The view that imaginary objects are actual abstract objects seems to be successful in accounting for our intuitions that (some) external sentences are literally true and that (all) internal sentences are literally false. However, it does not seem to be able to accommodate the intuitions that (some) internal sentences are nevertheless ‘ in some sense ’ true. The view that imaginary objects are possible concrete objects, on the other hand, seems to be partially successful in accounting for the fact that some internal sentences are ‘in some sense’ true. However, it seems to take those sentences too seriously for, on that view, those internal sentences that are true are literally true not just true ‘ in some sense ’. Moreover, on that view, it is not clear how to vindicate the intuition that (some) external sentences are literally true. This complementarity, I suspect, stems from the fact that both accounts fail to recognize the ‘dual’ nature of imaginary objects and attempt to fully reduce them to either abstract or possible objects. In this section, I argue that it is possible to defend an account that explicitly acknowledges the peculiar dual nature of imaginary objects and, therefore, combines the main advantages of possibilist and abstractist accounts without sharing their respective problems. I call this account the dualist account . According to the dualist account, an imaginary object is an abstract object that stands for a possible object. ‘Sherlock Holmes’ refers to an abstract object: a fictional character that has real properties such as that of having been created by Arthur Conan Doyle in the late nineteenth century. This actual abstract object, however, stands for one of the many merely possible objects that are compatible with the description of Sherlock Holmes in Conan Doyle’s novels: an exceptionally brilliant detective who, among other things, lives at 221b Baker Street and smokes a pipe. Sherlock Holmes, thus, is not one of the possible objects that have all the properties that are attributed to him in Conan Doyle’s stories but only stands for one of them. According to the dualist account, external

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Page 262 sentences such as (2) are literally true because ‘Sherlock Holmes’ refers to an abstract object that was actually created by Conan Doyle at the end of the nineteenth century. Internal sentences like (1), on the other hand, are all literally false because ‘Sherlock Holmes’ refers to an abstract object and abstract objects do not smoke pipes nor do they have any other concrete property. Nevertheless, the abstract object Sherlock Holmes acts as a stand-in for one of the possible objects who, among other things, are detectives, smoke a pipe, and live at 221B Baker Street. So, even if (1) is literally false, we usually consider it to be in some sense true—true ‘by proxy’ so to speak. (This is not unlike when we talk of an actor as if he was the character he plays in a movie. Although our assertions are literally false of the actor they are in some sense true because they are true for the character the actor plays in the movie.) Analogously, we consider some of them false ‘by proxy’ as well (not only literally false) if they are false of all the possible objects that the fictional character Sherlock Holmes stands for. Finally, we consider them neither true nor false (in the nonliteral sense) if they are true of some of the objects Sherlock Holmes stands for and false of the others. Three remarks are in order here. The first two remarks concern ontological economy. Admittedly, the dualist account is ontologically inflationary for it requires that we include both abstract objects and possible objects in our ontology. However, this, in and of itself, is not a reason to reject the dualist account. We are not supposed to accept the dualist account because it is more ontologically parsimonious than the other accounts. We are supposed to accept it because, unlike the other accounts, it is descriptively adequate—it vindicates a large number of intuitions that seem to underlie the way we talk and think of imaginary objects. Ockam’s razor urges us not to postulate entities unless they are indispensable. So, if there was an account of imaginary objects that was as descriptively adequate as the dualist account but more austere ontologically, I think we should prefer it to the dualist account. In lack of such an account, however, we have to accept the dualist account with all its ontological baggage. The question of ontological economy should be raised only when two equally descriptively adequate accounts are available. The second remark is that the ontological baggage that comes with the dualist account may be less heavy than it could seem at first. In fact, the dualist account does not commit us to any specific view about abstract and possible objects and most philosophers agree that, since our language seems to be committed to both categories of objects, we need to have some account of talk of abstract and concrete objects. I think that, insofar as one has some descriptively adequate way of accounting for the ordinary talk of abstract and possible objects, they will be able to adopt the dualist account. The third remark concerns the standing-for relation. Here, I only want to note that the relation that holds between the abstract object that is the

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Page 263 character and the possible object for which it stands is not some mysterious relation. Most philosophers accept that some objects stand for other objects. For example, the name ‘Julius Caesar’ stands for Julius Caesar, and that this blue area on this map stands for Lake Ontario, and, that when we count five objects on our fingers, each finger stands for one of those objects. The relation that holds between the abstract and the possible object is just another instance of this familiar stand-for relation. If we had a satisfactory philosophical account of it in all these other cases, we would have an account that applies to our case. As I have mentioned, I take it that the best argument in favour of the dualist account is that it combines the respective advantages of possibilist and abstractist accounts without sharing their respective disadvantages. Consider the problems of the possibilist account first. According to the dualist account, ‘Sherlock Holmes’ refers to an abstract object that actually exists. It is therefore metaphysically impossible for it to be an actual person in some other possible world. This is not to deny that there are to be possible worlds in which there is a brilliant detective who lives in Baker Street, and so on, and whom the inhabitants of that world refer to as ‘Sherlock Holmes.’ It is only to deny that that possible person is Sherlock Holmes (where ‘Sherlock Holmes’ is used as a rigid designator and refers to the same object in all possible worlds). In that possible world, Sherlock Holmes (where ‘Sherlock Holmes’ is used as a rigid designator and refers to the same object in all possible worlds) simply does not exist—it is a possible abstract object. The dualist account is not even affected by the various problems arising from the identification of a specific imaginary object among the possible ones. In fact, Sherlock Holmes is not a possible object—it is an abstract object that stands for one of the many possible objects that fit Conan Doyle’s description of Sherlock Holmes. Thus, in order to determine what the referent of ‘Sherlock Holmes’ is, we do not need to exactly identify the possible object for which ‘Sherlock Holmes’ stands insofar as it stands for one or other of the possible objects that have all the properties that Holmes is attributed in Conan Doyle’s stories. Since the description of this object that can be gathered from Conan Doyle’s story is necessarily incomplete, it will be always to a certain extent underdetermined exactly for which possible object Sherlock Holmes stands. But the fact that we cannot determine exactly which possible object Sherlock Holmes stands for does not seem to be a problem insofar as we can identify the abstract object denoted by ‘Sherlock Holmes’ (that is, one of the fictional characters introduced by Conan Doyle in A Study in Scarlet in 1887). Consider now the objections against the two versions of the abstractist account, which I discussed in ‘Abstractist Accounts’. The first problem with van Inwagen’s account is that it cannot account for the fact that imaginary objects seem to have properties that are not ascribed to them in the works of fiction of which they are part. The dualist account, however, does not

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Page 264 seem to have troubles in accounting for this. In fact, if the topography of Victorian London is assumed to be true of the possible world that the fiction describes, then anyone who lives in Baker Street in that world lives closer to Regent’s Park than to Hyde Park. The dualist account also avoids the second problem faced by van Inwagen’s account. The expression ‘Sherlock Holmes’ refers to the same object in both metafictional and object-fictional sentences and in both internal and external contexts, namely, an abstract object. However, in internal contexts, this object acts as a stand-in for a possible object. Those sentences in a work of fiction which ascribe concrete properties to a fictional character are thus to be interpreted, within that context, as descriptions of the possible object for which the fictional character stands and not as directly ascribing those properties to an abstract object. In other words, sentences like (1) and (8) are false if interpreted as sentences about the abstract object but are true of the possible object for which the abstract object stands. The dualist account is also immune to the difficulty that faced Salmon’s account. In fact, according to the dualist account, ‘his head’ in (10) does not refer to Sherlock Holmes’s head but to the head of (one of) the possible object(s) for which Sherlock Holmes stands. The dualist account which I have sketched in this paper still needs to be developed as there are some phenomena (such as the possibility of incoherent fictions) that need to be accounted for. However, the dualist account has already an advantage over its rivals—it succeeds in accounting for a set of phenomena that are not jointly accounted for by any of them—and as such is a very plausible candidate for an account of imaginary objects. NOTES 1. An additional footnote in the reprint of (Strawson 1950) seems to suggest that also Strawson subscribed to such a view of imaginary objects. 2. A similar view has been proposed by Gilbert Ryle (1933). 3. Such a formulation of the paraphrase schema is due to Charles Crittenden (1991). Even if Crittenden is a critic of the mention account, his formulation of the paraphrase schema underlying the mention account seems to be the best available one. 4. Neither Meinong nor Parsons however seem to accept the combinatorial account as outlined here (or any other of the accounts I consider here for that matter). Both Meinong and Parsons seem to believe that nonexistent objects have no reality whatsoever and yet they can be referred to. If this interpretation is correct, they both reject the Axiom of Existence altogether and their position cannot be identified with any of the positions I consider here. 5. In presenting the combinatorial account, I roughly follow Terence Parsons’ presentation of his own account. Parsons specifies that the properties must be nuclear where, intuitively, being red or being 6 meters tall are examples of nuclear properties and being existent and being possible are examples of nonnuclear ones. This distinction is of paramount importance for the combinatorial account, but we will not need to clarify it further in this context.

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Page 265 6. Similar objections to the combinatorial account have been put forward by Daniel Hunter (1981). A different set of problems for the combinatorial account has been presented by Barry Smith (1980). 7. This seems to be the position actually held by Parsons. 8. A similar problem about creationism in fiction in general has been inspired by Takashi Yagisawa (2001). As I argue, I think that creationism in fiction does not necessarily fall prey of this problem. REFERENCES Crittenden, C. (1991) Unreality: The Metaphysics of Fictional Objects, Ithaca, NY: Cornell University Press. Currie, Gregory (1990). The Nature of Fiction, Cambridge: Cambridge University Press. Evans, G. (1982) The Varieties of Reference, Oxford: Clarendon Press. Hunter, D. (1981) ‘Reference and Meinongian Objects’, Grazer Philosophischen Studien 14: 23–36. Kripke, S. (1980) Naming and Necessity , Cambridge, MA: Harvard University Press. Lewis, David (1978). ‘Truth in Fiction’, American Philosophical Quarterly , 15: 37–46. Loux, M. J. (2002) Metaphysics: A Contemporary Introduction , 2nd edn, London: Routledge. Parsons, T. (1980) Nonexistent Objects, New Haven: Yale University Press. Quine, W. V. O. (1948) ‘On What There Is’, Review of Metaphysics , reprinted in W. V. O. Quine, From a Logical Point of View , New York: Harper and Row, 1953. Russell, B. (1905) ‘On Denoting’, Mind, n.s. 14: 479–93. ——. (1957) ‘Mr Strawson on Referring’, Mind, n.s. 66: 385–89. Ryle, G. (1933) ‘Imaginary Objects’, Proceedings of the Aristotelian Society , Suppl. vol. 12: 18–43. Salmon, N. (1998) ‘Nonexistence’, Noûs 32: 277–319. Sawyer, Sarah (2002). ‘Abstract Artifacts in Pretence’, Philosophical Papers , 31: 283–98. Searle, J. R. (1969) Speech Acts: An Essay in the Philosophy of Language, Cambridge: Cambridge University Press. Smith, B. (1980) ‘Ingarden vs. Meinong on the Logic of Fiction’, Philosophy and Phenomenological Research 41: 93–105. Strawson, P. F. (1950) ‘On Referring’, Mind, n.s. 59: 320–44. ——. (1959) Individuals: An Essay in Descriptive Metaphysics , London: Methuen. van Inwagen, P. (1977) ‘Creatures of Fiction’, American Philosophical Quarterly 14: 299–308. Walton, K. L. (1973) ‘Pictures and Make Believe’, Philosophical Review 82: 283–319. ——. (1990) Mimesis as Make-Believe: On the Foundations of the Representational Arts, Cambridge, MA: Harvard University Press. Yagisawa, T. (2001) ‘Against Creationism in Fiction’, Philosophical Perspectives 15: 153–72.

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Page 266 13 Russell’s Definite Descriptions de re Gregory C. Landini DEFINITE DESCRIPTIONS IN PRINCIPIA MATHEMATICA The pure (unapplied) formal language of modern classical predicate logic contains denumerably many predicate letters Fij (where i indexes the number of places of arguments and j the number of the predicate letter) together with denumerably many variables, and denumerably many individual constants t1, … , tn . Where the term t is free for x in A (a well-formed formula of the language of the theory), classical logic counts every instance of ( x) Ax → A( t/ x) as an axiom. In classical logic, a free variable must be given an interpretation in the semantics for the theory and hence the domain of any model for the theory must be nonempty. This makes the inclusion of individual constants innocuous. There is always at least one entity in the domain to provide an interpretation of the individual constants of the language—though we may have to assign all the constants to this entity. Principia Mathematica (1910) has a quantification theory which is classical. It counts as an axiom every instance of the schema   where y is a variable free for x in A.1 More carefully, for philosophical reasons it adopted a system in section *9 from which the quantificational system of section *10 was to be derived. The analog of *10.1 in the system of section *9 is this:   where y is free for x in A. Principia cites the presence of a free variable in *10.1 (and *9.1) as the source of its existential commitment to at least one individual. We find: The assumption that there is something is involved in the use of the real variable, which would otherwise be meaningless. This is made explicit

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Page 267 in *9.1, and in the proof of *9.2 which is the same proposition as *10.1. (Whitehead and Russell 1964:225) In 1919, Russell had a change of heart. In his Introduction to Mathematical Philosophy he thought it a ‘defect of logical purity’ that Principia ’s quantification theory has existential theorems concerning individuals (1953:201). A purist will want to countenance the empty domain since he thinks that a proper calculus for logic must be free of existential commitment to individuals. In the 1925 secondedition of Principia , Russell took some steps in that direction. He offered a new quantification theory without free variables called ‘section *8’. Central to Russell’s system are definitions of subordinate occurrences of quantifiers in terms of formulas where all quantifiers are initially placed. Quine’s Mathematical Logic (1940) offered a deductive system without free variables fifteen years later. In Quine’s system, the axiom schema   where y is a variable free for x in A, is replaced by its universal closure

  where z 1, … , zn are all the variables free in A. Quine’s system exploits vacuous quantifiers that cannot be eliminated. The vacuous universal closure of an existential formula is a thesis of the system, even when the formula is contradictory. Russell’s system of *8 does better. It works without vacuous quantifiers (226). But Russell fell short of generating a quantification theory inclusive of the empty domain. Quine succeeded. Adjusting his system of quantification theory without free variables, Quine was able to accommodate the empty domain (see Quine 1995:220–23). Ineliminable vacuous quantifiers again play a central role. Quine countenances   as a theorem, since he regards it as tautologous in form. Russell would not, since he counts it as an abbreviation for the existential formula:   Russell’s approach is very appealing. Russell’s system of *8 can be adjusted to accommodate the empty domain without appeal to vacuous quantifiers (Russell 1953:203 fn; see Landini 2005). When logical purity is our focus, it seems quite inappropriate to allow the language of logic to include individual constants. Of course, it is quite natural to accept individual constants into the language of an applied

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Page 268 theory couched within predicate logic, adjusting the axioms accordingly. For instance, if the applied theory is elementary astronomy, and we want to have ‘all planets revolve around the sun’ as a proper axiom, then we assign ‘ Pv’ for ‘ v is a planet of our Solar System’, and ‘ R( v, u)’ for ‘ v revolves around u’, and add the axiom ( x)( Px → R( x, t 1)). In the intended interpretation, t 1 will be assigned to the Sun. In ‘On Denoting’, Russell admonishes us not to do this. We are not to form applied theories by adding proper axioms containing individual constants. Returning to our example of astronomy, Russell would have us add the proper axiom:   The intended interpretation then assigns ‘ S’ to a property that singles out the sun uniquely. Karel Lambert has helped pioneer systems of ‘free logic’ which embrace both the purity of quantification theory and yet allow individual constants. In such systems, individual constants are ‘free’ of ontological import. For example, if t is a variable or individual constant free for x in A, Lambert’s free logic allows neither ( x) Ax → A( t / x), nor A( t / x) → ( x) Ax . Rather, with E as a primitive, Lambert’s system accepts every instance of the following:   Moreover, where t and tn are individual constants, the system has the usual axioms of identity theory even when these constants do not denote. The following are axiom schemata   Astronomers—Lambert is fond of supposing—used the name ‘Vulcan’ with impunity, discovering only later that there is no such planet to account for the perturbations in the orbit of Mercury (2003a: 14). Russell’s approach to forming an applied theory will have nothing of this. If astronomers used a name, there is something they named! Though Principia maintains there are no terms besides variables in logic, the work does endeavour steadfastly to make it appear as though ‘ ι xφ x’ is a term. Principia has: Whitehead and Russell write: ‘Whenever we have E!( ιxφ x), ιxφ x behaves, formally, like an ordinary argument to any function in which it may occur’

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Page 269 (174). It is important, however, not to be misled by appearances. Principia ’s ‘ ιxφ x’ is not a genuine term. Unfortunately, the status of ‘ ιxφ x’ is obscured by views concerning the general nature of definitions in Principia . There are two approaches to formal definition. On one approach, definitions are simply notationally convenient stipulations. The definiendum of a definition is simply a convenient notation for the definiens . On the other approach, definitions are axioms extending the notation of the language (in a noncreative and eliminable way). Lambert assumes that the definitions of Principia are axioms introducing new signs which are, however, noncreative and eliminable in the sense that any formula in which they occur is equivalent to a formula of the language in which they do not occur (11). On this later approach, the definiendum counts among the well-formed expressions of the formal objectlanguage.3 Assuming that definitions in Principia are axioms, Lambert holds that Russell has two distinct theories of definite descriptions: one in ‘On Denoting’, where definite (and indefinite) descriptive phrases of ordinary language are eliminated by paraphrase when transcribed into a quasiformal language; and another in Principia , where incomplete symbols are added by means of axioms to form a definitional extension of the formal object-language (11). As a result, Lambert finds that the theory of definite descriptions in Principia is ‘weaker’ than that of ‘On Denoting’ because it is open to ‘technical complaints’. Lambert’s technical complaints derive from his assumption that in Principia , ‘definite descriptions occur in positions in statements often occupied by (logically proper) names or variables, and that E! occurs in positions in statements occupied by predicates’ (3). On this basis, Lambert holds that the statements ψ a and ψ(ιxφ x) have the same syntactic form in Principia but have different logical forms since the definiens of the latter is a quantification via the definitional axiom:   Lambert concludes that Principia ‘violates the condition that formal languages not be misleading in their syntax with respect to logical form’ (10). This is mistaken. The definiendum of *14.01 is ‘[ ιxφ x][ψ(ιxφ x)]’ not ‘ψ ( ιxφ x)’. In fact, one may exploit the scope operator as a variable binding operator, writing the definition thus:   The sole reason Principia uses [ ιxφ x][ψ(ιxφ x)] rather than [ ιxφ x][ψx] is to allow the convenience of omitting scope markers when smallest scope is intended. Principia ’s omission of scope markers makes it appear as though definite descriptions are genuine terms. But the convenience is not part of the formal symbolism. In Principia ’s formal language ιxφ x is never in the

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Page 270 subject position of a predication without its scope marker. This dispenses with Lambert’s ‘technical complaints’. Realizing that ‘ ιxφ x’ is not a term and ‘ψ(ιxφ x)’ is not a well-formed formula helps immensely to clear up misunderstandings. Consider Principia ’s   Lambert objects that the syntax of ‘E!(ιxφ x)’ puts ‘E!’ in the predicate position of ‘ψ’ in the formula ‘ψ(ιxφ x)’. But we have just seen that there is no formula ‘ψιxφ x’ in Principia and so no position of ‘ψ’ for ‘E!’ to occupy. Consider   This is not akin to a universal instantiation involving a term ‘ ιxφ x’. Recall that universal instantiation in Principia is this:   where y is a variable free for x in A. Removing abbreviations from *14.18 we have:   There is no instantiation involving a definite description in Principia . There is no term ‘( ιxφ x)’. Admittedly, there are passages of Principia which seem to conflict with this. Lambert calls attention to Principia ’s   At first blush, this definition seems illicit unless definite descriptions are genuine terms. But Whitehead and Russell explain that the complete form of the definition is:   The existence of *30.01 does no harm to Russell’s thesis that definite descriptions are not terms of the language of logic. It is widely thought that Principia ’s definitions do not determine an order of application when ‘ ιxφ x’ is involved. For example Principia has:   What in Principia determines the order of application of definitions? Are we to get

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Page 271  

or is it to be

  Only one can be correct, since a given definiendum cannot have multiple definiens . This is yet another misunderstanding produced by thinking that ‘ ιxφ x’ can occupy a subject position in a formula. The solution is simple. There is no formula ιxAx = y of Principia , so it cannot be an instance of the definiendum of definition *13.01. Definitions formed with free variables apply only to genuine terms (free variables) of the language of Principia . One of the great benefits of Principia ’s treatment of definite descriptions is that it provides an apparatus for clarifying ambiguous uses of definite descriptions in ordinary language—uses that Russell warns are apt to generate (among philosophers) speculative metaphysics. Russell’s example from ‘On Denoting’ is ‘The present King of France is not bald’. Russell wryly points out that what is needed is not a Hegelian synthesis here (1905). It is rather that there are two scopes:

  The primary scope is false, for there is no present King of France. The secondary is true. The distinction is also handy when it comes to evaluating sentences such as:   Russell’s technique admonishes us to replace the ordinary name ‘Holmes’ with an ordinary definite description involving the uniqueness property H. We can then distinguish the following:   The first is the primary scope and clearly false. The second is true. There is always exactly one primary scope, but there can be several secondary scopes. Where C is a truth-functional context, every instance of the following is a theorem of Principia governing the scope of a definite description:  

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Page 272 When we have E!( ιxAx ), and a truth-functional context C(…), primary and secondary scopes are equivalent. For instance we have:

  If C is not a truth-functional context, then scopes will not always be equivalent, even when the antecedent condition E!( ιxAx ) is met. A celebrated example occurs when C(…) is (necessity). We know that, if we count Pluto and no others from the Kuiper Belt, the number of planets (of our solar system) is 9. We have E!( ιxPx ), where ‘ Px’ stands for ‘ x numbers the planets’. Thus, it seems true that   There is an x that numbers the planets and necessarily it is greater than 7. But it is false that   It is false that necessarily there is an x that numbers the planets which is greater than 7. The number of planets in the solar system is contingent. There could well have been some other number of them. As we see, the theory of definite descriptions has many applications both in philosophy and outside of it. The apparatus can be wonderfully clarifying. Consider its use in explaining the logarithmic expression ‘Loga ( x)’. The conceptual clarity of replacing occurrences of ‘Loga ( x)’ by ‘( ιv)( av = x)’ speaks volumes. Another application, of course, is in the notation of functions and limits. We have:   With the help of Weierstrass and the clarity of Russell the calculus can be free from the metaphysics of infinitesimals. DEFINITE DESCRIPTIONS AND PRINCIPIA’S ‘NO-CLASSES’ THEORY The conceptual clarity brought about by the theory of definite descriptions does not automatically bring with it ontological parsimony. Russell’s theory of definite descriptions has a straightforward application to the development of a theory of sets. But using the theory of definite descriptions to single out sets obviously does not avoid the ontological assumption of sets. The theory of definite descriptions can be employed by a typed theory of classes. But it is also perfectly compatible with Zermelo-Frankel set theory which adopts

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Page 273 type-free axioms for set existence that are not logical truths. The use of definite descriptions simply enables one to avoid class abstract terms of the form {z : Az}. In a naïve ontology of classes, we have a comprehension principle for classes which takes the membership sign ‘ ’ as a primitive of the language:  

where x is not free in A. The principle of extensionality is this:

  To see how to avoid class abstract terms of the form {y : Ay}, we have only to notice that we can apply Russell’s theory of definite descriptions and use contextual definitions of   for the class of all and only those y satisfying the formula A. We arrive at the following:   Since the extensionality axiom schema assures the uniqueness of the class, we need not trouble over the uniqueness clause in the contextual definition of the definite description. Thus, for primary scope, we have:   For example, we arrive at:   Of course, definite descriptions introduce scope distinctions and these are tedious. Quine offered contextual definitions for class abstract terms that parallel the results of the theory of descriptions but avoid the attending scope distinctions (see 1980:259). He has:   In any event, we see that the mere employment of a definite description instead of a class abstract term does not do away with an ontology of classes.

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Page 274 So how does this square with Russell’s autobiographical comment that the theory of descriptions ‘was the first step toward solving the difficulties which had baffled me for so long’ (1967:79)? The baffling difficulties, of course, pertained to paradoxes such as that of the class of all and only those classes that are not members of themselves. The solution was Russell’s ‘no-classes’ theory according to which ‘classes, are in fact, like descriptions, logical fictions or (as we say) “incomplete symbols”’ (1953:182). How then is Russell’s theory of definite descriptions related to Principia ’s ‘no-classes’ theory? We must first come to appreciate that Principia is indeed a no-classes theory! Unfortunately, reductiveidentity interpretations of Principia abound. For instance, Linsky writes that ‘Russell is indeed ontologically committed to some logical constructions, despite their expression by “incomplete symbols”’ (1999:117). On Linsky’s view, there are classes in Principia —they are just identified with attributes (propositional functions in intension). Linsky writes: Seeing that classes are not objects is enough to resolve the paradox of sets. But this is not to say that classes simply do not exist. To see that they aren’t objects is rather to see that they really play the same role as higher-order entities, propositional functions, to which type distinctions do apply…. The technique used is contextual definition, rather than explicit definition, but the effect is not any more of a wholesale ontological elimination than is the theory of definite descriptions. (130, 131) It is important to see that this is quite mistaken. Principia is genuinely a ‘no-classes’ theory. Classes are not identified with any entities of the ontology of Principia . If classes were to be assumed, they would be extensional entities. Classes of classes (of individuals) are identical if and only if they have exactly the same classes (of individuals) as members. In contrast, attributes of attributes that are coextensive may fail to be identical. To solve this problem, a reductionist identification of classes with attributes relies on the existence of an extensional attribute correlated with each attribute. Let φ be an attribute of φ. Suppose χ is such that ψ x ↔x φ x fails to assure that χφ ↔ χψ. This happens, for example, when the context χ(φ) is φ = F . Now observe that corresponding to χ there is the attribute Σ, namely,   We now have that for any attributes (of individuals) φ and ψ,  

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Page 275 It is tempting to imagine that Principia recovers extensionality by finding an attribute Σ to stand in for a class. This is a reductive-identity interpretation; a class is an attribute such as Σ. This is not what is found in Principia . Quite literally Principia maintains that there are no classes. It is not a reductive identity. Rather, it offers a reconstruction of the structure of a type-theoretical ontology of classes without the ontology. Principia replaces statements in the type-theoretical language of classes with statements in the language of predicate variables. It begins from the following type-stratified comprehension principle:   where φ( t 1 … tn ) is not free in A. No new comprehension assumptions are needed to emulate a typetheory of classes. Instead, we find the following definition:   This is a stipulative definition. The left-hand side is a convenient way of abbreviating the right. Thus it immediately meets the criteria of eliminability and noncreativity central to proper definitions. To emulate the presence of a relation of membership central to the type-theoretical ontology of classes, Principia introduces the definition:   Again, this stipulative definition introduces a notational convenience. To see how the two definitions work, observe that by employing the definitions one immediately gets an analog of the type-theoretical class abstraction:   Principia emulates this with the following theorem schema:   This theorem schema is forthcoming because the definitions yield   But observe that Abstraction applies only to entities of type t . It does not apply to classes of classes of entities of type t . In order to emulate classes of classes, Principia offers a new definition. Suppressing type indices, we find:

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  To understand the definitions, we must examine Principia ’s use of bound lower-case Greek. Observe that definitions involving lower-case Greek must be applied before any contextual definitions of classes or definite descriptions. We have already seen that definitions framed with genuine variables do not apply to incomplete symbols. Thus, definitions framed with incomplete symbols must be applied before definitions framed with genuine variables. For instance, we find   In this definition, α and β are schematic and stand in for ŷAy and ŷBy, respectively. One must apply *22.03 before applying *20.01. Observe as well that scope markers are not part of the definitions of bound lower-case Greek because Whitehead and Russell intend that the scope of the class symbol be interpreted in its narrowest possible occurrence in the instances of these definitions. To see this, let us illustrate the recovery of Abstraction for classes of classes of individuals. Principia has:   Restoring the scope marker, we have:   To see how the type-theoretical analog of Abstraction is a theorem, remove the lower-case Greek by *20.07 to arrive at:

 

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Page 277 Putting all this together, we have:   This is how Principia emulates a type-regimented analog of Abstraction for classes of classes of entities of type t . The nature of Principia ’s emulation of a type-theory of classes should now be clear. Principia is not advocating a reductive identity theory which identifies classes with attributes in intention. We observed that by typical ambiguity, *20.01 emulates classes of entities of all types. But since Principia classes are not entities *20.01 does not emulate classes of classes of entities. Indeed, a similar result applies to *20.08. Although *20.08 emulates classes of classes (of entities of all types), it does not provide for classes of classes of classes of entities. The pattern is nonetheless clear. It is quite straightforward to see that what is needed is a recursive definition with respect to emulating classes. This would be done as follows:

 

Where t < o, we have:

  Observe, however, that general recursive definition does not show how to emulate classes of relationsin-extension (relations e of individuals), nor does it emulate relationse of classes (of individuals) and the like. Principia discusses the emulation of relationse in its section *21. There is clearly an analogy between the introduction of the membership sign for classes and its definition for membership with relatione symbols. We find:   A better notation would have preserved the membership sign thus:   No special problems arise for relatione symbols. Interestingly, the emulation of heterogeneous relationse (that is, relationse between individuals and

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Page 278 classes, or between classes of different types, and so on) is a central feature of Principia . The importance of understanding Principia as a ‘no-class’ (and no-relationse ) theory cannot be over emphasized. A recent objection to Principia ’s treatment of class symbols illustrates the point. Linsky reports that in conversation, Martin observed that some classes in Principia are coextensive over classes and fail to be coextensive over attributes (2004:4401). For instance, let F and G be coextensive attributes of individuals that are not identical. By Principia ’s definitions we arrive at the following:   This appears to Linsky and Martin to be a difficulty. There is no genuine difficulty, however. A typetheory of classes (as entities) naturally makes no distinctions between entities of type t that are classes and those that aren’t. This is because it takes membership xt y( t ) as a primitive relation involving entities of type t . Martin is concerned that Principia should distinguish classes of entities that are classes of type t and classes of entities of type t that are not classes. In failing to do this, he thinks that Principia has ‘too many’ classes. In truth, Principia has no classes at all. We cannot import into Principia the primitive notion of membership from the typetheoretical ontology of classes. In particular, Principia ’s   does not say that the class ŷt (φ( t ) yt ) is a member of the class ŷ( t )( y( t ) = F ( t )), where membership is the unanalysable or primitive notion of a type-theory of entities that are classes.9 Martin would be justified in regarding Principia ’s emulation of the type-theory of classes as problematic if one could find formulas B and C that are such that:   But there are no such formulas in Principia .10 There are no classes in Principia’s ontology. Principia ’s discussion of classes is an eliminativistic theory, not a reductive-identity theory. The eliminativistic technique of Principia ’s ‘no-classes’ theory originated with a theory that preceded Principia —a theory Russell called the ‘substitutional theory’ of propositional structure. Interpreting Principia as a theory of types of attributes in intension has as a consequence that the structure of types has no direct connection to the theory of definite descriptions. But the historical relationship between Russell’s ‘no-classes’ theory and the theory of defi** nite descriptions is that the original ‘no-classes’ theory was a technique

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Page 279 for emulating a type theory of attributes (and thereby classes) from within a type-free theory of propositions. Logic in this theory is designed to get along without comprehension principles for attributes. Prior to Principia , Russell held that logic is the science of the structure of the logical objects he called ‘propositions’. Propositions are akin to states of affairs; some obtain, others do not obtain. The language is one-sorted. There are no special styles of variables; all the variables are individual (entity) variables— including the letters ‘ p’, ‘ q’, ‘ r’, and so on. Russell held that there is a logical relation of ‘implication’ holding between propositions, and he used the sign ‘ ’ for the relation. The sign is to be flanked by terms to form a formula. Thus, ‘ x y’ expresses a relation between objects x and y no less so than ‘ xRy’. In order to facilitate this, nominalizing brackets are needed to transform a formula into a term— we must have terms {A} that are not variables. Hence, we put ‘ x {y x}’ or more conveniently, ‘ x . . y x’. We have:

  The language permits quantification such as ‘( x)( x . . y x)’. This is quite unlike the modern predicate calculus, which takes the sign ‘→’ as a connective between formulas A and B to form a formula A → B . As Quine pointed out long ago, to write ‘( P)( P . → . y → P)’ is a use-mention confusion. (In this paper, we have taken care to use different symbols to mark the difference, reserving the symbols , ~ for the early Russellian use.) Propositions are intensional objects with finely grained identity conditions. Even logical equivalence is not sufficient for their identity. For instance, we can have {x . . y x} ≡ {x x} and not {x . . y x} = {x x}. There is an easy transformation of the type-theoretical language of predicate variables into the type-free language of substitution. To see this, let us compare the comprehension principle of a type theory of attributes with the comprehension principle for substitution.11 We have:

 

The parallel is quite close. The type symbol on a given predicate variable in Principia is related to the number of variables needed in the language of substitution. A few examples clarify this:  

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Page 280   The substitutional analog of type is the number of substitutions. For the type ( o) of an attribute of individuals, substitution employs two variables p and a . The expression p/ a ; x abbreviates the definite description ( ιq )( p/ a ; x! q), that is, the q differing structurally from p at most in that x occurs in it at just those places in which a occurs in p. Removing the definite description in ( S)1 in accordance with *14.01, we have:   For the next type, we illustrate with ( S)2. Here we find the type (( o)) involves the use of three variables and the definite description ( ιq )( s / t , w; p, a ! q) of the entity q differing structurally from s at most in that p and a occur in it in exactly those places in which t and w occur in s (respectively). Removing the definite description in ( S)2 we arrive at:   The use of definite descriptions of propositions resulting from substitutions builds type into formal grammar. That is, there are no types of entities in the substitutional theory. Types of attributes are emulated by means of its constructions. In this way, types become part of logical grammar. The typefree substitutional logical reconstruction that emulates a typetheory of attributes in intension embodies a type structure. The substitutional theory of classes develops in a way that parallels that of Principia . More accurately put, Principia develops in a way that parallels the constructions of substitution. Indeed, we can translate anything in Principia’s primitive notation into substitution without much ado.12 On an objectual reading that makes the predicate variables of Principia range over a type-regimented ontology of attributes in intension, Russell loses his motivation for the ‘no-classes’ theory. One may as well embrace a typetheoretical ontology of classes. A type theory of attributes in intension seems every bit as ad hoc as a solution of the paradox as a typed theory of classes. Russell knew this, and it is prominently on his mind when, in 1907, during the era of his substitutional theory, he wrote: ‘Types won’t work without noclasses. Don’t forget this’ (1907). By ‘no-classes’ he meant that some construction must be found that builds the structure of type distinctions into logical grammar.13 A naïve formal system which embraces Russellian propositions together with bindable predicate variables (even restricting them to predicate positions alone) is contradictory. The contradiction is simple. Consider the property φ such that:

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Page 281   We get the contradiction: φ({φ x xx}) ≡ ~φ({φ x xx}). Russell knew of this contradiction in 1903. A paradox very similar to it appears in Appendix B of Principles and is discussed in letters to Frege (Landini 1992). At first, Russell wondered if the lesson of this sort of paradox is that there are logical paradoxes that type theory cannot address. But the paradox did not dissuade him in 1905 from embracing a type- and order-free theory of propositions, for he had then rejected bindable predicate variables in favour of his substitutional theory. Interestingly, in that same year Russell did consider an Epimenides paradox of propositions (1994). The paradox did not detain him. It involves essential appeal to contingent psychological notions of ‘assertion’ or ‘belief’ which he then viewed as outside the purview of pure logic. Matters were not so sanguine in 1906, when Russell discovered a paradox unique to his substitutional theory of propositional structure.14 Comprehension of propositions in substitution yields the following:   This yields:   Investigating Liar paradoxes of propositions to facilitate ideas towards solution, Russell reluctantly came to conclude that an ontological commitment to propositions requires that they be ramified into a hierarchy of orders.15 That is, the language of the substitutional theory would have to be regimented with order indices on its variables. The language now requires the restriction that fixes the order m of a term of the form {A}m . The restriction is this: if n is the highest order subscript of any variable v (bound or free) in A, then m = n if v is free and m = n + 1 if v is bound. Of course, in an identity statement the orders must be the same, and universal instantiation must respect order. If we demand:   The paradox cannot go through. Similarly, consider the following version of the Liar:

Regimenting the language by orders, we have

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Page 282   Ramification thus avoids the contingent propositional liar. But ramification is the devil—as Russell came to realize. Without mitigation, it destroys the impredicative quantifiers that are essential to mathematics. In the end, he abandoned his ontology of propositions and with it his substitutional solution of the paradoxes plaguing logicism. DEFINITE DESCRIPTIONS AND INTENTIONALITY Outside of the eliminativistic aims of the constructions of the substitutional theory, Russell’s theory of descriptions is perfectly compatible with Zermelo-Frankel sets. Indeed, it is every bit as compatible with Homeric gods, nonexistent objects and even a ‘Meinongian jungle’16 of incomplete and impossible objects. The theory does, however, undermine a central impetus in natural language for postulating entities of such a jungle. It untangles the old conundrum that we seem to refer to (or think about) nonexistent entities, if only to affirm their nonexistence. On Russell’s view, we cannot refer to or think about what is not. Rather we refer to and think about everything. We do this (admittedly by an as yet unresolved mystery) by employing quantification. We do not refer to Pegasus in affirming his nonexistence; rather, we think that everything fails to be uniquely winged and a horse. Ontological commitment, Quine was fond of saying, comes only through the bound variables of quantification. The doctrine is shared by Russell.17 What then is a Meinongian? If one’s motivations for postulation of nonexistent objects lie in metaphysical postulations grounding causal possibilities of nature law, logic, logical modalities and the like, one is not, ipso facto, a Meinongian. Quite distinct motivations underly the adoption of Meinongian ontologies. The differences lie in the motivations, not the objects. I propose that we define a Meinongian as one whose motivations for postulating nonexistent particulars stem from the quest to form a theory of intentionality. With a resolve and bravery that is exemplary, Meinong confronted the phenomenological datum that a thought can point towards an object other than itself. Focus on intentional contexts led him to the following lesson: If a thought points to an object so and so, there is an object so and so to which the thought points. To state what object a referential mental act is directed towards seems to require that there is an object —if only one that is intentionally inexistent. Consider, the following:

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Page 282   Ramification thus avoids the contingent propositional liar. But ramification is the devil—as Russell came to realize. Without mitigation, it destroys the impredicative quantifiers that are essential to mathematics. In the end, he abandoned his ontology of propositions and with it his substitutional solution of the paradoxes plaguing logicism. DEFINITE DESCRIPTIONS AND INTENTIONALITY Outside of the eliminativistic aims of the constructions of the substitutional theory, Russell’s theory of descriptions is perfectly compatible with Zermelo-Frankel sets. Indeed, it is every bit as compatible with Homeric gods, nonexistent objects and even a ‘Meinongian jungle’16 of incomplete and impossible objects. The theory does, however, undermine a central impetus in natural language for postulating entities of such a jungle. It untangles the old conundrum that we seem to refer to (or think about) nonexistent entities, if only to affirm their nonexistence. On Russell’s view, we cannot refer to or think about what is not. Rather we refer to and think about everything. We do this (admittedly by an as yet unresolved mystery) by employing quantification. We do not refer to Pegasus in affirming his nonexistence; rather, we think that everything fails to be uniquely winged and a horse. Ontological commitment, Quine was fond of saying, comes only through the bound variables of quantification. The doctrine is shared by Russell.17 What then is a Meinongian? If one’s motivations for postulation of nonexistent objects lie in metaphysical postulations grounding causal possibilities of nature law, logic, logical modalities and the like, one is not, ipso facto, a Meinongian. Quite distinct motivations underly the adoption of Meinongian ontologies. The differences lie in the motivations, not the objects. I propose that we define a Meinongian as one whose motivations for postulating nonexistent particulars stem from the quest to form a theory of intentionality. With a resolve and bravery that is exemplary, Meinong confronted the phenomenological datum that a thought can point towards an object other than itself. Focus on intentional contexts led him to the following lesson: If a thought points to an object so and so, there is an object so and so to which the thought points. To state what object a referential mental act is directed towards seems to require that there is an object —if only one that is intentionally inexistent. Consider, the following:

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Page 283 Ponce de Leon searches for the fountain of youth. Thus, there is something for which Ponce de Leon searches. The conclusion seems to be reached by existential generalization alone. But, in fact, there is no fountain of youth; there is nothing for which Ponce (in his present act) is searching. A Meinongian concludes that existential generalization should yield that there is something for which Ponce’s intentional act is aimed —that is, a fountain of youth, albeit only as an ‘intentionally inexistent’ fountain of youth. But there is no genuine term ‘the fountain of youth’ in Russell’s logic. The inference from premise to conclusion cannot be an instance of A( t / x) → ( x) Ax . How can a Russellian even represent the premise? Obviously, it will not be possible to construe the premise as:   From this, the conclusion that there is a fountain of youth would follow. The Russellian must resort to paraphrase to capture the intentional import of ‘searches’. But it is far from obvious how paraphrase together with the Russellian account of definite descriptions untangles the conundrum. What sort of ‘objects’ are Meinongian objects of intentionality? One might imagine grades of ontological status, ‘existence’, ‘being’ and so on to explain intentional inexistence. But this was not Meinong’s view. Maintaining an independence of sosein (being so) from sein (existence), Meinong held that there are objects of which it is true to say they are not. By this he meant that phenomenology should be ontologically free and he thought that logic must follow suit. Russell was sympathetic with the epistemic realism embodied in Brentano and Meinong’s thesis of intentionality, but he bridled at Meinong’s thesis that logic must be formed in such a way that the variables of quantification involved in ‘there is’ do not make an ontological commitment. A proper characterization of Meinongianism must be sensitive to the foundational motivations for Meinongian object theory. Russell’s motivations in ontology were not to provide an account of intentionality or reference. The difference is nicely illustrated by examining an argument by Lambert that Russell’s rejection of Meinong’s theory of objects was unprincipled and arbitrary.18 The argument runs as follows. In ‘On Denoting’, Russell criticized Meinong for ‘infringing the law of contradiction’ by holding that ‘every grammatically correct denoting phrase stands for an object ’ (107). Lambert observes that with ιxAx as a genuine referring expression for which the axiom   holds, one can derive A( ιxA ) from the very plausible principle MD:

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Page 284   Taking the class abstract notation {z : Bz} to abbreviate the definite description ( ιx)( y x ↔yBy ), we see that schema A( ιxAx ) readily yields naïve class abstraction: y ( ιx)( y x ↔yBy ) ≡yBy . (Simply let Aξ be y ξ ↔yBy .) Lambert concludes that Russell is arbitrary in having a negative attitude towards Meinongian object theory and yet a positive attitude towards a logical conception of a class (2003b). Lambert maintains that Russell’s paradox of the naïve theory classes and Russell’s paradox for naïve Meinongian theory of objects both stem from a common source—the naïve assumption that A( ιxAx ). Lambert’s argument assumes that Russell’s theory of definite descriptions is part of a theory of reference. But no theory of reference provides a ‘common source’ underlying both naïve class abstraction and Meinong’s account of intentionality. In fact, it is far from clear that a viable theory of intentionality requires a Meinongian theory of objects of thought. Russell’s logicism, on the contrary, requires a reconstruction and rehabilitation of the logical notion of a class. Russell’s theory of definite descriptions was not intended as part of a theory of reference or intentionality. In this respect, it is unfortunate that Russell’s theory of definite descriptions is often regarded as a part of the ‘linguistic turn’ in philosophy focusing on language, communication and reference. What motivates Meinongians is the problem of understanding intentionality. Caution is in order, however. There is significant disagreement as to what field the investigation of intentionality belongs. Does the analysis of intentionality belong to empirical psychology, cognitive science, theory of causation, biochemistry, philosophy of mind? Is the theory of intentionality a part of the philosophy of logic itself? With an ontology of propositions construed as necessary entities of logic, Russell found it hard to resist pressing them into service of his revolt against Idealism. Russellian propositions, as states of affairs containing physical objects themselves, are directly apprehended as objects of propositional attitudes. This is a comforting ally of Realism. But we must not be misled. The notion of a Russellian proposition, as a state of affairs, is not the notion of a ‘proposition’ as a meaning—an entity posited to explain what is preserved in translation of one language into another or what is conveyed in acts of communication and reference. Russellian propositions are intensional entities, not intentional entities. This explains Russell’s insistence that in spite of its snowfields, Mt. Blanc is a constituent of the proposition ‘Mt. Blanc is white’ (see Frege 1980:163, 169). What is incredible is the thesis that a ‘meaning’ (intentional entity) contains a mountain with all its snowfields. That is surely absurd, but Russell never held it. In Principles , Russell advanced a theory according to which there are denoting concepts which are ‘about’ (other) entities. It will therefore be surprising to be told that the problem of intentionality was not driving

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Page 285 Russell’s early ontology of denoting concepts and propositions. Aboutness seems to concern intentionality. According to Principles , the denoting concept ‘ Every man’ is about every man. Indeed, it is in virtue of denoting concepts that Russell is able to assure that thinking about the infinite is possible. To think that every even natural number greater than two is the sum of two primes does not require the impossible mental act of entertaining infinitely many thoughts—one about each natural number. Instead, we entertain the proposition: Every even natural number greater than two being the sum of two primes which contains the denoting concept ‘ every even natural number ’. Russell explains that denoting concepts provide ‘the inmost secret of our power to deal with infinity’ (1964:73). Comments like these make it appear as though denoting concepts and propositions are advanced by Russell to provide a theory of meaning. In truth, denoting in Principles is a purely logical relation; it is part of the ontology of pure logic. As such, denoting concepts and propositions are postulated by Russell quite independently of his epistemic theory or his conception of mind. Russell’s early logic was a theory of propositional structure. He required an account of the constituents of those propositions indicated by nominalized formulas which are formal implications—formulas containing bound variables of the new quantification theory of Peano (and Frege). The theory of denoting concepts was Russell’s attempt to form a bridge between the Medieval/Aristotelian logic of categoricals and the bound variables occurring in the formal implications of quantification theory. Russellian propositions are intensional objects, not intentional objects. Principles spoke of those propositions containing denoting concepts (‘as concept’) as being about (in a logical and nonpsychological sense) objects. It is far from clear that this is the ‘aboutness’ of an intentional act. Russell came to abandon denoting concepts in 1905. The theory of denoting concepts of Principles faced ‘an inextricable tangle’. Russell could not solve the problem of what is to be the structure of propositions involving denoting concepts. Socrates (the person) can only occur in a proposition in one way. He occurs in the proposition Socrates’s being human as logical subject of the proposition. The property humanity, on the other hand, is capable of what Russell calls a ‘two-fold occurrence’ in a proposition. It occurs predicatively (or ‘as concept’) in the proposition Socrates’s being human and occurs as term in Humanity’s belonging to Socrates . Like properties, denoting concepts have a two-fold capacity. In the proposition: The centre of mass of the Solar System’s being a point the denoting concept ‘ The centre of mass of the Solar System ’ occurs in away akin to a predicative occurrence. It occurs as logical subject in the proposition:

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Page 286 ‘ The centre of mass of the Solar System ’ being a denoting concept. To display the difference, as we have above, one needs to use inverted commas to act as a genuine proper name (of a denoting concept). If there are no such genuine names, then we cannot display the ontological difference. But the difference remains. The problem is not about how to display it. The problem is that Russell could not devise a theory of propositional structure adequate to the two-fold occurrences of denoting concepts.19 Consequently, he abandoned the theory of denoting concepts in his article ‘On Denoting’. Russell still maintained, however, that Logic is the science of propositional structure. He had to concede that the constituents of propositions named by nominalization of formulas (formal implications) containing the bound variables of the new quantification theory could not be explained by means of the theory of denoting concepts. The bridge offered in Principles had its foundations in clay. When it collapsed, Russell was left with no solution of the problem of the ontological constituents of general propositions. By 1906 the problem was moot. Only those formulas that are quantifierfree can be nominalized to form singular terms for propositions. There are no general propositions—though there are plenty of general sentences that are meaningful. Propositional attitudes such as belief will have to be reconstructed—at least where belief of a ‘general proposition’ is concerned. By modern lights, ontological commitments in logic are questionable. Modern logic has been jaded by the discovery of paradoxes involved with the assumption of purely logical objects. But one should not fear that contradictions concerning ‘meanings’ will arise within formal theory for logic which embraces an ontology of Russellian propositions. There is no reason to be concerned over paradoxes such as that of a person S who believes that every proposition he now believes is false (and all of whose other beliefs are indeed false). Such a paradox is not part of pure logic. To be sure, on Russell’s account of logic as the science of propositions, every well-formed formula of the formal theory of logic can be nominalized to form a term. But this certainly does not assure that expressions such as ‘believes’, ‘asserts’ and such expressions of propositional attitudes are part of the formal language of the calculus for pure logic. Quite clearly they are not. They are part of an applied theory of psychology or philosophy of mind and reference. An ontology of Russellian propositions certainly does not require that belief be regarded as a ‘propositional attitude’ in a literal sense, that is, a relation of a mind to a Russellian proposition. Modern conceptions of logic will have nothing of Russellian propositions as logical objects. Indeed, it will not accept any intensional entities as a part of the ontology of logic. On the modern conception, pure logic should be ontologically free. Modern predicate calculi allow only individual variables as bindable. This means that the seemingly logical assertion that every x has some attribute will become a thesis of a nonlogical theory—a theory

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Page 287 of properties. Is logic captured by the modern predicate calculus? Some say that it is not. Indeed, some (Platonists, let us say) offer a calculus for logic that embraces logical objects—intensional entities such as properties and relations (that is, attributes). Attributes are intensional in the sense that coexemplification is not sufficient for their identity. (Renate and cordate are typical examples, for while they are coexemplifying—one has a kidney if and only if one has a heart—the attributes are not identical.) As objects, attributes can be exemplified by others—for example, goodness exemplifies the property of abstractness. Not everyone among us is a Platonist—not the least of which is because unbridled Platonism is inconsistent. Russell demonstrated this conclusively with the contradiction of the attribute that an attribute φ has if and only if φ does not have itself. Platonism is on the skids. But this does not force the position that logic is captured completely by the predicate calculus. There are those, shall we say Fregeans, who reject Platonism in favour of a conception according to which attributes are logical entities but not logical objects . (This may be paired with the thesis that there are no logical objects—logical objects being apt to produce contradictions.) Predicate variables must remain in predicate positions in the grammar of the calculus. Only object expressions can occupy subject positions. In this Fregean conception, quantification such as ( φ)φx is sui generis . No paradoxes arise in such a theory. On the Fregean theory, attributes live in the configurations of objects, and are not themselves objects for which identity or nonidentity relations hold. The expression ‘φ = ψ’ is illicit for this puts a predicate variable in a subject position. The Fregean will have to be content with φ y ↔y ψ y. How then is one to express what the Platonist so easily writes as ‘the attribute φ exemplifies the property of being exemplified by something’. The Fregean will have to be content with ‘( x)φ x’. But the Fregean can capture a version of the Platonist’s ‘φ exemplifies some property’ in a way that keeps the predicate expression ‘φ’ in a predicate position. He can write ‘( M ) Mxφ x’. The subscripted ‘ x’ in ‘ Mxφ x’ is to remind us that we are dealing with a form such as ‘( x)φ x’ where a bound individual variable is involved. Similarly, the Fregean can recover a version of the Platonist locution ‘the property of being exemplified by some object has the property of being such that every property exemplifies it’. The Fregean writes, ‘(φ)( x)φ x’. A Platonist will write that the property of being exemplified by some object has some property. The Fregean can write ‘( Σ)(Σφ( x)φ x)’. The theory of intentionality is not part of the philosophy of logic. Meinongian objects transcend the logical objects postulated as part of a philosophy of logic—including objects such as logically (or causally) possible worlds and their inhabitants. We may legitimately call upon intensional objects in an account of intentionality. But the challenge for Russellians (and anti-Meinongians) with a ‘robust sense of reality’ is to do justice to the data of intentionality without Meinongian objects. The challenge is daunting because the problem is little smaller in scope than the problem of

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Page 288 giving an adequate account of the mind itself. But this makes the research programme even more interesting. PUZZLES ABOUT PROPOSITIONAL ATTITUDES In ‘On Denoting’ Russell illustrated how his new account of descriptions can solve puzzles concerning propositional attitudes. One of his examples concerned the following argument. The conclusion seems to follow from the premises by application of logical principles. Yet the conclusion is false and the premises are true. We have:   To assess the logical form of the argument, and thereby determine whether its conclusion follows validly from the premises, we must first transcribe the argument into the formal canonical language of logic. To transcribe the ordinary language argument, Russell has:   Russell’s diagnosis of the puzzle is that there is a ‘logical mirage’ produced by the ordinary language use of the expression ‘the author of Waverley ’. This is not a genuine term of formal logic. Transcription of the argument into the language of logic reveals that the law of identity does not apply. The inference to the conclusion assumes that the following is an instance of the law of identity,  

According to Russell, the above is not an instance of the law of identity. The law is this:

  where A* is just like A except that y replaces one or more free occurrence of x in A and y is free for x in A. We cannot instantiate the quantifiers of the law of identity to ‘the author of Waverley ’ and ‘Scott’ since there are no

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Page 289 such terms in the formal language of Principia . Quantifiers always instantiate to variables—variables are the only terms. The sentence ‘George IV wished to know whether the author of Waverley is Scott’ does not lend itself naturally to an ambiguity of scope of the definite description ‘the author of Waverley ’ because it is clear in Russell’s example that George IV has the concept of authoring Waverley in mind.20 But certainly primary scopes concerning definite descriptions in the context of propositional attitudes are possible. Moreover, primary and secondary occurrences will not always be equivalent, even when the description is satisfied. For example, it may well be true that there is exactly one morning star and a person S who believes it to be bright, that is,

  It is false that S believes there is exactly one morning star and that it is bright. The first scope is a de re ascription of belief to S. The de re reading does not attribute to S the concept ‘morning star’. S may well have a quite different concept in mind in his belief about Venus. It is the person making the ascription that has this concept ‘morning star’ in mind, not the person S to whom the belief is ascribed. In a de re ascription, we may well not know what concept is used by the person to whom the belief is ascribed. Such de re ascriptions of propositional attitudes are certainly captured by Russell’s theory of definite descriptions. There is a problem, however, with pairing de re ascriptions with Russell’s early thesis that propositions are objects of propositional attitudes. At the time of publishing ‘On Denoting’, Russell held that propositions are the direct objects of the attitudes. Using our nominalizing brackets to mark terms for Russellian propositions, one may ask, what proposition is the object of S’s belief in the de re reading

  Since only Venus (the planet) satisfies the description, the proposition ascribed to S here is {Bv }, that is, {Venus is bright}. But this is certainly not intended by our de re ascription. The de re ascription intends to leave open how S refers to Venus—it certainly should not determine that S has the state of affairs {Venus is bright}, containing Venus itself, before his

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Page 290 mind. Rather, we want to say that S refers under some description or other and, though we don’t know which, we do know that that description picks out the morning star. We can, of course, avoid the difficulty if we rid ourselves of the early Russellian position that belief is a relation to a proposition. We can drop our nominalizing brackets and hold that the de re ascription   does not represent the structure of the cognition of the person S. This approach to quantification de re into propositional attitude contexts relies on a semantic distinction between ‘belief of … ’ and ‘belief that … ’. The distinction is not captured in the syntax of the ascription. Moreover, such a distinction must rely on pragmatic matters sensitive to the context in which the ascription is made. Either way, the distinction is out of sorts with Russell’s ‘logical mirage’ solution in ‘On Denoting’. Russell was surely after a syntactic solution, not a semantic/pragmatic distinction between ‘belief of … ’ and ‘belief that … ’ (and like distinctions for other propositional attitudes). A new application of Russell’s theory to de re ascriptions of propositional attitudes is needed if we are to preserve Russell’s assumption that propositions are objects of the ‘propositional attitudes’. A solution to the problem readily suggests itself. Quantification de re into propositional attitudes must make perspicuous the conceptual cognitive structures employed by the person having the propositional attitude. We can do this if we permit the language to include bindable predicate variables. We have:   Expanding the scope marker this is:   Our de re belief ascription asserts is that S employs some (unknown) concept φ in referring descriptively to the morning star. In this way, the Russellian can embrace quantification de re without relying on a semantic/ pragmatic distinction between ‘belief of’ and ‘belief that’. It is therefore attractive as a way of preserving the ‘logical mirage’ (or syntactic) solution that Russell was after. The fundamental maxim is this: In de re quantification into propositional attitude contexts, one must display the relevant structure of the cognition of the person having the attitude. On this approach, we have the following chart of forms for belief expressions:

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Page 291   No individual variable may occur free inside the context of a propositional attitude. Only predicate variables may occur free in such contexts. The maxim wrought from our examination of Russellian scope distinctions of definite descriptions is that quantification de re into propositional attitudes must display, to an appropriate degree, the structure of the cognitive state of the person engaged in the attitude. If we pair this with the thesis that the structure of cognition is quantificational, we arrive quite naturally at the thesis that the structures that must be represented in de re quantification into propositional attitudes are akin the Frege’s hierarchy of levels of concepts. The account merges Frege’s notation of levels of functions with Russell’s theory of definite descriptions. Frege’s hierarchy of levels must not be conflated with a hierarchy of types of attributes in intension. In a type of the form ψ( t )(φ t ) the attribute ψ( t ) is understood as unstructured. (An example might be redness exemplifying the property of being abstract.) Fregean hierarchy of levels is a quite natural feature of structure of conceptual processes—assuming that quantification structures of government and binding are essential to the cognitive processes underlying reference and predication. The Fregean hierarchy of types of quantifier concepts is founded upon the notion that concepts must fit together so that concept expressions always occur in predicate positions. As Frege puts it, level n and level n + 1 concepts ‘mutually saturate’. Let us adopt the following notation for the levels of concepts. We have Mxfx the mutual saturation of a first-level concept fx , with a second-level concept Mxφ x which can involve quantifier binding an individual variable. Similarly, Σφ[ Mxφ x] represents the mutual saturation of a second-level concept Mxφ x with a third-level concept Σφ[ξ xφ x] which may involve a bound firstlevel concept variable. This notation keeps concept expressions in predicate positions, and thus the hierarchy of levels of concepts is made perspicuous in the notation. By means of the Fregean expression of levels, we now have the following new expressions of our language of propositional attitudes:   The letters φ, M , Σ are variables and so may be bound de re by quantifiers. We can go further in this way, generating new variables for higher levels of concepts. This account of de re quantification into propositional attitude contexts suggests a straightforward solution of contingent liar paradoxes and like paradoxes of propositional attitudes. Frege’s hierarchy of levels is a natural component of our demand that de re quantification into propositional attitude

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Page 292 contexts give a syntactic representation of the structures employed in the process of cognition. Once such structures are in place, all attempts to formulate a liar paradox (of propositional attitudes) fail. In short, the hierarchy of levels (akin though it is to simple type theory) blocks paradoxes without ramification. Of course, the first step is to abandon Russellian propositions as entities to which propositional attitudes such as belief are related. The form ‘ s bel p’ with ‘ p’ as a variable is illicit. This variable does not display the cognitive structure of the belief. The general solution is that all contingent paradoxes of propositional attitudes involve such illicit de re quantification. Consider the following attempt to recover a contingent propositional liar with the modern connectives (without assuming a theory of Russellian propositions). We have:

One arrives at the contradiction: θy ↔y ¬θy. At first blush it may seem that our strictures on quantification de re into propositional attitudes do not block this contingent paradox. But the source of paradox (B) lies in a misconception about the mind’s ability to control the objects of its referential acts. Assumption #b is based on the reasonable intuition that we can determine our minds to refer to a particular object (insofar as that object satisfies a concept employed in a referential act of cognition). But upon reflection that is not what #b asserts, for ψ is not an object of S’s belief. The property ψ is used in the intentionality of the belief, in directing the belief to a specific object. Consider:

 

 

Suppose that we also have:

  Both beliefs are then cases of S having a belief about the entity a , via a definite description. But the concepts P and Q are not coextensive. For this reason, assumption #b should be rejected as impossible. On the basis of these successes, we have strong reason for thinking that paradoxes of propositional attitudes can be solved by a form of simple type-stratification—our stratification of Fregean levels together with our strictures governing quantification de re into propositional attitudes. Meinongians take intentionality as the raison d’etre for postulating inexistent objects of thought. Their mistake, as a Russellian would see it,

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Page 293 is in their failure to imagine quantificational logical forms for intentional attitudes. They are misled by the surface grammar of natural language. Consider again the puzzle: Ponce de Leon searches for the fountain of youth. Thus, there is something for which Ponce de Leon searches. Searching is an intentional act. It is quite distinct from non-intentionally finding (happening across) something. The logical form of the surface grammar makes it appear to be the same as that of the following argument. Ponce de Leon finds the fountain of youth. Thus, there is a something that Ponce de Leon finds. The logical form here is this:   If Ponce finds the fountain of youth, then there is an object that he finds. In contrast, intentionally finding (searching and finding what one searched for) and searching (which leaves open whether one finds what one is searching for) concern the intentionality of cognition. Thus, cognitive structures are now involved in ascriptions of such intentional acts. How shall the Russellian capture this? There is a scope ambiguity in the statement ‘Ponce de Leon searches for the fountain of youth’. The person ascribing the intentional state may be the one who uses the description ‘the fountain of youth’ and who aims only to ascribe to Ponce the use of some descriptive concept co-referential with it. On the other hand, the ascription may be read as saying that the descriptive property fountain of youth is employed by Ponce in his acts of searching in question. There are degrees of de re ascription in this case. Consider this:   Explanation of this unusual formula is in order. We have seen that in quantification de re into propositional attitudes we must represent (to an appropriate extent) the structure of the cognition of the person to whom the propositional attitude is ascribed. The idea is naturally allied to a theory according to which Ponce’s mind is (among other things) a system of interconnected quantificational structures. These quantificational structures are abstract entities which are exemplified by or implemented by physical processes of a sort that remains mysterious.22 We saw that the quantificational structures that constitute cognition can be modeled by means of the

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Page 294 Fregean language of levels of concepts. The Fregean language exploits the subscripted variables to indicate the presence of bound variables involved in those quantificational structures. That is why delta occurs as subscript to ‘Ponce’. The expression   says that Σ is a searching routine occurring among the quantification structures of Ponce’s mind. The clause, Σφ[ Mz φ z ], says that M is a quantificational structure involved in Σ. Thus the clause,   says that the quantificational concept ‘the fountain of youth’ is involved in Ponce’s searching routine Σ. This interpretation of the ascription does not assure that Ponce himself employs the concept Y (fountain of youth) in his cognitive act of searching. Nor is it committed to their being a fountain of youth. A de re ascription that does commit the person making the ascription to the existence of the fountain of youth is this:   From here, of course, we can existentially generalize to arrive that the conclusion that there is some object for which Ponce was searching, that is,   To make our ascription to Ponce de dicto, we have:   This says that Ponce himself uses the concept Y (fountain of youth) in his cognitive acts of searching in question. I have no doubt that this is yet too simplistic. What makes intentional ascriptions and quantification into propositional attitudes so difficult is that they require an adequate philosophy of mind. There is little consensus on what such a philosophy should look like. But the point should be made. Russell hoped that his theory of descriptions shows how to dissolve the ‘logical mirages’ found in puzzles and contingent paradoxes of quantifying into propositional attitudes. His hope was to find a syntactic (structural) representation of the logical forms involved. By uniting Fregean levels of quantifier concepts with Russell’s quantificational approach to definite descriptions, we can imagine some of the needed logical forms. Contingent Liar paradoxes of propositional attitudes are solved in this theory without ramification.

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Page 295 NOTES 1. More exactly, it adopted a ramified type-stratified analog. 2. The symbols for the logical connectives here differ from those in Principia for reasons that will be explained later. 3. Lambert’s account of definitions in Principia cannot be correct where the definitions of Principia ’s section *9 are concerned. The usual derivations underlying the validity of the replacement of logical equivalents in extensional contexts, essential to the axiomatic approach to definition, have to be proven using the definitions of *9 itself. 4. This device is used in Hughes and Cresswell, Introduction to Modal Logic , New York: Routledge, 1996:325. 5. We are omitting issues concerning predicativity. Thus we have removed the sign ! from Principia ’s definition of the identity sign. 6. We have added the scope marker ( Principia to *56 , p. 80) and neglected the issue of predicativity for convenience. Moreover, circumflex notation is removed to avoid controversies surrounding the interpretation of predicate variables in Principia . 7. I have added the scope marker. As with *20.01 the scope marker must be part of the definition *20.08. Its omission is an oversight. 8. Whitehead and Russell explicitly draw the analogy. See Principia to *56 , p. 81. 9. It says: . 10. Linsky’s reply to Martin’s problem focuses on *20.081 and the problematic use of circumflex Greek in Principia . On the present account, circumflex Greek (as with all occurrences of circumflex in Principia ) should be dropped from the work as it plays no role but to mark subject position occurrences of predicate variables. 11. Actually ( S) is a theorem schema derivable from the axiom schema for Russell’s substitutional theory. See Landini 1998a. 12. Russell clearly had this in mind. See Russell 1908. 13. In my view, Principia does not embrace a type-regimented or a ramified and type-regimented ontology of attributes. Instead it embraces a nominalistic semantics for its predicate variables and the notion that these variables are internally limited by their significance conditions. See Landini 1998a. 14. This is the po/ ao paradox. See Landini 1998a. 15. In my view, this was a mistake. Liar paradoxes of propositions are irrelevant to the substitutional theory. See Landini 2004. 16. This phrase is part of the wonderfully rich and interesting book by Richard Routley (Sylvan), Exploring Meinong’s Jungle and Beyond (Australian National University Monograph, 1980). 17. Russell, like Quine, demands an objectual account of the bound individual variables of quantification. 18. Lambert reports that he is developing an idea due to David Kaplan. 19. This is the Gray’s Elegy problem set out in ‘On Denoting’. See Landini 1998b. 20. In conversation with Nathan Salmon at the conference, it became clear that a de re reading of (1) is not indicated in Russell’s example. 21. This paradox is a version of a paradox discussed by Francesco Orilia (1996). 22. This account of mind may be attractive to the computational theory of mind because quantification structures seem amenable to emulation by recursive processes. But this may be too optimistic. The impredicative higher-level

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Page 296 quantifiers essential to Frege’s hierarchy of levels of concepts transcend first-order recursive functions. REFERENCES Frege, G. (1980) Philosophical and Mathematical Correspondence, G. Gabriel, H. Hermes, F. Kambartel, C. Thies, A. Veraart (eds.) and trans. H. Kaal, Chicago: University of Chicago Press. Lambert, K. (2003a) ‘Russell’s Version of the Theory of Descriptions’, in Free Logic: Selected Essays, Cambridge: Cambridge University Press: 1–15. ——. (2003b) ‘The Reduction of Two Paradoxes and the Significance Thereof’, in Free Logic: Selected Essays, Cambridge: Cambridge University Press: 33–43. Landini, G. (1992) ‘Russell to Frege 23 May 1903: I Believe I have Discovered that Classes are Entirely Superfluous ’, Russell, 12: 160–85. ——. (1998a) Russell’s Hidden Substitutional Theory , New York: Oxford University Press. ——. (1998b) ’ On Denoting Against Denoting’, Russell 18: 43–80. ——. (2004) ‘On Insolubilia and Their Solution by Russell’s Substitutional Theory’, in G. Link (ed.), One Hundred Years of Russell’s Paradox, Berlin: Walter de Gruyter: 373–99. ——. (2005) ‘Quantification in Principia ’s *8 and the Empty Domain’, History and Philosophy of Logic 26: 47–59. Linsky, B. (1999) Russell’s Metaphysical Logic , Stanford, CA: CSLI Publications. ——. (2004) ‘Classes of Classes and Classes of Functions in Principia Mathematica ’, in G. Link (ed.), One Hundred Years of Russell’s Paradox, Berlin: Walter de Gruyter: 435–47. Orilia, F. (1996) ‘A Contingent Russellian Paradox’, Notre Dame Journal of Formal Logic 37: 105–11. Quine, W. V. O. (1940) Mathematical Logic , Cambridge, MA: Harvard University Press. ——. (1980) Set Theory and Its Logic , Cambridge, MA: Harvard University Press. ——. (1995) ‘Quantification and the Empty Domain’, in Selected Logic Papers, Cambridge, MA: Harvard University Press. Russell, B. (1905) ‘On Denoting’, Mind 14: 479–93. ——. (1907) ‘On Types’, manuscript in Bertrand Russell Research Center, McMaster University. ——. (1908) ‘Mathematical Logic as Based on the Theory of Types’, American Journal of Mathematics 30: 222–62. ——. (1953) Introduction to Mathematical Philosophy, London: Allen and Unwin. ——. (1964) The Principles of Mathematics, New York: W.W. Norton. ——. (1967) Autobiography 1872–1914, vol. 1., Boston: Little Brown and Co. ——. (1994) ‘On Fundamentals’ in A. Urquhart (ed.), The Collected Papers of Bertrand Russell, vol. 4, Foundations of Logic, 1903–1905, London: Routledge: 359–413. Whitehead, A. N. and Russell, B. (1964) Principia Mathematica to *56, Cambridge: Cambridge University Press.

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Page 297 14 Quantifying in and Anti-Essentialism Michael Nelson Bertrand Russell’s theory of descriptions, doctrine of acquaintance, and distinction between knowledge by description and knowledge by acquaintance are truly brilliant, profound, and (even if not in the exact form proposed by Russell) correct.1,2 But these Russellian doctrines are sometimes misapplied. This is nowhere more the case than in their application to W.V.O. Quine’s famous attack on quantified modal logic (QML).3 Quine argued that QML is problematic and should be rejected. QML is the combination of standard firstorder quantification theory with sentential modal logic.4 The distinctive formulae of QML, and the ones that Quine found particularly problematic, are ones in which a quantifier is outside the scope of a modal operator and binds a variable within that operator’s scope. The following is an example. (1) x Gx. (1) is a natural formalization of the sentence ‘Something is necessarily a gorilla’, for example. Many have thought that Quine’s arguments are answered by carefully applying Russell’s theory of definite descriptions and his doctrine of logically proper names.5 I think it fair to say that this is the standard response to Quine. Yet it is this application of Russellian theory that I shall here bemoan. Once Quine’s argument is properly understood, it becomes clear that the Russellian response, as I shall call it, fails. These are the topics of the first four sections. This is not to say that Quine’s arguments are successful. Indeed, I think that there are several ways to undermine them. In the fifth section, ‘Quantifying in for the Anti-Essentialist’, I develop two responses. Both are independent of theses about the semantics of definite descriptions or proper names—theses essential to the Russellian response. THE PSEUDO-QUINEAN ARGUMENT AGAINST QML Before I can present the Russellian response, I need to present an argument. But the response in question is only a response to an argument that is not

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Page 298 Quine’s. So, in this section I shall present what I call the pseudo-Quine argument against QML. This argument captures a common understanding of Quine’s argument. In the second section I shall present the Russellian response. In the third and fourth sections, ‘The Real Quine’ and ‘The Failure of the Russellian Response’, I present what I think is Quine’s real argument and show how that argument is immune to the Russellian response. Pseudo-Quine’s argument turns on a(n attempted) derivation of a contradiction. Recall Frege’s famous case of Hesperus and Phosophorus. Pseudo-Quine uses a version of this case to show that ‘modal logic violates Leibniz’s principle’ (Smullyan 1948:31), or the Indiscernibility of Identicals (II), which is the principle that, for all x and y, if x = y, then, for all properties F , x is F iff y is F .6 From this pseudo-Quine concludes that quantifying into modal environments is nonsensical. Pseudo-Quine’s argument turns on two claims. The first is that modal logic violates II and the second is that such violations render quantified modal sentences unintelligible. In support of the first, consider the following trio of sentences. (2) Necessarily, Hesperus is a heavenly body seen first in the evening sky. (3) Hesperus is Lucifer. (4) Necessarily, Lucifer is a heavenly body seen first in the evening sky. We are supposed to agree that (2) and (3) are true and (4) is false.7 But (2), (3), and II entail (4). II is a metaphysical principle. What pseudo-Quine really needs is a semantic principle: A substitution principle. The following is a start. SUB: For any pair of singular terms a and b, if the identity statement a = b is true, then, for any pair of sentences s and s′ , where s′ differs from s only in the replacement of an occurrence of a in s with b, s is true iff s ′ is true.8 (4) differs from (2) only in the replacement of an occurrence of ‘Hesperus’ with the codesignating ‘Lucifer’. So, (2) and (4) seem to be the right form to satisfy the antecedent of SUB. So, SUB seems to require that (2) is true iff (4) is true. But the data seems to indicate that (2) is true and (4) is false. Above I identified two claims driving pseudo-Quine’s argument. The first was that modal logic violates II and the second was that such a violation renders quantified modal sentences unintelligible or otherwise problematic. I’ve discussed the first. Let me now turn to the second. Is (*) below true or false of the single object Hesperus/Lucifer/Venus? (*) Necessarily, x is a heavenly body seen first in the evening sky. Given that (2) is true, it would seem that we should say that (*) is true of that object; given the falsity of (4), it would seem that we should say that (*)

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Page 299 is false of that object. The same condition cannot both be true of and false of a single object (at a single time and in a single world). Assuming there is no equivocation or shift of context in the condition, this would require that a single object both have and not have some property, which violates the principle of noncontradiction. So, we cannot make coherent sense of (*)’s being true or false of an object like Venus. But then we cannot make sense of a quantified modal sentence like (5) below. (5) There is something x such that, necessarily, x is a heavenly body seen first in the evening sky. If we read the quantifier ‘there is’ objectually and we accept a standard semantics for such quantifiers, then the truth or falsity of (5) is defined in terms of the truth or falsity of (*) under an assignment of some object to the variable x. In general, the truth of a quantified sentence is defined in terms of the truth under an assignment of the relevant open sentence. We define (QF)’s truth   in terms of the truth under an assignment (of objectual value(s) to the free variable(s)) of the open sentence that results from dropping the initial quantifier; in our case, (OF) below.   So, because modal logic violates SUB, we cannot make sense of the distinctive formulae of QML. That is pseudo-Quine’s argument. The claim that the Russellian response targets is that (i) (2) and (4) differ in truth-value and yet, (ii) given SUB and the truth of (3), (2) and (4) should not differ in truthvalue. For ease of future reference, let’s call this the pseudo-claim. THE RUSSELLIAN RESPONSE Depending on how one understands the terms ‘Hesperus’ and ‘Lucifer’ in (2)–(4), the Russellian argues that either (i) or (ii) of the pseudo-claim is false. According to the Russellian, Quine’s argument turns on equivocating between these different ways of understanding those terms. To see why, we must first articulate some Russellian doctrines. I shall thus present a detour through Russell’s doctrine of acquaintance and Russell’s theory of definite descriptions—key doctrines employed in the Russellian response—before returning to the Russellian response itself.

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Page 300 Russell’s Doctrine of Acquaintance and Theory of Descriptions A full, or even adequate, account of Russell’s important notion of acquaintance is out of the question. But a brief description is both necessary and sufficient for present purposes. Russell maintained that every constituent of a thought that an agent is in a position to entertain is something with which she is acquainted.9 Being acquainted with x enables one to entertain thoughts that contain x as a direct, selfrepresenting constituent and one is in a position to entertain such a thought only when one is acquainted with x.10 Call this the Acquaintance Principle . Russell thought that we are acquainted only with our sense data and universals.11 So, Russell thought that we can only think directly about our own sense data and universals. Why did Russell maintain that we are not acquainted—and hence not capable of thinking directly about —material objects? A primary, although not exclusive, reason is broadly Fregean. One is acquainted only with that for which misidentification is rationally impossible. If one is presented with o and it is possible to be presented again with o and rationally not realize it is the same object as before, then one is not acquainted with o;12 one’s thoughts about o are, in that case, indirect. This line of reasoning relies on the Fregean claim that identity confusions are to be explained in terms of differences in thoughtconstituents. The thought that Hesperus is Hesperus is distinct from the thought that Hesperus is Lucifer precisely because of the possibility of misidentification. From this it follows that if one can be presented with an object and rationally not realize that it is the same object that one has been presented with before or in another way, then one’s thought is not directly about that object. For if the thought were directly about the object, there would be no difference in thought grasped, violating the above Fregean claim about cases of misidentification. If there were no difference in thought-constituents in cases of misidentification, then agents would be in a position to believe contradictions while having no internally accessible way of correcting them. And this Russell, like Frege, seems to have found unacceptable. This aspect of Fregeanism forced Russell to deny that we are acquainted with material objects and hence deny that our thought about such objects is direct.13 In claiming that Russell had Fregean motivations for a restrictive view of the objects of acquaintance I am not denying that there are important differences between Russell and Frege. There are significant differences, the most important being that acquaintance played no role in Frege’s view of how thoughts are about the world. Frege maintained that all thought is indirect; we do not think directly about anything, on Frege’s view. Russell, on the other hand, maintained that we think directly about certain entities and that this provides the foundation for all thought whatsoever, whether direct or indirect, about external reality, as we shall see below.14 The Acquaintance Principle is closely related to Russell’s notion of a logically proper name. A logically proper name has as its sole semantic

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Page 301 function that of contributing to the proposition expressed by a sentence in which it occurs its referent. Given the Acquaintance Principle, it follows that, if one understands a logically proper name, then one is acquainted with the object that name names. This is because understanding an expression involves, at least, grasping thoughts with the content of that expression as a constituent. We have seen above that the Acquaintance Principle, combined with Russell’s adoption of a Fregean attitude towards misidentification, led Russell to deny that we can think directly about material particulars. Russell admitted that there is a material reality filled with material particulars that we can and do think about. But all such thought, Russell insisted, is indirect in the sense that the items thought about are not direct constituents of the proposition grasped and that there are no logical proper names of such entities that any of us understand. Thought about material particulars, Russell claimed, is thought by description. By (1910), the canonical form that thought about a concrete particular existing in space and time took is something like the following: The thing that caused THIS [demonstratively referring to one’s occurrent sense datum] is such-and-such . An example is in order. Suppose I am sitting before a green apple and say to myself, ‘That apple is green’. I am acquainted with the universals APPLE and GREEN. But I am not acquainted with the individual apple itself, as misidentification with respect to it is possible. My thought about the apple is descriptive. In virtue of my visual experience of the apple, I am acquainted with a sense datum caused by the apple. Call this sense datum BILL . The content of my thought, according to Russell, is then something like the following.   Such propositions are general and thus indirect with respect to the external object (in this case, the apple) itself, but singular and thus direct with respect to the sense datum (in this case, BILL) being demonstratively referred to. Because this is the canonical form thought about material reality takes, such thought is ultimately grounded in acquaintance, albeit acquaintance with sense data as opposed to material reality itself. This is in stark contrast to the canonical form such thought takes in Frege’s system, in which there is no direct reference to sense data or any individuals at all.16 So far the discussion has focused on Russell’s views of acquaintance. This has led us to another famous doctrine of Russell’s—the theory of descriptions. Before spelling that view out in more detail, however, I would first like to discuss Peter Strawson’s (1990) critique of Russell’s view of thought about material reality.17 A key claim Strawson makes is that physical bodies are basic particulars , by which he means that we can identify material bodies without identifying other kinds of particulars (like mental particulars or events) but not vice versa. Strawson’s notion of identification

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Page 302 is related to the possibility of speaking (and presumably thinking) about an object and ascribing properties to it. For both Strawson and Russell, our ability to speak and think about objects in the world is based on demonstrative reference (what Russell called acquaintance). In this, both Strawson and Russell are opposed to Frege. But, whereas Strawson claimed that the objects demonstratively referred to are physical bodies in one’s immediate perceptual environment, Russell, as we have seen, maintained that such reference is to one’s occurrent sense data. In an apparent attempt to establish his view over Russell’s, Strawson writes: On other criteria than the present, private experiences have often been the most favoured candidates for the status of ‘basic’ particulars; on the present criteria, they are the most obviously inadmissible. The principles of individuation of such experiences essentially turns on the identities of the persons to whose histories they belong. A twinge of toothache or a private impression of red cannot in general be identified in our common language except as the twinge which such-and-such an identified person suffered or is suffering, the impression which suchand-such an identified person had or is having. Identifying references to ‘private particulars’ depend on identifying references to particulars of another type altogether, namely persons. (41) Russell should agree that private particulars (sense data) are dependent on persons in the sense that for any private particular m , there is some person p such that, necessarily, if m exists, then m is had by p. But from this it does not follow that in order to identify a private particular one must first identify the person to whom that private particular belongs. If it is my private particular and it is immediately before me, then, says Russell, I can think of it directly without first identifying the owner of the private particular; after all, the sense data is immediately present to me in my experience. Strawson conflates the metaphysical dependence of private particulars on persons and the semantic or psychological dependence of having to independently identify the bearer of a given private particular in order to identify, and hence think about, it. These two kinds of dependences come apart precisely in the firstperson case: Although all private particulars (mine included) are metaphysically dependent on their bearers, I can directly refer to my own occurrent private particulars without first independently identifying myself. Russell’s view is consistent with the ontological dependence of sense data. Strawson developed an influential ‘massive reduplication’ argument (20). One of the conclusions Strawson drew from this argument is that identifying, and hence talking and thinking about, objects outside one’s immediate perceptual environment ultimately rests on relating those objects spatiotemporally to objects in one’s immediate perceptual environment and their spatio-temporal location, where the latter are demonstratively identified. That is, Strawson takes the argument to support the broadly Kantian claim that

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Page 303 demonstrative identification of one’s spatio-temporal location in a system of particulars bearing spatiotemporal relations to one another ultimately grounds our ability to identify objects outside our immediate perceptual contact. This conclusion runs contrary to Russell’s view, according to which (to use Strawson’s terminology), it is mental particulars that are the (identificationally) basic individuals. But, I shall argue, Russell’s view can actually accommodate the insight behind Strawson’s reduplication argument. I was just sitting in my chair in my office and I am now standing outside in the hall thinking about that chair. But suppose that we live in a universe with massive reduplication in which there is a qualitatively indiscernible chair in a qualitatively identical office adjacent to a qualitatively identical hall on the other side of the universe. It is intuitive that I am nonetheless thinking about the chair in my office and not its qualitative twin. But then my thought is not purely qualitative, as otherwise it would not be determinately about one of the chairs rather than the other. Strawson concludes that I must relate the chair in the room I just left to my spatio-temporal location, which I think about demonstratively and hence nonqualitatively, in order to have a description that uniquely picks it out as opposed to its qualitatively twin. The first chair, and not its qualitative twin, bears the appropriate spatio-temporal relations to my present spatio-temporal relation, which I identify demonstratively. Hence, I am able to think determinately about objects outside my present perceptual environment by relating them spatiotemporally to my present spatio-temporal location, where I pick the latter out demonstratively. I think that the reduplication argument provides powerful support for the claim that our thought about material reality is not all purely qualitative.18 It thus succeeds in refuting a purely Fregean view. But it does not refute Russell’s view. Russell does not, remember, maintain that our thought about material particulars is all purely qualitative. He can deliver the intuitive results concerning reduplication cases. This is because demonstrative identification of our own sense data provides just as good an anchor as one’s spatio-temporal location; indeed, demonstrative identification of any individual that other individuals bear unique, discernible relations to will work. For Strawson, my thought is about the chair in the room next to me rather than the chair in the other region of the universe in virtue of its spatiotemporal relation to me now and my ability to think about my current spatio-temporal location directly. Russell gets the same result by relating the chair to my sense data. Just as the locations of the two chairs in the reduplication universe are different, so too are the sense data they cause. Only the chair in my office is the cause of the sense datum that, on Russell’s view, I demonstratively identify; the other chair causes a numerically distinct sense datum. So, if I can demonstratively identify my own sense data and then identify other objects in relation to those sense data, I have met the theoretical challenges the possibility of reduplication present. I have located, as it were, my thoughts in such a way as to make them about the proper objects, even in the reduplication universe.

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Page 304 Strawson’s reduplication argument, whatever its exact intended effect, does not offer reason to abandon Russell’s view. Let’s move now to Russell’s theory of description. We have seen that Russell’s notion of thought by description is supposed to enable one to think about items with which one is not acquainted consistent with the Acquaintance Principle. In order for descriptive thought to play this role, one must have a theory of descriptive thought according to which the individual the thought is (indirectly) about is not a constituent of that thought. Russell had just such a theory, first presented in his classic (1905) and more rigorously in Alfred North Whitehead and Russell (1925). Whitehead and Russell introduced into their formal language an operator—the iota-operator—to translate sentences with definite descriptions in subject position—sentences of the form The F is G . This addition did not constitute an extension of their formal language; iota-phrases are mere ‘abbreviations of convenience’, always eliminable in terms of other pieces of vocabulary of the language. So, for example, the ‘iota-sentence’   is definitionally equivalent, by *14.01, to the following ‘iota-less sentence’.   Definite descriptions are thus, in their logical form, quantificational phrases. The sentence ‘The heavenly body seen first in the evening sky is a heavenly body seen first in the evening sky’, for example, is logically equivalent to and analysed in terms of the sentence ‘There is exactly one heavenly body seen first in the evening sky and that object is a heavenly body seen first in the evening sky’. The combination of definite descriptions and sentential operators create scope ambiguities. To use Russell’s favourite example, (6) below is ambiguous. (6) The present King of France is not bald. This sentence as a whole can be taken either to be primarily a quantificational sentence or primarily a negated sentence. If the first, we are ‘giving the definite description wide scope’; if the second, we are ‘giving the definite description narrow scope’. We can represent these options as follows:   As iota-formulae are definitional shorthands for iota-less-formulae, (6w) and (6n) are equivalent to the following iota-less-formulae.

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Page 305   (6wexpanded) and (6nexpanded) are not truth-functionally equivalent.20 In truth-functional environments, scope differences affect truth-value—that is, there is a difference in truth-value between the wide and narrow scope readings—only when the unique existence assumption is not satisfied, as *14.3 claims. But Russell was clear that, outside truth-functional environments, scope ambiguities do lead to differences in truth-value even when the existence assumption is satisfied, as his case of George IV puzzlement over who authored the Waverley series in (Russell 1905) makes clear. Although George IV wonders whether or not Scott is the author of Waverley , he does not wonder whether or not the author of Waverley is the author of Waverley . There is a scope difference that leads to a difference in truth-value here, even though the existence assumptions are satisfied, because of the nontruthfunctional environment created by the attitude verb. Russelling Quine We now have the needed machinery to present the Russellian response to Quine’s argument against QML. Recall (2) and (4). (2) Necessarily, Hesperus is a heavenly body seen first in the evening sky. (4) Necessarily, Lucifer is a heavenly body seen first in the evening sky. According to the pseudo-claim , (i) (2) and (4) differ in truth-value and yet, (ii) given SUB and the truth of the identity claim (3), (2) and (4) should not differ in truth-value. Appealing to Russell’s distinction between logically proper names and definite descriptions, we can distinguish two ways of understanding (2) and (4). First, ‘Hesperus’ and ‘Lucifer’ might both be logically proper names; second, ‘Hesperus’ and ‘Lucifer’ might be disguised definite descriptions.21 And, given the interaction between definite descriptions and modal operators, the second comes in two varieties: One in which the definite description takes wide scope with respect to the modal operator and another in which it takes narrow scope. Because the modality creates a nontruth-functional environment, this scope ambiguity might affect truth-value even when existence assumptions are satisfied. The Russellian claims that, in the first case, (2) and (4) have equivalent truth-values and, in the second, they either have equivalent truthvalues or else (4) does not follow from (2) and (3) by SUB. But in neither case does both (i) and (ii) obtain. So, either way, the pseudo-claim is false. Let me fill this out in more detail. Suppose first that both terms are logical proper names. Call this option (A). Then (2) is true just in case (4) is. This is because under option (A) (2) and (4) express exactly the same proposition, as both singular terms ‘Hesperus’ and ‘Lucifer’ are, given the truth of the identity statement (3),

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Page 306 logical proper names of the same individual and hence contribute the same object to the proposition they express.22 So, in this case, (i) of the pseudo-claim is false. Suppose, then, that both ‘Hesperus’ and ‘Lucifer’ in (2) and (4) are disguised definite descriptions. For simplicity, let’s suppose that the first is equivalent to ‘the heavenly body seen first in the evening sky’ and the second to ‘the heavenly body seen last in the morning sky’. Then (2) and (4) should be read as (2d) and (4d) below, respectively. (2d) Necessarily, the heavenly body seen first in the evening sky is a heavenly body seen first in the evening sky. (4d) Necessarily, the heavenly body seen last in the morning sky is a heavenly body seen first in the evening sky. Let us further suppose Russell’s theory of definite descriptions, a theory Quine accepted.23 Then we face a choice. Given that ‘necessarily’ functions as a sentential operator, (2d) and (4d) are ambiguous in terms of scope. That is, there is both a wide and narrow scope reading of each (2d) and (4d), as follows. (Let Ex abbreviate ‘ x is a heavenly body seen first in the evening sky’ and Mx abbreviate ‘ x is a heavenly body seen last in the morning sky’.)

  We shall show that, in the first case, (i) of the pseudo-claim is false and, in the second case, (ii) of the pseudo-claim is false and hence that, either way, the pseudo-claim is false. Suppose first that we give both descriptions wide scope. Call this option (B). Then we understand (2) and (4) as having the logical forms given by (2dw) and (4dw). But (2dw) and (4dw) do not differ in truth-value, as the object that uniquely satisfies the condition Ex also satisfies the condition Mx . If we assume that Venus is only accidentally seen first in the evening sky, then both are false; if we assume otherwise, then both are true. So, under option (B) there is no variance of truth-values between (2) and (4) and hence (i) of the pseudo-claim is false. Suppose then that we give both descriptions narrow scope. Call this option (C). Then there is indeed a difference in truth-value between (2) and (4), as (2dn) is true and (4dn) is false (assuming, as seems evident, that it is possible for a heavenly body to be seen first in the evening sky without being seen last in the morning sky). So, we secure (i) of the pseudo-claim only with option (C). But in that case, we jeopardize (ii) of the pseudo-claim, for the variance in truth-value does not, in that case, violate ‘Leibniz’s principle’, or, more precisely, SUB. It is a misapplication of SUB to use it to derive (4dn)

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Page 307 from (2), taken in any way, and (3) or (4), taken in any way, from (2dn) and (3). a and b in SUB range over only genuine singular terms, which, given Russell’s theory of descriptions, definite descriptions are not. We have considered three options for understanding (2) and (4). No understanding has led to a variance in truth-values that violates Leibniz’s principle. It is only by equivocating between these options that we secure both (i) and (ii) of the pseudo-claim. Quine has not shown that QML violates Leibniz’s principle and has failed to derive a contradiction. THE REAL QUINE24 Smullyan first applied Russell’s doctrines to Quine’s argument against QML in the way detailed above.25 Although the application is brilliant, it also rests on a misunderstanding of Quine’s argument. In all fairness to Smullyan, he was responding to Quine’s (1947),26 which was, even by Quine’s own lights, confused in important ways27 and failed to bring out the heart of Quine’s objection. But, by 1953, when Quine significantly rewrote and combined (1943) and (1947) to create the first version of ‘Reference and Modality’, the best statement of Quine’s objection to QML, it became clear that Quine’s argument does not turn on deriving a contradiction, as Smullyan and his followers conceived it. Instead, Quine’s argument turns on attempting to show that interpreting the characteristic formulae of QML requires Aristotelian essentialism. The Russellian response is simply silent about any alleged connections between QML and Aristotelian essentialism and thus fails to truly address Quine’s argument. Quine thought that modality requires a reduction to the notion of analyticity and ultimately logical truth. But this reduction is at odds, Quine argued, with the combination of modal logic and standard first-order quantification logic. For the combination requires Aristotelian essentialism, which is contrary to the original reductionist project of grounding modality in analyticity and ultimately logical truth and the notion of synonymy. So much the worse, concluded Quine, for QML.28 The intelligibility of QML requires that we make sense of an object, independently of how and even if it is designated, satisfying the condition Gx. (Equivalently, we need to make sense of the open sentence Gx being true of an object, independently of how and even if it is designated.) This is because QML is intelligible only if formulae like (1)—( x) Gx—are intelligible and the intelligibility of such formulae require the intelligibility of the notion of an object satisfying the condition Gx. Quine’s challenge is then to make coherent sense of this notion without resort to Aristotelian essentialism. He claimed the challenge could not be met. We need two things to spell this line of argument out in more detail: First, we must characterize Aristotelian essentialism; second, we must be more precise about the condition Gx.

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Page 308 One might think that it is straightforward to characterize the thesis of Aristotelian essentialism. One would expect Quine to have given a clear and careful characterization of the thesis and then proceed to operate only with that characterization, given the crucial role the thesis plays in his argument. But things are not, I fear, as one would expect. Fully working this out exposes a serious set of equivocations in Quine’s argument, as I argue in the fifth section, ‘Quantifying in for the Anti-Essentialist’. But we need at least a working conception to get going. For this, we turn to Quine’s own words. Reversion to Aristotelian essentialism is required if quantification into modal contexts is to be insisted on. An object, of itself and by whatever name or none, must be seen as having some of its traits necessarily and others contingently, despite the fact that the latter traits follow just as analytically from other ways of specifying it. (Quine 1980:155) This means adopting an invidious attitude toward certain ways of uniquely specifying x, for example [as ‘Hesperus’, say], and favouring other ways, for example [as ‘Lucifer’, say], as somehow better revealing the ‘essence’ of the object. (155) We can glean the following characterizations of the thesis of Aristotelian essentialism from these sampled passages. The thesis of Aristotelian essentialism is the thesis that there is a privileged proper class of designators of an object that best reveal that object’s necessary properties:29 the ‘essence revealing’ designators. And this despite the fact that those properties do not analytically follow from some nonprivileged designators of the object and other, contingent properties do analytically follow from some nonprivileged designators. Later I shall distinguish other characterizations of the thesis of Aristotelian essentialism present in the passages. Let’s turn to explicating the condition Gx. There are at least three ways of construing . We might first construe it in terms of logical truth. Then, in making sense of an object satisfying the condition Gx, we need to say what it is for an object to logically satisfy a condition Gx.30 Second, we might construe it in terms of analytic truth. Then, in making sense of an object satisfying the condition Gx, we need to say what it is for an object to analytically satisfy a condition Gx. Finally, we might construe it in terms of metaphysical necessity. Then, in making sense of an object satisfying the condition Gx, we need to say what it is for an object to ( metaphysically ) necessarily satisfy a condition Gx. Quine is clear that his concern is with strict necessity analysed in terms of logical and analytical truth.31 Although it is an interesting and important question whether or not a Quinean argument works when is construed in terms of metaphysical necessity—and in particular whether or not understanding the notion of an object, independently of how and even whether

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Page 309 it is designated, satisfying a condition as a matter of metaphysical necessity requires some philosophically controversial thesis of essentialism—it is a question I shall not here pursue. Following Quine, I shall be concerned with a construal of necessity in terms of analytical and logical truth. Quine claims that (2) is true, which is likely to sound strange to contemporary ears. First, most of us naturally read an unadorned ‘it is necessary that’ in terms of metaphysical necessity and it is indeed hard to think that as a matter of metaphysical necessity Venus is seen first in the evening (unless one is a metaphysical necessitatarian). But Quine had in mind strict necessity. Second, like Russell, Quine typically thought of ordinary proper names as disguised definite descriptions and so naturally read ‘Hesperus is a heavenly body seen first in the evening sky’ as equivalent to something like ‘The heavenly body seen first in the evening sky is a heavenly body seen first in the evening sky’. So, putting these two points together, the claim that (2) is true comes to, according to Quine, the claim that the sentence ‘The heavenly body seen first in the evening sky is a heavenly body seen first in the evening sky’ is analytically true. This does not sound strange, even if it is strange to think that that is what (2)’s truth involves. We now have all the pieces to spell out Quine’s argument in detail. Quine claims that making sense of the distinctive formulae of QML requires making sense of an object, independent of how it is designated, analytically and ultimately logically32 satisfying a condition. And he thinks that the fact that (2) is true and (4) is false proves an insurmountable problem to this task, provided we are to avoid commitment to Aristotelian essentialism.33 Avoiding Aristotelian essentialism involves not privileging one way of designating an object over others when determining whether or not that object necessarily has some given property. But without such a privileging, we are at a loss when asked whether or not Venus, for example, necessarily has the property of being a heavenly body seen first in the morning sky. Because (2) is true, we should say that it does; because (4) is false, we should say it does not. We get a consistent answer concerning whether or not Venus analytically satisfies the condition ‘ x is a heavenly body seen first in the evening sky’ only if we privilege one of these ways of designating Venus, letting, say, what analytically follows from the designator ‘the heavenly body seen last in the morning sky’ be determinative of what conditions Venus analytically satisfies and ignoring the fact that some of those conditions do not analytically follow from other ways of designating Venus. Hence, QML is committed to Aristotelian essentialism. But Aristotelian essentialism is contrary to properly grounding modality in analyticity. Thus, QML should be rejected. Quine’s argument against QML turns on what we can call Quine’s Challenge: The challenge of explicating the notion of an object logically or analytically satisfying a condition in terms of the more familiar notion of a (closed) sentence being logically or analytically true without committing

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Page 310 oneself to Aristotelian essentialism and while recognizing the fact that, for some objects, different ways of designating it are analytically tied to different predicates. Now it might seem tempting to simply insist that the truth of (2) and falsity of (4) are irrelevant to whether or not Venus analytically satisfies the condition Ex. But that is a hard pill to swallow. The notions of (syntactic) logical and analytic truth primarily apply to closed sentences. So if we are going to make sense of an open sentence being (syntactically) logically or analytically true of an object, it must be in terms of the logical or analytic truth of a closed sentence. And to make sense of an object analytically satisfying the condition Gx just is to make sense of the open sentence Gx being analytically true of that object. But then the fact that (2) is true and (4) false, given the identity statement (3), is very relevant to whether or not Venus analytically satisfies Ex. The notions of logical and analytic satisfaction are dependent on the notions of logical and analytic truth. A strong case can be made, supported by standard model theory for first-order predicate logic, that the order of dependence is reversed for the notion of truth (conceived of as a property of sentences) and the notions of satisfaction and true of. The truth of a simple sentence Fa is explicated in terms of an object (the object assigned to a ) satisfying the condition Fx . But the notions of logical and analytic satisfaction simply cry out for analysis in terms of logical truth and the analyticity of closed sentence. Quine’s problem is a problem only if one adopts an objectual theory of quantification. If we adopt a substitutional theory, then we would explicate the truth of a quantified sentence like (1) in terms of the truth of some closed sentence and so would not have to avail ourselves of (and hence make sense of) the notion of an object satisfying the condition Gx.34 Similarly, if we treated the quantifier in (1) as a conceptual quantifier, then, again, we would not have to make sense of the notion of an object satisfying the condition Gx. This is because conceptual quantifiers range not over objects but rather over individual-concepts (that is, concepts that uniquely determine a single object). Although this point is correct as far as it goes, it is irrelevant to Quine’s Challenge. If it is standard, firstorder quantification theory that we are adding to sentential modal logic, then we must make sense of an object satisfying the condition Gx. Quine’s argument against QML assumes that the Q is standard, objectual quantification theory. As Quine says: ‘What I’ve been talking about is quantifying, in the quantificational sense of quantification, into modal contexts in a modal sense of modality’ (Marcus et al. 1963:116). (By ‘quantificational sense’ he clearly means objectual; by ‘modal sense’ he means strict modality.) So we cannot simply reject the demand to explicate the notion of analytic satisfaction. We can change the subject, if we like, and we might even be able to justify changing the subject by showing that the alternative substitutional and conceptual conceptions of quantification

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Page 311 are superior to the standard objectual conception. But that is not to answer Quine’s argument, as that argument is targeted against objectual quantification into modal environments. I think that the foregoing discussion captures the essence of the strongest version of Quine’s argument against QML, although I certainly have not followed Quine’s own presentation. Indeed, in presenting Quine’s argument I have not explicitly employed the notions of purely referential and nonpurely referential occurrences of singular terms (or what in (1943) Quine called purely designative occurrences ) and opaque environments. And I have not relied on Quine’s Thesis—the thesis that quantifying in to an opaque environment is incoherent—which is essential to some understandings of Quine’s argument. David Kaplan (1986:230) distinguished two kinds of arguments Quine raised against quantifying in: Logical arguments, which aimed to establish the incoherence of quantifying into opaque environments in general, and nonlogical, metaphysical or epistemological arguments, which aimed to show that there were suspect metaphysical or epistemological theses underlying the attempt to quantifying in to a particular opaque environment. I have here focused on Quine’s nonlogical, metaphysical argument against QML.35 This, I think, is where Quine’s insights are to be found. Quine’s worry was that QML required the suspect metaphysics of Aristotelian essentialism. He thought this because he saw that different designators of a single object are analytically connected to different predicates and so, he concluded, in saying what is analytically true of an object we must privilege certain such singular terms as ‘better revealing’ that object’s essence, which is just to embrace Aristotelian essentialism. Answering Quine’s worry thus requires showing that QML is free of essentialist commitments and thus answering Quine’s Challenge. THE FAILURE OF THE RUSSELLIAN RESPONSE In the previous section I described what I take to be Quine’s argument against QML. The key difference, for present purposes, between that argument and pseudo-Quine’s argument, described in the first section, is that, whereas pseudo-Quine attempts to derive a contradiction from the fact that (2) and (3) are true and (4) false, relying on SUB, Quine did no such thing. I claim that, although successful against pseudo-Quine’s argument, the Russellian response is unsuccessful against Quine’s argument. The Russellian response turns, remember, on showing that either (i) that (2) and (4) do not differ in truthvalue; or (ii) (2) and (3) do not entail, via SUB, (4). The response is successful, I claim, in this. But it is simply irrelevant to Quine’s argument. To respond to Quine one needs to show either that interpreting the characteristic formulae of QML does not require commitment to Aristotelian essentialism and more particularly that we can make sense of the notion of an object, independently of how and even

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Page 312 whether it is designated, logically satisfying a given condition without privileging a proper class of designators of the object, or that Aristotelian essentialism is not as problematic as Quine made it out to be. That is, one needs to either meet head-on what I called Quine’s Challenge or develop a defensible essentialist metaphysics. Nothing the Russellian says helps on either of these fronts. The Russellian response does not help answer Quine’s Challenge as it either assumes the sense of the notions of logical or analytic satisfaction that we have been asked to explicate (when we consider the terms to be descriptions with wide scope, or something just as problematic when we consider the terms to be logically proper names) or simply confirms one of the points that pushes Quine’s argument (when we consider the terms to be descriptions with narrow scope). And, of course, the Russellian does not help with an essentialist metaphysics either. Let me spell this in more detail. Earlier I distinguished three ways of understanding (2) and (4) the Russellian offers—options (A)–(C). The Russellian rightly points out that none of those options allow us to say both that (2) and (4) differ in truth-value and that (4) should follow from (2) and the true (3) by SUB. Quine can and should admit this;36 it is simply irrelevant to Quine’s Challenge. Option (A) is the most delicate, so I shall postpone its discussion. Option (B) offers no help in answering Quine’s Challenge. Under this option, we understand (2) and (4) as (2dw) and (4dw) respectively, reproduced below.   Both (2dw) and (4dw) involve occurrences of applying to an open sentence. But then in claiming that (2dw) and (4dw) have the same truth-value—or indeed any truth-value at all—we have simply helped ourselves to the very notion we have been asked to analyse. Answering Quine’s Challenge, remember, requires explicating the truth or falsity of quantified modal sentences in terms of modal sentences with applying only to a closed sentence. Option (C) is more promising on this front. On this option, recall, we understand (2) and (4) as (2dn) and (4dn), respectively, reproduced below.   Both (2dn) and (4dn) only have closed sentences within the scope of . But the problem with (2dn) and (4dn) is that, if we are to avoid Aristotelian essentialism and so treat all ways of designating an object as equally telling of what conditions it logically satisfies, then we seem forced into the contradiction of saying that one and the same object—Venus—both does and does not logically satisfy the condition Ex. This contradiction does not

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Page 313 involve any application, questionable or otherwise, of SUB. So the Russellian’s complaint with option (C) is irrelevant. What drives Quine’s argument at this point is the desire to treat all designators of Venus on a par when it comes to determining Venus’s necessary properties. And this does not rest on attempting to substitute one definite description for another within the scope of . Rather, it rests on a desire to eschew commitment to Aristotelian essentialism. I said above that option (A) raises delicate issues. Let me now take them up. Under option (A), we understand (2) and (4) as (2lpn) and (4lpn), respectively. (Let h and l be logically proper names both assigned Venus as values.)   It might be thought that (2lpn) and (4lpn) avoid the problems I raised for options (B) and (C). Unlike (2dw) and (4dw), neither contain an open sentence governed by ; unlike (2dn) and (4dn), (2lpn) and (4lpn) seem to have the same truth-value. Quine wants us to explicate what it is for an open sentence to be analytically true of an object in terms of the analytic truth (or lack thereof) of a closed sentence. We now see that the reduction should be carried out in terms of closed sentences containing logically proper names of the object in question. Venus analytically satisfies the condition Ex, we might say, because the closed sentences Eh and El are analytically true (or, alternatively, Venus does not analytically satisfy the condition Ex because the closed sentences Eh and El are not analytically true). Just what we wanted, right? No. First, notice that if we go this route we must still exclude from the class of ‘essence revealing’ designators of Venus either ‘the heavenly body seen first in the evening sky’ (if we count both (2lpn) and (4lpn) as true) or ‘the heavenly body seen last in the morning sky’ (if we count both (2lpn) and (4lpn) as false). (Even if definite descriptions are neither genuine names nor singular terms, surely they are designators.) But this is just the kind of privileging that a denier of Aristotelian essentialism seeks to avoid. Ruth Barcan Marcus famously distinguished a tag for an individual from a singular description of that individual (1963:85). The distinction is consciously reminiscent of Russell’s distinction between logically proper names and definite descriptions. ‘This tag’, Marcus writes, ‘a proper name, has no meaning. It simply tags’ (84). By saying that a tag ‘has no meaning’, Marcus means that it does not contribute a descriptive condition to the proposition expressed by a sentence in which it occurs. By claiming that ‘it simply tags’, Marcus means that is simply introduces an individual directly for the rest of the sentence to then go and attribute a property to. If we help ourselves to the traditional notion of a proposition (something Marcus seems not terribly comfortable with), we then get that sentences with tags

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Page 314 express singular propositions—exactly what Russell thought of sentences with logically proper names. Marcus claimed, in effect, that if there are two tags a and b of the same individual, then a = b is a tautology and indeed analytic. She suggests ‘there would be a way of finding out, such as having recourse to a dictionary or some analogous [nonempirical] inquiry, which would resolve the question as to whether the two tags denote the same thing’ (Marcus et al. 1963:115).37 Marcus is here pursuing option (A). Saul Kripke responded to Marcus’s proposal by claiming that it requires acceptance of Aristotelian essentialism. That seems to me like a perfectly valid point of view. It seems to me the only thing Professor Quine would be able to say and therefore what he must say, I hope, is that the assumption of a distinction between tags and empirical descriptions, such that the truth-values of identity statements between tags (but not between descriptions) are ascertainable merely by recourse to a dictionary, amounts to essentialism itself. The tags are the ‘essential’ denoting phrases for individuals, but empirical descriptions are not, and thus we look to statements containing ‘tags’, not descriptions, to ascertain the essential properties of individuals. Thus the assumption of a distinction between ‘names’ and ‘descriptions’ is equivalent to essentialism. (Marcus et al. 1963:115) Kripke is right that option (A) leads to Aristotelian essentialism and hence does not constitute a solution to Quine’s Challenge.38 When Kripke went on to develop his distinction between rigid and nonrigid designators—a distinction related to, although importantly different from, as there are rigid definite descriptions, Marcus’s distinction between tags and descriptions—and argue that identity sentences with rigid designators are, if true, necessarily true and that modal sentences containing rigid designators reveal the necessary properties of individuals, in (1971) and (1980), he was clear that he was simply embracing essentialism, not eschewing it. There are further reasons to be suspicious of the doctrine of logical proper names and the appeal to (2lpn) and (4lpn) in answering Quine’s Challenge. We should remind ourselves of the peculiar nature of l and h. As logically proper names, their sole semantic function is to introduce an object into the proposition expressed by sentences in which they occur. Thus, the sentences Eh and El closely resemble the open sentence Ex under an assignment of Venus for x. The most plausible way of assigning propositions to these sentences has them all expressing the same singular proposition containing Venus and the property being a heavenly body seen last in the evening sky . Their only differences reside in the fact that the valuation of variables, as opposed to the interpretation of the individual constants, supply Venus as value in the latter case. Given this similarity, it seems strange to say that the alleged analyticity of the one is any less problematic than the alleged analyticity of the other, even if the other is a closed sentence.

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Page 315 If one were puzzled with the attribution of analyticity to a valuated open sentence Ex, as Quine evidently was, this puzzlement is not dispelled by appealing to an attribution of analyticity to sentences like Eh and El. We have little more understanding of what is involved in their logical or analytic truth than we have understanding of the notion of analytic satisfaction. We have a more or less good understanding of why a sentence like ‘The heavenly body seen first in the evening sky is a heavenly body seen first in the evening sky’ is a (syntactic) logical truth and a sentence like ‘The heavenly body seen last in the morning sky is a heavenly body seen first in the evening sky’ is not. This is made all the more apparent if we assume something like Russell’s theory of descriptions, whereby the first is analysed as [ ιxEx ] Ex and the second as [ ιxMx] Ex. We can then point out that anything that satisfies the condition Ex is thereby guaranteed to satisfy the condition Ex, but not so for satisfying the condition Mx . It is for this reason that the first is guaranteed to be true in virtue of its form alone whereas the second is not. And if we help ourselves to the notion of synonymy, then, again, we can explain the analytic status of a sentence like ‘Everything that is a vixen is a female fox’ by pointing out that ‘vixen’ and ‘female fox’ are synonymous and so, by replacing synonym with synonym, we get the logically true syntactic form ‘Everything that is a vixen is a vixen’. But we lack a similar grip on why we should count a sentence like Eh as logically (in the syntactic sense) or analytically true. Indeed, once we see that Quine intended to mean either ‘is a logical truth that’ or ‘is analytic that’, where analyticity is explicated in terms of synonymy and logical truth, it seems to me that we should not be so willing to take as unproblematic the truth of sentences like (2lpn) and (4lpn). If anything, we should be explicating what it is for such a sentence to be logically (in the syntactic sense) or analytically true in terms of the less problematic sentences that do not contain logically proper names. Indeed, it is very hard to see how anything beside identity claims (like l = l) could be thought to be logically or analytically true. (If we focus on a syntactic (as opposed to propositional) conception of logical truth, it is hard to see how we could count h = l as logically true. But if it is not logically true, we have to once again be discerning about what designators we consult in determining whether or not Venus satisfies the condition x = l.) Option (A), although initially attractive, is a dead-end. I conclude that the Russellian response is ineffective against Quine. An effective anti-essentialist response must answer Quine’s Challenge and doing that requires very different resources from those employed by the Russellian response. QUANTIFYING IN FOR THE ANTI-ESSENTIALIST There are three broad attitudes one may take towards the argument ascribed to Quine in ‘The Real Quine’, given the failure of the Russellian response.

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Page 316 The first two are alike in that they do not attempt to pry apart QML and Aristotelian essentialism and thus do not take up answering Quine’s Challenge, while the third does just that. My primary focus here shall be on articulating a version of the third. The first broad attitude one might take is that of Quine himself: Accept Quine’s conclusion and reject QML as ‘conceived in sin’ and unfit for use (and perhaps even mention).39 Although some—some even distinct from Quine40—have gone down this dark road, I think it too drastic this early in the game. The second reaction is to accept that QML requires or at least is best articulated in light of Aristotelian essentialism and embrace Aristotelian essentialism. I think this is the typical reaction to Quine, even if its proponents do not always appreciate that that is what they are doing. I have argued that that is where options (A) and (B) of the Russellian response lead and we have already seen that Kripke is consciously a proponent of this response. Although I am most sympathetic with this line of response,41 in this paper I wish to explore a third reaction to Quine’s argument, which is to seek to sever Aristotelian essentialism and QML. There are, broadly, two ways to develop an anti-essentialist version of QML. Both turn on offering nonstandard semantics for de re modal claims. Crudely, the first makes their truth ‘all too easy’ and the second makes their truth ‘all too difficult’. Although my focus here shall be on a version of the latter, I shall begin by briefly presenting a version of the former. David Kaplan, in (1968), showed us how to make de re modal claims cheap and consistent with antiessentialist commitments.42 Kaplan proposed that we posit extra quantificational structure when analysing modal operators. Let c range over individual-concepts, φ be the determining relation that obtains between an individual-concept and the individual that falls under it,43 G be the concept associated with Gx, and A be short for ‘is analytically connected to’;44 so, for example, A(G, c) should be read as ‘G is analytically connected to c’. Then we can say that the open sentence Gx is analysed as c(cΔx & A(G, c)) (read ‘there is an individual-concept that determines the value of x and that individual-concept is analytically connected to the concept G’). It is important to note that the freevariable x takes individuals as value and so is set to be bound by an ordinary, objectual quantifier. Kaplan’s proposal is within the framework of a theory of objectual quantification. Positing this extra quantificational structure proves useful in defusing Quine’s argument because it allows us to distinguish two ways in which an object might ‘fail to satisfy’ the condition Gx. (Kaplan works the account out more fully for the case of propositional attitudes, articulating the notion of suspended judgement, which he distinguishes from not believing. I am here making the analogous distinction for the case of modality.) The Kaplanesque analysis of that condition allows for a choice regarding the scope of any negation operators, much as Russell’s theory of definite description predicts scope interactions between definite descriptions and negation. So, we should distinguish (7) and (8).

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Page 317   (7) is true of an object o just in case there is no individual-concept determining o that is analytically connected to G, whereas (8) is true of o just in case there is an individual-concept determining o that is not analytically connected to G. (8) is consistent with there being other individual-concepts determining o that are not analytically connected to G, given that a single object can fall under multiple individualconcepts. With the distinction between (7) and (8) in hand, one can be nondiscriminating about the designator one consults in determining which conditions an object analytically satisfies, thus avoiding Aristotelian essentialism, without producing contradiction and while admitting that (2) is true and (4) is false. (2) is true, we are supposing. So we should infer, given the existence of Venus, that Venus satisfies the condition Ex. (4) is false, we are supposing. So we should infer that Venus—the very same object!— satisfies the condition ~ Ex. This does not lead to a contradiction because Venus satisfies that last condition when it is construed as c(cΔx & ~A(E, c)) and, remember, one and the same object can consistently satisfy both the conditions c(cΔx & A(E, c)) and c(cΔx & ~A(E, c)), provided different individual-concepts provide the grounds of their truth.45 In general, it is not contradictory to say that one and the same object satisfies the conditions Gx and ~ Gx, as long as the negation in the second condition is construed as taking narrow scope with respect to the posited extra quantificational structure. So, we have avoided both contradiction and Aristotelian essentialism. The Kaplanesque response is brilliant. But it has several odd consequences.46 I discuss these consequences, as well as different versions of the basic strategy (some of them not requiring that extra quantificational structure be posited in the logical form of modal sentences to achieve the desired result), in Nelson (unpublished a). I mention the strategy here not to recommend it but rather to highlight the fact that there are a number of anti-essentialist strategies for making sense of QML available. My focus in the remainder of this paper, however, shall be on a very different anti-essentialist strategy that does not have these odd consequences. The strategy is based on a response to Quine first presented, to my knowledge, by Ruth Barcan Marcus in (1967) and later developed by Terence Parsons in (1967) and (1969). Marcus distinguished what we can call trivial and philosophically problematic necessary properties.47 She then argued that interpreting the characteristic formulae of QML only requires ascribing trivial necessary properties to objects and that an object’s having trivial necessary properties is consistent with the motivating spirit of anti-essentialism. So, QML is free of any philosophically problematic essentialist theses; Quine’s Challenge is met. I shall call this the Marcus/Parsons response . The strategy allows us to recognize a distinction between necessary and contingent properties and see these as genuine properties of objects (as

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Page 318 opposed to the Kaplanesque strategy considered above, which leads to a collapse of that distinction and the Quinean view, which entails that no objects have any properties as a matter of necessity). So, for example, it is Venus itself, independently of how or even whether it is designated, that is necessarily such-and-such and contingently so-and-so. But this is a long way from embracing anything that runs contrary to the analysis of necessity in terms of analyticity. The proponent of the Marcus/Parsons strategy maintains that there is a middle ground between a form of essentialism that sees objects, independently of how or even whether they are designated, having certain properties necessarily and a form of essentialism that runs contrary to the linguistic conception of necessity, according to which all necessity is ultimately linguistic or conceptual necessity. Occupying this middle ground provides for a powerful response to Quine’s Challenge. We need three things to spell this out more fully. First, we need a characterization of the distinction between trivial and philosophically problematic necessary properties. Second, we need support for the claim that QML only requires that objects have trivial necessary properties. And third, we need support for the claim that anti-essentialism is compatible with objects having trivial necessary properties. A necessary property of o is a trivial necessary property just in case necessarily every object necessarily has it. A philosophically problematic necessary property of o, on the other hand, is a necessary property that o necessarily has but other objects do not. We can then say, again following Marcus, that philosophically problematic forms of essentialism48 are ones that not only distinguish the necessary properties an object has from its contingent properties, but that go on to deny that every necessary property is had by every object.49 That is, philosophically problematic essentialist theses ascribe not only trivial necessary properties but philosophically problematic necessary properties to objects. Take the property being either exactly 5′9″ or not exactly 5′9″. It is a logical truth that everything is either exactly 5′9″ or not exactly 5′9″. So it is unobjectionable to say of me in particular that I am necessarily either exactly 5′9″ or not exactly 5′9″. That does not make me special and does not require that I possess some metaphysically mysterious objective nature contrary to the linguistic doctrine of necessity. The necessity resides in the aforementioned linguistic necessity. We can go further. It is unobjectionable to say that I analytically or logically satisfy the condition ‘ x is either exactly 5′9″ or not exactly 5′9″’. We can acknowledge that analyticity and logical truth are fundamentally features of closed sentences and explicate the notions of analytic and logical satisfaction in terms of these more fundamental notions. The explication does not require Aristotelian essentialism, in any philosophically problematic form, and does not lead to contradiction. We can see this by noting that, for any designator t such that t designates me, the closed sentence t is either exactly 5′9″ or not exactly 5′9″ is analytically true. There is no need

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Page 319 to privilege any proper class of designators as being more ‘essence revealing’ than other designators, given that every sentence of the above form is analytically true and so substituting any designator of me is guaranteed to deliver the same results. The reduction of the notions of analytic and logical satisfaction to the notions of analytic and logical truth does not require Aristotelian essentialism. An ‘invidious’ form of essentialism is one that would see certain necessary properties attaching to certain privileged entities and not to other entities. Such a form of essentialism may well require the world, independently of how we talk about it, to be the ultimate grounds of such necessary properties and thus may run contrary to the linguistic and conceptual conceptions of necessity. But this is not true of trivial necessary properties. If QML only requires that objects have trivial necessary properties, it is free of any philosophically problematic essentialist theses. I said above that the Marcus/Parsons response required three ingredients. We have presented the first and the third and now it is time for the second: Supporting the claim that interpreting the characteristic formulae of QML requires only attributing to object trivial necessary properties. Quine challenges the proponent of QML to explicate the notions of analytic and logical satisfaction in terms of the more familiar notions of analytic and logical truth (conceived as properties of closed sentences). The explication must avoid Aristotelian essentialism and yet be consistent with the fact that different predicates are analytically and logically connected to different ways of designating a given object. We propose to do this by setting up our system so that objects only have trivial necessary properties. The following principle does the job. REDUC: For any object o and condition Fx , o analytically/logically satisfies Fx just in case the universal closure of that condition xFx is analytically/logically true (that is, ).50 REDUC entails that objects only analytically or logically have properties that are trivial properties. We can see this by noting that (9) below is a consequence of REDUC, where is taken to be ‘it is analytic that’. (9) (9) says that if something is analytically such-and-such, then everything is analytically such-and-such. If REDUC is true, then a given object analytically satisfies a given condition just in case the universal closure of that condition is analytic. So, if something analytically satisfies a given condition, everything analytically satisfies that condition. But then nothing about the particular object in question determines whether or not it analytically satisfies a given condition; that is completely a matter of the logical status of the condition itself.

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Page 320 We should distinguish three characterizations of the thesis of Aristotelian essentialism. (1) The thesis of Aristotelian essentialism0 (TAE0) is the thesis that an object, independently of how or whether it is designated, necessarily has some properties. (2) The thesis of Aristotelian essentialism1 (TAE1) is the thesis that an object, independently of how or whether it is designated, necessarily has some properties and contingently has other properties, despite the fact that some of those contingent properties analytically follow from some ways of specifying the object in question. (3) The thesis of Aristotelian essentialism2 (TAE2) is the thesis that there is a privileged class of designators of an object that best reveal that object’s necessary properties, despite the fact that those properties do not analytically follow from other, nonprivileged designators of the object and other, contingent properties do analytically follow from some other, nonprivileged designators. Quine’s argument that QML runs contrary to the linguistic doctrine of necessity because it requires the thesis of Aristotelian essentialism turn on conflating these theses. There really is no simple distinction between ‘essentialism’ and ‘anti-essentialism’, as Quine and his followers seem to think. While we can grant that Quine is right that TAE2 is incompatible with anti-essentialist motivations in general and the linguistic doctrine of necessity in particular, he fails to establish that interpreting the characteristic formulae of QML entails TAE2. And while TAE0 is indeed a consequence of any interpretation of QML and, given a plausible assumption to be spelled out below, TAE1 is too, neither of these principles are incompatible with either the linguistic doctrine of necessity or anti-essentialist motivations. Quine needs a single thesis of essentialism that is both required by QML and incompatible with the linguistic doctrine of necessity. But there is no single thesis with both features.51 Let me substantiate these claims. Interpreting the formulae of QML requires TAE0, given that we have adopted a standard objectual semantics for quantified sentences. Let’s take ‘ x is self-identical’ as our example, which I shall take to be equivalent to x = x. I aim to show that, insofar as there are any objects, something analytically satisfies that condition (provided QML is sensible). x( x = x) is a classical logical truth and so x( x = x) is true. Not even Quine would balk at this, given his acceptance of the notion of logical truth. What I want to show now is that this is incompatible with claiming that x x = x is false, assuming the latter claim is deemed sensible. This would be straightforward if we were operating with a metaphysical notion of necessity, explicable in terms of truth at all possible worlds. x( x = x) is true just in case every world w is such that, for every individual o Dw, o = o at w. But if x x = x is false, then there is some object

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Page 321 o such that there is some world w at which there is a representer of o—say o′, which may just be o itself—such that o′ Dw and o′ ≠ o′ at w, which contradicts the conditions under which x( x = x) is true. Things are not so simple for us, however, as we are operating with a notion of strict necessity. Part of the problem here is that the very notion of logical satisfaction is up for grabs. So we need to take more care in arguing for the incompatibility of the truth of x( x = x) and falsity of x x = x. Suppose x x = x is false. We should then ask why. Not because there is some instance of t = t that is not logically true. x( x = x) is logically true and so every instance of t = t is logically true. But then surely every object is such that it satisfies x = x, assuming we are to make sense of an object analytically or logically satisfying a condition at all. There is no way of admitting that the characteristic formulae of QML are meaningful but simply insisting that we ‘count them all as false’ in order to avoid all commitments to any essentialist theses. Let’s grant that TAE0 is a consequence of claiming that the characteristic formulae of QML are meaningful. Should this be cause for fear? Not if we explicate the notion of logical satisfaction in terms of REDUC. There is nothing foreign to the spirit of anti-essentialism in TAE0, providing we are willing to saying that the only necessary properties any object has are necessary properties every object has, which is just what REDUC tells us. Let’s move, then, to TAE1. Whereas TAE0 is the thesis that objects have necessary properties, TAE1 is the thesis that an object has some properties necessarily and others contingently. TAE0 is weaker than TAE1, as TAE0 is compatible with there being only one way an object has a property: namely, necessarily. To see why this distinction is significant, recall the Kaplanesque view. This view falsifies TAE1. It is easiest to see this if we conceive the posited extra quantificational material introduced into de re modal claims as quantifying over designators rather than individual-concepts. (The argument works without this simplification.) So conceived, the Kaplanesque view says that o analytically satisfies the condition Fx just in case there is some designator t such that t designates o and Ft is analytically true. Suppose that o satisfies the condition Fx ; that is, suppose that o just plain old possesses the property associated with the condition Fx . Then there is guaranteed to be a designator that both designates o and is analytically connected to the condition Fx , assuming that there are any designators of o. The argument for this employs a trick Quine used to answer Church, discussed in note 27. Suppose that n is an individual constant with o as value and that the G designates o. Then both the object identical to n that is F and the G that is F designate o as well. Both descriptions are unique, as we have already supposed that n names only one object o and so only one object o satisfies x is an object identical to n and we have already supposed that the G designates o and so (assuming Russell’s theory of definite descriptions) there is only one object o that satisfies Gx and

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Page 322 we have already assumed that o also satisfies the condition Fx . So, putting it all together, we are guaranteed that o uniquely satisfies the condition x = n & Fx and the condition Gx & Fx . In both cases, the extra that is F in the two designators simply goes along for the ride, if you like. But notice that the sentences the object identical to n that is F is F and the G that is F is F are analytically true (assuming the descriptions designate). So, insofar as an object satisfies a condition, then, given the understanding of the notion of logical satisfaction provided by the Kaplanesque view, it analytically and logically satisfies that condition. Here’s the basic idea behind this argument. Insofar as we have a designator of an object, we can build a definite description of that object that contains any predicate that it satisfies. But then we are guaranteed to have a designator of that object that is analytically connected to any predicate it satisfies. So, given the Kaplanesque view, every object analytically satisfies any condition that it satisfies, which entails that no object contingently possess any property. So the Kaplanesque view leads to an obliteration of the distinction between necessary and contingent possession of a property and hence entails that TAE1 is false. Of course the Kaplanesque view requires TAE0, given that the view requires that objects necessarily satisfy conditions. (This follows, indeed, from the fact that the Kaplanesque view treats the quantifiers in the characteristic formulae of QML as standard objectual quantifiers.) REDUC and the claim that some closed sentences are analytically true and others, although true, are not analytically true, however, entails TAE1. For example, although I satisfy the condition ‘ x is writing’, I do not, given the understanding of the notions of analytic and logical satisfaction provided by REDUC, analytically or logically satisfy that condition, as the universal closure of that condition (that is, ‘Everything is writing’) is neither analytically nor logically true. So, I am mere contingently writing, although I am (for example) necessarily self-identical, given REDUC. Unlike the Kaplanesque view, the Marcus/Parsons view entails TAE1. But like TAE0, TAE1 is consistent with the reduction of all necessity to analyticity and logical truth, construed as properties of closed sentences, as I have argued, and thus deserves the title ‘anti-essentialist’. Let’s move to TAE2. We can admit that this thesis is indeed at odds with the reductionist ambitions of the linguistic doctrine of necessity. So, Quine must have TAE2 in mind when he writes: ‘Essentialism is abruptly at variance with the idea, favoured by Carnap, Lewis, and others, of explaining necessity by analyticity’ (Quine 1980:155). Privileging a proper class of designators is indeed at odds with seeing all necessity as fundamentally flowing from verbal necessity and not having an ontological basis in a mindindependent reality. For one owes some explanation for why that class of designators is being privileged and it seems hard to see how one could appeal to anything other than extra-linguistic facts in offering such an explanation.

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Page 323 The quote continues: ‘For the appeal to analyticity can pretend to distinguish essential and accidental traits of an object only relative to how the object is specified, not absolutely. Yet the champion of quantified modal logic must settle for essentialism’ (155). This claim is true only if Quine has in mind TAE0 and, given the assumption of a genuine distinction between contingently and necessarily having a property, TAE1. But it is decidedly false for TAE2. The champion of QML can avoid TAE2 by accepting either REDUC or the Kaplanesque view, both of which imply that TAE2 is false, as we have seen. To summarize, insofar as we assume standard objectual quantification theory, then the proponent of QML is committed to TAE0. And insofar as the system of QML allows for false instances of the schema , then TAE1 is also true. But both TAE0 and TAE1 are consistent with the linguistic doctrine of necessity. TAE2, on the other hand, is indeed inconsistent with this form of anti-essentialism. But interpreting the characteristic formulae of QML simply does not require TAE2. So Quine is wrong in thinking that the project of interpreting the characteristic formulae of QML—where quantifiers are objectual and necessity is strict—requires a philosophically problematic form of essentialism. The form of essentialism QML requires is philosophically unproblematic; the form of essentialism that is philosophically problematic is not required by QML. John Burgess, in (1997), is one of the few proponents of Quine’s argument against QML to address the possibility of analysing the truth-values of the characteristic formulae of QML in terms of the analytic status of closed sentence via REDUC.52 It is instructive to look at Burgess’s treatment of the matter. Burgess claims that Quine’s critique is limited to what Burgess calls ‘non-trivial de re modality’, by which he intends to exclude interpreting the characteristic formulae of QML in terms of REDUC (27). Burgess is not explicit about what he means by ‘ de re modality’ and there are at least three very different conceptions of the de re/de dicto distinction: One characterizing the distinction syntactically, in terms of whether or not open sentences are governed by a given operator; the other semantically, in terms of whether or not substitution of codesignating expressions within a given operator preserves truth-value; and the third metaphysically, in terms of whether or not given predicates correspond to genuine properties of objects.53 It is reasonable to interpret Burgess as being primarily concerned with a syntactic characterization of that distinction, as that is most directly related to QML. The characteristic formulae of QML are syntactically de re precisely because they involve open formulae governed by modal operators whose free variables are then bound by a quantifier outside the scope of that modal operator. In saying what he means by the ‘non-trivial’ in ‘non-trivial de re modality’, Burgess offers the example of explicating in terms of the trivialization axiom TA.

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Page 324   TA eliminates any doubt that the modal operator is intelligible, but only at ‘the cost of making the introduction of the modal notion pointless’ (28). And there is a very clear sense in which the modal notion we have interpreted has been rendered pointless by our efforts: TA (together with its converse, evidently valid of any alethic necessity operator) obliterates the distinction between material truth and necessary truth as it renders every truth necessarily true. Introducing is worth the trouble only if there are true claims that are not necessarily true and so only if TA is invalid. We have in TA a model of a problematic trivialization. With this example in mind, Burgess moves to trivializations of de re modality. A modal trivializing axiom is one that leads to a collapse of necessary truth to material truth. By analogy with the case of TA, a de re modal trivializing axiom is one that leads to a collapse of de re modality to de dicto. Burgess offers the following as an example of what he has in mind.   (10) is an immediate consequence of REDUC. So, if Burgess is right, then any interpretation of QML that entails REDUC—like the Marcus/Parsons view—simply fails to address Quine’s argument as, according to Burgess, Quine’s argument is targeted at nontrivializing interpretations of QML that invalidate (10).54,55 TA is our model of a problematic reduction. But is (10) similarly problematic? Burgess writes: (10) corresponds to the trivializing definition to which F holds necessarily of a thing just in case it is necessary that F holds of everything—a definition that could silence any critic who claimed the notion of de re modality to be more obscure than that of de dicto modality [that is, a critic just like Quine—see in particular (1943)], but would do so only at the cost of making the introduction of de re notation pointless. (28, bold added) Burgess is too quick in assimilating the problematic character of TA to (10) and REDUC. TA is troubling because it leads to a collapse of material and necessary truth. The worth of modal logic rests precisely on drawing this distinction. But what is the similarly crucial distinction that a proponent of REDUC fails to preserve? Burgess never spells it out. There still is a difference between de re and de dicto formulae, if one cashes that distinction out syntactically. Now granted, the truth-value of any de re formulae is defined in terms of the truth-value of de dicto formulae. But a proponent of Quine’s argument can hardly complain about that; Quine’s Challenge requires that we explicate the de re formulae in terms of de dicto formulae! If we were

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Page 325 allowed to explicate the de re formulae entirely independently of any de dicto formulae, Quine’s argument would never get off the ground. Burgess’s ban on trivializing axioms is tantamount to a demand that one’s QML be problematically essentialist. But then Burgess’s ban reduces Quine’s complaint that QML requires a philosophically problematic essentialism to the banality that, provided proponents of QML are to interpret the characteristic formulae of QML in such a way as to be problematically essentialist, then they are committed to problematic essentialism. We should all agree with that. But, it would leave unsettled the interesting question whether or not proponents of QML need to interpret the characteristic formulae in a problematically essentialist (that is, nontrivializing) manner. I claimed that the ban on trivializing axioms is equivalent to the requirement that the system be essentialist in a philosophically problematic way. Here’s why. Suppose all trivializing axioms are false. In particular, suppose that the trivializing axioms that both REDUC—(10) reproduced below—and the Kaplanesque view—(11) reproduced below—entail are false.   Let us grant Quine’s point that there are pairs of designators t and t ′ that both designate the same object but that are analytically connected to different predicates. (Only the most extreme necessitarians —a conceptual necessitarian, according to whom every truth is analytically true—would claim otherwise. And such a view entails (11), assuming there is room in such a view for de re modality, and so has already been excluded by our assumption above.) Then one can consistently ascribe necessary properties to objects only if one privileges a certain subclass of designators in determining which conditions an object necessarily satisfies. But this is our TAE2, which we know to be philosophically problematic. Burgess does not justify the claim that the trivializing axioms (10) and (11) make ‘the introduction of de re notation pointless’ in the way in which accepting TA makes ‘the introduction of the modal notion pointless’. The trivializing axioms (10) and (11) do make necessary properties less interesting. It is only the substantive, philosophically problematic necessary properties that are interesting and their interest brings with it their problematic character. But this essentialism is not intrinsic to the characteristic formulae of QML. The interesting necessary properties are philosophically problematic necessary properties like necessarily being greater than 7 and necessarily being human; properties that a proper subset of the objects there are necessarily have. I am not arguing that we should refuse to ascribe philosophically problematic necessary properties to objects. Rather, I am arguing that such ascriptions are independent of thinking that QML is coherent. If one has no qualms about ascribing such properties to objects

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Page 326 and looks to QML to formalize such attributions, there is no question that in interpreting the characteristic formulae of QML one will deny the trivializing axioms. But that is only because one has brought philosophically problematic essentialist theses to QML; it is not forced on one merely in virtue of sitting at QML’s table. Quine’s argument is worth worrying about only if he can show that those who are not antecedently inclined to think that objects have problematic essences are forced to ascribe such essences in interpreting QML. And that requires rejecting Burgess’s ban on trivializing axioms. But once the ban is lifted, as I have argued, Quine’s argument is unconvincing, as it turns on an equivocation between distinct essentialist theses. My claim that Quine’s argument turns on equivocating between distinct theses of essentialism parallels Parsons’s (1967) and (1969) response to Quine, who in turn was following points implicit in Marcus (1967). Parsons too accused Quine of equivocating on his use of ‘Aristotelian essentialism’, or, when the argument did not employ that term, of equating claims like ‘Everything is necessarily self-identical’ with claims like ‘Something is necessarily greater than 7’ or ‘Something is necessarily human’. There is, I hope, something to be said in favour of resurrecting this response, as these points have either been completely ignored—as they are, for example, in Neale (2000)—or misappreciated—as they are, for example, in Burgess (1997). But I do not think that Marcus and Parsons were completely successful in developing an interpretation of QML free of all problematic essentialist theses. This is because Marcus’s and Parsons’s systems validate the necessity of identity, which is contrary to the spirit of antiessentialism and incompatible with the linguistic doctrine necessity. I show this by arguing that the necessity of identity leads to TAE2. After supporting this contention I shall show how to free the Marcus/Parsons view from these remaining essentialist commitments. In claiming that identity properties are problematic as necessary properties, one must distinguish selfidentity properties from being-identicalto-x properties. It is only the latter kind of identity properties that are problematic as necessary properties. Let’s take a particular example of the second kind of property: the property being identical to George W. Bush . GW instantiates both the properties being identical to GWB and being self-identical . But GW, and GW alone, instantiates the former whereas every object instantiates the latter. So the two properties are distinct, as there are objects (everything other than GW) that instantiates the one but not the other. The first property is referential with respect to GW or individual-involving . Indeed, on my view this property is constructed from GW and the two-place relation is identical to by abstraction. The second property, on the other hand, is individual-independent. Whereas the first property presupposes the existence of a particular object—GW—the second property does not. Indeed, the notation of attribute abstraction well encodes this

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Page 327 difference. With that notation, the property being identical to GWB is represented as whereas the property being self-identical is represented as

 

  This is all to follow quite closely (Marcus 1967:94). So, in claiming that identity properties are problematic as necessary properties, I mean individualinvolving identity properties; the individual-independent identity property is a paradigm of a trivial necessary property. The necessity of identity is the following thesis.   Why does NI commit one to a problematic form of essentialism? There are several reasons. First, it is philosophically problematic precisely because so many have been keen to reject it, as it witnessed by the work of Allan Gibbard (1975) and David Lewis (1986), to name just two opponents of the thesis. And the rejection of this thesis is, in some minds, tied to an adequate resolution of certain philosophical puzzles, like the puzzle of material constitution, the problem of qualitative change across time, and the problem of accidental intrinsics. Marcus and Parsons are correct in thinking that commitment to just the necessity of identity is less problematic than commitment to other essentialist claims, like the claim that some things are necessarily human. There are grades of problematic essentialist attributes and necessary identity attributes are surely the lowest grade. One might think that I am necessarily MN, for example, without thinking that I thereby have an Aristotelian essence or a substantive nature. One might say that the only general necessary properties objects have are trivial necessary properties and the only discriminating necessary properties objects have are necessary identity attributes. This is surely a weaker form of essentialism than claiming that objects also have general necessary properties like being human as well; that is, necessary properties that are both discriminating, in the sense that they are not possessed by all objects, and general. But there is a clear sense in which any theory that entails that I am necessarily MN, for example, is stronger than a theory that denies that any object has any philosophically problematic property. But there is a more robust reason for an anti-essentialist proponent of QML to reject NI. Proponents of NI widely recognize that NI is true only if

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Page 328 a and b are what Saul Kripke calls rigid designators (1971, 1980). ‘George Bush is the current president of the US’ is true even though, on the intuitive view, ‘Necessarily, George Bush is the current president of the US’ is false. The common explanation is that ‘the current president of the US’ nonrigidly designates GW in virtue of contingent properties he instantiates, whereas ‘George Bush’ does not. But, as we have seen in ‘The Failure of the Russellian Response’, this distinction between rigid and nonrigid designators requires embracing the very ‘invidious’ distinction between ways of designating objects Quine challenged proponents of QML to avoid; it leads directly to TAE2. So, a proponent of NI is either left with no explanation of the intuition that, although ‘George Bush is the current president of the US’ is true, its necessitation is false, or else embracing TAE2. We can go a step further. Employing once again Quine’s trick of building richer descriptions from others, we can see that accepting both NI and the ‘equal-treatment to all ways of designating an object’ attitude Quine’s anti-essentialism forces on us requires the claim that an object necessarily possesses every property it possesses, which is bad news indeed to the Marcus/Parsons view. Suppose o in fact satisfies the condition Fx , whether uniquely or not. Then we can construct a definite description that designates o and includes the predicate Fx by using the Quinean trick—say, the description the G that is F , where we assume o to uniquely satisfy the condition Gx. Let n be any designator of o. Then the G that is F = n is true. But, given NI, so too is its necessitation. But then o necessarily satisfies the condition Fx . For if it did not, the necessitation of the above identity would not be true. The idea behind the argument is easiest to see if we wax metaphysical and speak in terms of possible worlds. Suppose the G that is F = n , where n is any arbitrary designator of o, is true just in case its necessitation is true. Then the G that is F designates o with respect to every world w (at which it designates anything at all). But the G that is F designates an object with respect to a world w only if that object satisfies both Gx and Fx at w. But then o satisfies Fx in every world w (in which o exists). So o necessarily satisfies Fx if it satisfies Fx at all. This result is highly problematic for the proponent of the Marcus/Parsons view. Because objects evidently satisfy different conditions—that is, there evidently are pairs of objects o and o′ and condition Fx such that o satisfies Fx and o′ does not satisfy Fx —the elimination of the distinction between necessarily having a property and merely contingently having a property is incompatible with the claim that objects only have trivial necessary properties, in the sense that the only necessary properties any object has are necessary properties every object has. So, the very strategy employed by the Marcus/Parsons response is incompatible with both NI and the indiscriminating attitude towards ways of designating objects Quine’s anti-essentialism requires.56 The Marcus/Parsons response itself thus requires that NI be false.

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Page 329 Grant me that the necessity of identity (NI) is problematic in a way that the necessity of self-identity (NSI) is not. NI: If a = b, then, necessarily, a = b. NSI: Everything is necessarily self-identical. Then our problem becomes: How do we devise our modal logic so that it allows necessitation on the instantiation of self-identity, thus allowing us to infer from the fact that something is self-identical that it is necessarily self-identical, but not the instantiation of an individual-involving identity properties? That is, how can we validate NSI and invalidate NI? It turns out that we have already done it. We should simply accept an unmodified form of REDUC. REDUC: For any object o and condition Fx , o analytically/logically satisfies Fx just in case the universal closure of that condition xFx is analytically/logically true. GW analytically and logically satisfies ‘ x is self-identical’ (or x = x) because the universal closure of that open sentence (that is, x( x = x)) is analytically and logically true. But the universal closure of the condition x = GW (that is, x( x = GW )) is neither logically nor analytically true. Indeed, it is false under every interpretation with a domain with more than two objects or in which GW does not exist. So GW does not analytically or logically satisfy ‘ x is GW’. Everything is logically (and hence analytically) selfidentical, but nothing, including Bush himself, is logically (or analytically) identical to GW. So, NSI is valid but NI is not. We have banished the last remnants of the philosophically problematic essentialist consequences left in Marcus’s and Parsons’s views. CONCLUSION The Russellian response to Quine’s argument against QML was presented and evaluated. It was found to rest on a misunderstanding. Rather than turning on deriving of a contradiction from the failure of intersubstitutivity of codesignating singular terms within modal sentences, as the Russellian reads Quine, Quine’s argument turns on the allegation that QML requires a problematic form of Aristotelian essentialism. Once Quine’s argument is properly understood, we find that the Russellian response simply fails to adequately address its main contention. But Quine’s argument fails to convince. The argument conflates different conceptions of the thesis of Aristotelian essentialism. QML does indeed

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Page 330 require one form of that thesis: The thesis that an object, independently of how or whether it is designated, necessarily has some properties. But that thesis is consistent with the linguistic doctrine of necessity. Another form of the thesis is indeed inconsistent with the linguistic doctrine of necessity: The thesis that there is a privileged class of designators of an object that best reveal that object’s necessary properties, despite the fact that those properties do not analytically follow from other, nonprivileged designators of the object and other, contingent properties do analytically follow from some other, nonprivileged designators. But QML does not require that thesis. I developed two ways of interpreting the characteristic formulae of QML, both of which entail the first thesis and the negation of the second. These interpretations silence any Quinean worries that QML is at odds with a robustly anti-essentialist metaphysics. Philosophically suspect essentialist metaphysics are not built into the fabric of QML but rather brought to QML from some external source. NOTES 1. Thanks to the members of my fall 2004 opacity class at Yale University—Christopher Holownia, Samuel Newlands, Gaurav Varirani, and Leslie Wolf—where this material was first worked out. Thanks also to numerous discussions with Troy Cross, Michael Della Rocca, and Robin Jeshion. I presented this material at the ‘Russell vs. Meinong’ conference at McMaster University in May 2005. Thanks to those present for discussion and especially the organizers, Nicholas Griffin and Dale Jacquette, for the opportunity to participate in such a unique event. I have also presented versions of these ideas at Arizona State University, University of Toronto, University of Massachusetts-Amherst, University of California-Riverside, and at a lunch philosophy discussion at Yale University. ‘The real Quine’ and ‘Quantifying in for the Anti-Essentialist’ of the present paper overlap with Nelson (‘Anti-Essentialism and the de re ’), which in turn is the first of a trio of papers exploring the relationships between essentialism and modal metaphysics (the other members being Nelson (‘On the Contingency of Existence’) and (‘Necessary Essence’)). 2. Both the theory of descriptions and the views of acquaintance were present in Russell (1905), but the former was more fully developed in Whitehead and Russell (1925) and the latter in Russell (1903) and (1905). 3. Quine developed his attack on QML in a number of papers, especially (1943), (1947), (1953a,b), and (1961). 4. There are perplexing issues concerning how this combination is to be pulled off, even after Quinean worries with the bare possibility of such a combination are settled. Most of these issues revolve around whether to employ fixed or varying domains. I discuss this issue in Nelson (forthcoming). Also, it is contentious whether or not the characteristic S4 and S5 axioms constitute part of a system of our ordinary modal thinking. (See Salmon (1989) for compelling arguments that they do not.) For the present paper, however, we can set these concerns to the side. 5. Smullyan, in (1947) and (1948), was the first to present this response, followed by Fitch (1949) and Marcus (1948) and (1963). Russell himself never, to my knowledge, discussed this use of his doctrines.

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Page 331 6. The evidently true II is distinct from its evidently, at least after due reflection, false converse— the Principle of the Identity of Indiscernibles (PII), that, for all x and y, if, for all qualities F , x is F iff y is F , then x = y. Qualities are object-independent properties. So, for example, the property being identical to Adam is not a quality of Adam (although it is a property of Adam), precisely because it is dependent on Adam. If object-dependent properties were included in the scope of the second-order quantifier in PII, then we would have a principle even more evident than II. (Both Adam and Bill having the property being identical with Adam is obviously sufficient for Bill’s being identical with Adam.) PII is philosophically interesting only when the indiscernibility is qualitative indiscernibility. Historical proponents of the principle, and in particular Leibniz, clearly intended the principle in this way. For an excellent discussion of this matter, see Adams’s classic (1979). 7. I shall discuss why Quine thought that (2) is true in ‘The Real Quine’. For now, we shall simply grant it. 8. SUB is obviously invalid. The truth of ‘“Hesperus” starts with the letter “h”’ and ‘Hesperus is Lucifer’ hardly suffices for the truth of ‘“Lucifer” starts with the letter “h”’. We at least need to exclude substitution within quotation. We also need to exclude substitution that affects the semantic values of other elements of the sentence. Quine’s example of ‘so-called’ most plausibly fit this bill. Because an occurrence of ‘so-called’ refers to the name that occurs before it, the truth of ‘Giorgione was so-called because of his name’ and ‘Giorgione is Barbarelli’ does not guarantee the truth of ‘Barbarelli was socalled because of his name’, as the substitution affects the semantic value of ‘so-called’. (This is not Quine’s description of why substitution fails, but it comes to more or less the same thing. For Quine’s account, see 1980:140–41, where Quine proposes to analyse ‘so-called’ sentences explicitly in terms of quotation-sentences. Quine appreciated that we do not need to analyse all opaque environments in terms of quotation (1980:144), even if Quine clearly preferred such reductions, analysing ‘believes that’ in terms of ‘believes true’ and ‘it is necessary that’ in terms of ‘is analytically true’, the latter of each pair taking sentence-names as objects.) Some would say that substitution within the scope of propositional attitude verbs like ‘believes’ are not truthpreserving. But this is controversial and I think false. Propositional attitude verbs do not create counterexamples to the simplistic form of SUB given in the text. For a defence of this claim, see Salmon (1986). I argue for the claim in Nelson (2005). Present purposes do not require a precise formulation of SUB. The formulation presented in the text suffices. 9. I am attributing to Russell a structured proposition view, which he seems to have held early in his career (for example, in (1903) and (1905)), where a proposition is the bearer of truth-value, what a sentence says, and the object of propositional attitudes and so what an agent grasps, entertains, believes, and asserts. Such entities are structured in the sense that they are built from prior materials and have constituents as parts. (Frege too held a structured proposition view, although Frege differed sharply with Russell about their constituents.) Russell was not easy with this ontological commitment, even when he was espousing it. Part of what Russell found worrisome was the classic problem of the unity of the proposition: The problem of accounting for what ‘glues’ the disparate constituents of a proposition together into a single entity capable of bearing a truth-value. By (1906) Russell began developing his multiple relation theory of judgement, which received its fullest development in (1913), which allowed him to eschew commitment to propositions, at least as the objects of the attitudes. For simplicity, I shall ignore

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Page 332 these developments and present Russell as an unequivocal proponent of the structured proposition view. 10. The Acquaintance Principle makes an appearance in Russell (1905). But it is not until (1910) and (1912) that the views being described here are fully developed. 11. Russell sometimes claimed that we are also acquainted with ourselves. But he typically seems to have been convinced by Humean doubts about the self’s self-presentation and hence he seems to have been dubious of one’s acquaintance with one’s self qua substance as opposed to acquaintance with one’s mental states. 12. In an ingenious case, Austin, in (1990), shows that Frege-cases do not require temporally separated presentations of the same object. He describes a case—what he calls ‘the two tubes case’—in which an agent looks through two tubes, one for each eye, at a single object but is unsure whether the object seen with her right eye is the same as the object seen with her left eye, as she knows that the tubes can be directed in independent directions. (The object perceived, we can suppose, is a simple object—a paper clip, say—that the agent knows has many indistinguishable, as far as the agent is concerned, twins about it.) For simplicity, however, I shall deal in the text solely with temporally separated presentations of a single object. No significant issues turn on this. 13. Contemporary neo-Russellians who follow Russell in thinking that we can think directly about certain items have a more permissive view of the objects of acquaintance, including material particulars in this class. (Kaplan’s pioneering work (1989) is typically the starting point for such work, although Russell himself started out with such a position, maintaining, for example, that Mount Blanc itself is a constituent of the thought that Mount Blanc has snowfields .) They must thus deny the Fregean claim that whenever misidentification is possible, there is a difference in thought constituents. Neo-Russellians might still agree with Fregean intuitions about the truth and falsity of belief and other propositional attitude ascribing sentences, but insist that those truth deliverances do not require a difference at the level of thought constituents (following, for example, Crimmins and Perry 1989 or Richard 1990), or they may go on and deny as well the Fregean intuitions about the truth and falsity of propositional attitude ascribing sentences (following, for example, Salmon (1986)). But, given that misidentification of material particulars is obviously possible, a permissive theory of acquaintance requires denying what I called in the text the Fregean attitude towards misidentification, according to which all cases of misidentification are to be explained in terms of a difference in thought constituent. I am conceiving of the acquaintance relation as whatever enables direct thought. Jeshion (2002) presents a view according to which there is acquaintanceless direct thought about concrete objects. What I have been saying here is, however, consistent with her view, as her main aim is to show that the capacity to directly think about an object does not require causal contact with that object and can be achieved by descriptive thought, provided the thought plays a certain cognitive role; it is the cognitive role, not some other factors, that is determinative of whether an act of thinking is directly about its object or indirectly about it. I have not committed myself to any particular view on the perplexing matter of the conditions under which acquaintance is secured or direct thought is possible. 14. Kaplan’s (1975) is a very insightful discussion of the differences between Frege’s and Russell’s philosophies of language and thought. 15. I shall be more precise regarding the ultimate form of this thought on Russell’s view below, when discussing Russell’s theory of descriptions.

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Page 333 16. Thanks to Nicholas Griffin for correcting my misunderstanding of Russell’s views on sense data as mental entities. 17. Strawson does not, in all of Part 1, mention Russell by name. But it seems that he had Russell in mind as his target, as the opening sentence of the passage quoted in the text strongly suggests. 18. This intuition is even stronger with thoughts about oneself. When I think to myself, ‘I am hungry’, my thought is about me, not the guy who looks just like me and is having the same form of thought. I do not think about myself, as opposed to someone else, in virtue of having a purely qualitative description that determines me, for otherwise, in the reduplication universe, I could not succeed in thinking about myself. 19. This notation for marking scope distinction does not correspond to the notation used by Whitehead and Russell, although it achieves the same effect. I get it from Neale (2000). 20. As things actually are, (6nexpanded) is true because nothing uniquely satisfies ‘ x is present King of France’. (6wexpanded) is false because its first conjunct is false for the same reason (6nexpanded) is true. 21. It is also possible, of course, that one of the terms is a logically proper name and the other a disguised definite description. I only consider the unmixed possibilities as the mixed possibilities do not change the situation. 22. In claiming that in this case (2) and (4) express the same proposition, I am assuming a simple view of the semantics of ‘necessarily’. In particular, I am assuming that modals like ‘necessarily’ are only sensitive to the content of the expressions they govern. This can be denied, as I show in my ‘AntiEssentialist and the de re ’. I there show that one can claim that both ‘Hesperus’ and ‘Lucifer’ are genuine proper names and hence that both subsentences of (2) and (4) express the same proposition, but insist that nonetheless (2) and (4) themselves differ in truth-value because ‘necessarily’ is sensitive to more than just the content of the expressions it governs. For simplicity I shall stick with a simplistic understanding of how ‘necessarily’ functions. It should be noted that the more complex understanding is no help to Quine as his argument fails if we accept it. 23. Here is a sampling of passages in which Quine endorses Russell’s theory of descriptions: Quine 1937:85; 1948:5–7; 1951:30; 1953a: 173. 24. My understanding of Quine’s argument owes much to Fine’s excellent (1989) and (1990). 25. Burgess (1997:44–45, including n25), accuses Marcus of not giving Smullyan priority credit in developing the Russellian response. He notes that in Marcus (1963), Marcus does not cite Smullyan but instead calls the scope response ‘familiar’ and notes that in an earlier paper Marcus cites Fitch but not Smullyan. However, Marcus reviewed Smullyan’s paper (Marcus 1948), where, of course, she credits Smullyan, and she writes in the republished version of ‘Modalities in intensional languages’ included in her (Marcus 1993): ‘It is worth noting that in saying, in the text that follows, that “I have never appreciated the force of the original argument” about failures of substitutivity in modal contexts, I had assumed that Smullyan’s paper “Modality and Description” . . . was fully appreciated. Smullyan had shown that Russell’s theory of descriptions, properly employed with attention to scope, dispelled the puzzles’ (3). 26. Quine’s earlier (1943), however, did not suffer from these problems. 27. The flaws Quine recognized are independent of the Russellian response. Quine (1947) purports to show that there are intractable problems in providing modality a solid foundation ‘if one cares to avoid a curiously idealistic ontology which repudiates material objects’ (43). More precisely, Quine there

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Page 334 argued that QML ‘is committed to an ontology which repudiates material objects (such as the Evening Star properly so-called [i.e., the planet Venus itself]) and leaves only multiplicities of distinct objects (perhaps the EveningStar-concept, the Morning-Star-concept, etc.) in their place’ (47). By (1953b), Quine saw that not even the banishment of material objects and the replacement of the ‘curiously idealistic’ entities in their place suffices to avoid the problem. The argument for this, found in Quine (1980:152–53), is ingenious. In essence, Quine notes that the same intensional object is picked out by both A and ( ιx)[ p & ( x = A)], insofar as p is a true sentence. But if p is contingently true, then the replacement of A with its codesignating ( ιx)[ p & ( x = A)] within the scope of a modal can affect truthvalue. The move to intensional entities was supposed to solve Quine’s problem by delivering entities such that all of the different ways of designating them are analytically equivalent. But, as the above argument shows, not even intensional entities satisfy this condition; indeed, no object satisfies that condition, as long as we have descriptions and any contingency. 28. Quine (1980:156) turns this argument back against modal logic itself in an ingenious way. Given that the modal operator is to be explicated in terms of analyticity, if we only allow modal operators to attach to closed sentences, which is what we must do if we are to stop just short of QML, then we have robbed ourselves of any reason for introducing them. This is because every modal formula p will be equivalent to a nonmodal sentence like ‘The sentence “ p” is analytically true’. Assuming is to be explicated in terms of analyticity, it is only from the promise of quantifying in that modal logic proves its worth. 29. Quine tends to speak of essential and accidental properties when it is clear what he means is merely necessary and contingent properties. An essence, properly called, rather than a mere necessary property, is a property that answers the What is it? question. The distinction is present in Aristotle, but it is Fine (1994) and (1995) who is responsible for bringing this important distinction back into focus. As Quine’s argument targets the notion of a necessary property (as opposed to an essential property properly called), I shall replace his talk of the former for the latter. 30. There are at least two ways of construing the notion of logical truth. The first is syntactic, as truth in virtue of syntactic logical form, and the second is propositional, as truth in virtue of propositional logical form. We can see how these two conceptions come apart by considering the possibility of two distinct, nonlogical expression types, e and é , with the same content. Both is and is e xpress the same proposition. But because e and é are not part of the logical vocabulary, it is highly plausible to insist that the first is a logical form that is true in any interpretation of the nonlogical vocabulary whereas the second is not, in which case the first is true in virtue of syntactic logical form alone whereas the second is not. If, however, we are operating with a propositional conception of logical truth, then, as both sentences express the same proposition, it is implausible to think that the one is a propositional logical truth and the other is not and indeed it is highly plausible that both are logically (under the propositional conception) true. This divergence is most clear for the neo-Russellian, who insists that ordinary proper names like ‘Hesperus’ and ‘Lucifer’ are directly referential expressions. Because such expressions are pieces of the nonlogical vocabulary, there is a clear difference in the syntactic logical form of ‘Hesperus is Hesperus’ and ‘Hesperus is Lucifer’. At the level of syntactic logical form, the first is of the form is whereas the second is of the form is . There is a clear sense in which the first is guaranteed to be true by its logical form

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Page 335 alone whereas the second is not. But at the propositional level, because both sentences express the very same proposition (again, assuming neo-Russellianism), it is hard to see how we are going to find any way to similarly distinguish the logical form of what they express. On standard neo-Russellian views, both sentences express the singular proposition represented as <, IDENTICAL WITH>. It is extremely plausible to say that the form of this proposition is guaranteed to be true and so both identity sentences are logically true under the propositional conception. In the text I shall focus exclusively on syntactic logical form, which was clearly Quine’s focus. The propositional conception raises important and fascinating issues, but they are beyond the scope of the present paper. Thanks to Nathan Salmon for very helpful discussion of this topic. 31. ‘The notion [of analyticity, although, as Quine says, itself lacking a satisfactory foundation] is clearer to many of us, and obscurer surely to none, than the notions of modal logic; so we are still well advised to explain the latter notions in terms of it’ (1947:45). ‘The general idea of strict modalities is based on the putative notion of analyticity’ (1980:143). 32. Why ultimately logical truth? Because Quine explains analyticity in terms of logical truth and synonymy. A statement is analytic ‘if by putting synonyms for synonyms (e.g., “man not married” for “bachelor”) it can be turned into a logical truth’ (1947:44), where two expressions are synonyms just in case they mean the same thing (see paragraph 5 of the same paper) and a truth is a logical truth just in case it is deducible by the logic of truth-functions and quantification from true statements containing only logical signs (see paragraphs 2 and 3 of the same paper). 33. As we have the Russellian response fresh in mind, I should stress that Quine can stipulate that (2) is to be taken as (2dn) and (4) as (4dn). The Russellian agrees that, so understood, (2) is true and (4) is false. That is all Quine needs. In particular, he does not further need to maintain that that variation in truth-value itself violates Leibniz’s principle or SUB. We will see that that plays no role in the argument, as I present it. 34. Marcus makes this point in (1963). It was also discussed in the famous general discussion that followed her presentation, an edited transcript of which is published as (Marcus et al . 1963). I think it unfortunate that this point was not sufficiently separated from the other objections Marcus raised to Quine’s argument, as it really stands on its own. If one insists on treating quantifiers substitutionally, then Quine’s arguments against QML, in the form he presents them, do not get off the ground. There are, however, two points to be made. First, as I say in the text, this fact should not really bother Quine, as his intended target is the combination of standard, objectual quantification theory and modal logic. Second, it is not clear that the move to substitutional quantification avoids all Quinean worries. The Hesperus case is supposed to establish that all of the following sentences being true: t = t′ , Gt , and ~ Gt′ . If the quantifiers are substitutional, there will be no problem in accounting for the consistency of and , even when we have just a single object in our domain, provided we can account for the consistency of Gt and ~ Gt′ when we have just a single object in our domain (and where all individual constants have values). This is because the first only requires there be some singular term s such that the relevant substitution instance is true and the second only requires there be some singular term s′ such that the relevant substitution instance is true. But there is still a problem. We need to either block the derivation of x(φ Gx & ~φGx) or, if the derivation is allowed, explain why it is not contradictory. The simplest form the derivation will take will involve substituting t for t′ in ~φGt ′, conjoining

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Page 336 the result with Gt , and then applying EG. One might deny the validity of the substitution, of course, but nothing about operating with a substitutional conception of quantification is going to help here. Also, there may well be more devious ways of deriving the result. On the other hand, one might allow the derivation and show that the derived result is (strangely!) consistent by claiming that different occurrences of x governed by the same substitutional quantifier can take different terms as substitutional instances. I’m not sure how to make this idea precise in the model theory, but I do not doubt that it can be done. 35. In (1956), Quine presented a similar argument against quantifying in to propositional attitude verbs like ‘believes’ and ‘knows’. Quine took a very different attitude towards the results, however. Whereas he was inclined to dismiss as completely misguided any notion of quantifying in to modal operators, he found quantifying in to propositional attitude verbs—or something that looks very much like that— indispensable and so posited a semantic ambiguity in ‘believes’, positing (or is it uncovering?) a relational, three-place verb and a distinct nonrelational, two-place verb. The former permitted quantification (although not into an opaque position) and the latter did not. Although the arguments are similar—indeed, both of Kaplan’s two critiques of Quine are simultaneously run as critiques of both Quine’s arguments concerning modality and propositional attitudes—I think that fundamentally different considerations are raised, given that Quine’s most powerful arguments against quantifying in, in my opinion, are his nonlogical arguments, which turn on very different metaphysical and epistemological assumptions: The argument against QML turns, as we have seen, on antiessentialist assumptions and ultimately reductionism of all forms of necessity to linguistic necessity, whereas the arguments against quantifying in to propositional attitude verbs turn on Fregean assumptions about cases of misidentification. 36. Quine’s ‘Reference and Modality’ went through three versions, with the three printings of From a Logical Point of View . Although Quine did finally come around to seeing what is right about the Russellian response in the third version—he writes: ‘Then, taking a leaf from Russell [namely (1905)], he [Smullyan] explains the failure of substitutivity by differences in the structure of the contexts, in respect of what Russell called the scopes of the descriptions’ (Quine 1980:154)—Quine’s initial response to Smullyan was confused. In the first version of ‘Reference and Modality’, Quine responded to Smullyan by claiming that his ‘argument depends on positing a fundamental division of names into proper names and (overt or covert) descriptions, such that proper names which name the same object are always synonymous … He observes, quite rightly on these assumptions, that any examples which … show failure of substitutivity of identity in modal contexts, must exploit some descriptions rather than just proper names. Then he undertakes to adjust matters by propounding, in connection with modal contexts, an alteration of Russell’s familiar logic of descriptions. [Footnote:] Russell’s theory of descriptions, in its original formulation, involved distinctions of so-called “scope”. Change in the scope of a description was indifferent to the truth-value of any statement, however, unless the description failed to name. This indifference was important to the fulfillment, by Russell’s theory, of its purpose as an analysis or surrogate of the practical idiom of singular description. On the other hand, Smullyan allows difference of scope to affect truth-value even where the description concerned succeeds in naming’ (Quine 1953:155). (The same passage survives the first revisions of 1963; see Quine 1961:154.) Quine is simply wrong that Smullyan is revising Russell’s

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Page 337 theory of descriptions by finding scope ambiguities that affect truth-value without failures of existence. Whitehead and Russell are clear that scope ambiguities between operators and descriptions do not result in differences of truth-value unless the description does not designate holds only for extensional environments. Indeed, as mentioned above, Russell’s own solution to King George’s wonderment requires as much. (Marcus notes these changes in Quine’s argument and the mistakes of his earlier attitudes (1990:236).) Quine is extremely nonchalant about this radical revision from the first to second set of revisions; see Quine 1980: vii. 37. Neale writes: ‘It would seem that if the common-sense mode of inference [of substituting salva veritate codesignating singular terms] is to be maintained in modal logic, co-referential names will have to be synonymous. No-one has rushed to embrace this view yet. Perhaps they will’ (2000:297). Neale seems unaware that Smullyan, Fitch, and Marcus all clearly endorse the view he cites as something someone might embrace. I have already cited Marcus’s endorsement of the view. Smullyan writes: ‘However, we observe that if “Evening Star” and “Morning Star” proper-name the same individual they are synonymous and therefore B [the sentence “Evening Star is congruent with Evening Star & ~(Evening Star is congruent with Morning Star”] is false’ (Smullyan 1947:140). Fitch references Smullyan on this point with approval (Fitch 1949:138). Furthermore, critics of the Smullyan/Fitch/Marcus view have noticed it too. Church’s review of Fitch (Church 1950) focuses primarily on this point, which he finds objectionable. Church writes: ‘It would seem to the reviewer that, as ordinarily used, “the Morning Star” and “the Evening Star” cannot be taken to be proper names in this sense [i.e., synonymous]; for it is possible to understand the meaning of both phrases without knowing that the Morning Star and the Evening Star are the same planet. Indeed, for like reasons, it is hard to find any clear example of a proper name in this sense’ (63). (It should be noted that Church’s argument against Fitch’s view can just as easily be used to show that any contentious philosophical analysis—even Frege’s own analysis of number —is not sense preserving and hence the explicans and explicandum of a successful philosophical analysis are not synonymous. I think that this should cast doubt over this form of argument.) 38. Quine seems to not have appreciated Kripke’s comments. In the published version of the discussion, Quine follows Kripke’s remarks by more or less changing the subject, talking about substitutional quantification and complaining that Marcus does not properly understand the nature of quantification. Kripke brings him back to the point of appealing to tags as the essence-revealing designators by saying: ‘Now then granted this, why not read “there exists an x such that necessarily p of x” as (put in an ontological way if you like) “there exists an object x with a name [i.e., tag] a such that p of a is analytic”. Once we have this notion of name, it seems unexceptionable’ (116). Quine then comes around to Kripke’s earlier point that, although not contradictory and in no way involving the rejection of objectual quantification, contrary to his previous complaint, the suggestion requires accepting the Aristotelian essentialist privileging of a proper class of designators as revealing the essence of an object. It doesn’t appear, however, that he appreciates that that was exactly what Kripke had originally said. 39. It was Marcus who first characterized Quine’s attitudes towards QML as that of being conceived in the sin of confusing use and mention (Marcus 1963:77). Quine embraced the characterization (Quine 1963:97). 40. Recently both Burgess (1997) and Neale (2000)—the later reversing his assessment of Quine’s arguments in his earlier (Neale 1990), where he defended the Russellian response—have taken this attitude.

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Page 338 41. I take up the task of attempting to articulate such a view, developing a broadly Aristotelian conception of substance and essence, in Nelson (unpublished b). 42. Kaplan developed a very different response to Quine in (1986). I think this later response suffers from some of the difficulties I argued afflict option (A). A detailed discussion of Kaplan’s rich and difficult paper is, however, not possible here. 43. I follow Kaplan in using Church’s ∆-notation, although this is, strictly speaking, a relation between expressions and individuals. Kaplan knowingly vacillates between having the extra quantifier range over individual-concepts (his preferred conception) and expressions (following Quine’s preference of avoiding intensional entities). As Church famously pointed out—in, for example (Church 1943:45)—construing propositional attitude verbs as relating agents to sentences seems to require that the agent in question understands the language used in the report, which is very much at odds with our practice of reporting beliefs using embedded sentences that the alleged believers would not use to express their beliefs and might not even understand. I do not think that Quine ever met this worry. He famously wrote: ‘We may treat a mouse’s fear of a cat as his fearing true a certain English sentence. This is unnatural without being therefore wrong. It is a little like describing a prehistoric ocean current as clockwise’ (Quine 1956:186). Although an excellent turn of the pen, it seems clear that Quine fails to explain how we can truly say that a mouse fears-true an English sentence. Ascribing a clockwise current to a prehistoric ocean does not require the existence of clocks in prehistoric time, any more than our using actual resources to describe a counterfactual circumstance in which, say, there are no words, requires that there are words in that counterfactual circumstance being described. But this is a false comparison to the case of treating a mouse’s fear of a cat as fearing-true an English sentence when one is fairly certain the mouse does not understand English. Here we are not describing one situation from the perspective of another. Even if avoiding intensional entities were desirable, I do not think Quine has succeeded in showing how it is possible. 44. The notion of analytic connection can simply be taken as a primitive. Alternatively, if we assume a realist attitude of structured concepts, we can explicate the notion in Kantian terms, as follows. One concept is analytically connected to another just in case the one is a literal constituent of the other. For example, the concept being a two-legged animal is connected to the concept being an animal as the former literally contains the latter as a constituent part, in much the way the expression ‘animal’ is contained in the complex expression ‘a two-legged animal’. 45. It would indeed lead to contradiction if we concluded from the falsity of (4) that Venus satisfies the condition ~ c ( c∆x & A(E, c )). But we should not be tempted by this inference (and all the more so in light of the truth of (2)). Such an inference would be like concluding that there is no way I went to work from the fact that I did not run to work naked, given the Kaplanesque analysis of the structure of modal sentences. 46. One of its more striking consequences is that every object necessarily has every property it has; that is, there is only one way for an object to have a property and that is to necessarily have it. The account also entails, given the most straightforward extension to ◊, that every object possibly has every consistent property. (I set aside identity properties, which I shall discuss below.) Kaplan saw these consequences. He writes: Although our analysis of Nec avoids essentialism, it also avoids rejecting: (42) Nec (‘ x = the number of planets’, nine), which comes out true on the understanding

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Page 339 (43) α(∆(α, nine) & N = the number of planets ) in view of the facts that N the number of planets = the number of planets ) and ∆(‘the number of planets’, nine). (1968:221–22) That is, because there is a designator of nine analytically tied to the condition ‘ x = the number of planets’—to wit, ‘the number of planets’—it turns out, given Kaplan’s analysis, that nine analytically satisfies that condition. (I present a more rigorous argument for this in the text.) Kaplan continues: ‘In a sense, we have not avoided essentialism but only inessentialism, since so many of nine’s properties become essential. Small consolation to know of our essential rationality if each blunder and error is equally ingrained’ (222). Kaplan similarly complains that his analogous account of de re belief puts ‘Ralph en rapport with an excess of individuals’ (222). In §§8–9, he adds conditions that make de re modal properties and de re belief much more difficult by restricting the class of designators one looks to in determining whether or not an object necessarily satisfies a condition to the names ‘necessarily denote’ their objects, in the case of modality, and to designators that are vivid representations of their objects (for the believer) in determining what believer believes of, in the case of propositional attitudes. These restrictions demonstrate, early on, the seeds of Kaplan’s rejection of his anti-essentialist (antiessentialists should not want to carve off a special class of designators as revealing objects’ real, mindindependent and substantive nature) and his Fregeanism (Fregeans should deny that there is any substantive notion of rapport). 47. Like Quine, both Marcus and Parsons speak of essences. But, again like Quine, it is clear that what they meant by ‘essence’ is just a necessary property. (See n29.) Trivial necessary properties are not essences, properly called, as they hardly make a start at answering Aristotle’s What is it? question. Indeed, they make absolutely no distinction among the class of individuals there are, as every individual has every trivial necessary property and no individual has any nontrivial necessary property, as we shall see. This is what makes them so anti-essentialist friendly and so radically unfit to be genuine essences. So, I read Marcus and Parsons as intending to speak of necessary properties in general as opposed to essences in particular. 48. In calling such theses ‘philosophically problematic’, we are not calling them false. (Indeed, as I already said, I am a proponent of such a philosophically problematic thesis.) Even the most avid essentialists should admit that the necessary properties they acknowledge are more problematic— although they may wish to say richer and more useful for it—than the trivial necessary properties discussed below. 49. Marcus also distinguishes weakly essentialist theses from strongly essentialist theses. A thesis is weakly essentialist just in case nothing is such that it could contingently possess a problematically necessary property; that is, just in case everything is such that, necessarily, if it possesses a problematic necessary property at all, then it does not possess it contingently. A thesis is strongly essentialist , on the other hand, just in case it is possible for an object to contingently possess a problematically necessary property. To see the distinction, compare the property being human with the property being statueshaped. A standard essentialist about humanity will claim that, although not every object is necessarily human and so we have ourselves a problematic necessary property, every object that is human is necessarily human. (So, nothing is contingently human.) And this fact is itself nonaccidental, being constitutive of the property being human. A standard essentialist about being statue-shaped who denies that composite entities are identical to the matter out of which they are composed

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Page 340 will claim that the bronze statue is necessarily statue-shaped while the piece of bronze out of which the bronze statue is composed, albeit statue-shaped, is not necessarily statue-shaped, as it could have survived being squashed. (See, for example, Wiggins (2001).) If every problematic necessary property were like being human (according to the standard essentialist about humanity), then only weak essentialism would obtain. But if there are necessary properties like being statue-shaped (according to the standard constitution theorist), then strong essentialism is true. This distinction, although both insightful and important, is inessential to the present discussion. 50. Note that it would not do to say that o analytically or logically satisfies Fx just in case xFx is true, given that xFx might be nonanalytically true. 51. This line of argument draws on Parsons (1967) and (1969). 52. This possibility is not even mentioned, for example, in Neale’s defence of Quine in (Neale 2000). Neither Burgess nor Neale address (or even cite) Kaplan’s view. 53. I discuss these three conceptions of the de re / de dicto distinction and explore their inter-relations in more depth in Nelson (unpublished a). 54. Burgess says that Quine’s critique is limited to nontrivial de re modality. However, he offers no textual evidence that Quine appreciated the difference between trivial and nontrivial de re modality. Indeed, the ease with which Quine slides between claiming that proponents of QML must count as true statements like ‘Everything is necessarily self-identical’ to claiming that proponents of QML must count as true statements like ‘Something is necessarily greater than 7’ strongly suggests that he did not appreciate the difference. 55. I take it that Burgess would similarly object to the Kaplanesque view sketched above precisely because it has a ‘trivializing’ effect, albeit of a different sort from the trivializing effect of the Marcus/Parsons strategy. (This is but a guess, as Burgess does not discuss Kaplan (1968).) Although (10) is invalid on the Kaplanesque view, something perhaps just as bothersome is valid: Namely, (11). x( Fx Fx ). (11) can be seen to be ‘trivializing’ because it obliterates the distinction between necessarily having a property and contingently having a property. I believe my discussion of (10), which follows, can be applied to (11) as well. 56. Now no doubt Marcus herself would respond to this by rejecting the indiscriminate attitude. If one wants to get at the essence of an object, one should look at tags and not descriptions of the object. But, as I have already argued in ‘The Real Quine’, the very distinction between tags and definite descriptions is already essentialist, in Quine’s sense of the notion; that is, appealing to such a distinction will lead one to TAE2. REFERENCES Adams, R. (1979) ‘Primitive Thisness and Primitive Identity’, Journal of Philosophy 76: 5–26. Austin, D. (1990) What’s the Meaning of ‘This’?, Ithaca/London: Cornell University Press. Burgess, J. (1997) ‘Quinus ab omni naevo vindicatus’, in A. Kazmi (ed.), Meaning and Reference. Canadian Journal of Philosophy , Suppl. vol. 23: 25–65. Church, A. (1943) Review of Quine ‘Notes on Existence and Necessity’, Journal of Symbolic Logic 8: 45– 47. ——. (1950) Review of Fitch’s ‘The Problem of the Morning Star and the Evening Star’, Journal of Symbolic Logic 15: 63.

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Page 341 Crimmins, M. and Perry, J. (1989) ‘The Prince and the Phone Booth: Reporting Puzzling Beliefs’, Journal of Philosophy 86: 685–711. Fine, K. (1989) ‘The Problem of de re Modality’, in J. Almog, J. Perry and H. Wettstein (eds), Themes from Kaplan, New York: Oxford University Press: 197–272. ——. (1990) ‘Quine on Quantifying In’, in C. Anderson and J. Owens (eds), Propositional Attitudes, Stanford, CA: CSLI Publications: 1–25. ——. (1994) ‘Essence and Modality’, Philosophical Perspectives 8: 1–16. ——. (1995) ‘The Logic of Essence’, Journal of Philosophical Logic 24: 241–73. Fitch, F. (1949) ‘The Problem of the Morning Star and the Evening Star’, Philosophy of Science 16: 137– 41. Gibbard, A. (1975) ‘Contingent Identity’, Journal of Philosophical Logic 4: 187–221. Jeshion, R. (2002) ‘Acquaintanceless de re Belief’, in J. Campbell, M. O’Rourke and D. Shier (eds), Meaning and Truth: Investigations in Philosophical Semantics, New York, NY: Seven Bridges Press: 53– 78. Kaplan, D. (1968) ‘Quantifying In’, in D. Davidson and H. Hintikka (eds), Words and Objections: Essays on the Work of W. V. Quine , Dordrecht: Reidel: 206–42. Originally published in Synthese 19: 178–214. ——. (1975) ‘How to Russell a Frege-Church’, Journal of Philosophy 72: 716–29. ——. (1986) ‘Opacity’, in E. Hahn and P. Schilpp (eds), The Philosophy of W. V. Quine , La Salle, IL: Open Court: 229–89. ——. (1989) ‘Demonstratives’, in J. Almog, J. Perry and H. Wettstein (eds), Themes From Kaplan, Oxford: Oxford University Press: 487–504. Kripke, S. (1971) ‘Identity and Necessity’, in M. Munitz (ed.), Identity and Individuation, New York: New York University Press: 135–64. ——. (1980) Naming and Necessity , Cambridge, MA: Harvard University Press. Based on lectures delivered at Princeton University in 1970. Lewis, D. (1986) On the Plurality of Worlds , Oxford: Blackwell. Marcus, R. B. (1948) Review of Smullyan’s ‘Modality and Description’, Journal of Symbolic Logic 13: 149–50. ——. (1963) ‘Modal Logics I: Modalities in Intensional Languages’, in M. W. Wartofsky (ed.), Proceedings of the Boston Colloquium for the Philosophy of Science , Dordrecht: Reidel: 77–96. ——. (1967) ‘Essentialism in Modal Logic’, Noûs 1: 90–96. ——. (1990) ‘A Backward Look at Quine’s Animadversion on Modalities’, in R. Barrett and R. Gibson (eds), Perspectives on Quine , Oxford: Blackwell: 230–43. ——. (1993) Modalities: Philosophical Essays, New York: Oxford University Press. ——. et al. (1963) ‘Discussion’, in M. W. Wartofsky (ed.), Proceedings of the Boston Colloquium for the Philosophy of Science , Dordrecht: Reidel: 105–16. Neale, S. (1990) Descriptions, Cambridge, MA: MIT Press. ——. (2000) ‘On a Milestone of Empiricism’, in A. Orenstein and P. Kotatko (eds), Knowledge, Language and Logic, Dordrecht: Kluwer: 237–346. Nelson, M. (2005) ‘The Problem of Puzzling Pairs’, Linguistics and Philosophy 28: 319–50. ——. (forthcoming) ‘On the Contingency of Existence’, in L. Jorgensen and S. Newlands (eds), Essays in Honor of R. M. Adams , Oxford: Oxford University Press. ——. (unpublished a) ‘Anti-Essentialism and the de re ’. ——. (unpublished b) ‘Necessary Essence’. Parsons, T. (1967) ‘Grades of Essentialism in Quantified Modal Logic’, Noûs 1: 181–200.

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Page 342 ——. (1969) ‘Essentialism and Quantified Modal Logic’, Philosophical Review 78: 35–52. Quine, W. V. O. (1937) ‘New Foundations for Mathematical Logic’, American Mathematical Monthly 44: 70–80. Reprinted in his From a Logical Point of View , 80–102. Citations to reprinting. ——. (1943) ‘Notes on Existence and Necessity’, Journal of Philosophy 40: 113–17. ——. (1947) ‘On the Problem of Interpreting Modal Logic’, Journal of Symbolic Logic 12: 43–48. ——. (1948) ‘On What There Is’, Review of Metaphysics 2: 21–38. Reprinted in his From a Logical Point of View , 1–20. Citations to reprinting. ——. (1951) ‘Two Dogmas of Empiricism’, Philosophical Review 60: 20–43. Reprinted in his From a Logical Point of View , 20–47. Citations to reprinting. ——. (1953a) ‘Three Grades of Modal Involvement’, Proceedings of the XIth International Congress of Philosophy 14: 65–81. Reprinted in his 1976 The Ways of Paradox, rev. and enlarged edn, New York: Random House: 185–96. Citations to reprinting. ——. (1953b) ‘Reference and Modality’, in From a Logical Point of View , Cambridge MA: Harvard University Press: 160–67. ——. (1956) ‘Quantifiers and Propositional Attitudes’, Journal of Philosophy 53: 177–87. ——. (1961) ‘Reference and Modality’, in From a Logical Point of View , 2nd edn rev., Cambridge: Cambridge University Press: 160–67. ——. (1963) ‘Reply to Professor Marcus’ in M. W. Wartofsky (ed.), Proceedings of the Boston Colloquium for the Philosophy of Science , Dordrecht: Reidel: 97–104. ——. (1980) ‘Reference and Modality’, in From a Logical Point of View , 2nd edn rev., New York: Harper and Row: 139–59. Richard, M. (1990) Propositional Attitudes: An Essay on Thoughts and How We Ascribe Them , Cambridge: Cambridge University Press. Russell, B. (1903) The Principles of Mathematics, Cambridge: Cambridge University Press. ——. (1905) ‘On Denoting’, Mind 14: 479–93. ——. (1906) ‘On the Nature of Truth’, Proceedings of the Aristotelian Society 7: 28–49. ——. (1910) ‘Knowledge by Acquaintance and Knowledge by Description’, Proceedings of the Aristotelian Society 11: 108–28. ——. (1912) The Problems of Philosophy , Oxford: Oxford University Press. ——. (1913) Theory of Knowledge , in E. Eames (ed.), The Collected Papers of Bertrand Russell, vol. 7, London: George Allen and Unwin, 1984. Salmon, N. (1986) Frege’s Puzzle , Cambridge, MA: MIT Press. ——. (1989) ‘The Logic of What Might Have Been’, Philosophical Review 98: 3–34. Smullyan, A. (1947) Review of Quine’s ‘The Problem of Interpreting Modal Logic’, Journal of Symbolic Logic 12: 139–41. ——. (1948) ‘Modality and Description’, Journal of Symbolic Logic 13: 31–37. Strawson, P. F. (1990) Individuals: An Essay on Descriptive Metaphysics , London: Routledge. Originally published in 1959, Taylor Francis Group. Whitehead, A. N. and Russell, B. (1925) Principia Mathematica , vol. 1, 2nd edn, Cambridge: Cambridge University Press. Wiggins, D. (2001) Sameness and Substance Renewed, Cambridge: Cambridge University Press.

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Page 343 15 Points, Complexes, Complex Points, and a Yacht Nathan Salmon I comment here on two puzzling passages in Russell’s masterpiece, ‘On Denoting’.1 One is the famous ‘Gray’s Elegy argument’, as it is usually called.2 Afterward, I discuss errors in the famous discussion of the small yacht and its touchy owner. THE ‘GRAY’S ELEGY’ ARGUMENT Russell’s famous argument, as I interpret it, is aimed against a popular theory of the semantics of definite descriptions: ST : A definite description designates by virtue of the description’s semantic content, which fixes the designatum of the description to be (if anything) the individual or thing that uniquely answers to the description; further, when the definite description occurs in a declarative sentence, the description’s content represents the description’s designatum in the proposition expressed. ST fleshes out the simple and seemingly innocuous thesis that definite descriptions are singular terms. It had been held by Russell in The Principles of Mathematics. It is also held by theorists as diverse as John Stuart Mill, Gottlob Frege, Alexius Meinong, and legions of others. Here in a nutshell is Russell’s reductive argument against ST : The attempt to form a proposition directly about the content of a definite description (as by using an appropriate form of quotation) inevitably results in a proposition about the thing designated instead of the content expressed. I call this phenomenon the Collapse . In light of the Collapse, Russell argues, the ST theorist must accept that all propositions about a description’s content are about that content indirectly, representing it by means of a higher-level descriptive content. And this, according to Russell, renders our cognitive grip on definite descriptions inexplicable. On my interpretation, Russell may be seen as arguing in eight separate stages (at least), as follows: At stage ( I) he argues that there is some awkwardness in so much as stating the very theory ST . At stage ( II) he argues that once a way of stating ST is found, the theory, so stated, gives

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Page 344 rise to a peculiar phenomenon: The attempt to form a singular proposition about the content of a definite description inevitably results instead in a general proposition about the individual designated by the description. This is the Collapse. At stage ( III) the Collapse leads to a preferable formulation of ST . At stage ( IV) Russell shows that the Collapse remains a feature of the reformulated theory. At stage ( V) Russell argues that the Collapse commits ST to a very sweeping conclusion: that no singular term designating the content of a definite description can be what Russell will later call a logically proper name ; instead any such term must be itself a definite description, or function as one. As Russell puts it, on our theory ST , ‘the meaning cannot be got at except by means of denoting phrases’ (p. 486). At stage ( VI) he argues furthermore that the content of a definite description cannot be a constituent of the content of any definite description of it. Russell proceeds to complain at stage ( VII ) that the results of the preceding two stages are philosophically intolerable. At stage ( VIII ) he provides a complementary argument for the conclusion that ST ignores that which, by its own lights, is philosophically most significant about propositions. In Russell’s terminology, a denoting phrase is a noun phrase beginning with what linguists call a determiner , like ‘every’, ‘some’, or ‘the’. Both definite and indefinite descriptions are denoting phrases, in Russell’s sense. A definite description of a given language is said to mean —in a more standard terminology, it expresses—a denoting complex c as its meaning. The denoting complex c , in turn, denotes—in Church’s terminology, it is a concept of—an object as its denotation . I here translate Russell’s term ‘meaning’ as ‘content’.3 Russell does not use any special term for the binary relation between a definite description and the object of which the expression’s content in the language is a concept. Instead Russell speaks of “the denotation of the meaning”, saying that a definite description α “has a meaning which denotes” an object x. Sometimes he says that α itself (as opposed to its content) denotes x. Here I avoid Russell’s term ‘denote’ altogether. Instead I use ‘determine’ for the relation between a complex c and the object x of which c is a concept, and I call x the ‘determinatum’ of c . I use ‘designate’ for the relation between the expression α and x, and I call x the ‘designatum’ of α. Russell uses ‘ C’ as a variable ranging over determining complexes, and sometimes instead as a metalinguistic variable ranging over determiner phrases. Frequently he uses ‘ C’ as a schematic letter (a substitutional variable), sometimes standing in for an arbitrary definite description, sometimes for a term designating an arbitrary determining complex. Any sentence in which ‘ C’ occurs as schematic letter is strictly speaking a schema, of which Russell means to assert every instance. With a little finesse, Russell’s intent can often be captured by taking ‘ C’ as a variable either ranging over definite descriptions or ranging over determining complexes. I here use ‘α’ as a metalinguistic variable, and upper case ‘ D’ as a schematic letter

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Page 345 standing in for an arbitrary definite description. I use lower-case ‘ c ’ as a determining-complex variable. I use Quine’s quasi-quotation marks, ‘ ’ and ‘ ’ in combination with ‘α’. In quasi-quotation, all internal expressions are quoted, that is, mentioned (designated), except for metalinguistic variables, whose values are mentioned. I use single quotation marks for direct (expression) quotation. Following David Kaplan, I use superscripted occurrences of ‘ m ’ as indirect-quotation marks, and superscripted occurrences of ‘ M ’ as indirect-quasi-quotation marks (1971:120–21).4 In indirect-quasiquotation, the contents of all internal expressions are mentioned, except for determining-complex variables, whose values are mentioned. Here I avoid double quotation marks, except as scare-quotes when using another’s words. Departures from the original appear in boldface. Analytical Translation of the Famously Obscure Passage ( A′ ) The relation of the content to the designatum involves certain rather curious difficulties, which seem in themselves sufficient to prove that the theory which leads to such difficulties must be wrong. ( B′ ) ( I) When we wish to speak about, that is, to designate, the content of a determiner phrase, that is, of a definite description, as opposed to its designatum, the present mode of doing so is by indirect-quotation marks. Thus we say: The centre of mass of the Solar System is a point, not a determining complex; m The centre of mass of the Solar System m is a determining complex, not a point. Or again, The first line of Gray’s Elegy expresses a proposition. m The first line of Gray’s Elegym does not express a proposition. Thus taking any determiner phrase, for example, taking any definite description … , α, we wish to consider the relation between α and where the difference of the two is of the kind exemplified in the above two instances.5 ( C′ ) We say, to begin with, that when α occurs it is the designatum of α that we are speaking about; but when occurs, it is the content. Now the relation of content to designatum is not merely linguistic through the phrase, that is, it is not merely the indirect product of the semantic relations of being the content of a phrase and designating: there must be a direct, nonlinguistic, logico-metaphysical relation involved, which we express by saying that the content determines the designatum. But the difficulty which confronts us is that we cannot succeed in both preserving the connexion of content to designatum and preventing them—the content and the designatum —from being

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Page 346 one and the same; also that the content cannot be got at except by means of determiner phrases.6 This happens as follows. ( D′i) The one phrase α was to have both content and designation. But if in an effort to designate the content, we speak of , that gives us the content (if any) of the designatum of α. ‘The content of the first line of Gray’s Elegy’ designates the same complex as ‘The content of m The curfew tolls the knell of parting day m ’, and … not the same as ‘The content of m the first line of Gray’s Elegym ’. Thus in order to get the content we want, we must speak not of , but of , which designates the same as itself.7 ( D′ii ) Similarly does not designate the determinatum we want, the determinatum of α’s content, but means something, that is, expresses a determining complex, which, if it determines anything at all, determines what is determined by the determinatum we want. For example, let α be ‘the determining complex occurring in the second of the above instances’. Then and ‘The curfew tolls the knell of parting day’ are both true.8 But what we meant to have as the determinatum was m the first line of Gray’s Elegym . Thus we have failed to get what we wanted from 9 ( E′i) ( II) The difficulty in speaking of the content of a determining complex, that is, in using a phrase of the form , may be stated thus: The moment we put the complex in a proposition, the proposition is about the determinatum;10 and hence if we make a proposition in which the subject component is M the content of cM , for some determining complex c , then the subject represents the content (if any) of the determinatum of c , which was not intended.11 ( E′ii ) ( III) This leads us to say that, when we distinguish content and determinatum of a determining complex, as we did in the preceding paragraph, we must be dealing in both cases with the content: the content has a determinatum and is a determining complex, and there is not something other than the content, which can be called , and be said to have both content and a determinatum. The right phraseology, on the view in question, is that some contents have determinata. ( F′i) ( IV) But this only makes our difficulty in speaking of contents more evident. For suppose c is our target complex, and let ‘ D’ represent in what follows a determiner phrase that expresses c (for example, let c be m the centre of mass of the Solar Systemm and let ‘ D’ stand in for the phrase ‘the centre of mass of the Solar System’); then we are to say that mDm , that is, c , is the content of the phrase ‘ D’, instead of saying that mDm itself has a content. Nevertheless, whenever ‘ D’ occurs without indirect-quotation marks, what is said is not about mDm , the content of ‘ D’, but only about D, the designatum of ‘ D’, as when we say:

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Page 347 The centre of mass of the Solar System is a point. ( F′ii ) ( V) Thus to speak of mDm itself, that is, to express a proposition about the content of ‘ D’, our subject component must not be mDmitself , but something else, a new determining complex, which determines mDm .12 Thus m mDm m —which iterated indirect quotation is what we use when we want to speak of the content of ‘ mDm ’—must be not the content of ‘ D’, that is, not mDm itself, but something which determines the content. ( F′iii) ( VI) And mDm , that is, c must not be a constituent of this higher-level complex m mDm m (as it is of M the content of cM ); for if mDm occurs in the complex, it will be its determinatum, not the content of ‘ D’, that is, not mDm itself, that will be represented and there is no backward road from determinata to contents, because every object can be designated by an infinite number of different determiner phrases.13 ( G′i) ( VII ) Thus it would seem that m mDm m and mDm are altogether different entities, such that m mDm m determines mDm ; but this cannot be an explanation of m mDm m , because the relation of m mDm m to mDm remains wholly mysterious; and where are we to find the determining complex m mDm m which is to determine mDm ?14 ( G′ii ) ( VIII ) Moreover, when mDm occurs in a proposition, it is not only the determinatum that occurs (as we shall see in the next paragraph); yet, on the view in question, mDm represents only the determinatum, the content ( that is, the representing of mDm itself) being wholly relegated to m mDm m . This is an inextricable tangle, and seems to prove that the whole distinction of content and designation has been wrongly conceived. ( H′ ) That the content is relevant when a determiner phrase occurs in a sentence expressing a proposition is formally proved by the puzzle about the author of Waverley . The proposition m Scott is the author of Waverleym has a property not possessed by m Scott is Scottm , namely, the property that George IV wished to know whether it was true. Thus the two are not identical propositions; hence the content of ‘the author of Waverley ’ must be relevant to the proposition as well as the designatum, if we adhere to the point of view to which this distinction belongs. Yet, as we have seen, so long as we adhere to this point of view, we are compelled to hold that only the designatum can be relevant. Thus the point of view in question must be abandoned.15 Some previous interpreters do not so much as mention what I am calling the Collapse . Others have extracted the alleged phenomenon from ( Ei), but place little or no importance on it. Some have depicted its occurrence in the ‘Gray’s Elegy’ passage as little more than a clever observation, characteristic of Russell but one that he makes only in passing and is of limited significance in the grand sweep of the overall argument. In sharp contrast, on my interpretation the Collapse is the very linchpin of the ‘Gray’s Elegy’

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Page 348 argument, and plays a pivotal role in later stages that constitute the heart of the argument.16 At stage ( V) (the middle section of paragraph ( F )), Russell argues by means of the Collapse that on ST , m mDm m ≠ mDm , where ‘ D’ stands in for any definite description.17 We may designate a particular complex, say m the centre of mass of the Solar System m , in order to express a proposition about it. However, any proposition in which the complex itself occurs is about the centre of mass of the Solar System, that is, the determinatum of the target complex rather than the complex itself. A singular proposition about a determining complex is an evident impossibility; hence, any proposition that is about a complex must involve a second-level determining complex that determines the target complex. Hence, any term for a complex must function in the manner of a definite description. Even our indirect quotation, ‘ m the centre of mass of the Solar System m ’ (the closest thing there is to a standard name of the complex), must be a disguised definite description, expressing a second-level determining complex, m m the centre of mass of the Solar System m m , as its content. Furthermore, m m the centre of mass of the Solar System m m is distinct from, and in fact determines, m the centre of mass of the Solar System m . It is in this very concrete sense that on ST , ‘the meaning cannot be got at except by means of determiner phrases’. The only way to designate a determining complex is by expressing a higher-level determining complex.18 Russell has thus far argued that the theory ST is committed, by the Collapse, to denying the very possibility of singular propositions about contents. Some commentators have construed this argument as an objection to Frege’s theory, which rejects singular propositions.19 Such an argument would be a howler. On the contrary, Fregeans should welcome the conclusion derived at stage ( V), which provides a reductio argument against ST in conjunction with singular propositions of unrestricted subject matter— a theory like Mill’s or that of Russell’s Principles . The incoherence of these non-Fregean versions of ST may even be given a kind of proof, using the principle of Compositionality (which Russell relied on at least implicitly and Frege explicitly endorsed), according to which the content of a compound expression is an effectively computable function of the contents of the contentful components. Compositionality is subject to certain restrictions. For example, the content of a compound expression containing a standard (syntactic) quotation is a function of the content of the quotation itself, together with the contents of the surrounding subexpressions, but not of the content of the quoted expression. Subject to such restrictions as this, Compositionality evidently entails a similarly restricted principle of Synonymous Interchange , according to which substitution of a synonym within a larger expression preserves content. (I here call a pair of expressions synonymous if there is something that is the content of both.) To give the argument its sharpest focus, we consider Russell’s example:

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Page 349 (1) The centre of mass of the Solar System is a point. According to ST , the grammatical subject of (1), ‘the centre of mass of the Solar System’, expresses the determining complex m the centre of mass of the Solar System m as its English content. According to the non-Fregean version of ST , the content of the indirect quotation ‘ m the centre of mass of the Solar System m ’ itself is this same determining complex, and sentences containing the indirect quotation express singular propositions about the complex. Hence, the description and the indirect quotation are synonymous according to the non-Fregean version of ST . Therefore, by Synonymous Interchange, so also are (1) and (2) m The centre of mass of the Solar System m is a point. But (1) is true while (2) is necessarily false, indicating that they do not express the same thing. The content of (2) must invoke the second-level complex m m the centre of mass of the Solar System m m to represent the firstlevel complex. The same argument may be given using the free variable ‘ c ’ in place of the indirect quotation. On the supposition that the content of the variable under the established assignment is its value, the variable has the very same content as the definite description ‘the first line of Gray’s Elegy’. The Collapse then follows directly by Synonymous Interchange. This refutes the assumption that the variable under its assignment is a logically proper name for the complex in question. The theory ST is thus committed to extending its content/designation distinction for definite descriptions to all terms that designate determining complexes. The argument can be repeated in connection with the content of the indirect quotation itself. The argument is thus converted into an argument by mathematical induction for an infinite hierarchy of contents associated with ‘the first line of Gray’s Elegy’. Indeed, the postulated second-level complex m m the first line of Gray’s Elegym m is, for Frege, the content that the description expresses when occurring in ungerade (‘oblique’) contexts, like the contexts created by ‘believes that’ and by indirect quotation marks.20 He called this the indirect sense of ‘the first line of Gray’s Elegy’. The series beginning with ‘The curfew tolls the knell of parting day’, followed by m the first line of Gray’s Elegym , m m the first line of Gray’s Elegym m , m m m the first line of Gray’s Elegym m m , and so on, is precisely Frege’s infinite hierarchy of senses for the definite description (treating designation as the bottom level in the hierarchy). Not all of Frege’s disciples have followed the master down the garden path to Frege’s jungle. Two noteworthy deserters are Carnap and Dummett.21 But Church has followed Frege even here.22 In fact, at least one of the loyal opposition has as well. Russell’s argument via the Collapse for ST ’s commitment to the hierarchy was independently reinvented closer to the end of the previous century by Tyler Burge.23

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Page 350 Russell clarifies the nature of the hierarchy at stage ( VI ), which makes up the final third of ( F ). A feature of ( Fiii) that is typically overlooked is that it again invokes the Collapse.24 Russell observes that the target complex is not only distinct from the postulated second-level complex we seek; it is not even a constituent of the latter complex (as it is of m Russell has memorized the first line of Gray’s Elegym , and of m the content of the first line of Gray’s Elegym ). Here Russell pursues the obvious question: Given that the indirect quotation ‘ m the first line of Gray’s Elegym ’ must express a second-level complex that determines our target complex, which second-level complex does it express? The best way to identify the sought after second-level complex would be to provide a definite description of the form ‘the determining complex that is such-and-such’ which is fully understood (independently of indirectquotation), and which is synonymous with ‘ m the first line of Gray’s Elegym ’. Given Compositionality, it might be hoped that the suitable definite description will incorporate something expressing the designated target complex itself. We would thus construct the postulated second-level complex using the target complex. However, the desired description cannot be ‘the complex that determines the first line of Gray’s Elegy’, for there are infinitely many and varied complexes each of which determines the words ‘The curfew tolls … ’. Let us try a different tack. Let ‘ c ’ name the target complex, and consider: the determining complex that is c . Russell observes that this will not do either. Indeed, no description of the form ‘the determining complex that bears relation R to c ’ will succeed. Or to put the same point somewhat differently, our postulated second-level complex cannot be M the determining complex that bears R to cM , for some binary relation R. (Note the indirect-quasi-quotation marks.) For the Collapse occurs with determining complexes just as it does with propositions. The content of the description collapses into: m the determining complex that bears R to the first line of Gray’s Elegym . The problem here is that there is no ‘backward road’ from the words ‘The curfew tolls … ’ to their particular representation by m the first line of Gray’s Elegym , and likewise no backward road from the Solar System’s centre of mass to its particular representation as such. That is, there is no relevantly identifiable binary relation R whose converse is a ‘choice’ function that selects exactly our target complex, to the exclusion of all others, and assigns it, and only it, to its determinatum. If R is taken to be the relation of determining , then the collapsed second-level complex fails to determine a unique complex because there are too many complexes (infinitely many, in fact) that bear this relation to the first line of Gray’s Elegy. And if R is taken to be the relation of identity, then the resulting secondlevel complex fails to determine a unique complex because there are too few complexes that bear this relation to the first line of Gray’s Elegy. More generally, if c is our target complex, the postulated second-level complex cannot be of the form Mf ( c ) M , where ‘ f ’ designates a choice function that selects a distinguished or privileged determining complex from the class of all complexes that determine a given object. It is important to notice that

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Page 351 the missing choice function f goes not at the level from the target complex to the second-level complex, but at the bottom level from the determinatum to the complex itself. A ‘low’ backward road might enable us to construct the postulated second-level complex from the target complex. But high or low, no backward road is forthcoming. So ends stage ( VI). Because there is no backward road from ‘The curfew tolls …’ to m the first line of Gray’s Elegym , it follows via the Collapse that the second-level complex m m the first line of Gray’s Elegym m is not constructed from the target complex m the first line of Gray’s Elegym . Indirect quotations thus constitute a restriction on a principle of Strong Compositionality (also endorsed by both Frege and Russell), according to which the content of a compound expression is not only a function of, but is in fact a complex composed of, the contents of the contentful components. Russell might have taken the argument a step further. Continuing and embellishing the argument on Russell’s behalf, although the indirect quotation ‘ m the first line of Gray’s Elegym ’ expresses, and thereby uniquely fixes, the postulated second-level complex, the target complex designated by the indirect quotation does not itself uniquely single out the second-level complex. It is a serious mistake, for example, to suppose that m m the first line of Gray’s Elegym m can be described as the content of m the first line of Gray’s Elegym . (Russell believes he has shown that on ST , this description designates the target complex itself, whereas the description actually designates nothing. The alternative phrase, ‘the content of “the first line of Gray’s Elegy”’ does designate the target complex itself. Still, we do not get at the postulated second-level complex.) But neither can m m the first line of Gray’s Elegym m be described as the complex that determines m the first line of Gray’s Elegym . For any given object there are infinitely many complexes that determine it. Our target complex is also determined by such second-level complexes as m the determining complex occurring in the second of Russell’s instances m and m the determining complex that has given Russell’s readers more headaches than any other m —neither of which is suited to be the content expressed by ‘ m the first line of Gray’s Elegym ’. Thus not only is it the case, as Russell explicitly argues, that the target complex is altogether different from the postulated second-level complex. The target complex does not even uniquely fix the second-level complex. Never mind the Collapse. If there is no backward road from determinata to determining complexes, then not only is there no low road from the first line of Gray’s Elegy to m the first line of Gray’s Elegym ; there is likewise no high road from m the first line of Gray’s Elegym to m m the first line of Gray’s Elegym m . We have no way to go from the content of a definite description to the content of its indirect quotation. Our indirect quotation marks thus yield a restriction also on the weaker principle of Compositionality: The content of an indirect quotation is not even a computable function of (let alone a complex composed partly of) the content of the expression within the quotes. This result is stronger than the conclusion that Russell explicitly draws. If the

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Page 352 target complex were a constituent of the postulated second-level complex, presumably it would single out the latter complex. But the mere fact that the target complex is not a constituent of the secondlevel complex does not yet rule out the possibility that the target complex uniquely fixes the secondlevel complex in some other manner. The fact that there is a multiplicity of complexes determining any given object seems to do just that. (By contrast, the indirect quotation ‘ m the first line of Gray’s Elegym ’ singles out the second-level complex, as its English content.)25 SIZE MATTERS Having disposed of ST once and for all with his ‘Gray’s Elegy’ argument (so he believes), Russell moves on to illustrate the important distinction between primary occurrence and secondary occurrence with his famous example of the touchy yacht owner: I have heard of a touchy owner of a yacht to whom a guest, on first seeing it, remarked, ‘I thought your yacht was larger than it is’; and the owner replied, ‘No, my yacht is not larger than it is’. What the guest meant was, ‘The size that I thought your yacht was is greater than the size your yacht is’; the meaning attributed to him is, ‘I thought the size of your yacht was greater than the size of your yacht’. (p. 489) Speaking on ‘Russell’s Notion of Scope’ at Rutgers University in May 2005 (and also in conversation some years earlier), Saul Kripke pointed out a significant snag in Russell’s treatment of his yacht example. The meaning Russell attributes to the guest cannot be correct. Indeed, the guest might well have thought that the yacht was larger than it turned out to be without there being any particular size the guest thought the yacht was. Much more likely, the guest, on the basis of the owner’s boasts, had merely judged the yacht to be, at a minimum, grander than it turned out on visual inspection to be, that is, to be some size or other among a range of sizes (perhaps indeterminately delineated), each noticeably greater than the yacht’s actual size. In that case, the description, ‘the size I thought your yacht was’ is improper. Russell’s distinction of primary and secondary occurrence therefore appears to be of no help in removing the misunderstanding. Indeed, it seems that definite descriptions, as such, are entirely irrelevant to the example. In his talk Kripke said, ‘So Russell’s analysis in terms of his theory of descriptions, as stated, is incorrect … How to fix up Russell’s example is a little complicated, and not clear. Maybe it has relatively little to do with the definite descriptions themselves.’26 Any such conclusion robs Russell of credit he richly deserves. The correct conclusion is that although Russell’s theory of descriptions indeed applies to the case at hand, he misapplied it. Correctly applied, Russell’s theory

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Page 353 provides insight into an example that, at least on the surface, does not appear to invoke definite descriptions, or indeed any determiner phrases of the sort to which Russell’s theory directly applies.27 The sentence that is supposed to be subject to the primary/secondary occurrence ambiguity is: S: I thought your yacht was larger than it is. Now in general, a statement of the form, L: α is larger than β is plausibly analyses into α is greater in size than β is , which plausibly analyses into α has a greater size than β has . This last, in turn, plausibly analyses into The size that α has is greater than the size that β has , or more simply: L′: The size of α is greater than the size of β. This analysis uncovers two definite-description occurrences that remain concealed in L’s surface form. Plugging this analysis of L into S, letting both α and β be ‘your yacht’, yields the following: S′: I thought the size of your yacht was greater than the size of your yacht. Contrary to appearances, this analysis of S does not remove all ambiguity. The ambiguity is evidently preserved intact; S′ is evidently ambiguous in the same way that S is. What is significant is that the ambiguity of S′ is evidently one of scope. The definite description ‘the size of your yacht’ occurs twice in S′. Russell should probably be seen as maintaining that the same description therefore implicitly occurs twice in S itself. The touchy yacht owner deliberately misinterprets the guest’s remark, precisely as Russell indicates, by giving both the left-hand (first) and right-hand (second) description occurrences in S′ their secondary-occurrence readings: I thought: that there is a size s that was uniquely a size of your yacht and a size s ′ that was also uniquely a size of your yacht and s was greater than s ′, or more simply, S2,2 : I thought: that a unique size of your yacht was greater than a unique size of your yacht. By contrast with S2,2 , and by contrast also with Russell’s careless stab at capturing the guest’s intent (and contrary to the thrust of Kripke’s remark),

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Page 354 giving the right-hand description occurrence its primary-occurrence reading while still giving the lefthand description occurrence its secondary-occurrence reading yields precisely what the guest did mean: There is a size r that is uniquely a size of your yacht and I thought: that there is a size s that was uniquely a size of your yacht and s was greater than r, or more simply, S2,1 : There is a size r that is a unique size of your yacht and I thought: that a unique size of your yacht was greater than r. This result should not be underappreciated. It appears to vindicate Russell on two counts: ( i) the deep structure of the original problem sentence S evidently involves a definite description, ‘the size of your yacht’, hidden in the surface form; and as a result ( ii ) Russell’s theory of descriptions, with its distinction of primary and secondary occurrence, is indeed evidently applicable to the case, roughly as he says. Kripke is correct that S does not involve the improper description, ‘the size that I thought your yacht was’, but everything Russell says about the example is correct once his sloppy ascription is replaced with a more careful formulation, like ‘The size of your yacht is such that I thought the size of your yacht was greater than that’.28 There remains a problem of a sort rather different from the problem that Kripke noticed, but one that genuinely calls Russell’s theory into question. According to that theory, the left-hand description occurrence in S′ is subject to the same two options of primary and secondary occurrence. Giving both description occurrences their primary-occurrence readings yields a result, S1,1 , analogous to S2,2 .29 Giving the left-hand description occurrence its primary-occurrence reading while giving the right-hand its secondary-occurrence reading yields yet another unintended interpretation, but this one is truly bizarre: S1,2 : There is a size r that is a unique size of your yacht and I thought: that r was greater than a unique size of your yacht. This says, in effect, that the guest thought the yacht was smaller than it is! The main problem with S1,2 is not merely that it is a misinterpretation of the guest’s intent (although it is certainly that). The main problem is not even merely that it imputes to the guest exactly the opposite of the guest’s intent (although it does that as well). The main problem with S1,2 is that it is not a possible reading of the original sentence S at all. Instead, it is perhaps a natural reading of a very different sentence: S″: Your yacht is larger than I thought it was.

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Page 355 Any theory entailing that S may legitimately be read as S″ is incorrect. It remains unclear whether Russell’s is such a theory. Insofar as Russell might have held that S may be read as S′, there is ample cause for worry on this score. Perhaps Russell may avoid the difficulty by analysing L differently in terms of ‘the size of your yacht’. More promising, perhaps some argument can be provided that whereas S2,1 and S2,2 are indeed possible readings of S—and hence the ‘misunderstanding’, precisely as Russell holds—S1,2 by contrast is precluded by considerations extraneous, and complementary, to the theory of descriptions. More plausible still, S2,2 may not be a legitimate reading of S any more than S1,2 is. The ‘was’ in the original sentence S (‘ was larger’) might be seen as somehow incorporating subjunctive mood, the ‘is’ (‘than it is’) as incorporating indicative mood. The contrasting moods may be taken as indicating that the left-hand occurrence of ‘the size of your yacht’ in S′ is to be a secondary occurrence (‘the size your yacht had ’), the right-hand a primary occurrence (‘the size your yacht has ’), thereby unequivocally yielding S2,1 . Instead, the owner misreads S as ‘I thought your yacht was larger than it was ’, yielding S2,2 . NOTES 1. I have had the essentials of the interpretations provided here since 1972, but many others have greatly influenced my thought on the topic, too many others to list here. No one influenced me more than David Kaplan. The Santa Barbarians Discussion Group patiently worked through my edited version of the crucial passage in 1997. I am indebted to them, especially C. Anthony Anderson, for their comments and our efforts. By not venturing to challenge the interpretation, the group shares some responsibility for the final product—how much responsibility depending upon the success or failure of the project. I am also grateful to Alan Berger, Saul Kripke, Teresa Robertson, the participants in my seminars at UCSB and UCLA during 1998–99, notably Roberta Ballarin, Stavroula Glezakos, David Kaplan, and D. Anthony Martin, and my audience at the McMaster University 2005 conference on ‘Russell vs. Meinong: 100 Years After On Denoting ‘, for their insightful comments, notably Matt Griffin. Finally, I am grateful to Oxford University Press for permission to incorporate portions of my article ‘On Designating’. 2. Previous discussions include the following, chronologically: Alonzo Church (1943:302); Ronald J. Butler (1954); John Searle (1958); Peter Geach (1959); Ronald Jager (1960); David Kaplan (1969); A. J. Ayer (1971:30–32); Chrystine E. Cassin (1971); Michael Dummett (1973:267–68; Herbert Hochberg (1976); Simon Blackburn and Alan Code (1978); Geach (1978); Blackburn and Code (1978); A. Manser (1985); Peter Hylton (1990:249–64); Pawel Turnau (1991); Michael Pakaluk (1993); Russell Wahl (1993); Michael Kremer (1994); Harold Noonan (1996); Gregory Landini (1998); William Demopoulos (1999); Gideon Makin (2000:22–45, 206–22); James Levine (2004). 3. Fregeans may substitute the word ‘sense’ wherever I use ‘content’. 4. Kaplan there calls indirect-quotation marks meaning-quotation marks. Indirect quotation quotes not expressions but their content.

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Page 356 5. That is, we wish to consider the relation between ‘the centre of mass of the Solar System’ and ‘ m the centre of mass of the Solar System m ’, between ‘the first line of Gray’s Elegy’ and ‘ m the first line of Gray’s Elegym ’, and so on. 6. It might have been more perspicuous for Russell to formulate his objection this way: We cannot succeed in both preserving the connection of content to designatum and allowing the content and the designatum to be one and the same. Moreover, we cannot even succeed in both preserving the connection of content to designatum and disallowing the content and the designatum from being one and the same unless the content cannot be got at except by means of determiner phrases. That is, if we preserve the connection whereby the designatum of a definite description is determined by the description’s content which is distinct from the designatum itself, then the content cannot be designated by means of a ‘genuine name in the strict, logical sense’. 7. This yields the awkward result that m αm = the content of m αm is true. I am here attributing to Russell a serious equivocation, resulting from his dual use of inverted commas both as direct–quotation marks and as indirect-quotation marks. He appears to believe that he has derived from the theory that definite descriptions have a content/designation distinction the consequence that in order to designate m the centre of mass of the Solar System m , rather than using the inappropriate phrase ‘the content of the centre of mass of the Solar System’ we must use ‘the content of m the centre of mass of the Solar System m ’ (which Russell fails to distinguish from the perfectly appropriate ‘the content of ‘the centre of mass of the Solar System’’), thus ascribing a content to a determining complex itself. As a criticism of the content/designation theory, or even as a neutral description, this is a red herring. Instead, the theory entails that one may designate m the centre of mass of the Solar System m using the functor ‘the content of’ in combination with ‘the centre of mass of the Solar System’ and direct quotation, not indirect. Russell has a stronger criticism to make of the theory, though his presentation is coloured somewhat by this red herring. 8. In the original text, Russell here uses ‘ C’ as a schematic letter standing in for a term designating a determining complex. The preceding two sentences should read: For example, let ‘ C’ [stand in for] ‘the determining complex occurring in the second of the above instances’. Then C = m the first line of Gray’s Elegym , and the determinatum of C = ‘The curfew tolls the knell of parting day’. I have reformulated this in the metalinguistic mode using ‘α’, quasi-quotation, and the predicate ‘is true’. 9. Pace Russell, his apparent observation that in order to designate the designatum of α we should use the determinatum of m αm rather than the determinatum of α , though correct, provides no support whatever for his apparent conclusion that in order to designate the content of α, rather than using the content of α we must use the content of m αm , which is in fact equally inappropriate. Instead we can designate α’s content by using the content of ‘α’ or m αm . Analogously, we can equally designate α’s designatum using the designatum of ‘α’ or α itself. 10. That is, as soon as we put a determining complex in a proposition, by using a sentence involving a singular term whose content is the complex, the proposition is about the complex’s determinatum. This generates what I call the Collapse . As Russell will argue below, this same phenomenon arises even when designating the complex by using the simple indirect quotation m αm . 11. Roughly, a proposition component represents an object x in a proposition p if p is about x in virtue of that component. This marks the first use by

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Page 357 Russell of his variable ‘ C’ as ranging over determining complexes rather than definite descriptions. Moreover, the quotation marks here are indirect-quasi-quotation marks. The quotation ‘ M the content of cM ’ designates the determining complex consisting of the content of the functor ‘the content of’ joined with the complex c . Let c be the particular determining complex, m the first line of Gray’s Elegym . When we attempt to form a proposition about it by using a sentence containing the indirect quotation ‘ m the first line of Gray’s Elegym ’ (Russell supposes that one way to do this on the theory he is criticizing is by means of the sentence ‘“The content of the first line of Gray’s Elegy” is intriguing’), if the quotation functions as a logically proper name of the determining complex, then the resulting proposition is that (the content of) the first line of Gray’s Elegy is intriguing, rather than a proposition about the intended determining complex itself. This is one particular form of the Collapse: In attempting to form a proposition about a determining complex c by using a sentence containing an indirect quotation m αm , where α is a definite description that expresses c , we generate a proposition not about c but about its determinatum. We might use the content of ‘α’ instead of the indirect quotation m αm , but having assimilated this to the content of m αm , or failing to distinguish the two, Russell believes he has just shown that use of such a phrase inevitably comes to grief, via the Collapse. In any event, the objective in ( D) was to form a singular proposition about a determining complex, not a proposition in which the target complex is represented as the content of this or that phrase. 12. In this sense, “the meaning cannot be got at except by means of determiner phrases”; it cannot be genuinely named , in the strict, logical sense. 13. For example, let us attempt to name a particular complex, say m the first line of Gray’s Elegym , in order to express a proposition about it. Any proposition in which the complex itself occurs is about the first line of Gray’s Elegy, i.e. the determinatum of the target complex rather than the complex itself. And any proposition that is about the complex itself will involve a second-level determining complex that determines the target complex. For example, the indirect quotation ‘ m the first line of Gray’s Elegym ’ itself must express a second-level determining complex, m m the first line of Gray’s Elegym m , as its content. Moreover, the target complex is not a constituent of the postulated second-level complex, as it is of m the content of the first line of Gray’s Elegym . The second-level complex cannot, for example, be of the form M the determining complex that bears relation R to cM , for some relation R and where c is our target complex, m the first line of Gray’s Elegym . For the Collapse occurs here just as it does with propositions; the complex just formed collapses into m the determining complex that bears R to the first line of Gray’s Elegym . If R is the relation of determining , then this second-level complex fails to determine a unique complex because there are too many complexes that bear this relation to the first line of Gray’s Elegy (infinitely many, in fact). And if R is the relation of identity, then this second-level complex fails to determine a unique complex because there are too few complexes that bear this relation to the first line of Gray’s Elegy (none, in fact). 14. We have no idea which determining complex m mDm m is of the infinitely many complexes that determine mDm . 15. The inextricable tangle does indeed seem to prove that the whole distinction of content and designation has been wrongly conceived … by Russell. On the theory that definite descriptions are singular terms, whereas the proposition is about the description’s designatum and not about the content, the content itself is relevant to the proposition’s identity, and especially to its distinctness from other propositions involving determining

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Page 358 complexes with the same determinata. This is the very point of the theory (and Russell knows it). 16. Blackburn and Code mention the Collapse only after presenting their rival interpretation, which does not rely on the Collapse (1978a: 76; crediting David Kaplan for showing them that the Collapse refutes the earlier theory of designating in Russell’s Principles ). In sharp contrast to my interpretation, they express uncertainty whether Russell is even aware of the Collapse by the time he writes ‘On Denoting’. As against the hypothesis that he was, they say that ‘although this is a problem as to how one refers to senses [contents], the obvious solution is not to attack Frege, but rather to insist that his three-entity view [distinguishing among an expression, its content, and its designatum] applies to all referring [designating] expressions’. There are at least five problems with this. First, Russell was explicitly aware of the Collapse already in the lengthy and rambling ‘On Fundamentals’, begun not two months prior to ‘On Denoting’ and posthumously published in The Collected Papers of Bertrand Russell (1994a: 363, 382, and passim). Indeed, some passages of ‘On Fundamentals’ appear virtually verbatim in the ‘Gray’s Elegy’ argument, which is in certain respects a streamlined version of the convoluted reasonings of the former. Second, whereas one might hope to solve the problem by insisting that any singular term that designates a content always has its own content distinct from its designatum, the same distinction does not have to be extended to all terms (including names for concrete objects) in order for the solution to work. Third, though Russell was aware of the possibility of a theory like the one Blackburn and Code call ‘the obvious solution’ (as is shown by a passage they quote from Principles ), he did not unequivocally endorse it. Fourth, on the contrary, a central purpose of ‘On Denoting’ is precisely to reject Frege’s ‘three-entity view’ in regard to all singular terms, and replace it with a two-entity view. Finally, and most importantly, the very point of paragraphs ( F ) and ( G) appears to be precisely that the very proposal in question utterly fails to solve the problem. 17. The expression ‘ m mDm m ’ may stand in for the iterated indirect quotation ‘ m m the centre of mass of the Solar System m m ’, which designates the content of the indirect quotation, ‘ m the centre of mass of the Solar System m ’. 18. This does not rule out that the content can also be “got at” by means of an indefinite description, even if it is deemed not a singular term. Since ST is neutral regarding indefinite descriptions, it is equally consistent with the view that definite and indefinite descriptions alike are singular terms. The latter view makes indefinite descriptions subject to the argument from the Collapse. On the Theory of Descriptions, by contrast, a definite description is analysed as a special kind of indefinite description, neither being a singular term. The interpretation of this stage of Russell’s argument is strongly supported by the fact that he also gives this argument in writings just prior to ‘On Denoting’ (posthumously published). Cf. his ‘On Fundamentals’ and ‘On Meaning and Denotation’, also in The Collected Papers of Bertrand Russell (1994b: 322). 19. Searle (1958:139–40) depicts Russell as arguing that in order for a term to designate, the designated object must, if we are not to “succumb to mysticism”, occur in the propositions expressed with the help of the designating term; but then the Collapse excludes the possibility of designating determining complexes. Searle complains that the whole point of Frege’s theory, which Russell is attacking, is to deny Russell’s premise. It is possible that Church construes the argument similarly. 20. In ‘ Über Sinn und Bedeutung ’ (1994:149), Frege identified the indirect sense of a sentence φ with the customary sense of the thought that φ , which phrase may be presumed synonymous with m φ m .

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Page 359 21. Carnap (1947:118–37, especially 129–33) may be profitably interpreted as rejecting singular propositions about individuals, while accepting that ungerade constructions (as occur in belief attributions, modal claims, etc.) express singular propositions about the contents of their complement clauses. Cf. Dummett (1973:267–68) and Parsons (1981). 22. Church disagrees with Frege on some details, and as I argue in (Salmon 1993), he may have been inconsistent regarding the issue of the hierarchy. 23. Burge argues (1979:271–72), as follows, specifically that Frege’s theory of Sinn and Bedeutung is committed to hierarchies of sense, when coupled with Church’s methodology of eliminating ambiguityproducing devices (like ‘believes that’) that shift expressions in their scope into ungerade mode in favour of fully extensional operators applied to univocal names of senses: Suppose for a reductio that the true proposition that Bela believes that Opus 132 is a masterpiece does not contain a second-level complex that determines the proposition that Opus 132 is a masterpiece, and that instead the latter proposition represents itself in the former proposition. In accordance with Church’s methodology, we introduce an artificial extensional two-place operator ‘Believes’ for the binary relation of belief (between a believer and the object believed), so that ‘Bela Believes ( m Opus 132 is a masterpiece m )’ expresses that Bela believes that Opus 132 is a masterpiece. Then according to Frege’s theory, the quasi-artificial expression E, ‘Bela Believes (Opus 132 is a masterpiece)’, expresses the bizarre proposition that Bela believes a particular truth-value —to wit, the truth-value that is truth if Opus 132 is a masterpiece, and is falsity otherwise. But by our reductio hypothesis, E expresses a content consisting of the very components of the proposition that Bela believes that Opus 132 is a masterpiece, composed the very same way. By Compositionality, E therefore expresses our target proposition. (This collapse is obtained, in effect, from the reductio hypothesis by Synonymous Interchange.) On Frege’s extensional semantics, substitution in E of any sentence materially equivalent with ‘Opus 132 is a masterpiece’ preserves truth-value. Since E expresses that Bela believes that Opus 132 is a masterpiece, it follows on Frege’s theory that if Bela believes that Opus 132 is a masterpiece, he believes every materially equivalent proposition, which is absurd. Striking evidence that the central thrust of the ‘Gray’s Elegy’ argument has been lost on Russell’s readers is provided by Burge’s remark (280, n8) that to his knowledge, the argument presented above was nowhere explicitly stated before. Burge’s argument employs a sentence in place of a definite description, but this difference from Russell’s examples is completely inessential to the general argument. Burge also frames his argument in terms of a Fregean conception whereby an artificial notation should be used to avoid natural-language ambiguities produced by ungerade devices (e.g., ‘Believes’ in place of ‘believes that’). This introduces additional complexity, also inessential to the general point and leading to an unnecessarily restricted conclusion. Burge’s argument may be strengthened as follows: Suppose for a reductio that the true proposition that m the centre of mass of the Solar System m is a sense does not contain a second-level complex that determines m the centre of mass of the Solar System m , and that instead the complex m the centre of mass of the Solar System m represents itself in the proposition. The English sentence S, ‘The centre of mass of the Solar System is a sense’—which contains no artificial notation—then expresses a proposition consisting of the very components of the proposition that m the centre of mass of the Solar System m is a sense, and composed the very same way. By Compositionality, S therefore expresses our target proposition. But this conflicts with the fact that S is false.

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Page 360 24. A notable exception is Kremer (1994:287–88). Though my analysis of the argument differs from his, I have benefited from his meticulous probing and careful analysis of the passage. 25. The argument just given on Russell’s behalf purports to prove that, in Frege’s terminology, the sense of an indirect quotation is not an effectively computable function of the customary senses of the expressions within the indirect quotes. Frege concedes that the sense of a compound expression is not always composed of the customary senses of the component expressions. Frege would insist, however, that indirect-quotation marks do not violate Compositionality, or even Strong Compositionality as he intends these principles, since an expression does not have its customary sense when occurring within indirect-quotation marks and instead expresses its indirect sense, which does uniquely fix the sense of the indirect quotation. He says something analogous in connection with direct quotation. Direct quotations of customary synonyms are not themselves synonyms. 26. [Added after original submission of this article.] Kripke’s criticism has since been published (2005: see 1021–23). I take this opportunity to correct Kripke’s characterization there (1022) of our communication concerning Russell’s example. In my earlier discussion with Kripke I emphasized a distinction in semantic content that I draw, and of which Kripke is dubious, between the binary-relational predication ‘ a is larger than a ’ and the monadic-predicational ‘ a is a thing larger than itself’—the latter symbolized as ‘(λ x)[ x is larger than x]( a )’. I used the distinction not to solve the problem Kripke noticed in Russell’s discussion of his example, but rather to support my contention (which Kripke does not accept) that it is possible for one to believe concerning a particular yacht y, that y is larger than y is, while not thereby believing that y is self-larger (i.e., a thing x larger than itself). Cf. my ‘Reflexivity’ (1986) and my ‘Reflections on Reflexivity’ (1992). I was aware that this distinction (even if it is legitimate, as I maintain) does not solve the problem Kripke had noticed. I have known the corrected “purely Russellian” analysis, and have so interpreted Russell’s intended treatment of the example, since I first studied ‘On Denoting’ in 1971–72 (in undergraduate courses given by Alonzo Church, David Kaplan, Kripke and others). I had given the example essentially the same Russellian analysis on first reading ‘On Denoting’. Each of Kripke’s explicit misgivings (1025, n45) concerning my former proposal can be met. In particular, on my proposal, although a formula φβ and its lambda-convert (λα)[φα](β) differ in semantic content, the two remain coextensional and indeed logically equivalent (at least in the absence of nonextensional devices). The distinction in content in no way undermines the observation that there is always a fact of the matter concerning whether x = x (just as there is a fact concerning whether x is self-identical—the two matters being equivalent), any more than it undermines the observation that it is a necessary truth that x = x. Furthermore, Kripke’s claim that “Church, inventor of the lambda notation, did not intend any such distinction” in semantic content between a formula φβ and its lambda-convert (λα)[φα](β) (as between ‘a is larger than a ’ and ‘(λ x)[ x is larger than x]( a )’) is historically incorrect. On Church’s Alternative (0), which he explicitly preferred over Alternatives (1) and (2) as an explication of having the same sense , such lambda converts are, as Church recognized, although logically equivalent, not synonymous—just as the mathematical expressions ‘3!’ (alternatively, ‘(λ x)[ x!](3)’) and ‘6’ are codesignative but not synonymous. I am in agreement with Church in this. (φ-converts are regarded as synonymous on the other two alternatives.) Cf.

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Page 361 Church (1993) and Anderson (2001:421–22). (Thanks to Anderson for discussion and bibliographical references.) 27. David Kaplan and Terence Parsons have noted related difficulties in Russell’s discussion of the example. I am grateful to Kripke, Kaplan, and Parsons for discussion. Kripke is now persuaded, whereas I believe Parsons remains unconvinced, that Russell’s distinction of primary and secondary occurrence, properly applied, nevertheless provides an insightful diagnosis of the ambiguity. See the following note concerning Kaplan. Russell correctly observes in the same paragraph of ‘On Denoting’ that the primaryoccurrence reading of ‘George IV wondered whether Scott is the author of Waverley ’ is true if King George glimpses Scott at a distance and asks ‘Is that Scott?’. Russell was likely assuming, at least for the purposes of illustration, a commonsensical epistemology on which visual perception of an object is sufficient to enable one to apprehend singular propositions about it, and thus to bear de re propositional attitudes towards it. However, Russell’s observation thus seems incompatible with his claim that ‘an interest in the [reflexive] law of identity can hardly be attributed to the first gentleman of Europe’. Kaplan, Kripke, and others have independently also noticed this flaw in Russell’s presentation. (See Kripke, 2005:1023–24.) Russell’s observation can be made consistently with Russell’s insistence that King George had no interest in the reflexivity of identity by distinguishing, as I do, the singular proposition about Scott that he is Scott from the singular proposition about Scott that he is self-identical (a thing identical with itself), so that one can in fact wonder about Scott whether he is him without thereby wondering whether he is self-identical. See the preceding note. Kripke argues (1024–25) that this distinction was not available to Russell given his logical apparatus. I never asserted that Russell’s account of sentences involving λ-abstraction is compatible with my own. I believe, however, that Russell could have distinguished (even if not through his apparatus for propositional-functional abstraction) between the singular propositions about Scott that he is him and that he is selfidentical (a thing identical with itself). He might also have interpreted the reflexivity of identity as not involving the property of being self-identical. In any event, King George’s wondering about Scott whether he is him (as glimpsed from a distance) should not be misrepresented as a concern about the reflexivity of identity. King George knows about Scott all the while (even while glimpsing him from a distance) both that he is him and that he is, as with everything else, self-identical. 28. Kaplan, in (1973) observes, ‘The yacht owner’s guest who is reported by Russell to have become entangled in ‘I thought that your yacht was longer than it is’ should have said, ‘Look, let’s call the length of your yacht ‘a russell’. What I was trying to say is that I thought that your yacht was longer than a russell.’ If the result of such a dubbing were the introduction of ‘russell’ as a mere abbreviation for ‘the length of your yacht’, the whole performance would have been in vain’ (501). The measurement term ‘russell’ in Kaplan’s disambiguation of S serves much the same purpose as the anaphoric pronoun in ‘The size of your yacht is such that I thought the size of your yacht was greater than that’. So does the variable ‘ r’ in S2,1 . This suggests that Kaplan had in mind the same correction proposed here. 29. A potential difference between S1,1 and S2,2 is that one might easily come to believe of a single thing x, de re , that x is greater than x is. I take it to be clear, however, that the guest did not believe this of the yacht’s size. See n26 above.

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Page 362 REFERENCES Anderson, C. A. (2001) ‘Alternative (1*): A Criterion of Identity for Intensional Entities’, in Anderson and M. Zeleny (eds), Logic, Meaning and Computation: Essays in Memory of Alonzo Church , Boston: Kluwer: 395–427. Ayer, A. J. (1971) Russell and Moore: The Analytic Heritage, London: Macmillan. Blackburn, S. and Code, A. (1978a) ‘The Power of Russell’s Criticism of Frege: On Denoting pp. 48–50’, Analysis 38: 65–77. ——. (1978b) ‘Reply to Geach’, Analysis 38: 206–7. Burge, T. (1979) ‘Frege and the Hierarchy’, Synthese 40: 265–81. Butler, R. J. (1954) ‘The Scaffolding of Russell’s Theory of Descriptions’, The Philosophical Review 63: 350–64. Carnap, R. (1947) Meaning and Necessity , Chicago, IL: University of Chicago Press (reprinted 1970). Cassin, C. E. (1971) ‘Russell’s Discussion of Meaning and Denotation: A Re-examination’, in E. D. Klemke (ed.), Essays on Bertrand Russell, Chicago/London: University of Illinois Press: 256–72. Church, A. (1943) Review of Carnap’s Introduction to Semantics, The Philosophical Review 52: 298–304. ——. (1993) ‘A Revised Formulation of the Logic of Sense and Denotation, Alternative (1)’, Noûs , 27: 141–57. Demopoulos, W. (1999) ‘On the Theory of Meaning of On Denoting ‘, Noûs 33: 439–58. Dummett, M. (1973) Frege: The Philosophy of Language, London: Duckworth. Frege, G. (1994) ‘ Über Sinn und Bedeutung ’ (translated as ‘On Sense and Reference’), in Robert M. Harnish, (ed.), Basic Topics in the Philosophy of Language, Boston, MA: Prentice-Hall: 42–60. Geach, P. (1959) ‘Russell on Meaning and Denotation’, Analysis 19: 69–72. ——. (1978) ‘Russell on Denoting’, Analysis 38: 204–5. Hochberg, H. (1976) ‘Russell’s Attack on Frege’s Theory of Meaning’, Philosophica 18: 9–34. Hylton, P. (1990) Russell, Idealism and the Emergence of Analytic Philosophy , New York/Oxford: Oxford University Press. Jager, R. (1960) ‘Russell’s Denoting Complex’, Analysis 20: 53–62. Kaplan, D. (1969) Reviews of Butler, Searle, Geach, Jager and Garver, Journal of Symbolic Logic 34, 1: 142–45. ——. (1971) ‘Quantifying In’, in L. Linsky (ed.), Reference and Modality, New York/Oxford: Oxford University Press: 112–44. ——. (1973) ‘Bob and Carol and Ted and Alice’, in K. J. J. Hintikka, J. M. E. Moravcsik, and P. Suppes (eds), Approaches to Natural Language, Boston: Reidel: 490–518. Kremer, M. (1994) ‘The Argument of On Denoting ‘, The Philosophical Review 103, 2: 249–97. Kripke, S. (2005) ‘Russell’s Notion of Scope’, Mind 114, 456: 1005–37. Landini, G. (1998) ’ On Denoting Against Denoting’, Russell, n.s. 18, 1: 43–80. Levine, J. (2004) ‘On the Gray’s Elegy Argument and its Bearing on Frege’s Theory of Sense’, Philosophy and Phenomenological Research 69: 251–95. Makin, G. (2000) The Metaphysicians of Meaning , London: Routledge. Manser, A. (1985) ‘Russell’s Criticism of Frege’, Philosophical Investigations 8: 269–87. Noonan, H. (1996) ‘The Gray’s Elegy Argument—and Others’, in R. Monk and A. Palmer (eds), Bertrand Russell and the Origins of Analytic Philosophy , Bristol: Thoemmes Press: 65–102.

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Page 363 Pakaluk, M. (1993) ‘The Interpretation of Russell’s Gray’s Elegy Argument’, in A. D. Irvine and G. A. Wedeking (eds), Russell and Analytic Philosophy , Toronto: University of Toronto Press: 37–65. Parsons, T. (1981) ‘Frege’s Hierarchies of Indirect Senses and the Paradox of Analysis’, in P. French, T. Uehling and H. Wettstein (eds), Midwest Studies in Philosophy , Minneapolis: University of Minnesota Press: 37–58. Russell, B. (1905) ‘On Denoting’, Mind 14: 479–93. ——. (1994a) ‘On Fundamentals’, in A. Urquhart (ed.), The Collected Papers of Bertrand Russell, vol. 4, Foundations of Logic, 1903–1905, London: Routledge: 359–413. ——. (1994b) ‘On Meaning and Denotation’, in A. Urquhart (ed.), The Collected Papers of Bertrand Russell, vol. 4, Foundations of Logic, 1903–1905, London: Routledge: 314–58. Salmon, N. (1986) ‘Reflexivity’, Notre Dame Journal of Formal Logic 27, 3: 401–29. Reprinted in N. Salmon and S. Soames (eds), Propositions and Attitudes, Oxford Readings in Philosophy, Oxford: Oxford University Press, 1988: 240–74. Also reprinted in Salmon, Content, Cognition, and Communication: Philosophical Papers II, Oxford: Oxford University Press, 2007. ——. (1992) ‘Reflections on Reflexivity’, Linguistics and Philosophy 15, 1: 53–63. Reprinted in Salmon, Content, Cognition, and Communication: Philosophical Papers II, Oxford: Oxford University Press, 2007. ——. (1993) ‘A Problem in the Frege-Church Theory of Sense and Denotation’, Noûs 27, 2: 158–66. ——. (2005) ‘On Designating’, Mind 114, 456: 1069–1133. Searle, J. (1958) ‘Russell’s Objections to Frege’s Theory of Sense and Reference’, Analysis 18: 137–43. Turnau, P. (1991) ‘Russell’s Argument against Frege’s Sense-Reference Distinction’, Russell, n.s. 2: 52– 66. Wahl, R. (1993) ‘Russell’s Theory of Meaning and Denotation and On Denoting’, Journal of the History of Philosophy 31: 71–94.

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Page 365 Contributors David Bostock has been a Fellow of Merton College, Oxford, since 1968. His publications, all with Oxford University Press, include several books on Plato and Aristotle, and in addition Logic and Arithmetic (vol. 1, 1974; vol. 2, 1979) and Intermediate Logic (1997). He is currently working on a book on the philosophy of mathematics. Gabriele Contessa is a visiting Assistant Professor in the Department of Philosophy at the University of Rochester. He did his graduate studies in the Department of Philosophy, Logic and Scientific Method at the London School of Economics. His research interests include (but are not limited to) scientific models, representation, fictional entities, laws of nature, counterfactuals, and dispositions. He has published in journals such as Philosophical Studies , Studies in History and Philosophy of Science , and Erkenntnis . He is currently working on a variety of projects, including a book with Nancy Cartwright. Nicholas Griffin is Director of the Bertrand Russell Centre at McMaster University, Hamilton, Ontario, where he holds a Canada Research Chair in Philosophy. He has written widely on Russell and is the general editor of The Collected Papers of Bertrand Russell, the author of Russell’s Idealist Apprenticeship, and the editor of The Cambridge Companion to Bertrand Russell, and two volumes of Russell’s Selected Letters . Dale Jacquette is Senior Professorial Chair in Theoretical Philosophy at the University of Bern, Switzerland. Author of numerous articles on logic, metaphysics, and philosophy of mind, he has recently published Meinongian Logic: The Semantics of Existence and Nonexistence; Wittgenstein’s Thought in Transition; On Boole; Ontology ; David Hume’s Critique of Infinity ; and The Philosophy of Schopenhauer . He has edited the Cambridge Companion to Brentano; Schopenhauer, Philosophy, and the Arts; the Blackwell Companion to Philosophical Logic ; Philosophy of Logic in the North-Holland (Elsevier) Handbook of the Philosophy of Science series; and has just released a new translation of Gottlob Frege’s

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Page 366 Grundlagen der Arithmetik: Eine logisch mathematicische Untersuchung über den Begriff der Zahl. His critical edition of Bertrand Russell’s Introduction to Mathematical Philosophy is soon to appear. Kevin C. Klement is Associate Professor of Philosophy at the University of Massachusetts, Amherst. He received his Ph.D. from the University of Iowa in 2000. He is the author of Frege and the Logic of Sense and Reference (Routledge, 2000), and several articles on the history of analytic philosophy, informal logic and related areas in philosophy. Gregory C. Landini is a Professor of Philosophy at the University of Iowa. He is author of Wittgenstein’s Apprenticeship With Russell (Cambridge University Press, 2008) and Russell’s Hidden Substitutional Theory (Oxford University Press, 1998). He has published articles in the history and philosophy of logic and metaphysics. His research interests include modal logic, the foundations of mathematics, philosophy of mind and the history of analytic philosophy. Bernard Linsky is a Professor of Philosophy at the University of Alberta in Edmonton, Canada. He is the author of Russell’s Mathematical Logic (CSLI, 1999) and numerous articles on Russell. Bernard Linsky and Edward Zalta have written a series of papers on object theory, including most recently a discussion of neo-Fregeanism. Linsky has published the complete notes that Russell made on Frege, as well as Russell’s marginalia in Frege’s works, from the materials in the Bertrand Russell Archives. Currently he is working on the manuscripts and notes from the Archives relating to the second edition of Principia Mathematica . Peter Loptson is a Professor of Philosophy at the University of Guelph. His primary areas of specialization are metaphysics, and history of early modern philosophy. He is the author of Reality: Fundamental Topics in Metaphysics (University of Toronto Press, 2001) and articles on Descartes, Spinoza, Leibniz, Locke, and Hume. Gideon Makin obtained his D.Phil. from Oxford in 1995. Since then he has held posts and taught at the Universities of Oxford, Stirling, and Birmingham. His book The Metaphysicians of Meaning—Russell and Frege on Sense and Denotation appeared in 2001 in Routledge’s ‘International Studies in Philosophy’ Series. He is currently an honorary Research Fellow at the University of Birmingham, England. Johann C. Marek, born in 1948, received his Ph.D. in 1975 at the University of Graz where he is currently Associate Professor of Philosophy and Chair of the Alexius Meinong Institute. He works in the area of

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Page 367 philosophy of mind, epistemology, ontology, metaphilosophy, and the history of Austrian philosophy. Omar W. Nasim is a postdoctoral fellow for the project ‘Knowledge in the Making,’ a joint project with two Max Planck Institutes, one for the History of Science (Berlin) and the other for the History of Art (Florence). Nasim’s research interests include: History of Analytic Philosophy, Philosophy of Mathematics and Science, Aesthetics, and the 19th century Kantian tradition. His forthcoming book, Bertrand Russell and the Edwardian Philosophers: Constructing the World reflects some of these interests. Nasim is currently working on the drawings of nebulae made by Victorian Astronomers and the notion of ‘scientific observation.’ Michael Nelson is an Assistant Professor of Philosophy at the University of California, Riverside. He has been an Assistant Professor of Philosophy of Yale University and a visiting Professor at the University of Arizona. He specializes in philosophy of language and metaphysics. His work has been published in Australasian Journal of Philosophy , Noûs , Philosophical Studies , Linguistics and Philosophy , and the Stanford Encyclopedia of Philosophy . Francis Jeffry Pelletier is a Canada Research Chair in Cognitive Science at Simon Fraser University, and a Professor of Philosophy and of Linguistics. He has published widely on topics in philosophy of language and logic, automated theorem proving, ancient Greek philosophy, and linguistic semantics. Of interest to readers of this anthology might be his ‘Did Frege Believe Frege’s Principle?’ ( J. Logic , Language, Information, 1999). Nathan Salmon is Professor of Philosophy at the University of California, Santa Barbara. He is the author of numerous articles in metaphysics and philosophy of language and four books, Reference and Essence ; Frege’s Puzzle ; Metaphysics, Mathematics, and Meaning ; and Content, Cognition, and Communication . Graham Stevens is Lecturer in philosophy at the University of Manchester. He is the author of The Russellian Origins of Analytical Philosophy (Routledge, 2005) and several articles on Russell’s philosophy as well as other areas of philosophy. Alasdair Urquhart teaches in the Department of Philosophy at the University of Toronto. He is the editor of The Collected Papers of Bertrand Russell, volume 4: Foundations of Logic, 1903–05 . He works in the areas of mathematical logic, complexity theory and the history of logic.

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Page 369 Index A aboutness, 6, 103–104, 108, 285 (see: intentionality) confined aboutness, 103 abstract entity, 257, 259–260; abstract object, 15, 72, 214, 249, 257–264 abstraction, abstraction operator, 6, 13–14, 20–21, 32, 70, 275–277, 284, 326, 361 false abstraction, 32 functional abstraction, 13–14, 21 acquaintance, 10, 15, 18, 29, 37, 95, 102, 110, 134, 144, 147–148, 152–156, 168, 182, 203, 297, 299– 302, 304, 330, 332, 342 (see: knowledge by acquaintance) principle of acquaintance, 29, 37, 134 act, 14, 73, 148–151, 154, 156, 164, 228, 238–239, 248, 282–283, 285–286, 292–294, 332 actual existence, 190 Adams, Robert, 331, 340–341 adequacy relation, 151–152 ambiguity, 44, 126, 131, 134, 138, 140–142, 277, 289, 293, 305, 336, 353, 361; ambiguous, ambiguous object, 45, 120, 129, 140, 230, 271, 304, 306, 353 Ameseder, Rudolf, 56, 63 analyticity, 244, 307, 309–310, 314–315, 318, 322–323, 334–335; analytic truth, 308, 310, 313, 315 Andersson, Stefan, 38 Annahme, 170 (see: assumption) anti-essentialism, 297, 299, 301, 303, 305, 307, 309, 311, 313, 315, 317–321, 323, 325–331, 333, 335, 337, 339, 341; anti-essentialist, 297, 308, 315–317, 320, 322, 327, 330, 333, 339 antiextension, 209, 229 antinomy, 68–71 antirealism, 26–27, 29, 31–33, 35, 37, 39 Aquinas, Thomas, 6 Aristotelian essentialism, 307–314, 316–320, 326, 329 associationism, 101 assumption, 6, 35, 68, 82, 85, 90–92, 96, 100, 103, 106, 116, 120, 126, 129, 133, 170, 179, 183, 187, 194, 199–201, 204–208, 211, 213–221, 228–229, 237, 254, 266, 269, 272, 284, 286, 290, 292, 305, 314, 320, 323, 325, 349 (see: Annahme) attribute, 27, 37, 40, 55, 80, 171, 185, 188, 201, 274–275, 280, 286–287, 289, 291, 313, 326

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Page 370 Außersein, außerseiend, 147, 158, 161–163, 165, 170, 172, 186, 200, 203 (see: extraontology) Austin, J.L., 142, 332, 340 axiom, 12, 16, 53, 61, 122, 132, 140, 142, 214, 248–249, 252, 261, 264, 266–269, 273, 283, 295, 323–324 axiom of choice, Zermelo’s 122 axiom of existence, 248–249, 252, 261, 264 axiom of extensionality, 132 axiom of infinity, 16 axiom of pairing, 122, 289 axiom of replacement, 122 axiom of union, 122 power set axiom, 65, 122 Ayer, A.J., 98, 100, 355, 362 B Barendregt, H.P., 14, 25 basic particulars, 301–302 Bedeutung , 19, 41–48, 51, 53–57, 61–63, 76, 144, 166–167, 172, 174, 187, 358–359, 362 (see: reference, referential meaning) Begriffsschrift (Frege), 43, 177, 182 being, 1, 4, 7–8, 13, 17, 26–28, 34, 38, 43, 45–48, 52, 60, 73–74, 78–81, 83–92, 94–95, 99–100, 104, 106–108, 111–112, 116, 119, 121–123, 136, 139, 142, 144–145, 147, 149, 151, 153, 155, 157–165, 167, 170–171, 173–179, 181–189, 193, 197, 199–202, 205–206, 208, 210, 212–215, 217–218, 222, 224, 227–229, 233–234, 236–239, 242, 245–246, 248, 250, 255–256, 258–259, 261, 264, 283, 285– 287, 291, 294, 299–301, 306–307, 309–310, 314, 317–319, 321–323, 325–327, 330–332, 335, 337– 340, 345, 347, 352, 356, 358, 360–361 (see: Sein) beingless object, beinglessness, 6–8, 147, 169–171, 175, 177 Berkeley, George 76, 167, 190, 198, 202, 231 Bestand , 163, 186, 236 (see: subsistence) bivalence (principle), 26, 34–37, 68 Black, Max, 61, 63, 141 Blackburn, Simon, 355, 358, 362 Bolzano, Bernard, 103, 105, 108–109, 149, 168, 174 Boole, George, 24, 365 Boolos, George, 139, 142 Borkowski, L.S., 141–142 Boutroux, Pierre, 23 Bradley, F.H., 3, 106 Brentano, Franz, 5–6, 8, 101, 103, 106, 145–146, 148, 150, 163, 170, 179, 187, 189–190, 228, 283, 365 Brock, Stuart, 243, 247 Brouwer, L.E.J., 24 Burali-Forti paradox, 23, 121 Burge, Tyler, 75–76, 349, 359, 362 Burgess, John, 323–326, 333, 337, 340 Butler, Ronald J., 355, 362 C Cantor, Georg, 65, 73, 116, 118, 121 Carnap, Rudolf, 41, 46–47, 61, 63, 75–76, 112, 236, 246, 322, 349, 359, 362 Cassin, Chrystine, 19, 25, 355, 362 categoricals, 285 Chalmers, David, 75–76 characterization, 26, 34–35, 42, 200, 205–206, 208, 211, 213, 215–216, 218–221, 228, 283, 308, 318, 323, 337, 360

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Page 371 characterization postulate, 200, 205–206, 213, 215–216, 219–221 characterizing property, 183 Chihara, Charles, 76 Church, Alonzo, 24–25, 75–76, 129, 140, 321, 337–338, 340, 344, 349, 355, 358–360, 362 class, 19–20, 22, 26–27, 29, 31–32, 34–35, 54–55, 69, 74, 86–87, 90–93, 113–118, 120–123, 131– 132, 137–139, 206, 212, 244, 273–276, 278, 284, 308, 312–313, 319–320, 322, 330, 332, 337, 339, 350 (see: set, set theory) class-as-many, 114–117, 139 class-as-one, 114–117 class-concept, 87 theory of classes, 22, 25, 30–31, 38, 123, 125, 132, 142–143, 272, 280 classical logic, 14, 60, 217, 235–236, 246, 266 Cocchiarella, Nino, 75–76, 129, 141–142 Code, Alan, 355, 358, 362 Coffa, Alberto, 103–105, 108, 112 cognition, 108, 290–293, 363, 367 collapse, the, 343–344, 347–351, 357–358 complex, 8–9, 13–16, 18, 21–22, 24, 47–48, 50, 54, 69–71, 75, 78, 80, 88, 91, 93, 96, 98–99, 104, 108, 110, 125– 126, 134, 140, 155–156, 165, 193, 217, 219–220, 236, 333, 338, 343–353, 355–357, 359, 361–363 complex points, 343, 345, 347, 349, 351, 353, 355, 357, 359, 361, 363 compositionality (principle), 348, 351 comprehension axiom, comprehension principle, 12, 66, 140, 191, 273, 275, 279 concept, 3–4, 27–29, 32, 41, 43, 45, 69–71, 76–77, 80, 86–87, 89, 91–94, 97–99, 103–105, 108–109, 111, 115–116, 119, 139, 147, 157, 171–173, 178, 184, 186, 188–190, 193, 199–200, 212, 241, 285– 286, 289–294, 316, 338, 344 conceptual content, 100, 152 consciousness, 3, 106, 145, 147 consistency, 181, 205–206, 208, 211, 215, 224, 229, 335 constant, 12, 23, 105, 131, 268, 321 constituent, 13, 15, 17, 27, 29, 95, 103, 105, 109, 155, 197, 218, 227, 284, 300–301, 304, 332, 338, 344, 347, 350, 352, 357 constitutive property, 159, 170, 176 construction, 11, 68, 121, 138, 181, 280 content, 26, 63, 100, 106–107, 109, 112, 144–145, 147–157, 159, 161, 163–168, 173, 180, 190, 228, 236–237, 253, 287, 301, 333–334, 343–352, 355–360, 363, 367 (see: Inhalt ) context of supposition, 220–227, 230 contradiction, 11–14, 17, 21–24, 30–31, 33, 62, 72–75, 95, 100, 109, 116–117, 120, 123, 126, 138, 140, 145–146, 160, 162–163, 180–181, 183–184, 186, 198, 202, 210, 230, 280–281, 283, 287, 292, 298, 307, 311–312, 317–318, 329, 338 contradictory entities, 90, 100 Copeland, B.J., 211, 231 Copi, Irving M., 141–142

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Page 372 correspondence, 34, 76, 102, 152, 171, 236–237, 296; correspondence theory of truth, 34 course of values, 44, 46, 61 Couturat, Louis-Alexandre, 22–24 Cresswell, Max, 295 Crimmins, Mark, 332 Crittenden, Charles, 243, 247, 264–265 Currie, Gregory, 252, 265 D Dau, Paul, 114, 139, 142 de dicto, de dicto belief ascription 294, 323–325, 340 De Morgan, Augustus, 24 de re , de re definite descriptions 266, 289–295, 316, 321, 323–325, 330, 333, 339–341, 361 de re belief ascription, 289 de re modal claims, modality, 316, 321, 323–325, 340–341 definite descriptions, 41, 193, 266, 272, 282 demonstrative reference, 302 Demopoulos, William, 355, 362 denotation, 10–11, 13, 15, 17–23, 25, 29, 46, 54–55, 61, 63, 65–66, 72–73, 75–76, 80, 83, 91, 97–99, 103, 173, 176, 180–182, 184–185, 187–190, 201, 203, 344, 358, 362–363, 366 denoting complexes, 13, 19, 69, 71, 94 denoting concept, 28–29, 69, 87, 94, 97–99, 104–105, 108–109, 111, 285–286 denoting concepts, 12, 28, 32–33, 65, 69, 74, 80–81, 83, 90, 92, 94–97, 100, 102–106, 108–109, 111, 114, 172, 179, 193, 231, 284–286 denoting function, 70 denoting phrase, 27, 55, 180, 283, 344 Descartes, René, 175, 190, 202, 366 description, 8, 13, 19–21, 34–35, 37, 44, 46–60, 62, 64, 66, 70–71, 73, 90, 100, 105, 110–111, 116, 147, 155, 163, 168, 182, 191, 193–198, 200–201, 203–204, 208, 214, 224, 239, 255–256, 261, 263, 270–271, 273, 280, 284, 289–290, 292–293, 297, 300–301, 303–305, 313, 316, 322, 328, 331, 333, 336–337, 341–345, 348–354, 356–359 description operator, 13, 19–20, 47, 71 description principle, 200–201 descriptive phrase, 65 descriptive sense, 66–68, 70–73 designation, 15, 50, 150, 246, 346–347, 349, 356–357; designator, 263, 309, 317–319, 321–322, 328, 339 determiner phrase, 345–347 determining complex, 344–351, 356–357 direct quotation, 356, 360 direct realism, 29, 33, 103–104 directedness, 148, 154–155 disguised definite description, 62, 91, 97, 305–306, 309, 333, 348 displacement identity, 241 doctrine of logical types, 33 Donnellan, Keith, 240 Dummett, Michael, 26, 29–32, 34–38, 349, 355, 359, 362 E eliminative materialism, 241 emotion, 6, 170, 199

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Page 372 correspondence, 34, 76, 102, 152, 171, 236–237, 296; correspondence theory of truth, 34 course of values, 44, 46, 61 Couturat, Louis-Alexandre, 22–24 Cresswell, Max, 295 Crimmins, Mark, 332 Crittenden, Charles, 243, 247, 264–265 Currie, Gregory, 252, 265 D Dau, Paul, 114, 139, 142 de dicto, de dicto belief ascription 294, 323–325, 340 De Morgan, Augustus, 24 de re , de re definite descriptions 266, 289–295, 316, 321, 323–325, 330, 333, 339–341, 361 de re belief ascription, 289 de re modal claims, modality, 316, 321, 323–325, 340–341 definite descriptions, 41, 193, 266, 272, 282 demonstrative reference, 302 Demopoulos, William, 355, 362 denotation, 10–11, 13, 15, 17–23, 25, 29, 46, 54–55, 61, 63, 65–66, 72–73, 75–76, 80, 83, 91, 97–99, 103, 173, 176, 180–182, 184–185, 187–190, 201, 203, 344, 358, 362–363, 366 denoting complexes, 13, 19, 69, 71, 94 denoting concept, 28–29, 69, 87, 94, 97–99, 104–105, 108–109, 111, 285–286 denoting concepts, 12, 28, 32–33, 65, 69, 74, 80–81, 83, 90, 92, 94–97, 100, 102–106, 108–109, 111, 114, 172, 179, 193, 231, 284–286 denoting function, 70 denoting phrase, 27, 55, 180, 283, 344 Descartes, René, 175, 190, 202, 366 description, 8, 13, 19–21, 34–35, 37, 44, 46–60, 62, 64, 66, 70–71, 73, 90, 100, 105, 110–111, 116, 147, 155, 163, 168, 182, 191, 193–198, 200–201, 203–204, 208, 214, 224, 239, 255–256, 261, 263, 270–271, 273, 280, 284, 289–290, 292–293, 297, 300–301, 303–305, 313, 316, 322, 328, 331, 333, 336–337, 341–345, 348–354, 356–359 description operator, 13, 19–20, 47, 71 description principle, 200–201 descriptive phrase, 65 descriptive sense, 66–68, 70–73 designation, 15, 50, 150, 246, 346–347, 349, 356–357; designator, 263, 309, 317–319, 321–322, 328, 339 determiner phrase, 345–347 determining complex, 344–351, 356–357 direct quotation, 356, 360 direct realism, 29, 33, 103–104 directedness, 148, 154–155 disguised definite description, 62, 91, 97, 305–306, 309, 333, 348 displacement identity, 241 doctrine of logical types, 33 Donnellan, Keith, 240 Dummett, Michael, 26, 29–32, 34–38, 349, 355, 359, 362 E eliminative materialism, 241 emotion, 6, 170, 199

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Page 373 empiricism, 6, 36–38, 199, 341–342; empiricist metaphysics, 5 empirical descriptive psychology, 6 empirical methodology, 171 empty descriptions, 80–81, 98 entity, 4, 15–16, 18–19, 21, 23, 28, 31, 45, 53, 65–67, 71, 73–74, 80–81, 85–87, 91, 93, 95, 98–99, 102, 106, 135, 140, 174, 185–186, 202, 250, 257, 259–260, 266, 279–280, 284, 292, 331 entity-occurrences, 22 epistemic realism, 283 epistemology, 1, 106, 178, 361, 367 Evans, Gareth, 252, 265 evidence, theory of, 6 exist, 6–7, 27–28, 35, 38, 56–57, 79, 81, 84–87, 89, 98–99, 106, 117, 121, 123, 133–134, 140, 150– 151, 154, 162–164, 169–171, 176–177, 179–180, 182–188, 190, 192–193, 197– 199, 201, 214–215, 220–221, 224–225, 234, 236, 238, 242, 244, 246, 248–251, 254, 261, 263, 274, 329 existence, 4, 7, 9, 17, 27–28, 35, 49, 54, 56–57, 62, 72, 80–81, 84–87, 91, 99, 108–109, 117, 122– 123, 132–133, 150, 157, 164, 166, 169, 176, 178–179, 182–183, 185–190, 193, 195–199, 202–203, 206, 212, 215, 217, 233–234, 236, 248–250, 252, 261, 264, 270, 273–274, 283, 294, 305, 317, 326, 330, 337–338, 340–342, 365 existent object, 169, 192, 196 existent, 4, 6–8, 56, 81, 102, 154–155, 162–163, 167, 169, 171–175, 179–184, 187, 191–193, 195– 196, 198–203, 207, 213–217, 238, 264 existential quantifier, quantification, 29, 49, 52, 80, 86, 100, 118, 181, 186, 188, 193, 195–196, 201– 202, 209, 225, 237, 266–267, 283 expressivism, 26 extension, 9, 32, 70, 116, 137, 156, 191–192, 209, 229, 250, 269, 304, 338 extensionalism, 8, 171–172, 174–175, 179, 184, 191–192, 197, 202 extensionalist theory of meaning, 171, 183, 191 extensionality, 132, 172, 273, 275 external relation, 153, 156 extraontology, 170 –171, 195–196, 201 (see: Außersein, außerseiend) extra-being, 186 extra-nuclear property, 215 F face-value semantics, 205, 228 fact, 7–8, 12, 14, 16, 18–19, 23–24, 27–31, 34, 43, 46, 55–57, 59, 61, 80–82, 84, 87, 89, 91–93, 96– 97, 99–101, 103, 105–107, 109, 111, 115–117, 119, 122, 125–126, 129, 133, 136, 138, 146, 151, 153, 155–156, 159, 164, 169–171, 173, 175, 177, 179, 181–182, 184, 186, 189, 199, 201, 206–208, 213– 214, 217, 219–223, 225–226, 228, 233–237, 239, 241, 245, 250–253, 255–264, 269, 274, 283–284, 308–311, 314, 317, 319–320, 322, 328–330, 335, 338–339, 348–352, 356–361

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Page 374 fiction, 202, 222, 232, 265 fictional objects, 247, 265 Findlay, J.N., 145, 159, 162, 165–166, 182, 184, 200–202, 212, 229, 231 Fine, Kit, 201–202, 333–334, 341 Fitch, Frederic B., 141–142, 330, 333, 337, 340–341 folk psychology, 241 Fraenkel, Abraham A., 122 free logic, 42, 64, 236, 268, 296 freedom of assumption, 6, 204–207, 211, 213–217, 219, 221, 229 Frege, Gottlob, 3–4, 9, 12, 14, 16–21, 24–25, 32, 35, 40–51, 53–59, 61–65, 68–72, 74–77, 85, 95–97, 99, 105, 108–109, 115–119, 128–130, 132, 134, 137, 139–140, 142, 146, 162, 171–182, 184–185, 187–191, 193, 203, 281, 284–285, 291, 296, 298, 300–302, 331–332, 337, 343, 348–349, 351, 358– 360, 362–363, 366–367 function, 13–14, 16–18, 21, 45, 48, 53, 61–62, 69–71, 75–77, 86, 95, 117–121, 123–127, 131, 133– 135, 138, 140, 194, 211, 268, 314, 344, 348, 350–351, 360 functional application, 13–14 G gap, 16, 78, 94, 114, 127–128, 130, 134, 139 gappy object, 17 Geach, P.T., 19, 25, 139, 142, 355, 362 Gegenstand, 105, 153–154, 158, 162, 165, 168 Gegenstandstheorie (Meinong), 1, 4, 25, 40, 64, 98–100, 162–164, 166–169, 171, 173, 176–177, 200, 203, 231, 236, 238 (see: object theory) generality, 52, 72, 104, 142, 228 Gibbard, Allan, 327, 341 Gödel, Kurt, 24, 76, 141 Goldfarb, William, 76 Grattan-Guinness, Ivor, 11, 25, 75–76 ‘Gray’s Elegy’, 19, 63, 98, 178, 188, 295, 343, 345–347, 349–352, 356–359, 362–363 Griffin, Nicholas, 1–3, 6, 8–40, 42–369 H Hazen, Allen P., 76 Hermes, Hans, 99, 296 hierarchy of levels, 291–292, 296 Hilbert, David, 24 Hochberg, Herbert, 355, 362 Hughes, G.E., 295 Hume, David, 5, 175, 190, 198, 202, 241, 366 Hunter, Daniel, 265 Husserl, Edmund, 179 Hylton, Peter, 28–29, 32, 38, 80–85, 87–88, 91, 93, 95, 99–100, 103–105, 112, 140, 142, 355, 362 I ideal relation, 151–152 idealism, 80, 100, 142, 284, 362 identity, 14, 42, 62, 72, 138, 141, 164, 172, 181–182, 193, 211, 213–214, 241, 268, 275, 277, 279, 281, 287–288, 295, 298, 300, 305, 310, 314–315, 326–329, 331, 335–336, 338, 340–341, 350, 357, 361–362 identity function, 14 identity property, 327 imagination, 6–9, 107, 190 imaginary object, 249, 253, 258, 261, 263

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Page 375 immanent object, 150 immigrant object, 222 implication, 13–14, 84, 170, 222, 279 imported object, 222, 224 impossibilia, 207–208, 210, 228 impossible object, 192, 211 improper description, 48–49, 53, 354 incomplete object, 160, 195 incomplete symbol, 111, 125 inconsistency, 12, 180–181, 183–184, 198, 211–212 independence principle, 158, 165 indeterminacy, 144–145, 147, 149, 151, 153, 155, 157, 159, 161, 163, 165, 167, 210 indeterminate entity, 95 indifference principle, 158–160 indirect quotation, 347–352, 355–358, 360 indiscernibility of identicals, 68 individual, 15–16, 20, 42, 50, 53, 62, 89, 91, 117, 121, 127, 130, 132, 134, 140, 174, 188, 244–246, 266–268, 279, 286–287, 291, 295, 301, 303–304, 306, 313–314, 316, 320–321, 335, 337, 339, 343– 344 Inhalt , 101, 105–106, 112, 153–154, 168 (see: content) intended object, 170, 182–183, 194 intension, 9, 76, 152, 174, 191, 274, 278, 280, 291 intensional entity, 74; intensional object, 334 intensionalism, 8, 174–175, 183–184, 191–192, 202 intentionality, 6, 145, 147, 228, 282–285, 287, 292–293 (see: aboutness) intentional entity, 284 intentional inexistence, 150, 283; intentional in-existent doctrine, 106 intentionalism, 8 intentionality thesis, 283 internal relation, 153 introspection, 156, 164 intuition, 52, 55, 57, 103, 224, 243, 251, 258, 261, 292, 328, 333 isolated object, 224 item, item theory, 41, 45, 48–49, 51–52, 54, 58, 63, 72, 93, 117, 139, 204 –217, 219–232, 242 J Jacquette, Dale, 1–369 James, Henry, 228 James, William, 157, 166 Jeshion, Robin, 330, 332, 341 Jespersen, Otto, 229, 231 Jourdain, Philip, 11, 25, 75–76 judgement, 6, 16, 24, 33–34, 39, 50, 98–99, 103, 105, 110, 112, 133–134, 141, 165, 170, 186, 199, 227, 316, 331 K Kalish, Donald, 44, 48, 59, 62–63 Kambartel, Friedrich, 99, 296 Kant, Immanuel, 5, 112, 177 Kaplan, David, 42, 61, 64, 295, 311, 316, 332, 336, 338–341, 345, 355, 358, 360–362 Kaulbach, Friedrich, 99 Kindinger, Rudolf, 162–163, 166–167, 203, 231 Klement, Kevin C., 9, 65–66, 68–70, 72, 74–77, 366 Kneale, William, 142, 145, 162, 166 Kneale, William and Martha, 141 file:///K|/A-DATA%20CH91%20(F)/BU3%20%20Incoming/Meinong/0415963648__gigle.ws/0415963648/files/page_375.html[2/12/2011 12:21:04 πμ]

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knowledge by acquaintance, 37, 110, 147, 182, 203, 297, 342 knowledge by description, 37, 110, 147, 182, 203, 297, 342 Kremer, Michael, 355, 360, 362

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Page 376 Kripke, Saul A., 201, 203, 256–257, 265, 314, 316, 328, 337, 341, 352–355, 360–362 Kuhn, Thomas, 174 L Lackey, Douglas, 39, 98, 100, 126, 142–143, 168, 232 lambda calculus, 14, 25 Lambert, Karel, 42, 64, 165–166, 268–270, 283–284, 295–296 Landini, Gregory, 9, 24–25, 37–38, 63, 74, 76–77, 125, 127, 140–142, 266–268, 270, 272, 274, 276, 278, 280–282, 284, 286, 288, 290, 292, 294–296, 355, 362, 366 law of contradiction, 95, 145–146, 162–163, 180–181, 283 law of excluded middle, 36–37, 55–56, 159–161, 210 law of identity, 211, 288, 361 law of noncontradiction, 159, 179, 208, 211, 228 Lehmann, S., 42, 48, 64 Leibniz, Gottfried Wilhelm, 24, 132, 175, 231, 298, 306–307, 331, 335, 366 Leibniz’s Law, 132 Leibniz’s principle, 298, 306–307, 335 Levine, James, 63, 355, 362 Lewis, A.C., 25, 64, Lewis, David, 256, 265, 322, 327, 341 limitation of size, theory of, 120–121 linguistic necessity, 318, 336 linguistic turn, 284 Linsky, Bernard, 9, 24–25, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60–64, 69, 77, 134, 141–142, 166– 168, 203, 243, 274, 278, 295–296, 366 Linsky, Leonard, 142, 243, 247, 362 logic, 1–4, 6–8, 10–15, 17, 19, 21–25, 31, 38, 40, 42, 44, 48–49, 56, 58, 60, 63–65, 68, 72, 75–77, 86, 89, 93, 96, 100, 102, 114, 116, 121–124, 126–127, 132–133, 138–139, 142–144, 146, 152, 163, 166, 168–169, 172–173, 176–178, 181, 188–189, 191, 193–196, 202–203, 211–212, 217, 222, 229– 232, 235–236, 246–247, 250, 265–268, 270, 279, 281–288, 295–299, 307, 310, 323–324, 329, 334– 337, 340–342, 362–363, 365–367 logical atomism, 113, 135–136, 141, 143, 168, 203, 237 logical entities, 89, 287 logical impossibility, 260 logical objects, 32, 279, 286–287 logical positivists, 237 logical subject, 28, 71, 119–120, 136, 142, 285 logical truth, 16, 50, 307–310, 315, 318–320, 322, 334–335 logical types, 33, 71, 114, 141–142 logically proper name, 300–301, 333, 344, 349, 357 logicism, 282, 284 Lotze, Rudolf Hermann, 84, 174 M MacColl, Storrs, 80, 99, 163 Makin, Gideon, 9, 38, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 200, 203, 355, 362, 366 Mally, Ernst, 40, 56, 63, 145–146, 162, 165, 182, 212–213, 229, 231 Manser, Anthony, 355, 362

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Page 377 Mar, Gary, 59, 62–63 Marcus, Ruth Barcan, 310, 313–314, 317–319, 322, 324, 326–330, 333, 335, 337, 339–342 Martin, D. Anthony, 278, 295, 355 massive reduplication, 302–303 materialism, 241 mathematics, 2–3, 11–13, 15, 18, 23–25, 27, 32–33, 36, 38, 42, 44, 46–47, 55, 64–65, 69, 76–77, 79– 81, 86, 89, 100, 103, 108, 112–114, 116, 121–122, 131, 133, 138–139, 141–144, 146–147, 167, 169, 172–175, 185, 199–200, 203, 231–232, 236, 282, 296, 342–343, 365–367 intuitionistic mathematics, 36 mathematical entities, 81, 86, 89–90, 99 mathematical functions, 12 mathematical logic, 3, 24–25, 76, 114, 116, 121, 126, 133, 139, 142–143, 169, 178, 181, 267, 296, 342, 366–367 mathematical objects, 33, 92, 170, 233 mathematical realism, 34 matrix, matrices, 31, 33 McMichael, Alan, 213–214, 229, 231 meaning, 2, 7–11, 15–22, 25, 32, 36, 38, 42–43, 54, 61, 63, 65, 73, 76, 79–80, 83, 87, 91, 93–94, 96– 97, 101, 110–111, 119–120, 124, 133, 135, 141, 143, 149, 152, 157, 169–172, 175–176, 178, 180– 183, 191, 197, 201, 203, 250–251, 284–285, 313, 337, 340–341, 344, 348, 352, 357–358, 362–363, 367 Meinong, Alexius, 1–9, 19, 25, 36, 38, 40, 55–57, 63–64, 79, 81–83, 85, 89–90, 92, 95, 97–101, 103, 144–192, 194, 197–205, 207–209, 211–216, 224, 227–229, 231–239, 241–245, 247, 254, 264–265, 282–284, 330, 343, 355, 366 Meinongianism, 8, 27–28, 35, 178, 191, 233, 235, 244– 245, 283 mental act, 154, 228, 282, 285; mental content, 147–150, 152, 154, 157 metaphysics, 1, 5–6, 29, 32–33, 38, 65, 72, 113, 134, 169–170, 173, 181, 189, 200, 202, 232, 235– 236, 242, 247, 249, 265, 271–272, 311–312, 330, 342, 365–367 metaphysical impossibility, 260 metaphysical necessity, 308–309 Mill, J.S., 343, 348 modal moment, Meinong’s doctrine, 183, 200, 202, 215–216, 231 modality, 232, 305, 307, 309–310, 316, 323–325, 333, 336, 339–342, 362 Montague, Richard, 44, 48, 59, 62–63 Moore, G.E., 18, 25, 94–95, 102, 110, 145, 156, 164, 167, 174, 362 Moore, G.H., 143 Morscher, Edgar, 42, 48, 58, 61–62, 64 multiple relation theory of judgement, 33, 134, 141, 331 mutual saturation, 291 N naïve item theory, 204–206, 209, 220 naïve realism, 29 name, 8, 15–16, 30–31, 41–45, 56, 61, 69–70, 80, 88, 91–92, 99–100, 119–120, 124, 129–131, 136, 138, 140, 146, 149, 153, 163, 172, 174–176, 230, 239, 250, 252, 256–257, 263, 268, 271, 286, 300– 301, 308, 313, 327, 331, 333, 336–337, 344, 348–350, 356–357

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Page 378 Neale, Stephen, 60, 64, 326, 333, 337, 340–341 necessary property, 318, 327, 334, 339–340 Nelson, Michael, 9, 297–298, 300, 302, 304, 306, 308, 310, 312, 314, 316–318, 320, 322, 324, 326, 328, 330–332, 334, 336, 338, 340–342, 367 Nichtsein , 1, 158, 168, 228 (see: non-being; non-existence) no-class theory, 131, 137 nominalism, 5, 35, 38 nominalist thesis, 34 nominalization, 132, 286 non-being, 158–159, 233, 242 (see: Nichtsein ; nonexistence) non-constitutive properties, 212 noncontradiction (principle), 299 nonexistence, 7, 166, 182, 188, 197, 203, 214, 230, 265, 282, 365 (see: Nichtsein ; non-being) nonexistent object, 154, 189–190, 192–195, 199–201, 214, 226 nonentity, 154, 216 non-functional concepts, 21 nonmathematical entities, 81, 83 nonrigid designators, 314, 328 Noonan, Harold, 355, 362 nuclear property, 198, 215 number, 3, 12, 19, 22, 24, 32, 34–35, 43, 56, 65, 77, 84, 86–87, 92–93, 95, 104, 115, 118, 121–122, 134, 137, 139, 145, 206, 209, 218, 250, 256, 259–260, 262, 266, 272, 279–280, 285, 317, 330, 337– 339, 347 number theory, 34–35 real numbers, 14, 135 Nunn, T.P., 101, 112 O object, 1–2, 4–7, 9, 15, 17–18, 20, 29, 41, 43, 45–46, 49, 52–53, 58, 60, 66, 70–72, 74, 80–81, 98– 99, 103–109, 111–112, 114–115, 119–121, 130, 132, 139, 144, 148–156, 158–162, 164–165, 168–173, 175–186, 188–204, 211–214, 222, 224, 226, 228–230, 232, 236, 239, 241–244, 249–250, 252–255, 257–264, 282–284, 287, 289, 292–294, 298–302, 304, 306–314, 316–323, 325–332, 334–340, 344, 347, 350–352, 356, 358–359, 361, 366 object-directedness, 6 story-bereft object, 244–245 story-embedded object, 244–245 object theory, 1–2, 4–7, 9, 43, 169–173, 175–185, 189, 191–201, 212–213, 232, 283–284, 366 (see: Gegenstandstheorie ) objective, 108, 149, 165, 190, 318, 357 objective presentation, 149 objectless presentation, 109 objects of consciousness, 106 Occam’s razor, 238 ‘On Denoting’ (Russell), 1–4, 7–9, 11, 15, 19, 24–25, 38, 40, 55, 63–65, 69, 75, 77–79, 94, 97, 100– 101, 103, 109–111, 113, 118–120, 131–132, 139, 142, 145, 147–148, 166–169, 172–173, 175–181, 185, 187, 191, 193, 198–200, 202–203, 231–232, 236, 265, 268–269, 271, 283, 286, 288–290, 295– 296, 342–343, 355, 358, 360–363

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Page 379 ontology, 14, 16, 18, 28, 32–33, 35, 38, 65, 76, 79–80, 82–83, 85, 87–90, 92–94, 97, 169–173, 177– 178, 181, 195–196, 201–203, 216, 250, 262, 273–275, 278, 280, 282–286, 295, 333–334, 365, 367 ontology of classes, 32–33, 273, 275, 278, 280 ontological commitment, 33, 91–92, 94, 237, 251, 281–283, 331 ontological economy, 10, 94, 262 ontological reduction, 22–24 Orilia, Francesco, 295–296 P Pakaluk, Michael, 355 paraconsistency, 180 paradox, 3, 12, 14, 24–25, 28, 30–31, 33, 37, 39, 65, 67, 72–74, 76–77, 118, 121, 124, 126, 140, 191, 232, 274, 280–281, 284, 286, 292, 295–296, 342, 363 Parsons, Terence, 201–204, 206, 210, 212, 215, 218–219, 229–231, 254, 264–265, 317–319, 322, 324, 326–329, 339–341, 359, 361, 363 particular, 2–4, 10, 14, 18, 26, 34, 49, 57, 62, 72, 75, 78, 85–87, 89, 92, 98, 103, 108, 110, 113, 116, 122, 127–129, 132, 141, 151, 169, 173, 175, 178, 198–201, 207, 221, 224–226, 228, 230, 240, 246, 253, 278, 292, 301–302, 308, 311, 318–320, 324–326, 331–333, 335, 339, 348, 350, 352, 357, 359– 360 Peano, Giuseppe, 3, 20, 114, 116, 146, 285 Pelham, Judy, 15–16, 24–25 Perry, John, 75, 77, 332, 341 perspicuity assumption, 237 phenomenology, 166, 168, 199, 231, 247, 283 phenomenological psychology, 190 philosophical logic, 1, 64–65, 76–77, 142, 172, 231–232, 341, 365 philosophical psychology, 6, 8, 101 philosophy of language, 1, 6, 75, 265, 362, 367 physical laws, 101 Plato, 10, 174, 186, 200, 248, 365; Platonism, 181–182, 287 plural object, 114–115, 120, 139 po/ao paradox, 295 points, 17–18, 29, 35, 45, 74, 78, 84, 87, 89, 94, 105, 112, 134, 164, 176, 199, 271, 282, 309, 312, 326, 335, 343, 345, 347, 349, 351, 353, 355, 357, 359, 361, 363 possibility, theory of, 109 possibilia, 210 possible worlds, 72–73, 256–257, 263, 287, 320, 328 predicate, 8, 23, 42, 46, 48, 50, 57–59, 63, 69, 117, 119, 121, 123, 127–131, 135–136, 138–139, 159, 161, 179, 181, 188–190, 192, 195–198, 205, 208–211, 214–215, 223, 228–229, 249–251, 266, 268, 270, 275, 279–281, 286–287, 290–291, 295, 310, 322, 328, 356 predication, 4, 7–8, 21, 166, 169, 171, 173–175, 177–178, 189, 193–194, 196, 199, 213–214, 223, 270, 291, 360

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Page 380 predicate negation, 159, 161, 208–210, 215, 229 predicative functions, 127, 141 presentation, 1, 6, 55, 75, 98–99, 109, 112, 149–151, 153–156, 164–165, 167, 170, 176, 199, 231, 264, 311, 335, 356, 361 (see Vorstellung) Priest, Graham, 229, 232 primary occurrence, 352, 355 primary scope, 271, 273 primitive proposition, 14, 17 private particular, 302 proper name, 41–43, 45, 69, 88, 99, 119, 153, 172, 174–175, 239, 286, 300–301, 313, 333, 337, 344, 349, 357 property, 4, 8, 46, 58, 65–69, 72–74, 84–86, 99, 120, 123, 133–134, 136, 138, 153, 159–160, 170, 173–174, 176, 179, 182–183, 186, 188–189, 192–198, 200–202, 205, 208–210, 212–219, 222, 225– 228, 234, 241–243, 250, 255–259, 262, 268, 271, 280, 285, 287, 291–293, 299, 309–310, 313–314, 318, 321–323, 326–328, 331, 334, 338–340, 347, 361 proposition, 13–17, 27–29, 31, 39, 54, 83–85, 87, 90, 93, 95–96, 98–99, 103–105, 108–111, 118–120, 124–126, 128, 131, 133–136, 140–141, 147, 163, 172, 183, 185–186, 189, 192–193, 197–198, 202, 237, 241, 244, 267, 284–286, 289–290, 301, 305–306, 313–314, 331–335, 343–348, 356–357, 359, 361 propositional attitude, 107, 286, 290–293, 331–332, 336, 338 propositional form, 17 propositional function, 17, 69–71, 86, 95, 117–118, 123–127, 133–135, 140 propositional logic, 14 propositional realism, 29, 32–33, 37 psychology, 5–6, 8, 101, 106, 112, 144–147, 157, 166–168, 190, 199, 241, 284, 286 psychological atomism, 101 psychological content, 144–145, 147–149, 151–153, 155–157, 159, 161, 163, 165–167 psychologism, 152, 177 Purtill, Richard, 243, 247 Pythagoras, 33, 35 Pythagorean realism, 36 Q quadratic function, 117 qualia, 151, 156 quality, 35, 151, 154–155, 331 quantifying in, 68, 75, 297, 299, 301, 303, 305, 307–311, 313, 315, 317, 319, 321, 323, 325, 327, 329–331, 333–337, 339, 341, 362 quasi-quotation, 345, 356 Quine, W.V.O., 10, 22, 25, 75–77, 79–80, 86–87, 89, 93, 98, 100, 121, 130, 140, 142, 236–237, 246– 247, 249, 265, 267, 273, 279, 282, 295–299, 305–326, 328–331, 333–342, 345 R Ramsey, F.P., 1, 4, 10, 25 range, 2, 16, 74, 89, 117, 124, 127, 135, 141, 180, 195, 204, 213, 216, 225, 280, 307, 310, 316, 338, 352

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Page 381 Rapaport, William J., 229, 232 realism, 8, 26–30, 32–38, 71, 103–104, 166, 231, 247, 283–284 realistic theory of propositions, 28 reality, 8, 28, 30, 38, 78–79, 81, 106–107, 145–146, 149, 163, 190, 235–236, 238, 241, 246, 264, 287, 300–301, 303, 322, 366 (see Wirklichkeit) reference, 7–8, 19, 31, 61, 65, 69–70, 77, 93–94, 96, 107, 110, 119, 123–124, 126–127, 132–134, 140, 142, 148, 169–175, 177–180, 184–185, 187–189, 191, 193–195, 197, 199, 201, 220, 239, 241, 248–250, 252, 254, 257, 265, 283–284, 286, 291, 299, 301–302, 307, 336, 340, 342, 362–363, 366– 367 (see: Bedeutung ) referential meaning, 7, 175 (see: Bedeutung ) Reicher, Maria, 162, 167, 200–201, 203 relation, 9, 21, 25, 29, 33, 66, 75, 84, 87, 91, 93, 95, 100–101, 105, 108, 111–112, 128–129, 133–134, 138–139, 141, 145, 147, 149–158, 169, 186, 196, 199, 206, 213–220, 229, 258, 262–263, 275, 278– 279, 285–286, 290, 303, 316, 326, 331–332, 338, 344–345, 347, 350, 356–357, 359 relational property, 218 reduced relation, 216 relations, theory of, 5 representation, 49, 103, 106, 108–109, 111, 165, 205, 292, 294, 350, 365 representational content, 109 representative content, 107 Restall, Greg, 211, 229, 232 Richard, Mark, 332, 342 rigid designation, 246; rigid designator, 263 Routley, Richard 167, 182, 200–201, 203–205, 207–210, 212, 216–219, 228–230, 232, 295 (see: Sylvan, Richard) Russell, Bertrand, 1–4, 6–41, 43, 45, 47–51, 53–65, 68–71, 74–105, 107–127, 129, 131–148, 152–157, 162–164, 166–203, 206–209, 215, 224, 228, 230–233, 236–238, 241–242, 244, 249–251, 265–274, 276, 278–291, 294–297, 299–307, 309, 313–316, 321, 330–333, 336–337, 341–344, 347–363, 365–367 Russellian proposition, 27–29, 284, 286 Russell-style paradox, 67 Ryle, Gilbert, 1, 145, 162, 168, 264–265 S Sainsbury, Mark, 129, 141, 143 Salmon, Nathan, 9, 63, 259–261, 264–265, 295, 330–332, 335, 342–344, 346, 348, 350, 352, 354, 356, 358–360, 362–363, 367 Sawyer, Sarah, 259–260, 265 Schilpp, P.A., 38, 99–100, 141, 143, 168, 341 scope, 38, 49–50, 53–54, 97, 100, 119, 196, 208–209, 219, 269–271, 273, 276, 287, 289–291, 293, 295, 297, 304–306, 312–313, 316–317, 323, 331, 333–337, 352–353, 359, 362 Searle, John R., 248, 265, 355, 358, 362–363

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Page 382 secondary occurrence, 119, 352–355, 361 secondary scope, 271 second-order logic, 72, 75 Sein, 1, 153–155, 157–158, 161–162, 168, 170, 177, 186, 189, 192, 200, 212, 236–238, 245, 283 (see: being) self-membership, 31 semantics, 4, 6–8, 25, 27, 34, 37, 46, 48, 60, 77, 136–137, 147, 166, 169–173, 175, 177–178, 182, 192–194, 200–205, 219, 222–223, 225–226, 228, 230–232, 242, 246, 251, 266, 295, 297, 299, 316, 320, 333, 341, 343, 359, 362, 365, 367 semantic dualism, 104, 107–108 semantic monism, 103–104, 108, 111 sense, 3, 7–8, 15, 19, 24, 28, 31–32, 35–36, 43, 54, 59, 61, 63, 65–68, 70–73, 75–77, 82–93, 95–96, 99, 104–105, 109–111, 115, 135, 137, 146, 148–150, 152, 158, 160, 170 –172, 174–179, 183–189, 191, 193, 201–203, 206, 209, 211–212, 216–219, 235, 237, 241, 243, 245, 249, 251–252, 257–258, 261–262, 269, 285–287, 299–303, 307–312, 315, 317, 321, 324, 327–328, 331, 333–334, 337, 339– 340, 344, 348–349, 355–360, 362–363, 366 (see: Sinn ) sense-data, 112 sentential negation, 208–209, 211, 215 set, 4, 11, 13–15, 17, 20–22, 33, 41, 44, 46, 48, 53, 56, 60–63, 65–66, 75, 77, 79–82, 85, 89–90, 95– 96, 113, 117, 120–123, 137–138, 142, 174, 177, 191, 194, 204, 214, 218, 225, 228–229, 234, 239– 240, 242–245, 250, 253–255, 264–265, 272–273, 295–296, 308, 316, 330, 337–338 set abstraction, 20 set theory, 22, 75, 77, 117, 121–123, 137–138, 142, 191, 272, 296 Simons, Peter M., 42, 48, 58, 61–62, 64, 162–163, 168, 202 singular terms, 34, 40–43, 45, 47, 49, 51, 53, 55–57, 59–63, 88, 230, 286, 298, 305, 307, 311, 313, 329, 337, 343, 357–358 singular description, 313, 336 Sinn , 19, 41–44, 46–47, 54–55, 57, 61, 63, 76, 170, 172, 174–175, 187, 358–359, 362 (see: sense) Smith, Barry, 202, 265 Smith, Janet Farrell, 162–163, 168, 185, 198–199, 202, Smullyan, Arthur, 298, 307, 330, 333, 336–337, 341–342 so-being, 361, 158, 160, 171, 182, 200 (see: Sosein) Sosein, 158, 165, 170, 182, 192, 194, 200, 212, 237–238, 244–245, 283 (see: so-being) space, 12, 81, 84–85, 87, 96, 113, 127, 146, 235, 237, 257, 301 speakers’ reference, 248 Stalnaker, Robert, 75, 77 states of affairs, 165, 233, 241, 279, 284 Stevens, Graham, 9, 26, 28, 30, 32, 34, 36–39, 367 Stout, G.F., 25, 101–103, 105–112 Strawson, P.F., 2, 47, 61, 64, 249, 251, 264–265, 301–303, 333, 342

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Page 383 structured proposition, 331–332 subset, 239–240, 255, 325 subsistence, 85–86, 162–163, 187, 189, 199, 233–234, 236 (see: Bestand ) substitution, 13–15, 23, 31, 33, 50, 126, 129, 140, 225, 279–281, 298, 323, 331, 335–336, 348, 359 substitutional theory of classes and relations, 30–31, 38, 123, 125, 143 substitutional theory of propositional structure, 278, 281 substitutional theory, 15, 23–25, 30–33, 37–38, 77, 123, 125–127, 131, 133, 140, 142–143, 278, 280– 282, 295–296, 310, 366 Swanson, Carolyn, 229–230 Sylvan, Richard, 167, 182, 205–206, 212, 217, 223, 225, 228, 230–232, 295 (see: Routley, Richard) symbolic logic, 3, 24–25, 76, 126, 142–143, 188, 340–342, 362 systematic ambiguity, 126, 138 T tag, 313, 337 Tarskian hierarchy of languages, 74 term, 5, 16, 18, 29, 34–35, 54–61, 63, 70, 85, 87–89, 104–105, 119, 146, 185, 187–189, 228, 230, 233, 266, 268–270, 273, 279, 281, 283, 285–286, 288, 326, 335, 344, 348, 356, 358, 361 time, 1–2, 4–6, 11, 13–19, 21–22, 26–27, 30–31, 33, 38, 59, 81–82, 85, 87, 90, 99, 101, 113–114, 116, 125, 134, 140, 143, 154–155, 164, 175–178, 190, 194, 202, 208, 243, 246, 257, 289, 299, 301, 319, 327, 338, 358 truth, 7, 16, 21, 27, 34, 36, 38, 42–43, 50, 58, 60, 62, 77, 99, 111–112, 132–133, 135, 138, 141, 143, 172, 174–175, 192, 195, 197–198, 223, 232, 237, 251–252, 255–258, 265, 278, 285, 299, 305, 307– 310, 312–313, 315–322, 324–325, 331–332, 334–335, 338, 341–342, 359–360 truth value, 62, 195 Turnau, Pawel, 355, 363 Twardowski, Kazimierz, 103, 106, 109, 112, 148–149, 168 type, 23, 60, 71, 104, 107, 116–118, 120, 126, 130–131, 135, 137–139, 141, 209, 211, 217, 223, 234, 242, 244, 274–275, 277–281, 291–292, 302 theory of types, 24–25, 30–31, 33, 71, 77, 113–114, 116, 123, 125–127, 129–130, 133, 135–139, 141– 143, 278, 296; type-theory, 31, 275, 277–278 simple theory of types, 113, 123, 125, 127, 135, 137, 139, 141 type hierarchy, 117 untyped terms, 12 U ultra-realism, 35–37 unity, 13, 39, 69, 331 universal, 10, 13–14, 17, 52, 69, 111, 116, 118, 121, 157, 177, 228, 267, 270, 281, 319, 322, 329 unsaturatedness, 16 Urquhart, Alasdair, 9–10, 12, 14, 16, 18, 20, 22, 24–25, 64, 76–77, 100, 102, 108, 112, 232, 296, 363, 367

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Page 384 V vagueness, 69, 210 value theory, 5–6 Van Fraassen, Bas C., 42, 64 variable, 16–19, 23, 94–95, 100, 102, 110, 118, 124–125, 127–128, 130–131, 134–135, 138, 141–142, 209, 266–270, 279, 281, 287, 291–292, 297, 299, 344–345, 349, 357, 361 vicious-circle principle, 74, 141 Voltolini, Alberto, 162, 168 Vorstellung, 6, 149, 153–155, 165, 170 (see: presentation) W Wahl, Russell, 355, 363 Walton, Kendall, 252, 265 Ward, James, 101 watered-down, watering-down, 183, 200, 215–217, 219–220 Weingartner, Paul, 202 Whitehead, A.N., 3, 11, 13, 22, 25, 30, 32–33, 39, 64, 76–77, 114, 126, 133–135, 138, 143, 267–268, 270, 276, 295–296, 304, 330, 333, 337, 342 Wiggins, David, 340, 342 Wirklichkeit, 236 (see: reality) Wittgenstein, Ludwig, 38–39, 75, 77, 136, 141, 143, 157, 166, 168, 172–174 Woods, John, 206, 222, 228–232, 241 Y Yagisawa, Takashi, 265 Z Zalta, Edward, 213–214, 229, 231–232, 366 Zermelo, Ernest, 24, 122 Zermelo-Fraenkel (ZF) set theory, 117, 121, 137–138

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