The New Theory of Reference: Kripke, Marcus, and Its Origins (Synthese Library)

THE NEW THEORY OF REFERENCE

SYNTHESE LIBRARY STUDIES IN EPISTEMOLOGY, LOGIC, METHODOLOGY, AND PHILOSOPHY OF SCIENCE

Managing Editor: JAAKKO HINTIKKA, Boston University

Editors: DIRK V AN DALEN, University of Utrecht, The Netherlands DONALD DAVIDSON, University of California, Berkeley THEO A.F. KUIPERS, University ofGroningen, The Netherlands PATRICK SUPPES, Stanford University, California JAN WOLEN-SKI, Jagielionian University, KrakOw, Poland

THE NEW THEORY OF REFERENCE: KRIPKE, MARCUS, AND ITS ORIGINS Edited by

PAUL W. HUMPHREYS University of Virginia, Charlottesville, VA, U S.A.

and JAMES H. FETZER University of Minnesota, Duluth, MN, US.A.

KLUWER ACADEMIC PUBLISHERS DORDRECHT / BOSTON / LONDON

Library of Congress Cataloging-in-Publication Data is available.

ISBN 0-7923-4898-2

Published by Kluwer Academic Publishers, P.O. Box 17, 3300 AA Dordrecht, The Netherlands. Sold and distributed in North, Central and South America by Kluwer Academic Publishers, PO Box 358, Accord Station, Hingham, MA 02018-0358, U.S.A. In all other countries, sold and distributed by Kluwer Academic Publishers, Distribution Center, P.O. Box 322, 3300 AH Dordrecht, The Netherlands

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© 1998 Kluwer Academic Publishers

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TABLE OF CONTENTS

PAUL W. HUMPHREYS and JAMES H. FETZER / Introduction

vii

PART I: THE APA EXCHANGE 1.

QUENTIN SMITH / Marcus, Kripke, and the Origin of the New Theory of Reference

3

2.

SCOTT SOAMES / Revisionism about Reference: A Reply to Smith

13

3.

QUENTIN SMITH / Marcus and the New Theory of Reference: A Reply to Scott Soames

37

PART II: REPLIES 4.

SCOTT SOAMES / More Revisionism about Reference

65

5.

JOHN P. BURGESS / Marcus, Kripke, and Names

89

6.

JOHN P. BURGESS / How Not to Write History of Philosophy: A Case Study

125

QUENTIN SMITH / Direct, Rigid Designation and A Posteriori Necessity: A History and Critique

137

7.

PART III: HISTORICAL ORIGINS 8. 9.

DAGFINN F0LLESDAL / Referential Opacity and Modal Logic, §§ 16-19

181

STEN LINDSTROM / An Exposition and Development of Kanger's Early Semantics for Modal Logic 203

10. QUENTIN SMITH / A More Comprehensive History ofthe New Theory of Reference

235

Name Index

285

Subject Index

287 v

PAUL W. HUMPHREYS AND JAMES H. FETZER

INTRODUCTION

On January 20th, 22nd, and 29th, 1970 Saul Kripke delivered three lectures at Princeton University. They produced something of a sensation. In the lectures he argued, amongst other things, that many names in ordinary language referred to objects directly rather than by means of associated descriptions; that causal chains from language user to language user were an important mechanism for preserving reference; that there were necessary a posteriori and contingent a priori truths; that identity relations between rigid designators were necessary; and argued, more tentatively, that materialist identity theories in the philosophy of mind were suspect. Interspersed with this was a considerable amount of material on natural kind terms and essentialism. As a result of these lectures and a related 1971 paper, 'Identity and Necessity' (Kripke [1971]), talk of rigid designators, Hesperus and Phosphorus, meter bars, gold and H 20, and suchlike quickly became commonplace in philosophical circles and when the lectures were published under the title Naming and Necessity in the collection The Semantics of Natural Language (Davidson and Harman [1972]), that volume became the biggest seller in the Reidel (later Kluwer) list. l The cluster of theses surrounding the idea that a relation of direct reference exists between names and their referents 2 is now frequently referred to as 'The New Theory of Reference'. 3 On December 28, 1994, Quentin Smith read a paper at the Eastern Division meetings of the American Philosophical Association that produced a different kind of sensation. In his paper, Smith suggested that most of the major ideas in the New Theory of Reference had been developed by Ruth Barcan Marcus in the period between 1946 and 1961. 4 Smith argued that Kripke had erroneously been given credit for these ideas and, more contentiously, that Kripke had heard some of these ideas at a lecture Marcus gave in February 1962, had unconsciously assimilated them (while not properly understanding them at the time) and had later incorporated them into his Princeton lectures. Word of Smith's paper had spread before the meetings and, perhaps attracted by a provocative sentence in the published abstract, 5 an overflow crowd assembled to hear the session. The proceedings were in sharp contrast to the sleepy atmosphere prevailing at most APA sessions. Smith was heckled by some members of the audience, others shouted down the chairman when he tried to limit the length of Smith's responses, and a few listeners walked out in apparent protest. The task of responding to Smith fell to Scott Soames6 who, in Vll

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PAUL W. HUMPHREYS AND JAMES H. FETZER

a paper twice as long as Smith's, provided a detailed set of arguments designed to show that all of Smith's claims on Marcus' behalf were groundless. Smith then read, in great haste due to time constraints, a response to Soames that was itself almost as long as Soames' reply. The session lasted for three hours and the polarized differences of opinion about the merits of the case - and the propriety of holding the session at all - continued to be discussed in the hallways at the convention, in a lead story in a mass circulation magazine, 7 in letters to the editor of the APA Proceedings,8 and elsewhere. 9 It is important to note that although Smith apparently was the first to publicly argue the misattribution claims, his paper did not emerge from a vacuum. In particular, at least as early as the mid-1980's, Ruth Marcus had sent out many copies of an eight page letter in which she made a case for her own priority in many of these matters. 10 What tended to be lost in the acrimonious debate were several important historical questions: how did the various ideas that are now known as the New Theory of Reference come to be developed? Was the picture conveyed by the casual attributions in the literature, that Kripke had created the theory from whole cloth, accurate? Was, as Smith originally claimed, the theory essentially due to Marcus or was the true history one of a cumulative set of contributions by various philosophers, with a particularly successful version of the theory eventually augmented by and effectively dramatized by Kripke? These are serious questions and ones familiar to historians dealing with older ideas. In the interests of starting an objective discussion of this question, we decided to publish the original APA papers in Synthese. We had originally planned to devote a second issue of Synthese to this topic, but the first issue generated so much interest that we arranged for the present collection of papers to be published in place of that second issue. This is an especially appropriate venue, for many of the original papers that bear on the issue originally appeared either in Synthese or in The Synthese Library. ADVICE TO THE READER

Because much of this dispute inevitably revolves around published work, one must be careful to note which version of a text is the relevant one. Both Kripke's and Marcus' work have been reprinted, sometimes many times, and changes and additions have been made in some of them, often by the authors themselves. So a few words of caution might be helpful to those readers - of whom we hope there will be many - who wish to read the original sources and to make up their own minds on the merits of the arguments presented in the collection. Marcus' paper 'Modalities and Intensional Languages' was presented at a meeting of the Boston Colloquium for the Philosophy of Science in February 1962. II It was published in an issue of Synthese XIII, noA (December 1961), pp.303-322, followed by Quine's response, op. cit., pp. 323-330. As often

INTRODUCTION

IX

happens with academic journals, that issue did not actually appear in print until some time later. 12 However, some reprintings of Marcus' paper, e.g., in her collection Modalities (Marcus, 1993) and especially in Zabeeh et al. (1974), pp. 838-853, contain changes and additions and are thus not reliable sources for historical research. In addition, a considerable portion of the disagreement between Smith and Soames revolves around remarks made by Marcus and Kripke during the discussion that occurred after Quine's response to Marcus' paper 'Modalities and Intensional Languages', this discussion being published in Synthese XIV, nos. 2/3 (September 1962), pp. 132-143. Naturally, the arguments of Smith, Soames, and others were based on the published transcript of that discussion (Marcus et al. (1962)). Having discovered that the early sessions of the Boston Colloquium were recorded on audio tape, we became curious as to whether the original recording of the discussion still existed. After an extended search, Robert S. Cohen, a former Director of the Boston Colloquium, located a large collection of unlabelled tapes and sent them to us. The relevant discussion turned out to be on the last tape sampled and a direct transcription was made from the tape. \3 It turned out that there were major differences between what was actually said at the discussion and what was eventually published in Synthese, most notably in the contributions of Ruth Marcus. Indeed, even a contemporary transcript that was circulated to the participants for approval contains many inaccuracies, omissions and changes. 14 We had originally hoped to include our new transcript as part of this collection. To this end we circulated a letter to all the participants in the original discussion informing them of our intention. Shortly thereafter, both editors were informed by Professor Marcus that she was adamantly opposed to our publishing the new transcript. As of this date, Professor Marcus is the only person who has voiced any objection to us about our publishing the new transcript. We hope, nevertheless, that at some point in the future this important part of the historical record will be made available to the philosophical community through an appropriate forum. THE PAPERS

Some comments are necessary on a few of the papers in order to provide relevant background information. The first section here, Part I, reproduces, as far as possible, the papers read at the 1994 APA session. ls Smith's paper is reprinted in its original form, with an addition to one footnote. The response by Scott Soames now includes four notes that were not part of the original. Consequently, with full concurrence on both sides, Quentin Smith has included replies to this new material in his response to Soames. These are clearly identified in the text. Part II begins with a new paper by Scott Soames that expands upon the criticisms he made in 1994 of Smith's arguments. This is followed by two

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PAUL W. HUMPHREYS AND JAMES H. FETZER

papers by John Burgess. The first (originally published in Philosophical Studies, reprinted here with an additional footnote) directly addresses the extent to which, if at all, Marcus' work anticipates Kripke's. This is followed by a second paper by Burgess in which he attacks the historiographical methods used by Smith in his two APA papers. The section concludes with a third paper by Smith extending his earlier arguments and responding to Soames' and Burgess' previously published papers. Part III begins with an excerpt from Dagfinn F011esdal's dissertation Referential Opacity and Modal Logic. F011esdal's dissertation was submitted to the Harvard University philosophy department on April 3 1961. 16 It has previously been available only in a mimeographed version, containing slight revisions and additions, from Oslo University Press (F011esdal (1966)). F011esdal's work is especially interesting because one finds in it explicit assertions of theses that later become widely accepted. One important example is this: "This solution leads us to regard a word as a proper name of an object only if it refers to this one and the same object in all possible worlds. This does not seen unnatural. Neither does it seem preposterous to assume as we just did, that if a name-like word does not stick to one and the same object in all possible worlds, the word contains some descriptive element.! eThis attitude towards proper names is not unlike that of [Neil] Wilson e.g., in The Concept of Language.}" (Ff1JllesdaI1961 §17)

Here, the proper names are terms such as 'Hesperus' and 'Phosphorus' and the quoted sentences occur in the course of a lengthy collection of arguments designed to show that a definite description ~[X(r, can be treated as a genuine singular term if and only if the condition, ~3yDllx(¢>(x) == x = yr, holds. In addition, the characteristic formula, IIxlly(x = y J D(x = y)), can also be preserved and substitutivity of identity can be maintained in modal contexts with an ontology of non-intensional objects if this condition is imposed. There is much of interest here, including a discussion of 'Aristotelian essentialism', but the reader can make his or her own way through the material. Next is Sten Lindstrom's paper on the development of modal semantics in the 1950's, focussing on the contributions of the Swedish logician Stig Kanger and of Saul Kripke, with attention given to work of Richard Montague and of Jaakko Hintikka. These contributions are highly relevant to the development of the New Theory. This is in part because the development of modal semantics involves delicate issues of how to handle names and descriptions in modal contexts and also because Quine's arguments against the very possibility of modal logic rest, amongst other things, on the difficulties of quantifying in to such modal contexts and on the role of referentially opaque contexts. Moreover, individual variables can be viewed as the archetypes of rigid designation (they have no descriptive content) and at least some of these priority disputes in reference revolve around the differences between asserting, say, the necessity of identity relations between variables and asserting the necessity of identity relations between names. Lindstrom's careful analysis concludes that Kanger's

INTRODUCTION

Xl

contributions to modal semantics (e.g., Kanger, 1957), which were made earlier than Kripke's, are distinctive and different in kind. Lindstrom contends that Kanger's semantics are adequate for logical necessities, whereas Kripke's are adequate for metaphysical necessities. This part then concludes with a long, final paper by Smith that attempts to put the central dispute into a broader historical context. We believe that there is more than enough material here to allow the reader to decide which of the various claims to priority has merit. It would hardly be surprising, however, if any attribution to a single figure turns out to be a gross oversimplification. The historical development of ideas is often a subtle process with contributions coming from many sources, even when individuals undeniably produce singularly creative advances. There is such a thing as philosophical novelty, but modern philosophers rarely work in such isolation as to insulate then from contemporary research. It is of great importance to properly attribute ideas to their originators, and we hope that this collection has served that end. THREE SUGGESTIONS

We conclude with three suggestions. First, that others who are interested in this important period of twentieth-century philosophy would do well to continue the research that is begun here in order to provide the philosophical community with a full account of the development of ideas that have been so influential on contemporary philosophy. Secondly, that the philosophical community develop more refined criteria for what counts as a genuinely novel contribution to an area of research and for attributing ideas to one individual rather than to another. This will not be an easy task, but it is one that is long overdue and, if accomplished, might help to resolve heated debates that disagreements over priority tend to generate. Thirdly, rather than suggesting that the APA repress public discussion of these issues, it would be preferable for that organization to formulate guidelines governing the appropriate attribution of sources. It is our impression as editors of some experience that many authors are very conscientious about citing sources, yet others are quite negligent about this, where the number of those who need to be reminded to cite prior work is growing. Such guidelines, which would have to rely on a successful outcome to the second project above and would necessarily have to be somewhat flexible, could then serve as a working standard for authors, publishers, editors and referees.

August 29, 1997 Corcoran Department of Philosophy University of Virginia Department of Philosophy University of Minnesota, Duluth

xii

PAUL W. HUMPHREYS AND JAMES H. FETZER ACKNOWLEDGEMENTS

The editors could not have carried out the difficult task of compiling this volume without the help and cooperation of the contributors. We gratefully acknowledge their assistance, despite occasional deep differences of opinion along the way. Saul Kripke and Ruth Marcus, the two individuals most directly affected by this dispute, were each invited on a number of occasions to contribute their own perspectives on the issue. It is unfortunate that they declined to participate, at least in the form of written papers. Finally, we take the opportunity here to thank those individuals who acted as referees and who in many cases offered unusually detailed comments to the authors. In addition we are grateful to Jaakko Hintikka, the editor-in-chief of Synthese Library, for his support of this project, to Robert S. Cohen, and to Dagfinn Fellesdal. NOTES Naming and Necessity was reissued in 1980 by Harvard University Press with a new preface by

Kripke and as the author put it: 'Obvious printing errors have been corrected, and slight changes have been made to make various sentences or formulations clearer'. (Kripke (1980), p. I). 2 The directly referential nature of terms is not restricted to names - some descriptions and ~enera1 terms also have this feature according to the theory. This terminology appears, for example, on the front cover of the 1977 anthology Naming, Necessity, and Natural Kinds (Schwartz (1977)), which describes itself as 'A challenging collection setting forth the new theory of reference expounded by Keith S. Donnellan, Saul Kripke, and Hilary Putnam .. .'. 4 In his response to Soames, Smith extends this period to 1943 when Barcan began to write her dissertation. 5 Proceedings and Addresses of the American Philosophical Association, 68:1, p. 94. The abstract reads: "It is arguable that the most serious and widespread error in the history of recent analytic philosophy is the misattribution of the New Theory of Reference to Kripke. This theory includes the epistemic argument that proper names are directly referential and are not equivalent to definite descriptions, the modal argument that proper names designate rigidly and are not equivalent to contingent definite descriptions, the argument that there are a posteriori necessities, the necessity of identity, and related ideas. Marcus had developed the New Theory by 1961; Kripke attended Marcus' presentation of her theory in 1962 and subsequently repeated with elaboration her ideas in Naming and Necessity (1972), without the expected attributions. This omission caused readers of Naming and Necessity to misattribute the New Theory of Reference to Kripke." This abstract had apparently not been read by the APA program committee when it accepted Smith's paper, but it should be noted that the APA did not at that time require an abstract to accompany a colloquium raper until after the paper had been accepted. Soames agreed to act as respondent after at least two other philosophers had declined invitations to do so. 7 Lingua Franca Volume 5, No.5 (January/February 1996), pp. 28-39. 8 Proceedings and Addresses of the American Philosophical Association 69:2 (November 1995), p. 121; ibid 69:5 (May 1996), pp. 141-2. 9 See e.g., The Australian, May 15, 1996, Higher Education Supplement, pp. 27-28. (This is an edited version of the Lingua Franca article.) 10 We note the existence of this letter because it affected the interpretation that some philosophers have placed upon the origins of the dispute, upon the nature of the dispute itself and, more bizarrely, even upon the authorship of Smith's original paper. The editors have a copy of the letter and have checked its contents against another copy. Aside from handwritten additions, and some short prefatory remarks, the contents of the two copies are the same. Earlier, and tangentially related, claims of misattributions can be found in Fogelin (1987), pp. 241-246, and F0llesdal (1994).

INTRODUCTION

XllI

II There is some unclarity in the literature about the exact date of the paper. It is identified in a footnote to Marcus (1961) as having been presented on February 7th 1962, but a corresponding note to the discussion suggests that it was given on February 8th 1962, the same day as Quine's response and the ensuing discussion. The reprint (Wartofsky (1963» also identifies the date as February 8th, which seems to be the most likely. The difference is important because the lapse of a day between the paper and discussion would mean that the comments during the discussion were more likely to be the product of considered reflection and, possibly, informal discussion. Marcus notes that her paper was announced under the title 'Foundation [sic] of Modal Logic'. 12 Marcus' paper, Quine's reply, and the discussion were also published in Wartofsky (1963), pp. 77-116. 13 The tape also contains Quine's comments on Marcus' paper, later published as (Quine (1961». It does not, however, contain a recording of Marcus's talk itself, nor did any of the other tapes that Professor Cohen located for us. 14 For example, it transcribes the spoken 'successor function' as 'Sheffer function'. Our understanding of the process that lead to the published version is that a preliminary transcript was circulated to the participants, changes were made at that stage, and the revised transcript was then circulated with additional changes being possible at that point. Correcting the page proofs also rresumably provided an opportunity for further emendation. S We make no claim that the papers here published are exactly those read at the APA. For example, the tumultuous atmosphere at the meetings led to parts of (at least) Smith's response to Soames being skipped on that occasion. 16 Follesdal says in the preface to Follesdal (1966) "I also owe a special thanks to Mr Saul Kripke, who in the spring of 1961 imparted to me virtually all the basic ideas on iterated modalities that he presented in his 1963 and 1964 papers [Follesdal must mean Kripke (l963a)(l963b) -ed!" but there is no indication that the indebtedness goes beyond that.

REFERENCES Davidson, D. and Harman, G.: 1972, Semantics of Natural Langage. D. Reidel Publishing Company, Dordrecht. Fogelin, R.: 1987, Wittgenstein (2nd edition). Routledge, London. Follesdal, D.: 1961, Referential Opacity and Modal Logic. Unpublished Ph.D. thesis, Harvard University. Follesdal, D.: 1966, Referential Opacity and Modal Logic. Filosofiske Problemes Nr. XXXII, A. Naess (ed), Universitetsforlaget: Oslo. (A slightly supplemented reprinting of Follesdal. (1961). Follesdal, D.: 1994, 'Stig Kanger in Memoriam', in D. Prawitz, B. Skyrms and D. Westerahl (eds), Logic, Methodology and Philosophy of Science IX. Elsevier, 885-888. Kanger, S.: 1957, Provability in Logic. Stockholm Studies in Philosophy, Vol. I, Almqvist and Wiksell, Stockholm. Kripke, S.: 1963a, 'Semantical Analysis of Modal Logic I: Normal Propositional Calculi', Zeitschriftfur Mathematische Logik und Grundlagen der Mathematik, 9, 67-96. Kripke, S.: 1963b, 'Semantical Considerations on Modal Logic', Acta Philosophica Fannica, lb, 83-94. Kripke, S.: 1971, 'Identity and Necessity', in Munitz, 135-164. Kripke, S.: 1972, 'Naming and Necessity', in Davidson and Harman, 253-355 and 763-769. Kripke, S.: 1980, Naming and Necessity. Harvard University Press, Cambridge. Marcus, R.: 1993, Modalities. Oxford University Press, Oxford. Marcus, R., W. Quine, S. Kripke, D. Follesdal, and 1. McCarthy.: 1962, 'Discussion on the Paper of Ruth B. Marcus', Synthese, 14,132-143. Marcus, R.: 1961, 'Modalities and Intensional Languages', Synthese, 13, 303-322. Munitz, Milton K.: 1971, Identity and Individuation. New York University Press, New York. Quine, w.V.0.: 1961, 'Reply to Professor Marcus', Synthese, 13, 323-330. Schwartz, S.: 1977, Naming, Necessity and Natural Kinds. Cornell University Press, Ithaca. Wartofsky, M.: 1963, Boston Studies in the Philosophy of Science: Proceedings of the Boston Colloquiumfor the Philosophy of Science 1961/1962. D. Reidel Publishing Company, Dordrecht. Zabeeh, F., E. Klemke, and A. Jacobson.: 1974, Readings in Semantics. University of Illinois Press, Urbana.

PART I THE APA EXCHANGE

QUENTIN SMITH

MARCUS, KRIPKE, AND THE ORIGIN OF THE NEW THEORY OF REFERENCE

The New Theory of Reference in the philosophy of language became widespread in the 1970s and is still flourishing today. The New Theory implies that many locutions (e.g., proper names) refer directly to items, which contrasts with the traditional or old theory of reference, which implies that names and relevantly similar locutions express descriptive senses or are disguised descriptions. The New Theory encompasses such notions as direct reference, rigid designation, identity across possible worlds, the necessity of identity, a posteriori necessities, singular propositions, essentialism about natural kinds, the argument from the failure of substitutivity in modal contexts that proper names are not equivalent to contingent definite descriptions, and related ideas and arguments. Some of the contributors to the development of this theory include Kripke, Kaplan, Donnellan, Putnam, Perry, Salmon, Soames, Almog, Wettstein and a number of other contemporary philosophers. The point of this paper is to correct a fundamental and widespread misunderstanding about the origins of the New Theory of Reference; the main misunderstanding is that it is widely believed that Kripke originated the major ideas of this theory, presented in his 1972 article on "Naming and Necessity" (Kripke, 1972) and his 1971 article on "Identity and Necessity" (Kripke, 1971). The fact of the matter is that the key ideas in the New Theory were developed by Ruth Barcan Marcus, in her writings in 1946-47 (1946; 1947) and especially in her 1961 article on "Modalities and Intensional Languages" (reprinted with small changes in (Marcus, 1993)). "Modalities and Intensional Languages" was presented in February, 1962 at the Boston Colloquium for the Philosophy of Science; Marcus' commentator was Quine and Kripke participated in the discussion which followed. II

I shall begin by adducing a number of representative instances where this historical misunderstanding is evinced. The point of the following series of quotations is to illustrate the nature and extent of the misunderstanding of the origin of the New Theory of Reference. 3 P. W. Humphreys et al. (eds.), The New Theory of Reference © Kluwer Academic Publishers 1998

4

QUENTIN SMITH

If one picks out at random any essay in the philosophy of language or essentialism in the past twenty-five years or so, then one will most likely find the New Theory of Reference attributed to Kripke (and some others, e.g., Kaplan and Donnellan) and that Marcus' name will only occasionally be mentioned. A recent example is Recanati's article in Philosophical Studies: "My starting point will be the ... notion or rigidity, introduced by Saul Kripke in the philosophical literature" (Recanati, 1988: 103). Paging through recent issues of Nous, one finds David Braun listing the proponents of the new "direct reference" theory of names: "Kripke (and) Donnellan's view strongly suggest direct reference. Almog, Kaplan, Salmon, Soames and Wettstein explicitly advocate versions of Direct Reference for proper names" (Braun, 1994: 465, n. 1). It is notable that the originator of the new "direct reference" theory, Marcus, is not even mentioned. Many misattributions of Marcus' ideas to Kripke and others can be found in the writings of contemporary philosophers, but what is even more surprising is that the leading developers of the New Theory do the same. Apart from Marcus, no one has done more to develop the New Theory of Reference than David Kaplan. David Kaplan, in some of his published works, attributes the New Theory of proper names to Kripke. He correctly notes that "the term 'rigid designator' was coined by Kripke to characterize those expressions which designate the same thing in every possible world in which that thing exists and which designate nothing elsewhere". But Kaplan proceeds to identify falsely the thesis or claim that proper names are rigid designators as Kripke's specific claim (rather than Marcus'); Kaplan writes: "He (Kripke) uses it in connection with his controversial, though, I believe, correct claim that proper names, as well as many common nouns, are rigid designators" (Kaplan, 1989: 492; my italics). Of course, Marcus did not make a claim for the rigidity of common nouns, and this idea is correctly credited to Kripke, but the same does not hold for the rigidity of proper names, as we shall shortly see. Even in cases where we find philosophers listing a series of contributors to the New Theory of Reference, Marcus is typically not mentioned. John Perry, who, along with Kaplan, is the leading exponent of the New Theory of indexicals, writes that "Lessons learned from the works of Donnellan, Kaplan, Kripke, Putnam, Wettstein and other New Theorists of Reference have convinced me to accept two theses. ... First, the references of the singular terms do not depend on Fregean senses, or identifying descriptions in the mind of the speaker. ... Second, each of these utterances expresses what David Kaplan has called a 'singular proposition'" (Perry, 1988: 108). The relevant lessons, however, were first taught by Marcus and repeated with elaboration by the named individuals. In Nathan Salmon's book on Reference and Essence, he writes that versions of the New Theory of Reference were "developed, to a considerable extent independently, by several contemporary philosophers of semantics, most notably Keith Donnellan, David Kaplan, Saul Kripke, and Hilary Putnam" (Salmon, 1981: 3). Another leading contributor

MARCUS, KRIPKE, AND THE ORIGIN OF THE NEW THEORY OF REFERENCE

5

to the New Theory, Howard Wettstein, writes such things as "New theorists like Keith Donnellan, David Kaplan, Saul Kripke, John Perry, and Hilary Putnam - and my own work falls into this tradition - proffer an account (of direct reference that is anti-Fregean)" (Wettstein, 1986: 185-186). Quotations such as these can be picked out at will from the current literature. I was once myself among the guilty, calling Marcus' theory of proper names "the KripkeDonnellan theory of proper names" (Smith, 1987: 387). Occasionally her work is alluded to in the literature on the New Theory! but her central role is overlooked. It seems to me that, from the point of view of the history of philosophy, correcting this misunderstanding is no less important than correcting the misunderstanding in a hypothetical situation where virtually all philosophers attributed the origin of the Theory of Forms to Plotinus. This correction is the aim of the following several sections. In these sections, I will outline some of the basic ideas in Marcus' work that also occur in Kripke's "Naming and Necessity" and "Identity and Necessity". As I shall explain later, I believe the two main causes of the subsequent failure of philosophers to mention her work is that attributions to Marcus did not appear in the relevant places in "Naming and Necessity" and "Identity and Necessity" and that many philosophers may have been insufficiently familiar with Marcus' earlier contributions. III

I shall quote some passages from Marcus' 1961 article that reveal six main ideas she contributed to the New Theory. First, let us start with the idea that proper names are directly referential and are not abbreviated or disguised definitions, as Frege or Russell and most philosophers up to the 1970s believed. Marcus writes: But to give a thing a proper name is different from giving a unique description .... (An) identifying tag is a proper name of the thing .... This tag, a proper name, has no meaning. It simply tags. It is not strongly equatable with any of the singular descriptions of the thing. (1961: 309-310).

This is the basis of the contemporary "direct reference" theory of proper names, where proper names are argued not to be disguised descriptions. For example, "Scott" refers directly to Scott and does not express a sense expressible by such a definite description as "the author of Waverly". A second idea that Marcus introduces is that we can single out a thing by a definite description, but this description serves only to single it out, not to be strongly equatable with a proper name of the thing. She says: "It would also appear to be a precondition of language [especially assigning names] that the singling out of an entity as a thing is accompanied by many ... unique descriptions, for otherwise how would it be singled out? But to give a thing a proper name is different from giving a unique description" (1961: 309). This idea later became widely disseminated through Kripke's discussion of how

6

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reference-fixing descriptions are sometimes used to single out a thing as a bearer of a name, but that the names are not disguised descriptions. Kripke writes: "It seems plausible to suppose that, in some cases, the reference of a name is indeed fixed via a description [but that the description is not "part of the meaning of the name"] (Kripke, 1972: 276). Kripke, however, added the novel idea (and this is one of the main original ideas in "Naming and Necessity") that in other cases names' reference may be secured by a historical causal chain stemming back to the original "baptism" (Kripke, 1972: 298-303). A third component of the New Theory of Reference introduced by Marcus is the famous modal argument for the thesis that proper names are directly referential rather than disguised contingent descriptions. Contrary to Nathan Salmon's claim that "The modal arguments are chiefly due to Kripke" (Salmon, 1981: 24), they are chiefly due to Marcus and presented by Kripke ("Naming and Necessity" (1972: 269ft) without reference to Marcus' earlier statement of them. Let us begin with this passage, where Marcus is discovering (10) and (15) (in her notation). (10) and (15) are (10) (15)

The evening star eq the morning star Scott is the author of Waverly

The symbol "eq" stands for some equivalence relation. Types of equivalence relation include identity, indiscernibility, congruence, strict equivalence, material equivalence and others. Marcus wants to argue that the equivalence relations to be unpacked in (10) and (15) are not strong enough to support the relevant theses of the "disguised contingent description" theory of proper names. She writes (1961: 308-309): If we decide that "the evening star" and "the morning star" are [proper] names for the same thing, and that "Scott" and "the author of Waverly" are [proper] names for the same thing, then they must be intersubstitutable in every context. In fact it often happens, in a growing, changing language, that a descriptive phrase comes to be used as a proper name - an identifying tag - and the descriptive meaning is lost or ignored.

Marcus will find that not all of the relevant expressions are names for the same thing. They are not intersubstitutable in modal contexts; Marcus writes: Let us now return to (lO) and (15). If they express a true identity, then 'Scott' ought to be anywhere intersubstitutable for 'the author of Waverly' in modal contexts, and similarly for 'the morning star' and 'the evening star'. If they are not so universally intersubstitutable - that is, if our decision is that they are not simply proper names for the same thing; that they express an equivalence which is possibly false, e.g., someone else might have written Waverly, the star first seen in the evening might have been different from the star first seen in the morning - then they are not identities. (1961: 311)

Marcus' modal argument shows why the 'disguised contingent description" theory of proper names is false. Since (10) and (15) do not express identities, the expressions flanking "is" are not proper names for the same thing. In (10) and (15) a weaker equivalence relation should be unpacked, for example, by a

MARCUS, KRIPKE, AND THE ORIGIN OF THE NEW THEORY OF REFERENCE

7

theory of descriptions. (By contrast, the sentence "Hesperus is Phosphorus" evinces an identity sign flanked by the two expressions; thus, it passes Marcus' modal test for containing two proper names of the same thing.) This modal argument goes back to Marcus' formal proof of the necessity of identity in her extension of S4 (Barcan, 1946; 1947), which is a fourth component she introduced into the New Theory of Reference. She showed that (T)

(xly) § O(xly)

is a theorem of QS4, QS4 being her quantificational extension of Lewis' S4. The quadruple bar here means strict equivalence. Since identities are necessary, a failure of intersubstitutivity in modal contexts will show that a proper name does not express the relevant descriptive sense. If "Scott" is not intersubstitutable with "the author of Waverly", "Scott" does not express the sense expressed by this definite description. This opens the door to the theory that proper names do not express descriptive senses but instead are directly referential. Of course, this argument does not prove that proper names do not express senses, merely that they do not express senses of contingent definite descriptions. Marcus' modal argument is consistent with the idea of L. Linsky (1977) and A. Plantinga (1978) that proper names express senses expressible by necessary definite descriptions, which are definite descriptions that express modally stable senses. For example, "Scott" may express the modally stable sense of "the actual author of Waverly". In order to rule out this modally stable descriptive theory of proper names, one needs further argumentation, such as the epistemic argument that proper names are directly referential. If the descriptive theory of proper names is true, Le., proper names are defined by descriptions, then "Venus is the evening star" should express a truth knowable a priori, i.e., knowable merely by reflection upon the concepts involved. But it cannot be known a priori that Venus is the evening star; this is known a posteriori, through observation of the empirical facts. As Marcus writes: You may describe Venus as the evening star, and I may describe Venus as the morning star, and we may both be surprised that, as an empirical fact, the same thing is being described. But it is not an empirical fact that (17) Venus I Venus. (1961: 310)

Here "I" is the identity symbol. If "Venus" expresses the modally stable sense expressible by "whatever is actually the evening star and morning star", then the persons designated by "you" and "I" in the passage quoted from Marcus' article should be able to know a priori, simply by reflection upon the semantic content of the expressions "Venus", "the morning star" and "the evening star" that Venus is both the morning star and the evening star. The fact that they cannot know this indicates that "Venus" does not express the modally stable sense expressed by "whatever is actually the evening star and morning star".

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Thus we have the irony that Plantinga's and Linsky's theory of proper names was refuted years before they formulated it, unbeknowst to themselves (and unbeknownst to later New Theorists)! Marcus' arguments for the "direct reference theory" make manifest her discovery of a fifth crucial component of the New Theory of Reference, the concept of rigid designation (although the name of this concept, "rigid designation" was first coined by Kripke). "Hesperus" is intersubstitutable salva veritate with either occurrence of "Phosphorus" in "Necessarily, Phosphorus is Phosphorus". Each of these two names actually designates Venus in respect of every possible world in which Venus exists and does not actually designate anything in respect of worlds in which Venus does not exist. If these two names were instead equivalent to contingent descriptions (e.g., "the morning star" and "the evening star"), they would not be intersubstitutable salva veritate in this modal context and thus would be non-rigid designators. Marcus notes in her 1970 APA paper, "Essential Attribution", presented at a symposium at which Kripke was one of the symposiasts, that "individual names don't alter their reference, except to the extent that in (respect of) some worlds they may not refer at all" (1971: 194). Although I have used the "rigid designation" terminology, Marcus does not use it, since Kripke's introduction of this expression in his "Identity and Necessity" (1971) assimilated proper names to some descriptions (viz., modally stable descriptions), which obscure their different semantic properties. Marcus' points can be accommodated, consistently with the continued use of "rigid designators", if we make the following classification, which is familiar to those working with the New Theory of Reference. Adopting the genus/species terminology, we may say that the genus is rigid designators, and the different species are (a) proper names, (b) referentially used definite descriptions (in Donnellan's sense), (c) attributively used definite descriptions that express a modally stable sense, (d) uses of indexicals, (e) natural kind terms, and certain other expressions. We avoid assimilating proper names to some modally stable descriptions, since proper names refer directly, whereas attributively used definite descriptions that express modally stable senses refer indirectly, via the expressed sense. A sixth idea introduced into the New Theory of Reference by Marcus is the idea of a posteriori necessity. Recall our earlier quotation of Marcus' remarks about Venus and the evening star: You may describe Venus as the evening star, and I may describe Venus as the morning star, and we may both be surprised that, as an empirical fact, the same thing is being described. But it is not an empirical fact that (17) Venus I Venus. (1961: 85)

Consider the expression "Hesperus is Phosphorus". We do not know this to be true a priori. It is not an analytic assertion whose truth value is known by analysis of the concepts involved. Nonetheless, it is necessarily true, since both

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names directly refer to the same thing, Venus. It is true that (a)

Hesperus I Phosphorus,

whereas, as before, "I" is the sign of identity. Given Marcus' theorem of the necessity of identity, it follows that (b)

Necessarily, Hesperus I Phosphorus.

Thus "Hesperus is Phosphorus" can be viewed as a synthetic a posteriori necessary truth. This belies Salmon's historical comment about the sentence "Hesperus, if it exists, is Phosphorous". He writes of Kripke's three 1970 talks at Princeton, published in 1972 as "Naming and Necessity", that "In 1970 Saul Kripke astonished the analytic philosophical community with his claim supported by the rich theoretical apparatus of possible-world semantics and his new 'picture' of reference - that [the mentioned sentences], though synthetic and a posteriori contain necessary truths, propositions true in every possible world" (Salmon, 1986: 2).2 A more accurate statement would be that Kripke eloquently elaborated upon Marcus' idea and extended it to new sorts of items, such as "water is H 2 0". What explains the wide misunderstanding of the historical origins of the New Theory of Reference, a major movement in the history of analytic philosophy? I have already suggested that two reasons may be that many philosophers were insufficiently familiar with Marcus' earlier work and that Kripke did not attribute the relevant ideas to her in "Naming and Necessity" and "Identity and Necessity" (despite the fact that he was present when she presented her seminal work in 1962 and was undoubtedly familiar with her earlier formal papers on modal logic). There seems to me a plausible explanation of why Kripke did not make these attributions. He writes in the Preface to the 1980 edition of Naming and Necessity that "The ideas in Naming and Necessity evolved in the early sixties - most of the views were formulated in about 1963-64" (1980: 3). Of course some of the ideas in "Naming and Necessity" are genuinely new, such as the causal chain picture of the reference of names, the idea that natural kinds are rigid designators and the theory of the necessity of origins. But since most of the views in "Naming and Necessity" occur in 1961 with Marcus' article "Modalities and Intensional Language" and in her formal work on modal logic in 1946-47, we need to look at Kripke's remark about the evolution of his views from this perspective. First, recall that Marcus presented her paper "Modalities and Intensional Languages" in February 1962 at the Boston Colloquium for the Philosophy of Science. Her paper was published, in conjunction with the colloquium, in the 1961 volume of Synthese. Kripke was present and participated in the discussion, which was subsequently published. Kripke, it seems, did not wholly grasp Marcus' ideas at this time. During the discussion of the paper at the 1962 colloquium, Kripke made

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the following remark about Marcus' theory: 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 aI., 1962: 142)

This is mistaken, since Marcus clearly did not claim in her article that things have their names essentially. As Marcus later explained, "that was not my claim. Socrates might have been named Euthyphro; he would not thereby be Euthyphro" (1993: 226-227). To the contrary, her claim was that names are what later came to be described as directly referential. They are not denoting phrases, essential or otherwise. This suggests how we may understand the statement in the 1980 Preface to Naming and Necessity that "most of the views were formulated in about 196364". We should interpret this as suggesting that Kripkefirst correctly understood Marcus' theory in 1963-64 and that before this time, he did not grasp what she conveyed in the presentation he attended. In particular, it was Marcus' theory of the necessity of identities, where names flank the identity sign, and the associated ideas of direct and rigid reference that became clear to Kripke in subsequent years. We should perhaps interpret this 1980 passage from Kripke in this light: He says "Eventually I came to realize - this realization inaugurated the aforementioned work of 1963-64 - that the received presuppositions against the necessity of identities between ordinary names were incorrect, that the natural intuition that the names of ordinary language are rigid designators can in fact be upheld" (1980: 5). But why does Kripke not say instead that at this time he first came to understand Marcus' arguments for the necessity of identity and the directly referential and rigid character of proper names? In the 1972 essay, he attributes one idea to Marcus: "Marcus says that identities between names are necessary" (1972: 305). But instead of explaining how this idea and Marcus' other ideas formed the theoretical basis of "Naming and Necessity", Kripke goes on to criticize a minor aside made by Marcus, viz., that a good dictionary should be able to tell one if "Hesperus" and "Phosphorus" have the same reference (1972: 305). (But as Marcus later explained, she should have made it clear that what she had in mind was a "dictionary" that functions as an encyclopedia, where coreferring names are listed as in a biographical dictionary (Marcus, 1993: 34, n. 1).) I believe a reasonable explanation of why Kripke did not attribute the central features of the "New Theory" to Marcus is that he originally misunderstood Marcus' New Theory of Reference. When he eventually understood it, after a year or two, the insight that came made it seem that the ideas were new. I suspect that such instances occur fairly frequently in the history of thought and art. 3 Philosophy Department Western Michigan University

MARCUS, KRIPKE, AND THE ORIGIN OF THE NEW THEORY OF REFERENCE 11 NOTES Some philosophers have noted in passing some of Marcus' contributions, but have not recognized their full extent. 1. Almog (1986: 220, n. 8) goes further than most in recognizing some of Marcus' contributions (e.g., the idea of direct reference), but confines this remark to a footnote in an article devoted to the theory that proper names are rigid designators, which he believes was originated by Kripke rather than Marcus. Another example is Alan Sidelle's recognition that Marcus, not Kripke, first formulated the idea of the necessity of identity (1989: 25), but Sidelle notes this in a book devoted to the idea of a posteriori necessity, which he believes was originated by Kripke rather than Marcus. John McDowell (1994: 105, n. 28) mentions the trend towards construing some expressions as directly referential and, after referring to Kripke and Donnellan as "early proponents of this trend", writes: "See also, predating the trend, Ruth Barcan Marcus, 'Modalities and Intensional Languages', Synthese, 27, (1962), 303-22". {Material added in May 1995: It should be added that in publications subsequent to the ones I quoted from Kaplan, N. Salmon, and H. Wettstein, each of them credits Marcus for developing at least one of the ideas for the New Theory of Reference. These appear in Salmon's Frege's Puzzle, Wettstein's Has Semantics Rested on a Mistake? and in Kaplan's contribution to Modality, Morality and Belief Essays in Honor of Ruth Barcan Marcus, Walter Simmot-Armstrong et al. (eds.).} 2 Of course Salmon is expressing here the nearly universal misunderstanding of the origin of this idea. For another example, consider Sidelle's comment in his book devoted to the idea of a posteriori necessity: "Enter Kripke and his Naming and Necessity. Kripke made it very plausible that there are necessary truths that are synthetic and knowable only a posteriori. Some of the more familiar examples are 'Hesperus and Phosphorus'" (Sidelle, 1989: 2). 3 Even official histories, such as Munitz's Contemporary Analytic Philosophy, get it wrong. In the chapter where the ideas developed by Marcus are explained, we find the chapter title "Referential Opacity, Modality, and Essentialism: Saul Kripke".

REFERENCES Almog, Joseph: 1984, 'Semantical Anthropology'. in P. French et aI., eds., Midwest Studies in Philosophy, 9, 479-90. Almog, Joseph: 1986, 'Naming Without Necessity', The Journal of Philosophy, 83, 210-42. Braun, David: 1993, 'Empty Names', Nous, 27(4), 443-69. Donnellan, Keith: 1966, 'Speaking of Nothing', The Philosophical Review, 83, 3-32. Kaplan, David: 1985, 'Dthat', in A. Martinich, ed., The Philosophy of Language. Oxford University Press, New York. Kripke, Saul: 1980, Naming and Necessity. Harvard University Press, Cambridge, Mass. Kripke, Saul: 1972, 'Naming and Necessity', in D.Davidson and G. Harman, eds., Semantics of Natural Language. Reidel, Dordrecht, pp. 253-355. Kripke, Saul: 1971, 'Identity and Necessity', in M. Munitz, ed., Identity and Individuation. New York University Press, New York. Linsky, Leonard: 1977, Names and Descriptions. University of Chicago Press, Chicago. Marcus, Ruth Barcan: 1993, Modalities. Oxford University Press, New York. Marcus, Ruth Barcan: 1971, 'Essential Attribution', Journal of Philosophy, 68, 187-202. Marcus, Ruth Barcan: 1961, 'Modalities and Intensional Languages', Synthese, 13, 303-22. [Marcus] Barcan, R.: 1946, 'A Functional Calculus of First Order Based on Strict Implication', Journal of Symbolic Logic, 11, 1-16. [Marcus] Barcan, R.: 1946, 'The Identity of Individuals in a Strict Functional Calculus of First Order', Journal of Symbolic Logic, 12, 12-15. Marcus, Ruth Barcan et al.: 1962, 'Discussion of the Paper of Ruth B. Marcus', Synthese, 14, 13243. McDowell, John: 1994, Mind and World. Cambridge, Mass. Munitz, Milton: 1981, Contemporary Analytic Philosophy. Macmillan Pub. Co., New York. Perry, John: 1977, 'Frege on Demonstratives', The Philosophical Review, 86, 474-97. Perry, John: 1988, 'Cognitive Significance and New Theories of Reference', Nous, 22, 1-18.

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Plantinga, Alvin: 1978, 'The Boethian Compromise', American Philosophical Quarterly, 15, 129-38. Recanati, F.: 1988, 'Rigidity and Direct Reference', Philosophical Studies, 103-17. Salmon, Nathan: 1981, Reference and Essence, Princeton University Press, Princeton. Salmon, Nathan: 1986, Frege's Puzzle. MIT Press, Cambridge, Mass. Sidelle, Alan: 1989, Necessity, Essence, and Individuation. Cornell University Press, Ithaca. Smith, Quentin: 1987, 'Problems with the New Tenseless Theory of Time', Philosophical Studies, 52, 77-98. Smith, Quentin: 1993, Language and Time. Oxford University Press, New York. Soames, Scott: 1987, 'Direct Reference, Propositional Attitudes, and Semantic Content', Philosophical Topics, 15, 47-87. Wettstein, Howard: 1986, 'Has Semantics Rested on a Mistake'?, The Journal of Philosophy, 83, 185-209.

SCOTI SOAMES

REVISIONISM ABOUT REFERENCE: A REPLY TO SMITH

My task today is an unusual and not very pleasant one. I am not here to debate the adequacy of any philosophical thesis. Rather, my job is to assess claims involving credit and blame. According to Quentin Smith, the central doctrines of Naming and Necessity were developed by Ruth Marcus in her pioneering papers on quantified modal logic in the late 40's, and in her paper, 'Modalities and Intensional Languages' in 1961. 1 Smith maintains that Saul Kripke learned these doctrines from her, initially misunderstood them, and, when he later straightened things out, mistakenly took the doctrines to be his own. Finally, Kripke is supposed to have published them without properly citing her. The entire profession was allegedly fooled, despite the fact that Kripke and Marcus were among its most well known members, and their work was familiar to leading researchers in the field. For years nobody said anything. Now, more than 20 years later, Smith claims to be bringing the truth to light. In what follows I show that the charges Smith makes against Kripke are false, and that the historical picture he paints is inaccurate. However, before I begin, I want to make clear that although Smith takes himself to be championing Marcus, my criticisms are of him, not her. I take a back seat to no one in my respect, admiration, and affection for both Ruth and Saul. As you will see from my comments on particular matters of substance, Marcus, along with certain other philosophers, do deserve credit for anticipating important aspects of contemporary theories of reference. However this credit in no way diminishes the seminal role of Saul Kripke. With this in mind let me review some ofthe accomplishments of Ruth Marcus. She is, deservedly, one of the most distinguished and well-known philosophers in America. She is widely recognized and admired for her pioneering work in quantified modal logic, and for her important contributions to a variety of related topics. In 1946 she published the first axiomatic systems of quantified modal logic, together with a collection of theorems provable in the systems, plus some proof theoretic metatheorems? In 1947 she extended her systems to include second order quantification, and defined identity in terms of secondorder indiscernibility. 3 She then established a variety of proof-theoretic facts concerning this conception of identity. One of these involved a quantified version of the thesis of the necessity of identity. Specifically, her axiomatic system of second order quantified modal logic (S4) had as one of its theorems the claim that for all individuals x and y, ifx = y, then necessarily x = y.4 13 P. W. Humphreys et al. (eds.), The New Theory of Reference © Kluwer Academic Publishers 1998

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In addition to developing these formal systems, Ruth Marcus successfully defended them in the early 1960's against Quine's influential, but ultimately wrong-headed, attacks on necessity in general, and on quantifying into formulas prefixed with modal operators in particular. In the course of developing this defense, she suggested that ordinary proper names might be Russellian logically proper names - terms whose meanings, or propositional contents, are nothing more than their referents. In the 60's and 70's she published important articles on essentialism as a plausible metaphysical doctrine, and helped clarify the minimal extent - namely its intelligibility - to which modal logic, as a system of logic, is committed to it. During the same period, she explored and defended substitutional interpretations of some quantifiers as both formally legitimate and potentially fruitful philosophically. The 1980's and 1990's have seen a series of papers on a wide range of topics, including belief, rationality, direct reference, moral dilemmas and moral consistency. This remarkable record of achievement is widely acknowledged and establishes Ruth Marcus as one of the leading philosophical logicians of the past 50 years. The question before us is whether a further accomplishment should be added to this already impressive list. I mentioned that in her early work Marcus suggested that ordinary proper names might be Russellian logically proper names. This raises a question regarding the relationship between her early work on this subject and the later development of contemporary non-Fregean theories of reference by philosophers such as Saul Kripke, David Kaplan, Keith Donnellan and others. Despite the similarity between some of the doctrines advocated by Marcus and those later incorporated into the new theories attributed to these philosophers, Marcus is generally not accorded a prominent role in the development of these theories. Quentin Smith claims there is an historical injustice here. On his view, the so-called "new theory of reference" is Marcus' theory. He claims that its main ideas were developed in her articles on modal logic in 1946 and 1947, and in her 1961 paper, 'Modalities and Intensional Languages.' Later theorists, especially Kripke, are viewed mainly as elaborating these ideas, and adding a few subsidiary points, while denying Marcus proper credit. A careful look at the historical record will show that this is not so. For example, Marcus' early papers on modal logic, in 1946 and 1947, developed certain formal systems in a language in which names do not occur at all, and in which the only singular terms are individual variables. The restricted version of the necessity of identity derived from the axioms of the system therefore does not involve names. These papers are not concerned with natural language, and do not contain formulations or defenses of any theses about proper names. Moreover, the distinction between proper names and descriptions, and the thesis that coreferential proper names are substitutable in modal contexts without changes in truth value, were not original with Marcus. These doctrines appeared in the literature on modal logic in response to Quine by Arthur

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Smullyan in 1947 5 and 1948,6 and Frederick Fitch in 1949. 7 In her later work, especially the 1961 paper cited by Smith, Marcus adopted these theses of Smullyan and Fitch, essentially suggesting that ordinary proper names might be Russellian logically proper names. However, even here names were not Marcus' main concern, and theses about their meaning and reference were only briefly indicated, rather than systematically explored and argued for. Her entire discussion of the meaning and reference of names, as well as their relations to descriptions, covers only five or six pages; and all of Smith's citations come from four of those pages. This is significant because it constitutes essentially all the evidence he provides for his claim that the central doctrines developed in the late sixties and seventies by Kripke are really due to Marcus. One clue that this claim cannot be correct comes from the observation that proper statements and defenses of the various doctrines of the so called "new theory" would not fit into such a small space. There is, of course, much more at issue than limitations of space. In what follows I will explain in detail why the historical picture Smith sketches is inaccurate. First, I will survey a series of relevant papers between 1943 and 1961 dealing with quantified modal logic and the behavior of names. These include papers and reviews by Ruth Marcus, Willard van Orman Quine, Arthur Smullyan, Frederick Fitch, and Alonzo Church. I will cite the origins in this literature of various theses about names, descriptions, identity, and modality; and I will explain the philosophical context in which those theses arose. Second, I will go through, one by one, Quentin Smith's claims about the six central ideas allegedly introduced into the new theory of reference by Ruth Marcus, and I will indicate the ways he goes wrong. Third, I will sum up the relationship between these theses about modality, identity, names, and descriptions in this early literature by Smullyan, Fitch, and Marcus, on the one hand, and the much more fully developed theses of the so-called "new theory of reference" that emerged in the 70s, on the other. The historical survey begins with Quine's 1943 paper, 'Notes on Existence and Necessity,.8 It was there that Quine first set out his argument that ordinary objectual quantification into any opaque construction is unintelligible, and hence illegitimate. For Quine, a construction is opaque iff for some pair of coreferential singular terms, substitution of one for the other in some formula within the scope of the construction changes truth value. Quine thought that such failures of substitution show that occurrences of singular terms within the opaque construction are not, as he put it, purely designative. By this he meant that their contributions to the truth values of the opaque sentences in which they occur are not exhausted by their reference. Using these notions, we may reconstruct his argument as follows: (P 1)

Occurrences of singular terms in opaque constructions are never purely designative.

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(P2)

Bindable occurrences of objectual variables must be purely designative.

(Cl)

An occurrence of an objectual variable within an opaque construction cannot be bound by a quantifier outside the construction.

(P3)

Modal constructions are opaque.

(C2)

Objectual quantification into modal constructions is illegitimate.

This conclusion was, of course, violated in Ruth Marcus' systems of quantified modal logic. With this in mind, Quine published a short article in 1947, 'The Problem of Interpreting Modal Logic',9 in which he reiterated his earlier conclusion and explicitly mentioned Ruth Marcus as one to which it applies. 1o Although Quine'S arguments were mistaken, they were enormously influential, and they baffled large numbers of the profession for decades. Fortunately, thanks in large part to recent work by David Kaplan, II Ali Akhtar Kazmi,12 and Mark Richard,13 we can now clearly see where they went wrong. Quine'S premises 1 and 2 are unjustified, and indeed false. 14 I won't go into a detailed explanation of this except to reiterate a certain point made by David Kaplan. Kaplan observed in his 1986 paper, 'Opacity', that it follows from Quine's characterization of a purely designative occurrence of a singular term that some occurrences of such terms in opaque contexts must fail to be purely designative; but it does not follow that all occurrences of singular terms in such contexts fail to be purely designative. If there are different kinds of singular terms - e.g., Fregean definite descriptions, proper names, individual variables - then it may be that occurrences of certain of these kinds fail to be purely designative within a given type of opaque construction, while occurrences of other kinds of singular terms remain purely designative. For example, one may have an analysis in which occurrences of Fregean definite descriptions within modal constructions are not purely designative,15 even though occurrences of names and variables are purely designative. 16 Or, one may propose an analysis in which neither occurrences of names nor occurrences of descriptions in propositional attitude constructions are purely designative,17 even though occurrences of individual variables in such constructions are purely designative. As Mark Richard and Ali Akhtar Kazmi have made clear, one can even invent constructions into which objectual quantification makes sense despite the fact that occurrences of objectual variables within such constructions are not always purely designative. IS In sum, there simply is no logical or semantic problem about quantifying into opaque constructions in general. None of these errors in Quine'S argument depends on special features of modality, or the behavior of names in modal contexts. However, quantified modal logic was Quine'S primary target, and the argument itself tended to get confused (both by Quine and by others) with a different criticism that was special to modality, namely the (equally mistaken) view that quantified modal

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logic was committed to an objectual form of essentialism. Thus it is understandable that the initial responses to the argument focused on the special case of modality. Quine's 1947 paper attacking the legitimacy of quantifying into modal constructions was quickly followed by a pair of responses by Arthur Smullyan in 1947 and 1948, and a further response by Frederick Fitch in 1949. The crucial point common to these responses was a sharp distinction between definite descriptions and genuine names. Smullyan and Fitch maintained that coreferential names are substitutable in modal constructions without change in truth value, whereas codesignative descriptions in general are not. They also accepted a corollary of this point, namely the claim that where a and f3 are genuine names, the sentence a = f3 is, if true, necessarily true. They recognized, of course, that an analogous point does not hold for definite descriptions. In fact, both Smullyan and Fitch denied that definite descriptions are singular terms at all, analyzing them instead as incomplete symbols, along Russellian lines. 19 Their basic criticism of Quine was that his argument wrongly treated definite descriptions as if they were genuine names, despite the fact that the two are logically quite different. Indeed, with definite descriptions not being counted as singular terms at all, the modal logician is free to restrict the class of closed singular terms to genuine names, in which case modal constructions won't count as opaque in the sense needed in Quine'S argument. There is no question, then, that Smullyan and Fitch regarded genuine names as fundamentally different from definte descriptions. Moreover, they regarded the behavior of the two in modal constructions as showing this. Neither Smullyan nor Fitch had the fundamental semantic notion of the referent of a term at a world, let alone the concept of rigid designation - i.e., the concept of a term that refers to the same thing at all worlds. Nevertheless, their recognition of the logical properties of genuine names in modal constructions led them to treat names in the way that one would treat them if one explicitly recognized them to be rigid designators. In this sense, which is the sense that applies to Ruth Marcus in her 1961 article, they can be credited with an implicit recognition that genuine names are rigid designators. In his 1947 review of Quine, Smullyan adds to this the claim that coreferential names are synonymous, which strongly suggests that genuine names have no meaning apart from their referents, another view later endorsed by Marcus. This was the point on which Smullyan and Fitch were criticized by Alonzo Church in one of his typically insightful reviews in The Journal of Symbolic Logic. Reviewing Fitch's article in 1950, Church says that Fitch "holds (with Smullyan) that two proper names of the same individual must be synonymous. 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; 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 ofa proper name in this sense".20 In this passage, Church uses

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the point about synonymy, and the meaning of proper names, to raise a critical issue about the discussions of Smullyan and Fitch. Both Smullyan and Fitch assumed that there is a class of singular terms - which I have been calling "genuine names" - that function exactly as what Russell called logically proper names, save for the fact that the referents of these names are not restricted to objects of direct Russellian acquaintance. Moreover, they seemed to suggest that at least some uses of ordinary proper names might qualify as names in this sense. However, they did not present any systematic examination of our use of ordinary proper names, nor did they produce a battery of arguments supporting their contentions. Because of this, it was inevitable that many readers of their discussions would retain substantial, and indeed unanswered, doubts about whether names as we ordinarily use them qualify as genuine names in their sense. Much the same can be said of Ruth Marcus' discussion of names in her 1961 article, "Modalities and Intensional Languages". As I indicated before, the discussion of names in the article is short, limited to just a few pages. The main themes of the article were first, that intensionality and extensionality come in degrees, and so there is no simple intensional/extensional distinction, and second, that Quine's attacks on modality in general, and quantifying into modal constructions in particular, are mistaken. The topic of names comes up, as it did with Smullyan and Fitch, in the course of answering Quine. In her discussion, Marcus reiterates the central points of Smullyan and Fitch namely that (i) coreferential names are substitutable in modal contexts without change in truth value whereas descriptions generally are not, (ii) identity statements involving proper names are necessary if true, (iii) names are not equivalent to descriptions, (iv) descriptions are not genuine singular terms, (v) proper names have no meanings over and above their referents, and (vi) coreferential names have the same semantic content, and are substitutable for one another in all nonquotational contexts. 21 It should be noted that although Marcus' discussion of these points is brief, it is more detailed and explicit than those of Smullyan and Fitch. For example, in discussing the necessity of identity statements involving genuine singular terms, she says that true statements of identity "must be tautologically true or analytically true".22 She also holds that only genuine singular terms can flank the identity sign, and that the terms involved in a true statement of identity must be intersubstitutable not just in modal constructions, but in every construction, including, presumably, attitude constructions such as those involving belief or knowledge. 23 The idea here, I take it, is the familiar Russellian view that since the meaning of a genuine singular term is its referent, any construction in which the meaning of the whole is a function of the meanings of its parts is one in which substitution of coreferential singular terms must preserve meaning, and hence truth value. Marcus treats names as genuine singular terms. In the text of her 1961 article, it certainly seems that when she speaks of

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names, Marcus means ordinary proper names. Nevertheless, essentially the same doubts that Church raised against Smullyan and Fitch arise against Marcus, and remain similarly unanswered. These doubts come up in a somewhat veiled way at one point in the discussion of her paper that occurred in 1962 at the Boston Colloquium for the Philosophy of Science. 24 Kripke (who was an undergraduate in the audience): Forgetting the example of numbers, and using your interpretation of quantification - there's nothing seriously wrong with it at all - does it not require that for any two names, 'N and 'B', of individuals, 'A = B' should be necessary, if true at all? And if 'N and 'B' are names of the same individual, that any necessary statement containing 'N should remain necessary if 'N is replaced by 'B'? Marcus: We might want to say that for the sake of clarity and ease of communication, it would be convenient if to each object there were attached a single name. But we can and we do attach more than one name to a single object. We are talking of proper names in the ideal sense, as tags, and not descriptions. Presumably, if a single object had more than one tag, there would be a way of finding out such as having recourse to a dictionary or some analogous inquiry which would resolve the question as to whether the two tags denote the same thing. If 'Evening Star' and 'Morning Star' are considered to be two proper names for Venus, then finding out that they name the same thing that 'Venus' names is different from finding out what is Venus' mass, or its orbit. It is perhaps admirably flexible, but also very confusing, to obliterate the distinction between such linguistic and properly empirical procedures. [my emphasisf5

Note the echo of Church here. 26 It is, I think, noteworthy that we find in this passage a hedged reference to "names in the ideal sense", and to the results of consulting a dictionary as opposed to invoking what Marcus calls "properly empirical procedures". The passage seems to suggest that it is to some degree an open question whether our ordinary use of proper names is one in which they are names in the "ideal sense" of Marcus' semantic theses. Altbougb I tbink ber intention in tbe paper was to take ordinary proper names to be names in tbe ideal sense, tbis cautious qualification seems to reflect an awareness of tbe continuing relevance of Cburcb-like doubts, and tbe lack of a battery of arguments sbowing tbat ordinary proper names really do have the semantic properties required by the Smullyan-Fitcb-Marcus response to Quine. So much for the historical background. We are now ready to examine Smith's contention that six fundamental theses of what he calls "the new theory of reference" were introduced by Ruth Marcus. In evaluating Smith's claims, I will put aside the qualification just noted and interpret Marcus, as well as Smullyan and Fitch, as suggesting that ordinary proper names are genuine names "in the ideal sense". Smith's first claim is that Marcus introduced the idea that proper names are not abbreviated or disguised descriptions, but rather are directly referential. This is false. Although Marcus did regard names as directly referential, and did not take them to be disguised descriptions, she did not introduce the idea; nor did she claim to. As we have seen, Smullyan and Fitch both invoked that idea in earlier responses to Quine that Marcus took herself to be repeating and elaborating. 27 ,28

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Smith's second claim is more elusive. He introduces the claim by saying "A second idea that Marcus introduces is that we can single out a thing by a definite description, but this description serves only to single it out, not to be strongly equatable with a proper name of that thing". The idea that we can single out a thing by a definite description is, of course, not new, and was not introduced by Marcus. The idea that a description which applies to a thing is not equivalent to a name of that thing was already covered in Smith's first contention - namely that Marcus supposedly introduced the idea that names are not abbreviated or disguised descriptions but rather are directly referential. So what new point is supposed to be covered by Smith's second contention? What is the second idea that Marcus is supposed to have introduced? Smith provides a clue when he says, "This idea [namely the second idea allegedly introduced by Marcus] later became widely disseminated through Kripke's discussion of how reference-fixing descriptions are sometimes used to single out a thing as a bearer of a name, but that names are not disguised descriptions." Smith contrasts this means of reference fixing with the historical chain mechanism, describing the latter, and only the latter, as original with Kripke. Thus it appears that Smith's second contention is that Marcus introduced the idea that the reference of a name may be semantically fixed by a description, even though the description is not synonymous with the name. If this is his contention, it is false. Here is the quote from Marcus that Smith gives to support his point. It would also appear to be a precondition oflanguage [especially assigning names] that the singling

out of an entity as a thing is accompanied by many ... unique descriptions, for otherwise how would it be singled out? But to assign a proper name is different from giving a unique description. (Bracketed words above inserted into the text by Smith.)

The problem here is that there is no way to get from this brief remark to the doctrine that sometimes the referent of a name is semantically fixed by an associated definite description. To see this, one must be clear what the content of that doctrine really is. It is not just that sometimes, or as Marcus seems to think, always, when we have an individual in mind for which we have a name, or to which we want to assign a name, we also have one or more descriptions that we are ready to apply to the individual. Rather, a specific description must, as a matter of semantics, be linked to the name. This means that if the referent of a name is semantically fixed by a certain description, then being a competent speaker who understands the name will involve knowing that if the name has a referent at all, it must be one that satisfies the description. Similarly, if a name N has its referent semantically fixed by a description D, then one who understands the sentence "If N exists, then N is D" will know, without empirical investigation, that it expresses a truth. Finally, if one later finds that the description one associated with the name fails to pick out anything, or fails to pick out the individual one had in mind, then it will follow that the name failed to refer, or at least failed to refer to the individual one had in mind. None

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of this is remotely suggested in the quotation from Marcus. The reason it isn't is that Marcus didn't have the doctrine in mind, as can be seen by quoting the full Marcus text from the beginning of the relevant paragraph, without ellipsis, or insertion of Smith's own words. That any language must countenance some entities as things would appear to be a precondition for language. But this is not to say that experience is given to us a collection of things, for it would appear that there are cultural variations and accompanying linguistic variations as to what sorts of entities are so singled out. It would also appear to be a precondition of language that the singling out of an entity as a thing is accompanied by many - perhaps an indefinite number - of unique descriptions, for otherwise how would it be singled out? But to assign a thing a proper name is different from giving a unique description. 29

What immediately follows in Marcus' text is an example in which we theorists assign random numbers as names for the entities singled out as things by a given culture. 30 These numbers are not intended as examples of names whose referents are semantically fixed by descriptions. On the contrary, Marcus calls such names "tags" and says they have no meaning. Marcus' point in the passage was not to sketch any particular theory about how names get their reference, but simply to distinguish names from descriptions. What she was really saying was that despite the fact that recognizing something as a thing presupposes a readiness to apply descriptions to it, nevertheless we have a linguistic device, the proper name, which allows us to refer to a thing without describing it. There is nothing here about semantic mechanisms by which the referents of names are fixed. Smith's third contention is that Marcus introduced "the famous modal argument for the thesis that proper names are directly referential rather than disguised contingent descriptions". Now Marcus did hold that names and descriptions typically behave differently in modal constructions, and so cannot be regarded as equivalent. Moreover, it is reasonable to take this as a version of "the modal argument", later made famous by Kripke. However, it was not introduced by Marcus, since Fitch and Smullyan made the same point earlier. It seems to me that all three of these philosophers deserve a degree of recognition that they are often not given. However, one should not lose sight of certain factors that made Kripke's presentation of the modal argument so compelling, whereas the others had not been. One such factor was the context of Kripke's presentation of the modal argument in conjunction with a whole battery of other arguments and significant distinctions, all designed to undercut description theories of proper names. To take one example, many philosophers find it much easier to accept the claim that coreferential proper names are substitutable without change in truth value in modal constructions than to accept the claim that they are similarly substitutable in all constructions, including propositional attitude ascriptions. By linking the two claims, Marcus made objections to the latter seem like objections to the former; by separating them, Kripke makes the claim about the substitutivity of names in modal constructions more palatable. 31

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Another point to keep in mind is that Kripke's presentation of the modal argument was not limited to the behavior of names in modal constructions, but was explicitly concerned with the evaluation of simple sentences (free of modal operators) at alternative possible worlds. 32 The basic intuition tapped by Kripke's version of the modal argument was not only about the truth value of modal sentences, like Necessarily Aristotle was a philosopher, but also about the truth value of simple sentences, such as Aristotle was a philosopher, when evaluated at alternative worlds. This not only added depth and plausibility to the discussion but also rendered the modal argument immune to certain types of objection. 33 Smith's fourth contention has to do with the necessity of identity. He says: This modal argument goes back to Marcus' formal proof of the necessity of identity in her extension of S4 (Barcan, 1946; 1947), which is a fourth component she introduced into the New Theory of Reference. She showed that (T)(x = y)

~

necessarily x = y)

is a theorem of QS4, QS4 being her quantificational extension of Lewis' S4 .... Since identities are necessary, a failure of intersubstitutivity in modal contexts will show that a proper name does not express the relevant descriptive sense.

There are two problems here. First, the priorities are wrong. We do not accept the modal argument because we know antecedently that identities involving ordinary coreferential names are necessary. Rather, we recognize these identities as necessary because the modal argument convinces us that ordinary names are rigid designators. 34 Second, the version of the necessity of identity proven by Marcus involved only variables, and had nothing to do with proper names. Here it is crucial to distinguish the thesis (NI-l), derived by Marcus in her 1947 paper, from the theses (NI-2) and (NI-3). (NI-l)

(x)(y)(if x = y, then necessarily x = y)

(NI-2)

for all proper names a and b, if a = b is true then necessarily a = b is true.

(NI-3)

for all singular terms a and b (including singular definite descriptions), if a = b is true then necessarily a = b is true.

Theses (NI-l) and (NI-2) are true; whereas thesis (NI-3) is false, at least in formal languages in which the class of singular terms includes Fregean definite descriptions. What must be noticed is that the quantificational version (NI-I) of the necessity of identity, articulated and derived by Marcus, no more provides a direct route to the true thesis (NI-2) involving ordinary proper names than it provides a direct route to the false thesis (NI-3). It simply leaves

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the status of these further theses open. For this reason it is just plain wrong to cite Marcus' early systems of quantified modal logic as introducing the version - (NI-2) - of the necessity of identity that corresponds to the modal argument. I should mention that, historically, there was a strong tendency, shared not only by those who accepted NI-l, but also those who rejected it, as well as those, like Quine, who rejected quantifying-in entirely, to think that ifNI-l was true, then NI-2 and 3 must also be true. I suspect that one important reason for this was the equally widely shared, and equally mistaken conviction that the intelligibility of objectual quantification depended upon universal instantiation and existential generalization being universally truth-preserving, where genuine singular terms are involved. In the hands of Marcus, Smullyan and Fitch, this led to the view that the necessity of identity not only required coreferential names to be substitutable in modal contexts, but also prevented us from taking definite descriptions to be singular terms. In the hands of their opponents, who were more inclined to accept descriptions as singular terms, it was taken as refuting the necessity of identity. What is interesting here is the false presupposition shared by both sides of the debate, tying the intelligibility of quantification to familiar extensional rules of inference. It seems plausible that what ultimately lay behind this error was an overly proof-theoretic perspective, and insufficiently developed model-theoretic conception of intensional logic according to which it is the semantics of various intensional constructions, plus the usual Tarski-like clauses for quantifiers, that have priority and determine which rules of inference are valid. Now that we have achieved the appropriate semantic perspective, there is no longer any excuse for running NI -1, 2, and 3 together, or for thinking that the truth of one establishes the truth of the others. As for the thesis, (NI-I), involving variables, I want to acknowledge that there is a way of viewing it as a genuine contribution by Marcus to contemporary theories of reference. One can think of it as the material-mode counterpart of the semantic thesis that individual variables are rigid designators. Although Marcus herself did not explicitly characterize variables in this way, and many years later suggested a more indirect way of understanding quantification via substitution of proper names, her original thesis (NI-l) can be interpreted as providing the basis for characterizing variables as rigid designators. 35 This brings us to Smith's contention that a fifth contribution of Marcus to the so-called New Theory of Reference was the concept of rigid designation. I have just indicated that there is a sense in which Marcus can be viewed as providing a material-mode basis for taking variables to be rigid (relative, of course, to assignments of values). Moreover, she can be seen, following Smullyan and Fitch, as implicitly treating proper names as rigid. However none of these philosophers had the concept of a rigid designation. This concept presupposes the more general notion of the referent of a term at a world. Neither Smullyan, Fitch, nor Marcus in her papers in the 1940's, provided any semantic framework for modal systems, let alone one involving this notion.

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Although an elementary semantic formalization is given by Marcus in her 1961 article, it did not invoke the notion of a referent of a singular term at a world, and did not make room for the full-blown concept of rigid designation as we now understand it. Rather, this semantic notion, though anticipated by Marcus, seems to be due to Kripke, and was present in his treatment of variables as rigid in his 1959, 'A Completeness Theorem in Modal Logic,.36 Smith's characterization of Kripke as contributing only the name 'rigid designation' for a concept discovered by Marcus is a grotesquely inaccurate caricature. Marcus did, of course, explicitly use the notion of rigid designation in her paper 'Essential Attribution', delivered at the December 1970 meetings of the APA. 37 Smith cites this paper, saying, "Marcus notes in her 1970 APA paper, 'Essential Attribution; presented at a symposium at which Kripke was one of the symposiasts, that "individual names don't alter their reference, except to the extent that in [respect ofl some worlds they may not refer at alf'.,,38 Why does Smith

feel that it is important to mention that Kripke was present at this symposium? Is he suggesting that Kripke's presence at the symposium supports the contention that he got the concept of rigid designation from Marcus? If so, why doesn't Smith also mention that the symposium occurred 11 months after Kripke had presented the three lectures of Naming and Necessity at Princeton University? Smith's final contention about the extent of Marcus' contributions to nonFregean theories of reference involves a pair of epistemological points he derives from the following one and one half sentence quote from Marcus' 1961 paper. You may describe Venus as the evening star, and I may describe Venus as the morning star, and we may both be surprised that, as an empirical fact, the same thing is being described. But it is not an empirical fact that (17) Venus I Venus. 39

Smith derives two conclusions from this brief passage. His first conclusion is that Marcus introduced the idea of a posteriori necessity into contemporary philosophy of language, since on her view the sentence Hesperus I Phosphorus is necessary, even though it is clearly a posteriori. Smith's second conclusion from the passage is that in it Marcus provided an epistemological argument against description theories of names to supplement the modal argument. Both of these claims are false. The first thing to do in showing this is to obtain an accurate quotation of the passage from Marcus. In presenting the passage, Smith breaks Marcus' final sentence in half, inserts a period immediately after her example sentence Venus I Venus, and omits, without any indication of ellipsis, the final half of her sentence. Here is the passage as it appears in Marcus.

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You may describe Venus as the evening star, and I may describe Venus as the morning star, and we may both be surprised that, as an empirical fact, the same thing is being described. But it is not an empirical fact that (17) Venus I Venus and if 'a' is another proper name for Venus that (18) Venus I a 40 [my emphasis]

What is Marcus saying here? She is saying that if a is any name for Venus, neither the sentence Venus = Venus nor the sentence Venus = a expresses "an empirical fact". If, as Smith maintains, Marcus is trying to make an epistemological point here, then by "an empirical fact" she must not mean "a contingent fact", for then there would be no epistemological point at issue. Rather, she must be taken to mean that these sentences do not express facts that are knowable only by empirical means. In other words they are knowable a priori. But if this is right, then true identity statements involving names are not characterized as examples of the necessary a posteriori, and Smith's contention that Marcus introduced this notion collapses. It should be noted that Marcus nowhere in the article says that there are true identity statements which are knowable only a posteriori. On the contrary, she says many things that strongly indicate the opposite. One remark that I cited earlier occurs in the paragraph immediately after the one just cited by Smith. There Marcus says" What I have been arguing is that to say truly of an identity (in the strongest sense of the word) that it is true, it must be tautologically true or analytically true".41 Thus, according to Marcus' true identity statements involving genuine names never express empirical facts, but rather are tautologically, or analytically true. Surely this is inconsistent with interpreting her as introducing the notion of necessary a posteriori identities. No author who was doing that would completely fail to use the notion a posteriori, while treating necessity, tautology, analyticity, and the notion of not expressing an empirical fact as if they were interchangeable. This point is reinforced by other things that Marcus says. For example, two pages before the passage cited by Smith, she says the following about the identity sentence alb (which is example 13 in her paper). Now if (13) is such a true identity, then a and b are the same thing. (13) doesn't say that a and bare two things that happen, through some accident, to be one. True, we are using two different names for that same thing, but we must be careful about use and mention. If, then, (13) is true, it must say the same thing as (14) ala. 42 [my emphasis]

The point to note here is that if a = a and a = b say the very same thing, then surely they express the same fact, in which case the fact expressed by one must be knowable a priori only if the fact expressed by the other is. Hence, on the view articulated by Marcus, true identity statements involving names are knowable a priori.

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Finally, you may recall that according to Marcus, coreferential proper names "must be intersubstitutable in every context".43 Thus, if prior to the relevant astronomical discovery Jones knew that Hesperus was identical with Hesperus, on the basis of reflection alone, then he also knew that Hesperus was identical with Phosphorus, by reflection alone - assuming that 'Hesperus' and 'Phosphorus' really are names in Marcus' sense. For all these reasons, it is as clear as anything can be that Marcus did not in her 1961 article embrace the notion of necessary a posteriori identities. What about Smith's contention that Marcus provided an epistemological argument against description theories of names to supplement the modal argument, and to rule out the possibility of modally rigid descriptive senses? Recall the passage cited. You may describe Venus as the evening star. and I may describe Venus as the morning star, and we may both be surprised that, as an empirical fact, the same thing is being described. But it is not an empirical fact that (I 7) Venus I Venus.

Smith claims to find in this passage an argument that where D is a description associated with a name N, the proposition expressed by N is D is not knowable a priori, contrary to the description theory. But there is no such argument. Moreover, once again what Smith says about the passage bears little relation to what is actually in it. Here is what Smith says: If 'Venus' expresses the modally stable sense expressible by 'whatever is actually the evening star and morning star', then the persons designated by 'you' and 'I' in the passage quoted from Marcus' article should be able to know a priori, simply by reflection upon the semantic content of the expressions 'Venus', 'the morning star' and 'the evening star' that Venus is both the morning star and the evening star. The fact that they cannot know this indicates that 'Venus' does not express the modally stable sense expressed by 'whatever is actually the evening star and morning star'.

Notice that in contrast to Marcus' passage, Smith reconstructs the example as one in which you and I both associate with 'Venus' the same description - the x: actually x is the morning star and x is the evening star. If we really did this, then, provided that we thought that we were successfully describing something, we certainly would not be surprised to find out that the morning star is the evening star (as Marcus says we are). Consequently, Smith's argument is his own invention; it is not in Marcus. In addition, the argument is no good. It assumes that if an expression r:t. means the same as the description the x: actually x is the morning star and x is the evening star, then, the claim expressed by r:t. = the x: actually x is a morning star and x is an evening star must be knowable a priori. But this is false, since that claim entails that there is something that is both the morning star and the evening star, it cannot be known a priori. Because of this the fact that it is not knowable a priori that Venus is both the morning star and the evening star does not establish that 'Venus' does not have the descriptive

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meaning under consideration. As a result, Smith's argument fails. 44 There is, however, a line of argument that can be constructed from elements in Marcus for the conclusion that neither the proposition that Hesperus is the evening star nor the proposition that Phosphorus is the morning star is knowable a priori. Ironically, however, the argument does no good for Smith, and cannot be used as an argument against descriptive senses. Recall the last line, omitted by Smith, of the passage cited from Marcus. "But it is not an empirical fact that Venus I Venus and if 'a' is another proper namefor Venus that Venus I a". If, as I have argued, Marcus is here expressing the view that identities between coreferential proper names do not express empirical facts, and so do not require empirical investigation to be known, then we can construct the following argument, which does not appear in her paper, on her behalf:

= Phosphorus.

(PI)

It is knowable a priori that Hesperus

(P2)

If it were also knowable a priori both that Hesperus is the (actual) evening star (if such exists) and that Phosphorus is the (actual) morning star (if such exists), then it would be knowable a priori that the (actual) evening star is the (actual) morning star (if there are such things).

(P3)

It is not knowable a priori that the (actual) evening star is the (actual)

morning star (if there are such things). (CI)

So it is not the case that it is knowable a priori both that Hesperus is the (actual) evening star (if such exists) and that Phosphorus is the (actual) morning star (if such exists).

(P4)

If one of these were knowable a priori, then the other would also be knowable a priori.

(C2)

Therefore neither is knowable a priori.

The first premise in this argument is, of course, incompatible with Smith's claim that for Marcus, the proposition that Hesperus is Phosphorus is an example of the necessary a posteriori. Thus, the argument is no good to him. However, given Marcus' treatment of proper names as Russellian logically proper names, and hence as supporting substitution without change of meaning in any non-quotational context, (PI) is plausible, as are the other steps in the argument. 45 Moreover, the conclusion is clearly incompatible with the description theorist's claim that the name 'Hesperus' has the same sense as 'the (actual) evening star', or any other plausible description that speakers might associate with the name. Why then isn't this precisely the epistemological argument against the

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description theory that we are looking for? The reason it isn't is that its first premise, namely that it is knowable a priori that Hesperus is Phosphorus, presupposes a prior rejection of the description theory. The basis for assuming this premise is simply a prior acceptance of Millianism. Given this, we can use the premise to draw out an epistemological consequence of Marcus' position, but we cannot use it in an argument against descriptivism. To get an epistemological argument against descriptivism one would have to argue directly, without appeal to any Millian premises, that one cannot know a priori that N is D, for relevant names N and descriptions D. Marcus does not do this. Thus, there is no epistemological argument in her paper which can be used to supplement the modal argument against the description theory. This concludes my critique of Smith's major contentions. There are a few other matters I would go into if there were time. 46 But since there is not, I will try to sum up. On the positive side, we can see in the writings of Marcus, Fitch and Smullyan, significant anticipations of some of the central theses of contemporary non-Fregean theories of reference. First, Marcus' quantified version of the necessity of identity anticipates the contemporary view that variables are rigid designators, with respect to assignments of values. Second, the claim, by Smullyan, Fitch, and Marcus, that substitution of coreferential names in modal constructions preserves truth value anticipates the view that ordinary proper names are rigid designators. Third, the use of this feature of names to discriminate them from some descriptions anticipates certain aspects of Kripke's modal argument against description theories. However, it is also important to notice how much of the development of contemporary theories of reference by Kripke and others is lacking from the earlier discussions of Marcus, Smullyan, and Fitch. First, we do not find Kripke's important distinction between the different ways that description theories can be understood - as theories of meaning vs theories of reference fixing. Second, apart from the modal argument, we do not find analogs to the battery of epistemological and semantic arguments against description theories that are given in Naming and Necessity. Third, there is no positive conception of how reference is determined - either by historical chain or by using descriptions to semantically fix reference. Fourth, there are no analogs of Kripke's doctrines of the necessary a posteriori and the contingent a priori. Fifth, the discussions of names are not set in the context of a wider theory of language, including, for example, natural kind terms. Sixth, there is no recognition that arguments stronger than those needed to establish rigidity are needed to support the claim that names are directly referentia1. 47 As a result, relatively uncontroversial claims, like the substitutability of coreferential names in modal constructions, were linked with highly controversial claims, like the substitutability of such names in all constructions, and thereby were rendered less persuaSIve. Don't get me wrong. I am not criticizing Marcus, Smullyan or Fitch for not having written Naming and Necessity. On the contrary, they should be praised

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for their prescient insight, despite the fact that they were not attempting anything so systematic or far-reaching. What I have tried to show is that providing them with proper credit does not result in a reassessment of the seminal role of Kripke and others as primary founders of contemporary nondescriptivist theories of reference. In fact, I think Smith does Kripke a grave injustice. Smith writes as if Kripke appropriated the major views expressed in Naming and Necessity from Marcus while denying her proper credit, and suggests that it is a scandal that the rest of the profession was thereby duped. We have not been duped; there was no misappropriation. Rather, what Smith has done is to mistakenly read many of Kripke's arguments and doctrines back into Marcus, and then to insinuate that Kripke is guilty of theft. This, it seems to me, is shameful. If there is any scandal here it is that such a carelessly and incompetently made accusation should have been given such credence. You may recall that, in hyping his accusations, Smith claimed to be correcting a misunderstanding in the recent history of philosophy "no less important than correcting the misunderstanding in a hypothetical situation where virtually all philosophers attributed the origin of the Theory ofForms to Plotinus". I hope that by now it is apparent how wildly exaggerated this remark really is. I also hope no one will be distracted by Smith's overheated rhetoric and irresponsible sowing of discord from the truly outstanding contributions of both Marcus and Kripke. Both have done work of great importance that should be appreciated and celebrated. They were never competitors in the past, and there is no need now to tear one down to elevate the other. 48 Department of Philosophy Princeton University

NOTES 1 Synthese, XIII, Dec. 1961,303-22. This paper is reprinted in Ruth Barcan Marcus, Modalities, (New York and Oxford: Oxford University Press), 1993. Citations from the paper will be from Modalities. 2 R.C. Barcan (Marcus), 'A Functional Calculus of First Order Based on Strict Implication', Journal of Symbolic Logic, 11, 1946, 1-16. Also, R.C. Barcan (Marcus), 'The Deduction Theorem in a Functional Calculus of First Order Based on Strict Implication', The Journal of Symbolic Logic, 11,1946,115-8. 3 R.C. Barcan (Marcus), 'The Identity of Individuals in a Strict Functional Calculus of Second Order', The Journal of Symbolic Logic, 12, 1947, 12-5. 4 In 'Modalities and Intensional Languages', pages 9 and 10, Marcus refers to theorem 2.32* -0(13, 1132) == (13, 1132)- of her 1947 paper as, in effect, establishing the necessity of identity. (The symbol 'I' is the (strict) identity predicate. The connective is strict equivalence, the terms are individual variables, and the theorem itself has the force of its universal closure.) Marcus derives this theorem in her quantified version ofS4 from her theorems 2.23 -0(13, 1m 132) == (13, 1132)- and 1.104* -OOA == OA. (The symbol '1m' stands for the material identity predicate. Material identity and strict identity are defined predicates that turn out to be provably strictly equivalent in Marcus' S4.) The point to note here is that Marcus' derivation of the necessity of identity depends on

30

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a controversial principle about the iterability of the necessity operator, which is not something that the thesis itself intuitively requires. (The proof also utilizes the Barcan and converse Barcan formulas. See below.) If variables are treated as rigid designators - with respect to assignments as in the now standard Kripke-style semantics for modal systems, the above version of the necessity of identity falls out automatically from the semantics without any special assumptions about the accessibility relation, or the corresponding axiomatic modal systems. In this connection, it is worth noting another theorem that Marcus refers to in 'Modalities and Intensional Languages' in her discussion of the necessity of identity. This is theorem 2.33* of her 1947 paper -(131 1m (32) == (131 I (32). This establishes the strict equivalence of Marcus' two forms of identity. (Theorem 2.32*, and hence the S4 premise guaranteeing the iterability of the necessity operator, is used in the proof of this.) The theorem itself is closely related to the necessity of identity. This can be seen as follows: First, we use the definition of 'I' (strict identity) to give the import of the theorem as (i) (i)

x 1m y

== (F)(Fx3 Fy)

Next we apply the definition of strict implication to give us (ii). (ii)

x 1m y

== (F)O(Fx:J Fy)

The combination of (ii) together with the second order Barcan formula -

N(l) ... N(m)P

for any natural number m. In a Russellian theory of descriptions, the condition 'N(x i- a*)' (or 'z could be dropped altogether, and we might conclude simply

i- a*')

p :::> N(l) ... N(m)P

(6")

for any natural number m. 4 So we may conclude: (XVI)

Let 3 be an interpreted system of modal logic got by supplementing G6del's basic system (or a stronger system, e.g., S4 or S5) by a standard set of axioms and rules for quantification theory with identity. Then if S contains a standard theory of descriptions (i.e., a theory of descriptions in which any well-formed sentence of the system with 'x' as the only free variable is permitted to take the place of 'Fx' in '(1X)Fx', then

1)

If descriptions are treated as names along the lines of Carnap's Meaning and Necessity, and if 'N(z of a*)' is true for some z, or if "Brouwer's axiom" ''P :::) NM'P~ is a theorem of S and 'z of a*' is true, then modal distinctions collapse in S.

2)

If a Russellian theory of descriptions is used, and if, as is usual in extensional logic, (1Q)'P is treated as a name when '(Ei3)(a)('P =.(3 = a)~is true, then modal distinctions collapse in S.

Similar awkward consequences follow, of course, in modal systems containing a theory of classes in which class abstracts are defined with the help of descriptions of the type above. Disastrous consequences follow also if one treats class abstracts as names, adopts the following identity condition for classes: (7)

a

= {3. =. (x) (x

E a. =. x E {3)

and allows substitutivity of concretion, viz. that

185

REFERENTIAL OPACITY AND MODAL LOGIC

(8)

'xEz( ... z ... )'and' ... x .. .'

may replace each other in all contexts. When Godel's basic system or a stronger system of sentential modal logic is supplemented by such a system of class theory, modal distinctions collapse unconditionally, as is seen from the following proof:

= x.p) = x(x = x)

*(1')

x(x

*(2')

(x)(x E x(x

*(3')

x E x(x

*(4')

x = x. p. =. x

*(5')

p

(7')

N(x(x

*(9')

x

=x

= x. p) = x(x = x). ~ p

x(x

p

= x. p). =. x E x(x = x)

(1') by (7) (2') (3') by (8) (4')

(6')

*(8')

= x. p). =. x E x(x = x))

= x.p) = x(x = x). ~ p)

= x.p.=.x = x = x.p). =.x E x(x = x)

* (5')

(6')RL

(8')

*(10')

x E x(x

*(11')

(x)(x E x(x

*(12')

x(x

*(13')

(x)(y)(x

*(14')

(y)(x(x

*(15')

x(x

*(16')

N(x(x N(x(x

*(17')

Np

(7') (12') (15') (16')

p~Np

* (17')

( 18')

= x. p). =. x E x(x = x))

= x.p) = x(x = x) = y. ~ N(x = y))

= x. p) = y. ~ N(x(x = x. p) = y))

= x. p) = x(x = x). ~ N(x(x = x. p) = x(x = x)) = x. p) = x(x = x). ~ p) ~. = x. p) = x(x = x)) ~ Np

(9') or (8) (10') x (11') by (7) Theorem I (or II)

(13') (14') GOdel's axiom A.2

By reasoning parallel to that which led to (6) above, we arrive at: (9)

p ~ N(l) ... N(m)P

We may therefore conclude: (XVII) Let S be a system of modal logic got by supplementing GOdel's basic system (or a stronger system, e.g., S4 or S5) by a system of class theory which contains a standard theory of identity (so that, in particular, the identity relation is substitutive with respect to all

186

DAGFINN F0LLESDAL contexts expressible in S), and such that classes are identical if they have the same members. Then if in S class abstracts are treated as names and substitutivity of concretion is allowed, modal distinctions collapse in S.

Among the proposed systems of modal logic, the second order functional calculi of Miss Barcan and Bayart permit class abstraction, but do not treat class abstracts as names. (Their class abstracts cannot be used to instantiate universal generalizations, and do not have access to identity contexts.) Carnap's system S2 in Meaning and Necessity is the only proposed system of modal logic which incorporates a theory of descriptions. In S2 descriptions may be used to instantiate universal generalizations and have access to '=:' contexts and to '~' contexts. The disastrous result XVI above is, however, avoided in S2 regardless of whether we construe the identity relation as '=:' or '~'. If we were to consider '=:' as an identity sign, then as we saw in § 13, S2 is incomplete since (1)

(x)(y)(x =: y.

~

N(x =: y))

is not among its theorem. But (1) is presupposed in the proof of theorem XVI (line 16». (1) would have been derivable in S2 if '=:' had been universally substitutive. So S2 is saved from a collapse of modal distinctions simply because identity of extension looks this most characteristic feature of an identity relation. What Carnap calls "identity of intension" behaves, however, as we saw in § 13 exactly the wayan identity relation is supposed to do. Nevertheless the disastrous result XVI is avoided in S2 when we use '~' for the '='. For in the proof of XVI, the description '1x)(x~z. p)' occurs in several of the lines. And since 'x~z' is short for 'N(x =: z)' (M&N 39-6), descriptions of this type are not permitted by Carnap, who on p. 184 of Meaning and Necessity states that "in order to avoid certain complications, which cannot be explained here, it seems advisable to admit in S2 only descriptions which do not contain 'N'''. Since in any proof of theorem XVI we must be able to prove that 'p' is true if and only if the entity described in a description is necessarily distinct from a *, it seems inevitable that at least one description in the proof contains the sign '~', i.e., an 'N'. So although S2 contains a theory of descriptions, S2 is saved from a collapse of modal distinctions by the circumstances that its theory of descriptions is not a standard one. (Cf. footnote 2 of this section.)

REFERENTIAL OPACITY AND MODAL LOGIC

187

17. Singular terms and the individuation of our objects

In § 13 we observed that in Carnap's system S2 the variables take as their values individual concepts, not individuals, properties, not classes, and propositions, not truth values (Theorem IV). One might be tempted to think that an intensional ontology is a price we have to pay for quantifying into modal contexts. But this is not so. The variables and quantifiers by themselves do not require us to individuate our entities finer than they are individuated in extensional logic. The trouble comes in with our definite singular terms. If, e.g., the descriptions 'the Morning Star' and 'the Evening Star' are among our singular terms, and if in some world which is possible with respect to the actual world these two descriptions refer to distinct entities, then by (1)

(x)(y)(x

=

y.:J N(x

=

y))

they have to refer to distinct entities also in our actual world. And the material object to which they both refer in non-modal logic therefore has to be expurgated from our universe of discourse. In order to avoid difficulties of this type, the only kind of descriptions which we may treat like singular terms are those descriptions ~ (1(}:)'P ~ in which 'P satisfies the condition: (2)

~(E,B)N(a)('P=.=,B)~

or in general, if we admit iterated modalities:

where the variables range over only the objects we want to admit in our universe of discourse, i.e., extensions. Abstracts, whether defined by descriptions or directly, are subject to parallel restrictions. Evidently words like 'Hesperus' and 'Phosphorus' give rise to similar difficulties. A natural way out of these difficulties would be to treat such name-like words just the way we would treat descriptions. We replace them in context using contextual definitions of the Russellian type, insisting with Quine on the "primacy of predicates" (Methods of Logic, p. 218). Instead of saying that Hesperus and Phosphorus are identical we might, e.g., say that there is one and only one object which Hesperizes and one and only one object which Phosphorizes, and these objects are identical. This solution leads us to regard a word as a proper name of an object only if it refers to this one and the same object in all possible worlds. This does not seem unnatural. Neither does it seem preposterous to assume as we just did, that if a name-like word does not stick to one and the same object in all possible worlds, the word contains some descriptive elements. 5 Frege held that "every grammatically well-formed expression representing a proper name always has a sense". 6 And Quine, by insisting on the primacy of predicates, 7 eliminates all

188

DAGFINN F0LLESDAL

definite singular terms along the above lines. Russell, in "Knowledge by acquaintance" held that 'I' and 'this' are the only two words "which do not assign a property to an object, but merely and solely name it".8 In a footnote added in 1917 Russell excluded 'I' from this list. The only remaining word 'this' will hardly be used as a definite singular term in any system of logic, modal or non-modal. The name-like words which disturbed Russell were the ones which fail to refer to one and only one object in our actual world. The ones which disturb us in quantified modal logic are the ones which fail to refer to one and the same object in all possible worlds. And the solution outlined above strongly resembles Russell's. Russell permitted a description '(1OO)t.p ~ to be treated as a singular term if and only if the following condition is satisfied (3)

'(E,6)(oo)(1j;)iffS~orSF1j;

(4)

SF '.

1= Dc/>, then 1= c/>. 1= ,Dc/>, then ~ c/>.

Since, by assumption, there is an effective enumeration of the logically true sentences of C, we can effectively decide which of F D¢ or F ...,D¢ holds. But, this means in virtue of (ii) and (iii) that we can effectively decide which of F ¢ or ~ ¢ that holds. By Godel's completeness theorem for the predicate calculus, for any sentence ¢ of Co, F ¢ holds if and only if ¢ is a theorem of the firstorder predicate calculus. But this is contrary to Church's theorem according to which the pure predicate calculus is undecidable (cf. Kleene 1967, § 45). Q.E.D.

The next step in the development of a viable semantics for quantified modal logic was taken by Stig Kanger in his dissertation Provability in Logic (1957a). Kanger's ambition was to provide a language of quantified modal logic with a model-theoretic semantics ala Tarski. For that purpose Kanger introduced the notions of a primary valuation and a system. A primary valuation for a language C of quantified modal logic is a function v which for every non-empty domain D assigns an appropriate extension in D to every individual constant, individual variable, and predicate constant in C. A system is an ordered pair S =< D, v>, where D is a (non-empty) domain and v is a primary valuation. Notice that v does not only assign extensions to symbols relative to the designated domain D, but relative to all domains simultaneously. In Kanger's dissertation there is to be found, for the first time in print, a semantics for modal operators in terms of so-called accessibility relations: each modal operator D is associated with an accessibility relation Ro between systems in terms of which the semantic evaluation clause for D is spelled out: S 1= Dc/> iff for every system S' such that SRoS', S'

1= c/>.

That is, D ¢ is true in the system S if and only if ¢ is true in every system S' that is Ro-accessible from S. One particular modal operator that Kanger introduces is one he calls logical necessity and which he provides with the following semantic clause: S 1= [Jc/> iff for every system S', S'

1= c/>.

Thus, R!!J is the universal relation between systems. Kanger points out that by imposing certain formal requirements on the accessibility relation, like reflexivity, symmetry, transivitity, etc., one can make the operator satisfy corresponding well-known axioms of modal logic. In this way, the introduction of accessibility relations made it possible to apply semantic and model-theoretic methods to the study of a variety of modal

KANGER'S EARLY SEMANTICS FOR MODAL LOGIC

207

notions other than logical necessity. Although Kanger was the first to publish, other researchers, among them Hintikka and Montague, also came up with the idea of utilizing accessibility relations in the semantics of modal notions. One source of inspiration for Kanger's use of accessibility relations in modal logic was no doubt the work of Jonsson and Tarski (1951) on representation theorems for Boolean algebras with operators. 3 Jonsson and Tarski define operators 0 on arbitrary subsets X of a set U in terms of binary relations R ~ U x U in the following way: oX = {x

E

U : 3y

E

X(yRx)},

that is oX is the image of X under R. They also point to correspondence between properties of 0 and properties of R. Among other things, they prove a representation theorem for so-called closure algebras that, via the TarskiLindenbaum construction, yields the completeness theorem for propositional S4 with respect to Kripke models with a reflexive and transitive accessibility relation. However, Jonsson and Tarski do not say anything about the relevance of their work to modal logic. Perhaps they considered the connection too obvious or of too little importance to mention it. A semantic approach to first order modal predicate logic that has a close resemblance to Kanger's was developed by Montague (1960).4 Like Kanger, Montague starts out from the standard model-theoretic semantics for nonmodal first-order languages and extends it to languages with modal operators. He defines an interpretation for an ordinary first-order predicate language £ to be a triple S =< D, I, g >, where (i) D is an empty set (the domain); (ii) I is a function that assigns appropriate denotations in D to the non-logical constants (predicate symbols and individual constants) of £;5 and (iii) a function g that assigns values in D to the individual variables of £. For each non-logical constant or variable X, let SeX) be the semantic value (i.e., denotation for nonlogical constants and value for variables) of X in the interpretation S. Then the notion of truth relative S is defined as follows: (1)

S F P(t\, ... ,tn ) iff < S(t\), ... ,S(tn )

(2)

S F (t\

(3)

SF'¢> iff S ~ ¢>.

(4)

SF (¢>

(5)

S F Vx¢> iff for every object a E D, S(a/x) F¢>'

=

->

t2) iff S(t\)

'l/!) iffS

~

=

>E

S(P).

S(t2)'

¢> or SF 'l/!.

Here, Sea/x) is the interpretation which is exactly like S, except for assigning the object a to the variable x as its value. Montague now asks the same question as Kanger: How can this definition of the truth-relation F be generalized to first-order languages with modal operators? As we recall, Kanger solved the problem by modifying the notion

208

STEN LINDSTROM

of an interpretation: a Kanger-type interpretation (what is called 'a system') assigns denotations to the non-logical constants and values to the variables not only for one single domain (the 'actual' one) but for all domains. Montague's approach is simpler than Kanger's: he keeps the notion of an interpretation S of first-order logic intact, and just adds semantic evaluation clauses for the modal operators. As in the Kanger semantics, each modal operator D is associated with an accessibility relation RD. Now, however accessibility relations are relations between interpretations S =< D, I, g > of the underlying non-modal first-order language. The semantic clause corresponding to the operator D, with associated accessibility relation R o , is: (6)

SF D¢ iff for every interpretation S' such that SRoS', S' F ¢.

Montague observes that for each variable x the universal quantifier Vx, that binds the variable x, can be viewed as a modal operator with the accessibility relation R\;ix defined by the condition:

< D, I,g > Rvx < D', I',g' > iffD every variable y different from x.

=

D', I

=

I' and g(y)

=

g'(y) for

Given this definition, (5) becomes a special case of (6). Montague associates with the operator [jJ of logical necessity the accessibility relation R[jJ defined by:

< D,I,g >R!D< D',I',g' > iff D = D' and g = g'. Thus, his semantic clause for (l)

[jJ

becomes:

< D, I, g > F I!J¢ iff for every I' defined over D, < D, I', g > F ¢.

This semantic clause should be compared with Kanger's stricter condition: (2)

S FI!J¢ iff for every system S', s'

F ¢.

The difference between (1) and (2) corresponds to a difference between two different conceptions of logical truth: Tarski's (1936) conception and the modern model-theoretic one. According to Tarski (1936), truth and logical truth are properties that primarily apply to interpreted formal languages. An interpreted first-order language L comes with a domain of discourse D and an interpretation function I that gives the denotations in D of the non-logical constants of L. Hence, the (absolute) notion of truth is well-defined for such a language. A formula ¢ of L is true relative to an assignment g of values in L to the variables of L if < D, I, g >F ¢. ¢ is true, simpliciter, if it is true relative to every assignment, that is if it is true in the intended model < D, I >.6 Now, according to Tarski (1936), a sentence (closed formula) ¢ of L is logically true if it is true and its truth is invariant with respect to all reinterpretations of its nonlogical constants relative to the given domain of discourse D. That is, ¢ is

209

KANGER'S EARLY SEMANTICS FOR MODAL LOGIC

logically true if and only if, for every interpretation < D, I', g' > with the given domain D, < D, I', g' >F ¢. If ¢ is a sentence (closed formula), then its truthvalue is independent of the assignment of values to the variables. Hence, Tarski's (1936) definition yields for sentences ¢ of £: ¢ is logically true iff for every I' defined over D, < D, I' ,g > p ¢,

where D is the domain of discourse of £ and g is any assignment of values in D to the variables. Hence, for closed formulas of the underlying first-order language, Montague's truth-clause (1) above coincides with Tarski's (1936) definition of logical truth. It also accords well with Carnap's definition of logical truth as truth in all state descriptions, provided that the language contains names for all the objects in a fixed domain of discourse. Tarski's (1936) definition yields the result that all true sentences of an interpreted language that do not contain any non-logical symbols are logically true. So, if the domain of discourse is infinite (and provided that = is taken as a logical constant), then all the sentences of the form: (n)

:JXl ... :JXn (Xl =1= X2 1\ ... 1\ Xl =1= Xn 1\ X2 =1= X3 1\ ...

. . . 1\ X2 =1= Xn 1\ ... 1\ Xn-l =1= Xn)

n

~

2, are logically true. So according to Montague (1960), the sentences:

([]n)

[]

:JXl ... :JXn(XI =1= X2 1\ . .. 1\ Xl =1= Xn 1\ X2 =1= X3 1\ ...

.. . 1\ X2 =1= Xn 1\ .. . 1\ Xn-l =1= Xn)

are true for an interpreted language with an infinite domain. Notice, however, that according to Montague (1960), it is not the case that:

P []:JXl ... :JXn(XI =1= X2 1\ . .. 1\ Xl

-1=

Xn 1\ X2 =1= X3 1\ ... 1\ Xn-l =1= xn),

that is the sentences ([iJn) are not logically true. This is so, since the definition of logical truth that Montague adopts in the metalanguage is the standard modeltheoretic one of truth in all interpretations, not just truth in all interpretations with a given domain. In conclusion, Montague's and Kanger's respective truth clauses for [iJ yield, for modality-free sentences ¢, []¢ is true iff ¢ is logically true in the sense of Tarski (1936) []¢ is true iff ¢ is logically true in the model-theoretic sense.

(Montague) (Kanger)

There are other possibilities for interpreting logical necessity within Montague's framework, one interesting alternative being: (3)

< D, I, g >p []¢ iff for every model < D', I' > such that ~ D', < D',I',g >p ¢.

D

Notice that on Montague's interpretation (1) of [iJ, both the Barcanformula:

210 (Ba)

STEN LINDSTROM

'v'xi!J¢>ex) ->l!J'v'x¢>ex)

and its converse: (CBa) i!J'v'x¢>ex) -> 'v'xi!J¢>ex)

are logically true. However, on the interpretation (3), (CBa) still holds, but the Barcan formula fails. Kanger's interpretation (2), finally, makes both (Ba) and (CBa) fail. As a matter of fact, on the interpretation (2) the following is a logical truth: i!J¢>(XI' ... ,xu)

+--+

I!J'v'XI ... 'v'Xn¢>(XI, ... , xn).

Hence, if we write, for example,

the initial quantifier does not really "bind" the free variables

Xl

in the formula

iff S ~ C¢>.

(3)

S FC (¢> -> 'Ij;) iffS

(4)

S FC 'v'x¢> iff, for every individual constant c, S FC ¢>(c/x).

(5)

S FC

~c

¢> or S FC 'Ij;.

D ¢> iff, for every state-descripition Sf in C, Sf FC ¢>.

KANGER'S EARLY SEMANTICS FOR MODAL LOGIC

211

Observe how the relativization of the definition to C changes the meaning of D. Instead of D¢ meaning that ¢ is logically true, it now means that ¢ is universally true relative to the given set of state descriptions. The metatheoretic

definition of logical truth must be changed accordingly: ¢ is logically true 0= ¢) if and only if, for every C and every SEC, S Fc¢. It is not difficult to axiomatize the quantified modal logic that corresponds to this semantics. As a matter of fact, Hintikka's and Kripke's innovation is essential for proving completeness results. The set C represents the space of possible words: not every state-description may correspond to a genuine possibility. The last step to possible worlds semantics, taken by Kripke, is to let the possible worlds be explicitly represented in the semantics by an index set W. Hence, by replacing the nonempty set of state-descriptions by an indexed family C = {Sw}weW of statedescriptions and utilizing accessibility relations between indices (possible worlds), we get something rather similar to possible worlds semantics. Sentences are now evaluated at indices rather than at state-descriptions: FC P(al, ... , an) iff(al, ... , an) E Sw.

(1)

W

(2)

W

(3)

W

Fc ..., O(x "'" y».

(Necessity of Distinctness)

The latter principles are controversial. Hintikka has repeatedly stressed that they are unacceptable for propositional attitude constructions like "John knows that ...", George the IV believes that ...", etc. 9 On the other hand, Kripke's formal semantics fits well with his conception of metaphysical necessity - as it is expounded in Kripke (1980) - and the possible worlds metaphysics that goes with it. In section 6.1, I shall argue for the thesis that (QS5=) is the (first-order) quantified modal logic corresponding to Kripke's conception of metaphysical necessity. And I shall write IMl rather than D when the necessity operator is interpreted as metaphysical necessity. The dual operator, metaphysical possibility, is written as ~ that is, E v(D, P).

(3)

S ~.L

(4)

S~(r,b-41/J)iffS~r,borS~1/J.

(5)

< D, I, g >~ Vxr,b iff < D, I, g >p r,b, for each g' such that g'

(6)

< D, I, g >~ 3xr,b iff < D, I, g' >p r,b, for some g' such that g'

(7)

for every operator 0, S ~ Or,b iff \;IS', if SRo S', then S' ~ r,b.

~

(t\ = t2) iffv(D, tJ) = v(D, t2).

=x g. =x g.

Explanation: g' is like g except possibly at x (also written, g' =x g) if and only if, for each domain D and each variable yother than x, g'(D, y) = g(D, y). In the

KANGER'S EARLY SEMANTICS FOR MODAL LOGIC

217

above definition, Ro is a binary relation between systems that is associated with the modal operator O. Ro is the accessibility relation associated with the operator O. Among the modal operators in £, there are two designated ones llil ("analytic necessity") and [j] ("logical necessity") with the semantic clauses: < D, l,g >p Iffiq., iff for every domain D',< D',I,g >p q.,. < D, I, g >p [Jq., iff for every system S, S p q.,. We define a Kanger model for £ to be an ordered pair Wl =< D, I> of a domain and an interpretation. Notice that for any D and any I, the structure < D,lo > is a model for the non-modal fragment £0 of £. Hence, an interpretation I can also be represented as a family {< D, 10 > }OED of firstorder models indexed by the collection V of all domains. Notice also that this family contains exactly one model for each domain D. A Kanger model can then be written as an ordered pair of the form Wl =< D, { < D, 10 > }OED >. A system, finally, can be represented as an ordered pair < Wl, g > of a Kanger model Wl and an assignment g. We say that formula ¢ is true in a Kanger model Wl (in symbols, Wl po ¢), if it is true in every system S of the form < Wl, g >. If g and g' are assignments that agree for each domain on all the variables that occur free in ¢, then < Wl,g >po ¢ iff < Wl,g' >po ¢. Hence, a sentence (closed formula) is true in a Kanger model Wl = {< D, 10 > bED iff it is true in some system < Wl, g >. A formula ¢ is said to be valid (logically true) if it is true in every system < D, v >. A formula ¢ is a logical consequence of a set r offormulas (in symbols, r po ¢) if ¢ is true in every system in which all the formulas in r are true. Kanger defines a proposition as an ordered pair < ¢, I > of a sentence (closed formula) ¢ and an interpretation 1. 14 An n-ary predicate is defined as an ordered pair < P, I >, where P is an n-ary predicate constant and I is an interpretation. A name is a pair < c, I >, of a constant c and an interpretation I. The proposition < ¢, I> is said to be true in the domain D if < D, I >po ¢. < ¢, I > is called analytic if it is true in every domain D. Notice that for any domain D, (I)

is analytic.

(2)

< [Jq." I > is true in D iff q., is logically true.

The notion of (non-relativized) truth is explained as followsY Let Do be the set of all "real" individuals. Let 10 be the interpretation which, for every domain D, assigns to the non-logical symbols the denotations that they have according to the intended interpretation of £.16 A proposition < ¢, I > is true if it is true in the domain Do. A sentence ¢ is true if the proposition < ¢,Io > is true. ¢ is said to be analytic if < ¢,Io > is analytic. Notice that llil ¢ is true iff ¢ is analytic. Similarly, [j]¢ is true iff ¢ is logically true.

218

STEN LINDSTROM

Let us say that a modal operator 0 is ontological if there exists a relation R such that for every domain D, every valuation v and every formula ¢:17

< D, v >p DqJ iff for every D', ifDRD', then < D', v >p qJ. In (1970) Kanger presents a version of his semantics where he considers ontological operators only. That is, every operator 0 is associated with a relation Ro between domains rather than between systems. In (1972) the ontological approach has become his official semantics for modal logic. 5. THE TREATMENT OF "QUANTIFYING IN" IN KANGER SEMANTICS

In Provability in Logic (1957a) and in "The morning star paradox" (1957b) Kanger gives the following evaluation clause for the universal quantifier: (i)

< D, I, g >p VXqJ iff < D, I, g' >p qJ for every assignment g such that g =x g.

According to this clause, the formula Vx¢ is true in the system < D, I, g > if and only if ¢ is true in every system < D, I, g' > which is exactly like < D, I, g > except, possibly, for the values it assigns to the variable x in the various domains. In (1957c) and (l957d) he considers the following alternative clause: (ii)

< D, I, g >p VXqJ iff < D, I, g' >p qJ for every g' such that (i) g' =x g; and (ii) g'(D',x) = g(D',x) for all domains D' that are distinct from D.

That is, the formula Vx¢ is true in the system < D, I, g > if and only if ¢ is true in every system < D, I, g' > which is exactly like < D, I, g > except possibly, for the value it assigns to the variable x in the domain D. Kanger (1957c) suggests the following informal readings of these two alternatives: (x)qJ is true iff qJ is true for every interpretation ofx

(Ux)¢ is true iff qJ is true whatever x may denote, writing (x) and (Ux) for the quantifiers with the first and the second evaluation clause, respectively. If ¢ is a non-modal formula, then, of course, (x)qJ



(Ux)qJ

is valid. However, (Ux) is really an odd quantifier, which does not even validate: (Ux) ~Fx

~

(Uy)

~Fy.

Consider, namely, a system S =< D, I, g > such that Fx is true in some domain D' different from D, and Fy is false in every domain. Suppose also that the extension of F in D is the empty set. Then, ~ Fx and --, ~ Fy are both true in S. By the semantic clause for (Ux), (Ux) ~ Fx will also be true in S. But, --, ~ Fy is

219

KANGER'S EARLY SEMANTICS FOR MODAL LOGIC

true for every assignment g satisfying the conditions (i) g' =y g; and (ii) for all domains D' that are distinct from D, g'(D', y) = g(D', y). Hence, (Uy) ~ Fy is false in S. That is, substitutivity of alphabetic variants fails for the operator (Ux). For this reason, I shall not consider it further. So, when I speak of Kanger's interpretation of the quantifiers, I shall understand the treatment in (l957a) and (1957b), according to which the universal quantifier \:I has the semantic clause (i) and the existential quantifier has the dual clause: (iii)

< D, I, g >F= ¢ iff < D, I, It >F= ¢ for some g' such that g'

=x

g.

In order to get a clearer understanding of Kanger's treatment of quantification, I shall speak of selection functions that pick out from each domain an element of that domain as individual concepts. To be more precise, an individual concept, in this sense, is a a function f, with the collection of all domains as its range, such that for every domain D, f(D) E D. We can think of a system S =< D, I, g > as assigning to each individual constant c the individual concept {< D, I(D, c) >: D is a domain} and to each variable x the individual concept {< D, g(D, x) >: D is a domain}. The formula P(t\, ... , t n) is true in S =< D, I, g > if and only if the individual concepts designated by t\, ... , tn pick out objects in the domain D that stand in the relation I(D, P) to each other. The identity symbol designates the relation of coincidence between individual concepts (at the "actual" domain D). That is t\ = t2 is true in a system S =< D, I, g > if and only if the individual concepts designated by t\ and t2, respectively, pick out one and the same object in the domain D of S. Kanger's quantifier \:Ix, with the semantic clause (i), can now be thought of as an objectual quantifier that ranges not over the "individuals" in the "actual" domain D, but over the (constant) domain of all individual concepts. That is, \:Ix¢ is true in a system < D, I, g > if and only if ¢ is true in every system which is exactly like < D, I, g > except, possibly, for the individual concept that it assigns to the variable x. Note, that interpreted in this way, the range of the quantifiers \:Ix and :3x is independent not only of the domain D but also of the system S: the range of the quantifiers \:Ix and :3x is fixed, once and for all, to be the collection of absolutely all individual concepts. While formulas of the form t\ = t2 express coincidence, identity between individual concepts is expressed by formulas of the form l1il(t\ = t2)' Writing x == y for l1il(x = y), the following principles are valid: (L ==)

\fx(x == x)

(I ==)

\fx\fy(x == y

--+

(¢(x/z)

--+

¢(y/z))),

that is, == satisfies the formal laws of the identity relation. None of the sentences:

220

STEN LINDSTROM

saying that the "actual" domain has at least n elements (for n 2: 2), is logically true according to Kanger's semantics. In contrast all sentences of the form: ::3xl··· ::3xn(·(Xl == X2) /\ ... /\ '(X2 == X3) /\ ... /\ .(X2 == xn) /\ ... /\ '(Xn-l == xn)),

are logically true. Intuitively, these sentences say that there are, for each n, at least n individual concepts. Consider now Kanger's (l957b) discussion of the so-called Morning Star paradox. The paradox arises from the following premises: (1)

(2) (3)

~ (Hesperus = Hesperus) Phosphorus = Hesperus • ~ (Phosphorus = Hesperus),

where, "Phosphorus" and "Hesperus" are two proper names (individual constants) and Iillis to be read "it is analytically necessary that". We assume that "Phosphorus" is used by the language community as a name for a certain bright heavenly object visible in the morning and that "Hesperus" is used for some bright heavenly object visible in the evening. Unbeknown to the community, however, these objects are one and the same, namely, the planet Venus. "Hesperus = Hesperus" being an instance of the Law of Identity is clearly an analytic truth. It follows that the premise (1) is true. (2) is true, as a matter of fact. "Phosphorus = Hesperus" is obviously not an analytic truth, "Phosphorus" and "Hesperus" being two different names with quite distinct uses. So, (3) is true. However, using sentential logic together with the following laws of predicate logic: (UI)

Vxq;

(I =)

VxVy(x = y ---+ (q;(x/z)

---+

q;(t/x),

(Universal Instantiation) ---+

q;(y/z))),

(Indiscernibility of Identicals)

we can infer from (2) and (3): (4)

•

~

(Hesperus = Hesperus).

But (1) and (4) contradict each other, so something must have gone wrong in this argument. According to Kanger's diagnosis of the Morning Star paradox it is (I =) that is at fault. Given Kanger's semantic clause (i) for the universal quantifier and his semantic treatment of individual terms, (UI) is valid but (I =) is not. Only the following restricted version of (I =) is valid: (I =')

VxVy(x = y ---+ (q;(x/z) ---+ q;(y/z))), provided that no free occurrence of z in q; is within the scope of a modal operator.

With this change in the underlying logic, (4) can no longer be inferred from (2) and (3).

KANGER'S EARLY SEMANTICS FOR MODAL LOGIC

221

As Kanger himself points out, there are still some difficulties left. From (UI) and the equivalence 3x¢ ...... -,\lx-,¢, we get: (EG)

¢(t/x)

--->

3x¢.

(Existential Generalization)

But, in view of (1 )-(3) and the Law ofIdentity, the following sentences are true: (5)

Phosphorus = Hesperus 1\

(6)

Hesperus = Hesperus 1\ IHI (Hesperus = Hesperus).

-,

IHI (Phosphorus = Hesperus).

So, it follows that: (7)

3x(x = Hesperus 1\

(8)

3x(x =Hesperus 1\ IHI (x = Hesperus».

-,

IHI (x = Hesperus».

Although unintuitive, this result is perfectly compatible with the interpretation of the quantifiers as ranging over individual concepts and of the identity symbol as designating coincidence between individual concepts. According to this interpretation, (7) and (8) mean: (7')

There is an individual concept x which actually coincides with the individual concept Hesperus but does not do so by analytical necessity.

(8')

There is an individual concept x which not only happens to coincide with the individual concept Hesperus but does so by analytic necessity.

As Quine (1947) was the first to point out, however, (7) and (8) are incompatible with interpreting \Ix and 3x as objectual quantifiers meaning "for all objects x (in the domain D)" and "for at least one object x (in D)" and letting the identity sign stand for genuine identity between objects (in D). Because, under this interpretation, (7) and (8) have the readings: (7")

There is an object x (in the actual domain D) which is identical with Hesperus and which is not necessarily identical with Hesperus.

(8")

There is an object x (in the actual domain D) which is identical with Hesperus and which is necessarily identical with Hesperus.

meaning that one and the same object, Hesperus, both is and is not necessarily identical with Hesperus, which is absurd. So Kanger's semantics for quantified modal logic is incompatible with interpreting the quantifiers as ranging over actually existing individuals (as opposed to individual concepts) and at the same time interpreting = as identity between individuals.

222

STEN LINDSTROM

In Kanger's semantics there are no means of identifying individuals from one domain to another. In particular, the truth-values of formulas will not be affected if we make all the domains disjoint, by systematically replacing every domain D by the set: {< D, a >: a ED}.

In other words, set-theoretic relations between domains like inclusion, overlap and disjointness, have no semantic significance. Suppose we make the claim: (9)

Something is such that it is the number of planets but might not have been so.

It seems reasonable to formalize this claim in quantified modal logic as: (10)

3x(Px /\ -.DPx).

We cannot use any of the Kanger's quantifiers for this purpose, however. Suppose, namely, that: g(D,x) E I(D,P),DRoD',D f:. D',g(D',x)

~

I(D',P).

Intuitively this means that one thing is the number of planets in the domain D and one thing or another is not the number of planets in the modal alternative D' to D. From this, we should not be able to conclude (10). But on any of Kanger's interpretations of the universal quantifier, (10) follows. So his approach does not allow us to express the claim that one and the same object has a given property in one domain and lacks that property in another domain. Now, we might ask how we could repair Kanger's semantics in order to allow for genuine quantification over individuals. There are many possibilities. One that is particularly straightforward technically is to adapt Kripke's (1963a) treatment of quantification to Kanger's approach. This means that we modify the notion of an assignment g in such a way that an individual variable x is assigned an object g(x) in a domain-independent way. That is, we make two changes with respect to Kanger's notion of an assignment: (i) the value g(D, x) of an individual variable x in a domain D is no longer required to be a member ofD; (ii) for all domains D and D', we require that g(D,x) = g(D',x). After these changes are made, an assignment simply becomes a function g that assigns to each variable x an object g(x). We then adopt the following evaluation clauses for the universal and existential quantifiers:

< D, I, g > PVxrj; iff < D, I, g' > p rj;, for every g such that (i) g is like g except possibly at x; and (ii) g'(x) ED. < D, I, g >p 3xrj; iff < D, I, g' >p rj;, for some g such that (i) g' is like g except possibly at x; and (ii) g'(x) ED.

223

KANGER'S EARLY SEMANTICS FOR MODAL LOGIC

With these clauses our previous objection to Kanger's approach that it could not make correct sense of sentences like 3x(Px 1\ 'DPx) seems to have been met. For this sentence to be true at < D, I, g >, there needs to be an element a E D such that: a

E

lCD, P) and for some D', DRoD' and a

~

I(D', Pl.

We have been able to express the claim that one and the same individual has the property P in domain D and lacks that property in some domain D' that is possible relative to D. Let us now see how the modified semantics might handle the Morning Star paradox. In this semantics, = is interpreted as genuine identity between objects. Accordingly the logical principles for = are the expected ones: (L =) Vx(x = x).

(I =)

(Law of Identity)

VxVy(x = y --> (¢(xjz)

-->

¢(yjz)).

(Indiscernibility of Identicals)

However, instead of (UI) we have: (UI')

Vx¢ 1\ :Jx(x = y)

-->

¢(y Ix).

Now, how should we handle individual constants within the modified Kanger semantics? An intuitively appealing approach is to assign denotations to constants in a domain-dependent way as before, but not require the denotation I(D,c) of a constant c relative to a domain D to be a member of D. With this treatment of individual constants, we cannot infer from (I =) to: (11)

Phosphorus = Hesperus --> (Iffi (Phosphorus = Phosphorus) Iffi (Phosphorus = Hesperus)),

-->

unless the following requirements are met: 3x !ill (x

=

Phosphorus),

3x!ill (x

=

Hesperus).

But these conditions hold, only if: 3x !ill (x

=

Phosphorus),

!ill (Phosphorus = Hesperus).

The last of these conditions contradicts (3), so it cannot be assumed. It would, presumably, hold only if "Phosphorus" and "Hesperus" were synonymous. Hence, we cannot infer (11) from (I =). We can also verify, directly, that the modified semantics does not allow the inference from (2) and (3) to (4). So the Morning Star paradox, in the form that Kanger presented it, is resolved. Let us say that a modal operator 0 is a constant assignment operator, if there exists a binary relation Ro between Kanger models < D, I >, such that for every assignment g,

224

STEN LINDSTROM

< D, I, g > F D4> if and only if for every Kanger model < D', I' > such that < D, I > Ro < D', I' >, < D', I', g > F 4>. Intuitively, constant assignment operators do not affect the values that are assigned to free variables within their scopes. In contrast, Kanger's operator of logical necessity, which is not a constant assignment operator, binds all free variables within its scope. Hence, quantifying in, past this quantifier, does not make sense. As Kaplan (1986) has shown, however, we can interpret logical necessity in a way that admits of quantifying in. Within the present framework, Kaplan's treatment of logical necessity amounts to the following semantic clause: < D, I, g > F [jJ 4> if and only if for every Kanger model < D', I' >, < D', 1', g >F 4>. Although, we do have for this operator, Barcan Marcus' (1947) Necessity of Identity principle: (D =) VxVy(x = y ->

[jJ

(x = y)),

we, of course, do not have: (12)

Phosphorus

=

Hesperus

->[jJ

(Phosphorus

=

Hesperus)

and this, we think, is as it should be. It is, of course, very doubtful whether Kanger would have approved of these changes to his semantics. 6. THE SET-DOMAIN VERSUS THE CLASS-DOMAIN SEMANTICS

Kanger presents his semantic theory within an informal set-theoretic framework, where all sets are treated on a par, as genuine objects that can be members of other sets. 18 This theory - what we might call naive Kanger semantics - is, however, threatened by paradoxes: given normal assumptions about sets the theory is inconsistent. For example, primary valuations are themselves non-empty sets, that is, domains. It follows that for any valuation v, v itself belongs to the first argument domain of v. In consequence, for an individual constant c, < < v, c >, v(v, c) >E v. This is contrary to the ordinary assumption of set theory that sets are well-founded. This consequence may not seem especially serious from Kanger's point of view, since in section 5.6 of [1957a] he briefly discusses the introduction of non-well-founded sets in set theory. However, there are more serious problems. Consider any valuation v. Its first argument domain is the collection U of all domains. But in order for v to be a set, the collection U must also be a set. Let r+(U) be the set of all non-empty subsets of U. Then, by Cantor's theorem, card (r-t (U)) > card (U). But this

KANGER'S EARLY SEMANTICS FOR MODAL LOGIC

225

contradicts the fact that p+(U) for the non-modal base language £0 are sets. An interpretation is a proper class {< D, In > }nEv of such models (relational structures) indexed by the class 'D of all non-empty sets. A Kanger (set-domain) model consists of a domain D and an interpretation 1= {< D, In > }DEV. Such a model (we use the notation (D, I) for it) cannot be a set nor, in fact, a class, since it is intuitively an ordered pair, one of the components of which is a proper class. Although, we cannot define it in the usual systems of set-theory (Zermelo-Fraenkel, G6del-Bernays-von Neumann, Kelley-Morse), it makes intuitive sense to speak of the ordered pair (D, I). An assignment g is now a functional class which for any domain D and any variable x assigns a value g(D, x) in D to x. A system is an ordered pair S = (Wl, g) consisting of a Kanger model Wl and an assignment g. The accessibility relation Ro that is associated with a modal operator 0 of £ is a collection of ordered pairs (S, S') of systems. Or, in the case of ontological operators: a collection of ordered pairs of domains. The following notions are defined exactly as before: (i) S F ¢ and Wl F ¢; (ii) a formula ¢ being valid or logically true (written as F ¢); (iii) logical consequence, r F ¢ where r is a set of formulas and ¢ a formula. The Kanger set-domain semantics presupposes a strong metatheory in which one can speak not only of the usual cumulative hierarchy of sets over a set of individuals, but also of classes that may contain sets and individuals, collections that may contain such classes, collections that may contain collections, and so on. Only the individuals and sets are regarded as genuine objects, while classes and collections are thought of as essentially predicative in nature. As a proper formal language for formalizing the metatheory, we think of a language of

226

STEN LINDSTROM

simple-type theory, where the individual variables (i.e., variables of type L) range over the elements of the cumulative hierarchy and the predicate variables of type (a\, ... ,an) range over arbitrary n-ary relations whose i'th domain for I :::; i :::; n consists of the class of all entities of type ai. So for instance, the variables of type (L) range over arbitrary classes of objects (urelements and sets). Variables of type ((t), (L)) range over arbitrary relations between classes of objects, etc. A metalanguage of this kind should be appropriate also to formalize the next version of Kanger semantics. 6.2. Kanger class-domain semantics

This semantics differ from the previous one in the following respects: A domain is now defined to be a non-empty class of elements of the cumulative set hierarchy, i.e., we also allow domains to be proper classes. A valuation is a function v, which given any domain 0, assigns appropriate denotations over 0 to the non-logical constants (propositional constants, individual constants and predicate constants) and individual variables of C. We now allow the denotation of an n-place predicate constant P of C to be a class of n-tuples of elements in O. The notions of an interpretation and an assignment are adjusted accordingly. Hence, we allow models (0,1 0 ) for the base language Co, where o is a class and 10 assigns appropriate classes to the non-logical predicate constants of C. Thus, Kanger models now have the form 9Jl = (0, {(O, Io)}o~:v)' 6.3. Comparing the two approaches

We might now ask how validity with respect to the class-domain semantics is related to validity with respect to the set-domain semantics. If the language C has sufficient expressive capacity, neither implies the other. Let, for example, C' be the language which is obtained from our language C by adding the generalized quantifier (::labs infX) as a new logical constant. 19 The intuitive reading of (::labsinfX)rj> is for absolutely infinitely many x, c/>(x),

which means that the class of all objects a that satisfy rj>(x) is a proper class. The conception of the absolutely infinite is due to Cantor. Intuitively, a class A is absolutely infinite if it does not have exactly Ii elements for any cardinal number Ii (compare, A being infinite if it does not have exactly n members for any natural number n). Consider now the sentence (::labs infX)(X = x). This sentence is true in a domain 0 iff the domain is a proper class. According to the class-domain semantics, there are domains that are proper classes. So, according to this semantics the following sentence:

KANGER'S EARLY SEMANTICS FOR MODAL LOGIC

(1)

~ (::JabsinfX)(X

227

= x)

is true in e\'.ery domain (and for every valuation v). Hence, it is logically true according to the Kanger class-domain semantics. On the other hand, according to the Kanger set-domain semantics the sentence (:Jabs infX) (x = x) is false in every domain. Hence, according to this semantics, it is instead (2)

-, ~ (::Jabs infX)(X

= x)

that is a logical truth. Here we have a dramatic difference between the two semantic theories. Clearly, it is the class-domain semantics that yields the intuitively correct result in this case. Instead of adding the "artificial" quantifier (:Jabs infX) to 1:, we could instead have assumed that I: contained a modal operator D with the semantic clause: (0, v)

F 0

of C supervalid if it is true in every interpretation of C and valid if it is true in every (QS5=)-model (that is, if it is (QS5=)-valid)?2 We now make the following conjecture: The logical truths of the language [. of metaphysical necessity are precisely those sentences of [. that are supervalid.

Adapting an argument due to Kreisel (1969), we can prove that supervalidity coincides with validity for the language C. The argument goes as follows: Since Kripke (QS5=)-models are interpretations, we have: (I)

if rp is supervalid, then

rp is valid.

The completeness theorem for the system (QS5=) yields: (2)

if rp is valid, then rp is (QS5=)-provable.

However, the system (QS5=) is intuitively sound with respect to supervalidity. That is the axioms are easily seen to be supervalid and the only rule of inference, modus ponens, preserves supervalidity. Hence: (3)

if rp is (QS5=)-provable, then

rp is supervalid.

(2) together with (3) yield: (4)

if rp is valid, then

rp is supervalid.

Hence, the notions of validity and supervalidity are co extensional for the language C. From this together with the conjecture, we conclude that (QS5=) is the first-order logic of metaphysical necessity.23 7.2. Logical necessity

An (interpreted) sentence 1> is metaphysically necessary if it is true in every possible world. It is logically necessary if it is true for every domain and every interpretation of its non-logical symbols. Given a certain conception of modal reality, I have argued that Kripke's (1963a) semantics for quantified S5 adequately captures the logic of metaphysical necessity. This means that the logic of metaphysical necessity is relatively meager. Although there are, on the Kripkean metaphysical picture, a wealth of metaphysically necessary truths, only a few of them are also logically necessary. For example, if the axioms of Zermelo-Fraenkel set theory are true, they are presumably true in all possible worlds, and hence metaphysically necessary. But they are not truths of logic, not even of the logic of metaphysical necessity.

230

STEN LINDSTROM

Consider now the sentences saying that there are at least n(n ?: 1) individuals: (n)

i- X2 /\ ... /\ Xl i- Xn /\ X2 i- X3 /\ ... i- Xn /\ ... /\ Xn-l i- Xn).

:JXl .•• :JXn (Xl . .. /\ X2

Each of these sentences is presumably metaphysically necessary. So for each positive n, the following is a truth of metaphysics: (1M] n)

i- X2 /\ ... /\ XI i- Xn /\ X2 i- X3 /\ ... i- Xn /\ ... /\ Xn-I i- xn).

1M] :JXl ... :JXn(Xl . .. /\ X2

It is, of course, not a logical truth. We do not have for any n ?: 1,24

F (QS5=) 1M] :JXl •.. :JXn(Xl i- x2 /\ ... /\ XI i- xn /\ x2 i- x3 /\ ... /\ X2

i- xn /\ ... /\ xn-I i- xn).

Nor do we have for any n,

F (QS5=) /\ X2

~:JXI ... :Jxn (XI i- x2 /\ ... /\ Xl i- Xn /\ X2 i- X3 /\ ... i- Xn /\ ... /\ Xn-I i- Xn).

In sharp contrast to this, Kanger's semantics for logical necessity validates every instance of

F ¢:JXI ... :JXn(XI i- X2/\···/\ XI i- Xn /\ X2 i- X3/\··· /\ X2

i- Xn /\ ... /\ Xn-l i- xn).

This is as I think it should be. It is a logical truth that it is logically possible that there are at least n objects. When comparing Kanger's semantics for modal logic with Kripke's we come to the conclusion that the former (at least in its class-domain version) is adequate for the notion oflogical necessity, while the latter adequately captures a form of metaphysical necessity. Neither semantics can handle adequately the notion that is captured by the other. To devise a semantics that can treat both notions is a challenge that still remains to be met. As we have seen, Kanger's model-theoretic semantics for quantified modal logic differs in many respects from modern possible worlds semantics. However, it raises sufficiently many questions both of a technical and of a philosophical kind to motivate an interest that is not merely historical. Department of Philosophy Umea University

KANGER'S EARLY SEMANTICS FOR MODAL LOGIC

231

NOTES At the 9th International Congress of Logic, Methodology and Philosophy of Science. See F Iilllesdal (1994). 2 Actually Carnap's state descriptions are sets of literals (i.e., either atomic sentences or negated atomic sentences) that contain for each atomic sentence either it or its negation. However, for our purposes we may identify a state description with the set of atomic sentences that it contains. Also, in order to make things simple, I am not discussing here Carnap's treatment of identity statements. 3 On p. 39 in (1957a) Kanger makes an explicit reference to Jonsson and Tarski (1951). 4 Montague (1960) writes: "The present paper was delivered before the Annual Spring Conference in Philosophy at the University of California, Los Angeles, in May, 1955. It contains no results of any great technical interest; I therefore did not initially plan to publish it. But some closely analogous, though not identical, ideas have recently been announced by Kanger [(I 957b)], [(l957c)] and by Kripke in [(1959)]. In view of this fact, together with the possibility of stimulating further research, it now seems not wholly inappropriate to publish my early contribution." 5 We are not going to consider languages that contain function symbols. 6 Here we ignore the possibility of D not being a set but a proper class and I not assigning sets but proper classes as extensions to the predicate symbols of C. If this were the case, then the intended interpretation of C would not be a model in the formal sense of model theory. Of course, there are interpreted first-order languages whose intended interpretations are not models in the formal sense, the first-order language of set theory, with the proper class V of all sets as its domain and the proper class {< x, y >: x is member of y} as the interpretation of 'E'. This opens up the possibility for a sentence of an interpreted formal language of being true although it may be false in all models in the sense of model theory. This possibility is precluded for first-order languages, by the LowenheimSkolem theorem: the truth of implies its consistency (by the intuitive soundness of first-order logic), which in turn, by the Lowenheim-Skolem theorem, implies having a (countable) model. But for formal languages that are able to express such notions as 'there is a proper class of x's such that ' the implication: (I)

if is true, then is true in some model (which is built up from sets).

fails. Let, for example, be the sentence "there is a proper class of x's such that x = x". This example is due to McGee (1992). 7 Cf. Kripke (1959, 1963) and Hintikka (1957a, 1957b, 1961). 8 For the standard-non-standard distinction, see also Cocchiarella (1975). 9 See, for example, Hintikka (1969). 10 We leave it open, for the time being, exactly what is meant by a (semantic) interpretation. II Kanger (1970), p. 49. 12 Kanger (1957b), p. 4. Cf. also Kanger (1970), p. 50. 13 Kanger uses the notation T(D, v, f= [g] and he speaks of the operation Twhich, for every domain D, every primary valuation v and every sentence , assigns one of the truth-values 0 or I to as the secondary valuation for C. 14 Actually he uses valuations here, but since the assignment of values to the variables is immaterial in this context it is more natural to work with interpretations. 15 Cf. Kanger (l957b), p. 4. 16 Kanger (1957b) uses the terminology "standard usage of C" instead of "intended interpretation ofe". 17 Here our terminology differs slightly from Kanger's. Our ontological operators correspond to what Kanger calls purely ontological operators. Cf. Kanger (1957a) p. 34. 18 In his definitions Kanger speaks of "classes' rather than "sets", but this terminological difference is inessential, since he does not make any distinctions within the category of all classes but rather treats all classes that he speaks of as genuine objects that can be members of other classes. 19 I have taken the quantifier (3 a bsinfX) from McGee (1992), where he uses it to show that there are interpreted formal languages for which the equivalence: (M) is logically true iff is true in every model (in the standard model-theoretic sense of "model" according to which models are sets).

232

STEN LINDSTROM

fails. He considers the language of set-theory with (:labs infX) added to it. The sentence (:labsinfX)(X = x) is then an example of a true sentence which is not true in any model (whose domain is a set). So if (M) were correct then ,(:labs infX) (x = X) would be an example of a false but logically true sentence. But there are of course no such sentences, so the equivalence (M) cannot hold in general. 20 If we are considering languages that are sufficiently strong in expressive power, then Kripke's model-theoretic semantics is not sufficient to capture the notions of metaphysical necessity and possibility. Consider, for example, the sentence: (*)

IMI (:labs infX)(X = X)

This sentence is presumably true in the intended interpretation. However, there is no Kripke model structure where it is true. 21 To be exact, we let QS5= by the system of free (i.e., 'free' of existential assumptions) modal predicate logic which is defined as follows. Axioms: (I) Any substitution instance of a theorem of propositional S5. (2) 'Ix¢! 1\ :ly(t = y) - t ¢!(t/x), provided that t is an individual constant or a variable that is free for x in ¢!. (3) Vx(¢! -t,p) - t ('Ix¢! - t Vx,p). (4) 'Ix¢! ¢!, provided x is not free in ¢!. (5) Vx:ly(y = x). (6) t = t. (7) t = tf - t (eb(t/x) - t ¢!(t' Ix)~, provided that t is an individual constant or a variable that is free for x in ¢!. Deduction rules: (MP) If ~ eb and ~ ¢! - t ,p, then ~,p. (Nec) If ~ ¢!, then ~ D¢!. (UG) If ~ eb, then ~ 'Ix¢!. Cf. Garson (1984) and Hughes and Cresswell (1996), chap. 16-17, where the this and similar systems are formulated and proved to be complete with respect to Kripke's (l963a) semantics (these are the systems that Garson refer to as

gIR).

The term "supervalidity" is due to Boolos (1985). The concept itself goes back to Kreisel (I 969). Here, we have, of course, presupposed Kripke's picture of metaphysical reality. Given another picture, for example that of Lewis (1985), we get a different logic of metaphysical necessity (but still a form of quantified S5). 24 Kripke's (1963) semantics allows the domains of quantification to be empty. 2

23

REFERENCES Barcan, (Marcus), R.: 1946a, 'A Functional Calculus of First Order Based on Strict Implication', The Journal of Symbolic Logic, 11, 1-16. Barcan, (Marcus), R.: 1946b, 'The Deduction Theorem in a Functional Calculus of First Order Based on Strict Implication', The Journal of Symbolic Logic, 11,115-118. Barcan, (Marcus), R.: 1947, 'The Identity of Individuals in a Strict Functional Calculus of Second Order', The Journal of Symbolic Logic, 12, 12-15. Boolos, G.: 1985, 'Nominalist Platonism', The Philosophical Review, XCIV(3), 327-344. Carnap, R.: 1946, 'Modalities and Quantification', The Journal of Symbolic Logic, 11, 33-64. Carnap, R.: 1947, Meaning and Necessity: A Study in Semantics and Modal Logic. University of Chicago Press, Chicago. Second edition with supplements, 1956. Cocchiarella, N.: 1975, 'On the Primary and Secondary Semantics of Logical Necessity', Journal of Philosophical Logic, 4, 13-27. Etchemendy, 1.: 1990, The Concept of Logical Consequence. Harvard University Press, Cambridge, Massachusetts. Follesdal, D.: 1994, 'Stig Kanger in Memoriam', in D. Prawitz and Westerstilhl, D. (eds), Logic, Methodology and Philosophy of Science, IX, 885-888. Elsevier, Amsterdam. Garson, 1.w.: 1984, 'Quantification in Modal Logic', in D. Gabbay and Guenthener, F. (eds), Handbook of Philosophical Logic, II, 249-307. D. Reidel, Dordrecht. Hintikka,1.: 1957a, 'Quantifiers in Deontic Logic', Societas Scientiarum Fennica, Commentationes humanarium lifterarum, 23(4). Hintikka, 1.: I 957b, 'Modality as Referential Multiplicity', Ajatus, 20, 49-64. Hintikka, 1.: 1961, 'Modality and Quantification', Theoria, 27, 110-128. Hintikka, 1.: 1969, 'Semantics for Propositional Attitudes', in 1.W. Davies et al. (eds), Philosophical Logic, 21-45. D. Reidel, Dordrecht. Reprinted in 1. Hintikka, Modelsfor Modalities. D. Reidel,

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Dordrecht, 1969; and in L. Linsky (ed), Reference and Modality. Oxford University Press, London, 1971. Hintikka, J.: 1980, 'Standard vs. Nonstandard Logic: Higher-Order, Modal, and First-Order Logics', in E. Agazzi (ed), Modern Logic - A Survey. D. Reidel, Dordrecht, 283-296. Hintikka, 1.: 1989, 'Is Alethic Modal Logic Possible?', in 1. Hintikka and M.B. Hintikka (eds), The Logic of Epistemology and the Epistemology of Logic. Kluwer, Dordrecht. Hughes, G.E. and M.1. Cresswell.: 1996, A New Introduction to Modal Logic. Routledge, London and New York. Jonsson, B. and A. Tarski.: 1951, 'Boolean Algebras with Operators', American Journal of Mathematics, 73, 891-939; 74, 127-162. Kanger, S.: 1957a, Provability in Logic, Acta Universitatis Stockholmiensis, Stockholm Studies in Philosophy 1, Almqvist and Wiksell, Stockholm. Kanger, S.: 1957b, 'The Morning Star Paradox', Theoria, 23, 1-11. Kanger, S.: 1957c, 'A Note on Quantification and Modalities', Theoria, 23,133-134. Kanger, S.: 1957d, 'On the Characterization of Modalities', Theoria, 23,152-155. Kanger, S.: 1970, New Foundationsfor Ethical Theory, in Hilpinen (ed.), Deontic Logic: Introductory and Systematic Readings, Reidel, 36-58. Earlier mimeographed version: New Foundations for Ethical Theory, Part 1, Stockholm, 1957. Kanger, S.: 19972, 'Law and Logic', Theoria, 38, 105-132. Kaplan, D.: 1986, 'Opacity', in Hahn and Schilpp (eds), The Philosophy of wv. Quine, The Library of Living Philosophers, Vol. XVIII, Open Court, La Salle, Illinois. Kleene, S.c.: 1967, Mathematical Logic, John Wiley & Sons Inc., New York. Kreisel, G.: 1969, 'Informal Rigour and Completeness Proofs', in I. Lakatos (ed), Problems in the Philosophy of Mathematics. North-Holland, Amsterdam. Kripke, S.: 1959, 'A Completeness Theorem in Modal Logic', The Journal of Symbolic Logic, 24, 114. Kripke, S.: 1963a, 'Semantical Considerations on Modal Logic', Acta Philosophica Fennica, fasc. 16, Helsinki, 83-94. Kripke, S.: 1963b, 'Semantical Analysis of Modal Logic I, Normal Propositional Calculi', Zeitschriftfur Mathematische Logic und Grundlagen der Mathematik, 9, 67-96. Kripke, S.: 1965, 'Semantical Analysis of Modal Logic II, Non-Normal Propositional Calculi', in I.W. Addison, L. Henkin and A. Tarski (eds), The Theory of Models. North Holland, Amsterdam, 206-220. Kripke, S.: 1980, Naming and Necessity. Basil Blackwell, Oxford. Lewis, D.: 1985, On the Plurality of Worlds. Basil Blackwell, Oxford. Lindstrom, S.: 1996, 'Modality Without Worlds: Kanger's Early Semantics for Modal Logic', in Odds and Ends, Philosophical Essays Dedicated to Wlodek Rabinowicz on the Occasion of His Fiftieth Birthday, Uppsala Philosophical Studies, 45, Department of Philosophy, Uppsala University. McGee, V.: 1992, 'Two Problems with Tarski's Theory of Consequence', Proceedings of the Aristotelian Society, new series, 92, 273-292. Montague, R.: 1960, 'Logical Necessity, Physical Necessity, Ethics and Quantifiers', Inquiry, 4, 259269. Reprinted in R. Thomason (ed), Formal Philosophy: Selected Papers of Richard Montague. Yale University Press, New Haven and London, 1974. Quine, W. Y.: 1947, 'The Problem of Interpreting Modal Logic', The Journal of Symbolic Logic, 12, 43-48. Tarski, A.: 1936, 'Uber den Begriff der logischen Folgerung', Actes du Congres International de Philosophie Scientifique, 7, I-II. (English translation: 'On the Concept of Logical Consequence', 409--420 in Logic, Semantics, Metamathematics, second edition, Hackett Indianapolis, 1983).

QUENTIN SMITH

A MORE COMPREHENSIVE HISTORY OF THE NEW THEORY OF REFERENCE

1. INTRODUCTION

This essay continues the effort of some previous essays to present a more accurate history of the origins of the New Theory of Reference. The "New Theory of Reference" is typically used by philosophers in different ways; for example, sometimes it is used to refer to a theory that essentially includes the historical chain theory of reference. But the consequence of this is that Kaplan, Perry, Salmon, Marcus, Wettstein, Almog and many others commonly identified with this theory are excluded. The "New Theory of Reference", which is used as a name or referentially used definite description, can be used to refer to many different ideas and in this essay I use it in the following narrow and broad senses. If the New Theory of Reference is defined in a narrow sense so that it includes all or virtually all of the philosophers who are standardly associated with this theory, then we may say someone is a New Theorist of Reference if and only if he or she presented an argument against the Frege-Russellian descriptivism that was the orthodox theory in the 1950s and early 1960s and replaced this descriptivism by a historical chain or direct reference theory (and perhaps an associated doctrine of singular propositions). There are many other ideas commonly associated with the New Theory of Reference, even though all of the New Theorists in the narrow sense do not subscribe to all of these ideas. These ideas include the notions of rigid designation, a posteriori necessity and metaphysical necessity, as well as other ideas. In this paper, I shall study contributions to the "New Theory of Reference" in the broad sense that includes these associated ideas. Someone contributes to or in some respect is a New Theorist of Reference in the broad sense if and only if she or he rejected some of the "Frege-Russell tradition" that was orthodoxy in the 1950s and early 1960s and argued for two or more of the following positions: (i) the idea that names are not disguised, contingent definite descriptions but are directly referential or refer by means of a historical chain, (ii) the idea that names are rigid designators and contingent definite descriptions are nonrigid designators, (iii) the distinction between logical and metaphysical necessity and (iv) the distinction between the necessary / contingent contrast and the a priori/a posteriori contrast.

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This system of classification enables us to consider the highly relevant ideas of philosophers who sometimes are not associated with the New Theory of Reference, such as Plantinga, the early Hintikka, Cocchiarella, F011esdal and others. A large number of later contributors may also be included, such as Graeme Forbes [1985; 1989] and Stephen Yablo [1992], and most of the philosophers of religion who write in the Plantingian tradition. Indeed, this classification would imply (correctly) that the New Theory of Reference is so widespread that a large number, if not most, analytic philosophers in the 1990s can be considered as contributing or belonging in some respects to this philosophical tradition. The use of this broad sense of "New Theory of Reference" is combined with talk of someone contributing to the New Theory or being in some respect a New Theorist of Reference, as distinct from the unqualified statement that someone is a New Theorist of Reference. For example, a philosopher may argue there are a posteriori necessities and metaphysical necessities and yet hold that names are disguised, contingent descriptions. It would be natural to say that such a philosopher is not a New Theorist of Reference in the narrow sense, but nonetheless made some contributions to the New Theory of Reference understood in the broader sense. The basic problem with the standard history of the New Theory of Reference (in the broad sense I am discussing in this essay) is the failure to make an adequate distinction between originators and developers of the basic ideas. The first wave of developers (mainly Kaplan, Donnellan, Kripke and Putnam) are mistakenly thought to be the originators of the ideas, who in fact include mainly Marcus, F0llesdal, Hintikka, Plantinga and Geach. These two groups need to be distinguished from the second wave of developers, who include Michael Devitt, Nathan Salmon, Howard Wettstein, John Perry, Joseph Almog, and many others. In previous essays, I largely concentrated on two of the originators (Marcus and Geach) and three of the members of the first wave of developers (Kripke, Donnellan and Kaplan), but in the present essay I will discuss more or less equally several philosophers who belong to the class of originators - Marcus, Plantinga, Hintikka, Geach, F0llesdal and some others. I will also discuss Kripke's main unknown contribution, his 1962 theory of descriptionally rigid proper names, and Cocchiarella's contribution to the logical/metaphysical distinction. But first we need to understand what it means to "originate" an idea in the New Theory of Reference. 2. DIRECT REFERENCE, SINGULAR PROPOSITIONS, A POSTERIORI NECESSITY, ETC., IN MOORE'S 1899 ESSAY "THE NATURE OF JUDGMENT"

One might say that British analytic philosophy began in August 1898 in a letter that Moore wrote to Desmond MacCarthy, in which Moore announced: "I have arrived at a perfectly staggering doctrine ...". [Moore, 1898]. This (eds.),

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staggering doctrine was an early version of some of the basic ideas in the New Theory of Reference that emerged in the late 1950s, 1960s and has been widely prevalent since the 1970s. This doctrine was first published in Moore's 1899 essay, "The Nature of Judgement", the first bona fide publication of British analytic philosophy, in which he laid out his theory of direct reference, singular propositions that include concrete objects as parts, a posteriori necessities, and other ideas that (in one version or another) later formed the foundation of the New Theory of Reference. The fact that the first publication in AngloAmerican analytic philosophy included an early version of many ideas in the New Theory of Reference is not widely known and it is worth explaining some of Moore's basic notions. Moore considers reality to be composed of (mind-independent) concepts; Moore uses "concept" to mean a universal; he holds a bundle theory of objects and that we directly refer to these objects (bundles of concepts) and their parts in our language. The concrete universe of stones, flowers and humans is made up of concepts and nothing more. Some sentences express propositions that consist of these concepts; these propositions are the analogues of what we today call "singular propositions" or "de re propositions". Two main aims of Moore's article is to reject the descriptivist theory of reference of Bradley and others and replace it with a theory of direct reference and singular propositions, and to reject the Kantian tradition that held all logical necessities are a priori and to replace this with a theory that some logical necessities are a posteriori. Some passages convey Moore's theory of direct reference and singular propositions: "When, therefore, I say 'This rose is red', I am not attributing part of the content of my idea to the rose, nor yet attributing part of the content of my ideas of rose and red together to some third subject. What I am asserting is a specific connexion of certain concepts forming the total concept [the concrete thing] 'rose' with the concepts 'this' and 'now' and 'red'; and the judgment is true if such a connexion is existent ... If the judgment is false, that is not because my ideas do not correspond to reality, but because such a conjunction of concepts is not to be found among existents ... A proposition is composed not of words, nor yet of thoughts, but of concepts ... All that exists is thus composed of concepts ... It seems necessary, then, to regard the world as formed of concepts" [1899: 179-182]. Moore also has a theory of a posteriori logical necessities. Moore considers existential propositions, e.g., Red exists, to be a posteriori and yet necessary. He argues that they are not a priori but nonetheless have the essential mark that Kant assigned to a priori propositions, namely, necessity. An existential and empirical proposition asserts that a simple concept exists in time. These propositions are a posteriori and "perception is to be regarded philosophically as the cognition of an existential proposition" [1899: 183]. Furthermore, "a simple concept cannot be known as one which could exist in time, except on the ground that it has so existed, is existing, or will exist. But we have now to point (eds.),

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out that even existential propositions have the essential mark which Kant assigns to a priori propositions - that they are absolutely necessity". [1899: 189, my italics]. If I assert that Red exists, I mean Red exists now, and "this connexion of red and existence with the moment of time I mean by 'now', would seem to be as necessary as any other connexion whatever. If it is true [which is discoverable by sense perception], it is necessarily true, and if false, necessarily false. If it is true, its contradictory is as fully impossible as the contradictory of2 + 2 = 4". [1899: 190, my emphases]. Accordingly, in the case of some propositions "there would seem no doubt that we mean by it [the proposition] to assert an absolute necessity; but between what precise concepts the necessary relation, of which we are certain, holds, we must leave to experience to discover". [1899: 188]. Since a theory of direct reference, singular propositions and a posteriori necessities appeared in the very first publication of Anglo-American analytic philosophy, the "excitement" expressed by some philosophers over the apparent novelty of ideas of this sort when they become popular in the 1970s may seem to some historians of philosophy to be a trifle ironic or misplaced. The specific versions of the 1960s-1990s theories of direct reference, singular propositions, a posteriori necessities, etc., differed from Moore's [1899], but the general ideas are significantly similar. Some philosophers correctly trace the general idea of directly referential ordinary names and singular propositions back to Russell's [1903], where a somewhat different and considerably more developed account is given than in Moore's [1899]; but the first statement of ideas of this general sort appears in Moore's earlier work, whose influence Russell acknowledged [1903: xviii]. However, in Russell's [1903] we already see the eclipse of some of Moore's anticipations of the New Theory of Reference, such as Moore's theory that there are a posteriori necessities, and in this respect as well Moore's [1899] may be seen as the most important precursor to the later works of the New Theorists of Reference. In 1903 Moore expanded on these ideas to include the distinction among physical necessity, metaphysical necessity and logical necessity. In Moore's [1903: 29] he says the existence of a natural part is a necessary condition for the existence of the good which is constituted by the whole. It is not "merely a natural or causal necessity" [1903: 29]. And yet the relation is synthetic, not analytic, and hence is not a logical necessity [1903: 7, 33]. The synthetic necessities are about what can or "cannot conceivably exist" [1903: 29]; they are metaphysical necessities, and the word "conceivably" is used in Kripke's [1959], Plantinga's [1970], Putnam's [1975] and Yablo's [1992] sense, as a less misleading term than "modal intuitions", which achieved a widespread use in the 1970s. This early appearance of ideas that would be revived in various forms in the late 1950s and 1960s was soon overshadowed by the appearance of Russell's 1905 article "On Denoting". This article initiated the eventual downfall of the "early" or "Moorian" version of the New Theory of Reference and its (eds.),

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replacement by (i) a descriptional theory of ordinary names, (ii) a restriction of directly referential names to demonstrative words in my private language for my sense data (foreshadowed in the second paragraph of "On Denoting"), (iii) an equation of necessity with the linguistically analytic and a priori, (iv) the theory that general rather than singular propositions are stated by sentences with ordinary names, (v) and the elimination of a "metaphysical necessity" that was broader than logical necessity and narrower than physical necessity. All or most of these ideas (or some variant upon them) became the orthodox theory up until the 1960s. This orthodoxy is often referred to as "the Frege-Russell tradition", which is an acceptable practice as long as this phrase is used as a name or referentially used definite description. (It needs to be kept in mind that Frege and Russell did not both hold all these doctrines and Frege's and Russell's theories are incompatible on some major points.) An early exception to this orthodoxy is Wittgenstein's [1922]. Wittgenstein [1922] anticipated the New Theory of Reference to a more significant extent than other logical atomists. He held that names directly refer to objects, that elementary sentences express singular propositions, and that names are rigid designators in that they refer to an object as it exists in each possible world (or state of affairs). Wittgenstein argued that these semantic facts are implied by the underlying structure of any logically possible language (disguised by what is used as "ordinary language"). The above considerations suggest that a point needs to be made about what "introducing an idea into the New Theory of Reference" means. This does not imply being original in the absolute sense, i.e., being the first person to discover or entertain or believe or write about the idea. It has been repeated many times since the early 1970s that the direct reference theory of proper names can be traced back to Mill, although it is rarely noted that this theory can also be found in Hume, Ockham, Plato and Parmenides, to name but a few others. Likewise, the nonequivalence of the a priori/a posteriori and the necessity/ contingent distinction is no more "new" than is the direct reference theory. This distinction was widespread in the scholastic period, with Aquinas and others arguing that some necessary truths (e.g., that God exists) are a posteriori. Some of Aristotle's metaphysical necessities, statements about natural kinds, are a posteriori and Plato argued that certain necessary relations between Forms are a posteriori. Virtually none of the main ideas in the New Theory of Reference are "original" in this absolute sense. Being "original" in the relative sense of introducing an idea or argument into the New Theory of Reference means this: being the first to put forth an argument against the "Frege-Russell orthodoxy" that remained predominant up until at least the 1950s and replacing a part of this tradition with one of the ideas or arguments that are associated with the New Theory of Reference (even if the idea or argument was previously presented by Parmenides, Aristotle, Locke, Aquinas, or others). Accordingly, the question we are addressing in the history of philosophy is this: What ideas and arguments were put forth that led (eds.),

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to the demise of the Frege-Russell tradition and the emergence of the New Theory of Reference in the late 1950s and 1960s (which then led to the New Theory's elaboration and wide acceptance in the 1970s)? 3. QUANTIFYING INTO MODAL CONTEXTS: 1918-1960

The New Theory of Reference is a theory about natural language, but an account of its origins requires us to discuss theories of logical languages, specifically, the languages used in interpretations of quantified modal logic. A syntactics for propositional modal logic appeared in c.l. Lewis' [1918] and a syntactics for quantified modal logic first appeared in 1946 with Marcus' [1946] and (two months later) in Carnap's [1946]. An interpretation or semantics for modal logic first appeared in Carnap's [1946] and [1947]. The key idea of Carnap's semantics is that the interpretation of "OA" was based on the Leibnizian idea that necessary truth is truth in all possible worlds (what Carnap called "state descriptions'); thus "OA" means A is true in all possible worlds (in all state descriptions). A state description is a maximally consistent set of atomic sentences. It is a logically consistent set W of sentences, such that for each atomic sentence S, either S is a member of the set W or the negation of S is a member of the set W. The route from logical languages to natural language followed a path started by Quine in 1941, in a footnote to an article he contributed to Schilpp's The Philosophy of Whitehead. Here Quine first stated his famous "paradox" about quantified modal logic. It is not widely known that Quine first started this paradox in 1941, four years before modal logic was first quantified by Marcus. This paradox is often traced back to a later writing of Quine, his [1947] or sometimes his [1943]. The paradox as it originally appears in Quine's [1941: 142, n. 26] comprises two sentences offootnote 26: "c.1. Lewis and C.H. Langford (Symbolic Logic, New York, 1932), e.g., use a non-truth-functional operator '~' to express logical possibility. Thus the statements: ~

(the number of planets in the solar system < 7)

~

(9

< 7)

would be judged as true and false respectively, despite the fact that they are interconvertible by interchanging the terms '9' and 'the number of planets in the solar system', both of which designate the same object."

If it were not for this footnote (which led to Quine's later restatements of the paradox) and the responses to this paradox, it is doubtful that the New Theory of Reference would have been developed. The traditional form of the paradox in virtually all later discussions is taken from Quine's [1947: 47] formulation, where "C" means congruence (which may be the relation of identity, but Quine does not wish to prejudge that):

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"Morning Star C Evening Star· D (Morning Star C Morning Star).

Therefore, according to (ii) ['An existential quantification holds if there is a constant whose substitution for the variable of quantification would render the matrix true']: (I) (:Jx) (x C Evening Star· D (x C Morning Star)).

But also: Evening Star C Evening Star . ~ D (Evening Star C Morning Star),

so that, by (ii) (2) (:Jx) (x C Evening Star . ~ D (x C Morning Star))."

Since (1) and (2) are mutual contraries, we have a paradox. Before we consider the first relevant response, Smullyan's in 1947, one other idea needs to be introduced which proved crucial for the New Theory of Reference. In his [1943] Quine discusses but rejects a principle of universal intersubstitutivity: "Given a true statement of identity, one of its two terms may be substituted for the other in any true statement and the result will be true". [1943: 113]. This statement may appear to be natural or plausible, given the indiscernability of identicals. If two individuals x and yare identical, they are indiscernible; this may suggest the idea that singular terms for x and y should be intersubstitutable in any context, including modal, temporal, deontic, epistemic and other intensional contexts. But Quine argues that singular terms are not intersubstitutable in modal and epistemic contexts. The idea that singular terms, most notably names, are always "purely designative" was associated with this universal intersubstitutivity thesis. Quine also rejects this idea: "Failure of substitutivity [in modal and epistemic contexts] reveals merely that the occurrence to be supplanted is not purely designative, and that the statement depends not only upon the object but on the form of the name". [1943: 114] Quine holds that names have a meaning ("criterion of application") in addition to their designative feature, and that the meaning, not just the designation, is relevant to modal and epistemic contexts. By rejecting the universal intersubstitutivity thesis and the associated thesis that names do not have a meaning but instead are purely designative, Quine has to mention these theses and make an issue about whether they are plausible, and his discussion of these theses was a motivating factor in the future discussions that led to the New Theory of Reference. (The impression should not be given that the conception of the universal intersubstitutivity thesis is "original" with Quine. This thesis has been regularly propounded or discussed throughout the history of philosophy, and can be traced at least as far back as Aristotle's Topics vii, I. The point is that Quine drew attention to it in a way that proved influential. The association of an intersubstitutivity thesis with the "purely designative" thesis became a central element of the New Theory of Reference that was not present in Moore's early theory.) (eds.),

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The theory Quine rejected (or rather, one largely similar to it) is also mentioned and rejected four years later, in Carnap's Meaning and Necessity; Carnap calls the theory "the name-relation method". Carnap writes [1947: 98] that the name-relation method is based on three principles (the numbers in brackets are my insertions) and is meant to apply to an artificial or logical language: " [I] Every expression used as a name (in a certain context) is the name of exactly one entity; we call it the nominatum of the expression ... [2] A sentence is about (deals with. includes in its subject matter) the nominata of the names occurring in it. [3] The principle of interchangeability (or substitutivity). This principle occurs in either of two forms: [3a] If two expressions name the same entity ... the two expressions are interchangeable (everywhere). [3b] If an identity sentence ['... is identical with - - -'] is true, then the two argument expressions ' .. .' and' - - -' are interchangeable (everywhere)."

Carnap rejects this name-relation method for several reasons, including the reason that expressions that name the same entity are not always intersubstitutable in modal contexts. The second relevant event in 1947 is Smullyan's innovative use of the "purely designative" and "substitutivity" theses in modal contexts to respond to Quine's paradox. Smullyan is responding to Quine's [1947], in which Quine's point is that "when modal logic is extended (as by Miss Barcan) to include quantification theory ... serious obstacles to interpretation are encountered". [Quine, 1947: 43-48]. Smullyan suggests two ways for interpreting quantified modal logic, each of which is able to resolve Quine's paradox; but only the first way is pertinent to the New Theory of Reference. This solution appears in the third sentence in this passage: "It is possible that by 'constant' is meant what is commonly understood by 'proper name'. Under this interpretation it appears evident to this reviewer that the principle of existential generalization is true. However, we observe that if 'Evening Star' and 'Morning Star' proper-name the same individual they are synonymous and therefore B is false." [Smullyan, 1947: 140]

B is the premise: Evening Star is congruent with Evening Star . rv D Evening Star is congruent with Morning Star. Smullyan's theory has been subjected to many mis-interpretations in recent years, including one of my previous discussions of his theory,l and consequently it is worth quoting enough material from his brief review (which is two and one-half pages in length) to provide sufficient textual evidence for a correct interpretation. In the abovequoted phrase, "what is commonly understood by 'proper name"', Smullyan is not referring to ordinary proper names, but to what philosophers of logic of that time commonly understood as proper names, i.e., proper names in Russell's sense (Russell's logically proper names, "this" and "that", which directly refer to my sense data). Smullyan characterizes his response to Quine's charge of contradiction as a response that employs Russell's theory of descriptions and proper names: "We have seen that in terms of Russell's theory ofdescriptions and proper names this contradiction can be avoided". [1947: 141;

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my italics]. Smullyan's employment of Russell's theory of logically proper names (as distinct from Mill's theory of ordinary proper names) in his first response to Quine was later noted by Prior [1967: 10-11] and others. Smullyan's second and preferred way of responding to Quine, in terms of Russell's theory of descriptions, is that the necessity of identity thesis for individuals is false, which is an implication of the following sentence, the crux of his second response: "For if it is not necessary that the morning star exists then it is not necessary that the morning star is self-congruent" [1947: 140]. This is a rejection of one of the premises of Quine's paradox, viz., "0 (Morning Star is congruent with Morning Star)". Smullyan is talking about artificial (formal or logical) languages (specifically, about artificial languages suitable for interpreting quantified modal logic), rather than natural or ordinary language. For this reason, Russell's argument that in ordinary language, expressions such as "Evening Star" or "Hesperus" are not proper names but truncated descriptions is not pertinent to the discussion. In his artificial language, Smullyan is not required to use words in the way they are ordinarily used. But Smullyan does remark that the treatment of "Evening Star" or "Hesperus" as a logically proper name in modal contexts does not accord with ordinary language and therefore that this particular solution to Quine's paradox is disadvantaged relative to his second solution. He prefers the solution in terms of Russell's theory of the primary and secondary occurrences of definite descriptions, which accords more with ordinary language. Thus, Smullyan concludes his review by saying: "In the judgment of the reviewer, the complications to which Carnap and Church resort underscore certain advantages obtained by retaining Russell's treatment of descriptions with its associated doctrine concerning the primary and secondary occurrence of descriptive phases. This doctrine, as Carnap admits [1947: 140), has the advantage of being in close accord with ordinary usage. It also permits a logical theory which unifies the theory of quantification with that of modality in a manner which Quine believes impossible. However, in defense of Quine's skepticism, in the reviewer's opinion, there is not a scintilla of evidence." [1947: 141).

At the risk of belaboring this point, Smullyan is noting that one of his ways of resolving Quine's paradox in an artificial language has, as an added advantage to its logical validity, the feature of "being in close accord with ordinary use". Being in accordance with ordinary language is not a necessary condition o((but merely an added advantage for) a solution to Quine's paradox, since Smullyan takes the discussion to be about logical language used in an interpretation of quantified modal logic, not about ordinary language. Smullyan is also saying that this added advantage belongs to the resolution in terms of primary and secondary occurrences of descriptive phases, not to the resolution in terms of logically proper names, which reflects Smullyan's belief that names in ordinary languages are not directly referential. (Smullyan reaffirms his preference for a descriptional theory in his [1948]). Here we are still a long way from the Millian theory of ordinary proper names, the necessity of identity for Millian names, the intersubstitutivity of Millian names in modal contexts, the rigidity of (eds.),

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Millian names, etc., that first appear in Marcus' [1961]. The next pertinent year in the route to the New Theory of Reference is 1949, which features Frederick Fitch's "The Paradox of the Morning Star and Evening Star". Fitch, like Smullyan, is talking about a logical language; his aim is to show that "the modal logician is free to deal directly with actual individuals and to employ the relation of identity between them". [1949: 138]. Fitch is criticizing Quine's argument that if we are to use quantified modal logic we must follow Carnap and let our variables range over individual concepts. (Quine rejected individual concepts, but had argued the modal logician is committed to them.) Fitch restates Smullyan's two arguments, including the argument employing Russellian logically proper names, to solve Quine's paradox. Fitch adds a third argument, based on using Marcus' 1946 theorem of the necessity of identity and considerations of scope differences for descriptive phrases. Although this third argument is the main point of the article, the significance of the article for "the route to the New Theory of Reference" is that we find a second person (Marcus' dissertation advisor) endorsing the validity of using Russellian proper names in modal contexts in an artificial language to respond to Quine's paradox. Fitch's 1950 article on "Attribute and Class" is more important since we find him going beyond Smullyan and mentioning the full universal intersubstitutivity thesis that Quine and Carnap discussed and rejected. (Smullyan mentioned only intersubstitutivity in modal contexts.) Fitch first writes about the import of Marcus' 1947 article on "The Identity of Individuals in a Strict Functional Calculus of First Order" for the identity of entities: "the system of modal logic developed by Ruth Barcan suggests that the simplest view is that no identities should be regarded as merely contingent and that identified entities should be everywhere intersubstitutable. (Indeed, no entity is correctly identifiable with any entity but itself, so permission of substitution of this sort is trivial anyway". [1950: 552]. Fitch mixes ontological with semantic theses in these two sentences, but proceeds to formulate a specifically semantic thesis: "Furthermore, if entities X and Y have been identified with each other, it seems reasonable to suppose that the names of X and Y should also be everywhere intersubstitutable". [1950: 552]. Fitch, however, no more endorses this view that Smullyan endorses the thesis about Russellian names in modal contexts. Fitch immediately adds: "According to Church's view, on the other hand, two names of the same thing might differ in sense and so not be intersubstitutable". [1950: 552]. Fitch later mentions Carnap's view, and Smullyan's two responses to Quine's paradox in terms of Russellian proper names and descriptions, but Fitch does not commit himself to anyone of these views (the universal intersubstitutivity thesis, Smullyan's two responses to Quine, Church's view, and Carnap's view.) Fitch's general point is the same point made in his [1949] and in Smullyan's [1947] and [1948], namely, that there are many ways to respond to Quine's paradox about quantified logic and to construct a valid logic of this sort. (eds.),

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As least three steps need to be made to get from Smullyan's and Fitch's papers to the New Theory of Reference. First, somebody needs to endorse, and not merely mention as one of the many possible solutions to Quine's paradox, the thesis that names are directly referential and intersubstitutable in modal contexts. Second, somebody must start talking about natural language and ordinary names, and not merely about names in an artificial language used for purposes of interpreting quantified modal logic. Third, the names need to be conceived as Millian names (in the broad and familiar contemporary sense) rather than as Russellian logically proper names. The first step (endorsing the direct reference and substitutivity thesis) is taken in 1960 in an article by Marcus, "Extensionality" [1960] and at greater length by F0llesdal in his 1961 Harvard dissertation on Referential Opacity and Modal Logic. (For my chronology to be accurate, I should point out that between Fitch's [1950] and Marcus' [1960] there appeared Kanger's [1957b] and Hintikka's [1957a; 1957b], which contained more extensive and logically original solutions to Quine's paradox than Smullyan's and Fitch's relatively brief responses. I shall discuss Kanger's and Hintikka's work separately when I discuss the origination of the concept of a metaphysical [as distinct from logical] semantics for modal logic.) In Marcus' [1960], she continues in the tradition of talking about artificial or logical languages that are suitable for interpreting quantified modal logic. She sums up her paper as follows: "I have tried in this brief paper, to characterize the theory of extensionality, and to show that logical systems are more or less extensional" [1960: 62]. In a footnote [1960: 61, n. 2] Marcus sees herself as continuing in the Fitch (and thus Smullyan) tradition of stating that one of the ways to resolve Quine's paradox is to treat the relevant expressions as proper names, in which case there is intersubstitutivity. She writes about the sentence "It is necessary that the evening star is the evening star" and she says that if it "involves proper names of individuals then 'the evening star' may replace 'the morning star' without paradox ..." [1960: 61]. In Marcus' [1960], we do not see the reservations expressed by Smullyan and Fitch about the response to Quine that involves treating "evening star" as a proper name, and we do not find here any sympathy with Smullyan's and Fitch's suggestion that a solution in terms of definite descriptions may be preferable because of greater conformity with ordinary usage. Marcus views the "proper name" solution as provably valid, given her theorems about identity, indiscernability, weaker equivalences, and about the intersubstitutivity of expressions; she argues that the "proper name" solution follows from her theorems. But Marcus in this article has her attention only on the interpretation of logical systems, and is not concerned to make any claims about ordinary usage. Further, we have as yet no indication that she has in mind Millian names as distinct from the Russellian names that Fitch and Smullyan used, although the reference to Fitch suggests that she does not at this time see herself as departing from the theory of names employed in Fitch's and (eds.),

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Smullyan's articles. The "Big Leap" into the New Theory of Reference is made next year, in her "Modalities and Intensional Languages" [1961]. But first we will consider Dagfinn F011esdal's 1961 theory, which is the most fully developed formal analogue (a theory of the language used in interpretations of quantified modal logic) to the theory of natural language in the New Theory of Reference. 4. F0LLESDAL'S 1961 THEORY OF DIRECTLY REFERENTIAL RIGID DESIGNATORS

Smullyan [1947], Fitch [1949; 1950] and Marcus [1960] discussed some formal analogues in the language of quantified modal logic to the natural language counterparts in the New Theory of Reference. By 1961, the philosopher who presented the most extensive formal analogue to the New Theory of Reference was Dagfinn F011esdal in his 1961 Harvard doctoral dissertation, Referential Opacity and Modal Logic. This was later privately published with minor additions in [F011esdal, 1966]. F0llesdal originates or develops the theory that genuine singular terms are rigid, the universal intersubstitutivity thesis, the necessity of identity thesis, the difference between rigid names and nonrigid definite descriptions, the difference between rigid definite descriptions and rigid, non-descriptional names, the modally oriented characterization of proper names in terms of the notion of possible worlds, the notion of a weak rigid designator, the endorsement of essentialism, and other theses that place him squarely in the conceptual context of the New Theory of Reference rather than of that of the Frege-Russell tradition that circumscribed the limits of Smullyan's and Fitch's discussion. F011esdal's original solution to Quine'S paradox is to reject the assumption that singular and general terms have the same semantics and to argue that genuine singular terms are characterized by the fact that they exhibit rigidity. F011esdal's "genuine singular terms" include variables, pronouns, and "genuine names" in the broad sense, which include both proper names and necessary descriptions. Genuine singular terms are defined as having a stable or rigid reference in terms of the notions of the referential transparency and extensional opacity of a construction. Constructions are referentially transparent in that whatever is said to be true of an object is true of the object regardless of how it is referred to. They are extensionally opaque in that we cannot substitute coextensional general terms or sentences for one another in modal contexts. In modal contexts, genuine singular terms refer to the same object in each possible world (or each possible world in which the object exists) and are intersubstitutable. F0llesdal presents three possible solutions to Quine's paradox, depending on which terms in our language are rigid, only variables and pronouns, or also genuine names. The solution involving "genuine names" includes both rigid definite descriptions and rigid names that have no descriptive context. (eds.),

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F011esdal defends at greater length than previous writers (specifically Marcus [1960)) the universal intersubstitutivity thesis and the strong identity thesis.

F011esdal holds that the identity sign cannot be flanked by a contingent description but only by a genuine singular term (a rigid designator). F011esdal sees the universal intersubstitutivity thesis as belonging to the meaning of identity and as a necessary premise in the derivation of the necessity of identity. [1966: 111-112]. (As I mentioned, F011esdal privately reprinted his 1961 dissertation in [1966] with an added preface and small additions to sections with which I am not here discussing or quoting; I quote and refer to only the parts of his [1966] that are unchanged from his [1961)). F011esdal is also the first to present a defense of the universal substitutivity thesis in both epistemic and modal contexts. (For example, Marcus endorsed the universal substitutivity thesis, but defended it only against objections pertaining to modal contexts in her [1960], [1961] and [1963].) F011esdal argues that the unrestricted substitutivity of identity in modal contexts amounts to essentialism: "if an attribute is necessary of an object, it is necessary of an object regardless of the way in which the object is referred to". [1966: 120]. F011esdal here is referring to Quine'S idea that an attribute is necessary of an object only relative to a certain way of describing it, and that denying this is tantamount to affirming essentialism. At the time of this dissertation (1961), the discussions by Marcus [1961; 1967; 1971], Parsons [1969] and others of the distinctions between trivial and nontrivial essentialism had not yet been published and F 011esdal has in mind only nontrivial essentialism in his dissertation. F011esdal characterized proper names in his 1961 Harvard dissertation as follows: "This solution [the second solution to Quine's paradox] leads us to regard a word as a proper name of an object only if it refers to this one and the same object in all possible worlds". [1966: 96-97]. F011esdallater discusses the problem of possible worlds in which the object does not exist and introduced what later became called [Kripke, 1972] "weak rigid designators". F011esdal formulates the notion of a weak rigid designator in [1966: 124-134]. In this discussion, F011esdal becomes the first to propose a theory ofa varying domain semantics combined with a theory that names are rigid designators, which is the first time the conceptual distinction between strong and weak rigid designation is made. A weak rigid designator designates the same object in every world in which that object exists, and designates nothing in worlds in which that object does not exist. A strong rigid designator designates the same object in every world and the object exists in every world. But note that F011esdal's distinction is made in the context of discussing the language of quantified modal logic, and Kripke's distinction is instead made in the context of analyzing ordinary usage [Kripke, 1971; 1972]. Quine was F011esdal's dissertation advisor and was a professor at Harvard University when F011esdal was a graduate student and Kripke an undergraduate student at this university. Quine has maintained that F011esdal's (eds.),

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concept of genuine names in the broad sense is the same as Kripke's concept of rigid designators, even as late as [1994]. Quine writes in [1981: 118] about Kripke's rigid designators and F0llesdal's genuine names and genuine singular terms: "a term thus qualified is what F0llesdal called a genuine name and Kripke has called a rigid designator. It is a term such that (Ex)D(x = a), that is, something is necessarily, where 'a' stands for the term .... A rigid designator differs from others in that it picks out its object by its essential traits". In Quine's [1994: 148] he writes: " ... Hence Dagfinn FeJllesdal's genuine singular terms, or Saul Kripke's rigid designators. These are the terms that obey substitutivity of identity even in modal contexts ... As we might say in a modal spirit, these are the terms that name their objects necessarily". Quine appears to be basically correct in his characterization. For example, Kripke [1971: 145] writes: "What do I mean by 'rigid designator'? I mean a term that designates the same object in all possible worlds". F0llesdal says the same of his genuine singular terms. For example, he writes in 1961 of some of his genuine singular terms, proper names, that we "regard a word as a proper name of an object only if it refers to this one and the same object in all possible worlds. This does not seem unnatural'. [F011esdal, 1966: 97]. Although F011esdal's statements (e.g., "this does not seem unnatural") suggest that he believes his theory also applies to ordinary language, he does not engage in the ordinary language analysis of Kripke's [1971; 1972] and has his attention on the language of quantified modal logic. This is the most important difference between the two theories that Quine does not mention. Furthermore, Quine is mistaken in believing that Kripke's rigid designators and F011esdal's genuine singular terms always refer in a descriptional way, i.e., that such an expression always "picks out its objects by its essential traits". As is well-known, Kripke held that proper names are not descriptionally rigid in his [1971] and [1972]. And F011esdal writes in his 1961 dissertation that if a name-like word is nonrigid, it is descriptional, and that proper names do not contain descriptional elements: we regard "a word as a proper name of an object only if it refers to this one and the same object in all possible worlds. This does not seem unnatural. Neither does it seem preposterous to assume as we just did, that if a name-like word does not stick to one and the same object in all possible worlds, the word contains some descriptive element'. [1966: 97]. F011esdal's and Kripke's proper names refer nondescriptivally to the same object in all possible worlds. They differ in that F011esdal does not subscribe to the historical chain theory of reference [Geach, 1969], whereas Kripke does subscribe to this theory, which is the main difference between the two theories if they are both taken to characterize natural language. The idea of directly referential rigid names appears again in F011esdal's [1967] recapitulation of some of the basic ideas in his 1961 dissertation, and he writes about epistemically possible worlds that: "The fact that the expressions 'the man who comes towards me' and 'Coriscus' change their reference from world to world in this manner, should perhaps be taken as evidence that they (eds.),

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contain some descriptive element, and that they should therefore not be regarded as genuine names. The only descriptions that should be regarded as genuine names are those which keep the same descriptum in every epistemically possible world". [1967: 11-12]. In 1961, F011esdal regards "a word as a proper name of an object only if it refers to this one and the same object in all possible worlds". [F011esdal, 1966: 96-96]. F 011esdal regards this as a necessary condition of a proper name, not as a sufficient condition, since the word in addition needs to be directly referential. A proper name does "not assign a property" to its referent and serves "merely and solely to name it" [1966: 97]. If "a name-like word does not stick to one and the same object in all possible worlds, the word contains some descriptive element" [1966: 97] and thus is not a proper name. According to Almog [1986] and Marcus [1993: 212, 248, n. 19], Kripke [1971; 1972] regards F011esdal's necessary condition ("refers to this one and the same object in all possible worlds") as a sufficient condition to be a proper name. Both Almog and Marcus criticize this approach since it fails to distinguish directly referential names from rigid definite descriptions. (Almog and Marcus only refer to Kripke in their discussion, not to F011esdal.) However, it seems Almog and Marcus are not correct on this matter, since Kripke held that names are connected to their referents by an historical chain and that they do not refer to the object descriptively; these two criteria distinguish names from rigid descriptions. According to Kripke, the condition ("refers to this one and the same object in all possible worlds") is merely a necessary condition to be a proper name. F011esdal interacted with the other philosophers who at this early time were discussing rigidity - Kripke, Marcus, Hintikka and others - but the lines of influence are not easy to trace. We do know that F011esdal [1961] and Marcus [1960] refer to the Smullyan and Fitch responses to Quine as their background material; F011esdal [1961] also expresses indebtedness to Hintikka's [1957a; 1957b] and extensively discusses Marcus' 1940 writings on quantified modal logic and the necessity of identity, as well as Carnap's [1946; 1947], and Quine's [1941; 1943; 1947]. Hintikka [1963: 71-72] refers to his earlier [1962: 138-158], F01lesdal [1961] and Quine's writings as the background for Hintikka's discussion of rigid names/nonrigid descriptions [1963], presented at a conference in August, 1962 at Helsinki attended by Marcus, Kripke and others [Marcus, 1993: 89]. F011esdal indicated [1966: 43, n. 1] he was indebted to conversations with Kripke (his fellow student at Harvard in the early 1960s) for Kripke's explanation to him (in Spring 1961) of Kripke's theory of iterated modalities. Kripke and F011esdal had extensive discussions in 1960 and 1961 (see [F011esdal, 1966: pp. v and 43, n. 1; 1994: 888, n. 7]); in their discussions, Kripke did not communicate to F011esdal (in 1961 or earlier) any ideas about the distinctions among directly referential names that were weak rigid designators, nonrigid definite descriptions, rigid definite descriptions or the idea about the necessity of identity between directly referential rigid names (Kripke (eds.),

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[1980: 3-5]; FlIlllesdal [1966: pp. v, and 43, n. 1]). Kripke at this time (19601961) had not developed and did not endorse a theory of the directly referential, rigid name/nonrigid description contrast or the necessity of identity between rigid names (see [Kripke, 1980: 3-5]. According to Kripke's account of his influences, it may appear that FlIlllesdal's 1961 theory, Marcus' 1961 theory, and the earlier writings of Fitch and Smullyan had no influence on his development in 1963-64 of the rigid name/nonrigid definite description theory, the direct reference theory, the theory of the necessity of identity between names, and related theories (see Kripke [1980: 3-5] and [1972: 342343, n. 2]. FlIlllesdal, Fitch and Smullyan are not mentioned in [Kripke, 1971; 1972]. This account may be natural inasmuch as [Kripke, 1971; 1972] is only about ordinary usage and FlIlllesdal, Fitch and Smullyan are concerned primarily with the language used in an interpretation of quantified modal logic; by comparison, in Kripke's work on quantified modal logic (e.g., [1963b, n. 1] he refers to Hintikka's influence and similar views. Marcus [1961] is in significant part about ordinary usage and her theory of ordinary language is mentioned in Kripke [1971; 1972], but Marcus is said to have had no influence (see Kripke's remark quoted in [Holt, 1996: 36]; also see an alternative hypothesis formulated in [Smith, 1995a; 1995b]). Only Rogers Albritton is specifically named in [Kripke, 1972: 342, n. 2] as having an influence on Kripke's [1972]: "Albritton called the problems of necessity and a prioricity in natural kinds to my attention ..." [1972: 342, n. 2]. Another sentence, "I also recall the influence of early conversations with Albritton and with Peter Geach on the essentiality of origins", is added to the footnote in [1980: 23, n. 2]. Putnam, Donnellan, Chastain, Slote and some "philosophers mentioned in the text" [1972: 342, n. 2] are mentioned as "independently" [1972: 342, n. 2] expressing some similar views. There are also the following two sentences in the footnote [1972: 342, n. 2]: "The apology in the text still stands; I am aware that the list in this footnote is far from comprehensive. I make no attempt to enumerate those friends and students whose stimulating conversations have helped me". As this section indicates, FlIlllesdal made a number of largely unrecognized contributions to the New Theory of Reference in [1961]. To summarize a few, he integrates the universal intersubstitutivity thesis and the thesis of the necessity of identity, holds that only rigid designators flank the identity sign, holds that proper names are weak rigid designators and are not disguised descriptions, and defends the universal intersubstitutivity thesis against objections based on both epistemic and modal contexts. Earlier [Marcus, 1960] and independently [Marcus, 1960; 1961], Marcus made some partly similar points (and additional points). F0llesdal had extensively studied Marcus' 1940s writings, but not her [1960; 1961] before finishing his dissertation [F0llesdal, 1961: 54-59]. Marcus did not read F011esdal's dissertation until after it was privately printed in 1966 [Marcus, 1993: 231]. One of the crucial differences (among many) between Marcus (eds.),

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[1961] and F01lesdal [1961] is that Marcus explicitly intends her theory to be about ordinary usage. F011esdal remains in the tradition of Smullyan, Fitch and Marcus [1960] of centering his discussion on the language of quantified modal logic. If F011esdal's theory had been explicitly developed as a description of ordinary language in his [1961], then he and Marcus would have both (independently) made the breakthrough to the New Theory of Reference in 1961. 5. THE BREAKTHROUGH TO THE NEW THEORY OF REFERENCE: MARCUS, 1961

The striking feature about Marcus' [1961] is that she restates the "proper name" solution to Quine's modal paradox and then proceeds to show its conformity to ordinary language and that the relevant "proper names" are ordinary names in the Millian sense and exhibit necessity of identity. She further argues that Millian names are stable in modal contexts and are rigid designators. She later in the article provides a possible world semantics for quantified S4, which includes rigid individual constants, and thereby provides a formal backing to her theory of rigid names in natural language. The New Theory of Reference makes its first appearance in this article. In addition to the ideas mentioned, other ideas belonging to the New Theory of Reference also first appear in her [1961]. The relevant quotes and discussion appear in my [1998a; 1995b; 1995a] and I refer the reader to these three essays. There is a historical and logical connection between the theses discussed by Quine and Carnap in the 1940s and Marcus' first statement of the New Theory of Reference. Marcus applies to natural language something analogous to Quine'S "universal intersubstitutivity thesis" and the idea that names are always "purely designative", and also something relevantly analogous to Carnap's "name-relation method". Quine and Carnap rejected this position for both natural and artificial languages, but Marcus adopts a version of this position for both logical and natural languages. We have seen how these theses were discussed by Quine, Carnap, Smullyan, Fitch, F011esdal and Marcus [1960] in the interpretation of quantified modal logic; Marcus' [1961] stands out by virtue of her arguments that these theses apply to ordinary language. In her [1961] Marcus only addresses the objections to intersubstitutivity in modal contexts in natural and artificial languages. She did not address the objections to intersubstitutivity in epistemic contexts and does not develop a theory of epistemic contexts, although her direct reference theory of names would seem to imply the sort of theory of epistemic contexts that was later developed by New Theorists (including herself) in the 1980s. More importantly, F011esdal developed a relevant theory of epistemic contexts in his [1961; 1967] in which he defended the universal intersubstitutivity thesis for both modal and epistemic logic.

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Marcus discusses F"lllesdal's [1966] in an April 1988 talk at Washington University in St. Louis (see Marcus [1993: 215-232]. She characterizes F0llesdal's "second solution" to Quine's paradox as follows: "The second solution seems to accommodate what Kripke [1971] later called 'rigid designators', which include proper names as well as some descriptions." [1993: 231]. Thus, both Marcus and Quine [1981; 1994] believe F0llesdal's "genuine singular terms" express the same concept as Kripke's "rigid designators". I have discussed the merits of this belief in the earlier section on F0llesdaI. Marcus also believes F0llesdal [1966] did not hold the theory that proper names are directly referential and she refers to F011esdal's [1986] as F011esdal's endorsement of the direct reference theory. Marcus is correct inasmuch as the directly referential character of proper names is only very briefly discussed in F011esda1 [1966] and is not the focus of his discussion, as it is in Marcus' [1961]. But F011esdal does hold proper names are directly referential in [1966: 96-97], with the only caveat being that F0llesdal did not present his theory as an analysis of ordinary language but as a theory of quantified modal logic. 6. KRIPKE'S 1962 THEORY OF DESCRIPTIONALLY RIGID NAMES

After Marcus' [1961], the next relevant development in the theory of ordinary names appeared in the February, 1962 discussion of Marcus' [1961] among Kripke, F01lesdal, Quine, Marcus and others. Kripke did not have a theory of rigid names in 1961 (see Kripke [1980: 3-5], but we can see sketches ofa theory of descriptionally rigid names in Kripke's 1962 remarks in [Marcus et aI., 1962]. This counts as one of Kripke's original and important contributions to the New Theory of Reference, for Marcus [1961] and F011esdal [1961] held that rigid proper names (in ordinary or logical language) are directly referential. The theory of descriptionally rigid proper names is standardly said to be originated by Linsky in [1977] and Plantinga in [1978], but I think the following texts show that Kripke has priority in this regard. On February 7, 1962, we see some relevant ideas discussed by Quine, Kripke, F01lesdal, Marcus and others at the Discussion following Marcus' talk [Marcus et aI., 1962]. At this time, Kripke held a Fregean-Russellian descriptional theory of proper names and he appears to have misunderstood Marcus' theory in a fruitful way by trying to assimilate it to this paradigm. First, we should note how Kripke (in 1980) described the theory he held in 1962. He recounts that: "the ideas in Naming and Necessity evolved in the early sixties - most of the views were formulated in about 1963-64 .... Eventually I came to realize - this realization inaugurated the aforementioned work of 1963--64 - that the received presuppositions against the necessity of identities between ordinary names were incorrect, that the natural intuition that the names of ordinary language are rigid designators can in fact be upheld .... Thus at this stage I rejected the conventional description theory as an account of meaning.... Let me not pay inadequate tribute to the power of the then prevailing complex of ideas, emanating from Frege and from Russell, that I then abandoned ....

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Although I, with others, always felt some strain in this edifice ["the description theory of proper names"), it took some time to get free of its seductive power." [1980: 3-5).

As Kripke indicates, he "abandoned" the Frege-Russell "description theory of proper names" in 1963-64. This account accords well with his remarks on February 7, 1962, which reveal him trying to understand Marcus' theory of proper names in terms of the descriptional theory of proper names he then held. I will quote the entire, continuous text [Marcus et aI., pp. 142-143] that is relevant to his theory. (The printed transcript is a heavily edited version of the original remarks; all the discussants approved of the edited version prior to its publication.) I will put the quoted passages in italics, to separate them clearly from my extensive interpolations regarding Kripke's and Quine's remarks. My interpolations are placed in brackets. We begin with Marcus' "dictionary remark": "Presumably, if a single object had more than one tag, there would be a way of finding out such as having recourse to a dictionary or some analogous inquiry, which would resolve the question as to whether the two tags denote the same thing. If "Evening Star" and "Morning Star" are considered to be two proper names for Venus, then finding out that they name the same thing as "Venus' names is different from finding out what is Venus' mass, or its orbit. It is perhaps admirably flexible, but also very confusing to obliterate the distinction between such linguistic and properly empirical procedures."

[Kripke responds:] "That seems to me like a perfectly valid point of view': [Here Kripke is agreeing with what he takes to be Marcus' theory. Kripke continues:] "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'. Here Kripke misinterprets what Marcus just said; Marcus said recourse to a dictionary is an example of a way of finding out if two names are co-referring, and Kripke mis-states this as saying that the truth-values of identity statements between tags are always ascertainable "merely by recourse to a dictionary". In his [1971: 142-143] and [1972: 305] Kripke quoted or restated his own remark here about a dictionary, stated that he had in mind "ideal dictionaries", attributed this remark to Marcus, and thereby mistook Marcus to be saying that identity statements between names are a priori. This is the theory of Kripke held in February 1962 (as we shall see), but it is not Marcus'. A second point to make about this sentence of Kripke's (the last italicized sentence I quoted) is that it reveals the Frege-Russellian descriptional theory of proper names he held in February 1962; he regards the theory arrived at via his (mis)- interpretation of Marcus as a "perfectly valid point of view" that implies that identity statements between names are known a priori merely by recourse to a (an ideal) dictionary. The reason he thinks this implies essentialism is stated in his next sentence:] "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 indivi(eds.),

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duals. Thus the assumption of a distinction between 'names' and 'descriptions' is equivalent to essentialism':

[Marcus (see [Marcus, 1993: 142]) and my first essay on this topic [Smith, 1995a], contain a misinterpretation of this sentence. Marcus' interpretation of this sentence (which I endorsed in my [1995aD is that it implies that an individual, say Socrates, has the essential property of being named "Socrates". But this is not what Kripke is saying. Rather, Kripke is saying here what Quine and F011esdal- participants in this 1962 discussion - took Kripke to be saying. Consider this later remark by Quine: " ... Hence Dagfinn F",J1esdal's genuine singular terms, or Saul Kripke's rigid designators. These are the terms that obey substitutivity of identity even in modal contexts. These are the terms, also, that support inferences by existential generalization, even in modal contexts: other terms do not. As we might say in a modal spirit, these are the terms that name their objects necessarily. They name them on the score of essential traits, not accidental ones." [Quine, 1994: 148].

Here "name their objects necessarily" does not mean the objects have the same name in each possible world (contra Marcus [1993: 142]) and contra my earlier self [Smith, 1995a: 187]. It means what Quine explains it to mean in his next sentence: "They name them on the score of essential traits, not accidental ones". [Quine, 1994: 148]. The phrase "naming or referring to an object necessarily or essentially" was the sort of language used in the early 1960s to talk about rigid designation. Thus in Hintikka's August, 1962 talk at a conference with Marcus and Kripke, he presents his theory of rigid designators in these terms; he writes of a singular term: "But referring to it [the object] in all these alternatives ["possible worlds"] is tantamount to referring to it necessarily". [1963: 73]. Kripke's remark (the last sentence in italics I quoted) shows his assimilation of Marcus' theory of the distinction between proper names and contingent descriptions to his own Frege-Russell descriptional theory of names. Kripke believes that Marcus' distinction implies that names refer to objects rigidly via identifying them in terms of their essential properties. Using Frege's language (which is not Kripke's), Kripke's theory is that the sense of names includes the essential properties of the object referred to. Using Russell's language (which is not Kripke's), Kripke's theory is that names are truncated definite descriptions that describe objects in terms of their essential properties. Let us continue with Quine's response to Kripke in the 1962 discussion, which is a rejection of Kripke's theory: "Professor Quine: My answer is that this kind of consideration is not relevant to the problem of essentialism because one doesn't ever need descriptions or proper names. If you have notations consisting of simply propositional functions (that is to say predicates) and quantifiable variables and truth functions, the whole problem remains. The distinction between proper names and descriptions is a red-herring. So are the tags. (Marcus: Oh, no.)"

[Here Quine seems to be getting at the point that if we interpret quantification objectually, we do not need to phrase the problem of essentialism in terms of a special class of rigid singular terms, proper names. It can be phrased in (eds.),

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terms of quantifiable variables, propositional functions and truth functions. F011esdal [1961] argued that quantifiable variables are rigid singular terms and F011esdal might agree that the "problem" of essentialism remains even without considering Marcus' distinction between proper names and descriptions. Quine continues:] "All it is a question of open sentences which uniquely determine. We can get this trouble every time as I proved with my completely general argument of p in conjunction with ¢x where x can be as finely discriminated an intension as one pleases - and in this there's no singular term at all except the quantifiable variables or pronouns themselves. This was my answer to Smullyan years ago, and it seems to me the answer now. Mr Kripke: Yes, but you have to allow the writer what she herselfsays, you see, rather than arguingfrom the point of view ofyour own interpretation of the quantifiers." [Kripke here is saying that for purposes of evaluation of Marcus' talk we should allow Marcus' substitutional interpretation of quantification, and not assume Quine's objectual interpretation ("the quantificational sense of quantification", as Quine puts it).] "Professor Quine: But that changes the subject, doesn't it? I think there are many ways you can interpret modal logic. I think it's been done. Prior has tried it in terms of time and one thing and another. I think any consistent system can be found an intelligible interpretation. What I've been talking about is quantifying, in the quantificational sense of quantification, into modal contexts in a modal sense of modality. Mr Kripke: Suppose the assumption in question is right - that every object is associated with a tag, which is either unique or unique up to the fact that substituting one for the other does not change necessities - is that correct? Now then granted this, why not read 'there exists an x such that necessarily p ofx'as (put in an ontological way ifyou like) 'there exists an object x with a name a such thatp ofa is analytic: Once we have this notion of a name, it seems unexceptionable. Professor Quine: It's not very far from the thing I was urging about certain ways of specifying these objects being by essential attributes and that's the role that you're making your attributes play. Mr Kripke: So, as I was saying, such an assumption of names is equivalent to essentialism." [Kripke is reaffirming his position that names denote objects by way of specifying their essences and that 'a is p' is analytic if "a' is a name and p an essence of a. At this point he is prepared to accept the conventionally accepted equivalence between the analytic, the a priori, the necessary and the essential. He does not appreciate Marcus' point that "the kind of uses to which logical modalities are put have nothing to do with essential properties in the old ontological sense. The introduction of physical modalities would bring us closer to this sort of essentialism". (Marcus et aI., p. 141). At this time, only Marcus distinguishes between non-trivial essential attributions (e.g., 'Cantor is a mathematician') and what is logical and analytic.] "Professor Cohen: I think this is a goodfriendly note on which to stop."

The transcript of the discl,lssion ends here. All of the italicized sentences form a continuous text in [Marcus et aI., 1962, pp. 142-143]. Kripke maintains that if we assume Marcus' tag theory of names, then we have esentialism since her tags (allegedly) involve designating objects in terms of their essential attributes. Kripke misinterprets Marcus' naming relations to objects as ways of specifying these objects by essential attributes and Kripke holds that sentences with names and essential predicates are analytic. Quine rejects this theory but Kripke finds it to be "a perfectly valid point of view" and holds that "once we have this notion of a name, it seems unexceptional". (eds.),

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[Marcus et aI., pp. 142-143]. F0llesdal, who had developed his own theory of modally stable and non-descriptional proper names a year earlier, did not misunderstand Marcus. See [F0llesdal, 1986: 105]. It seems that Kripke was under the influence or "seductive power" (as Kripke later put it [1980: 5]) of the then prevalent descriptional theory of names and thereby did not fully comprehend Marcus' theory that names pick out their objects non-descriptionally. More important than this misunderstanding is the positive theory that resulted, namely, Kripke's origination of the theory that names are de scriptionally rigid. Kripke's remarks in this 1962 discussion suggest that his 1980 recollection of when he first came to believe that rigid names are directly referential is better supported by the textual evidence than his 1996 recollection. In [1980: 5] Kripke says "the ideas in Naming and Necessity evolved in the early sixties most of the views were formulated in about 1963-64 .... Eventually I came to realize - this realization inaugurated the aforementioned work of 1963-64 that the received presuppositions against the necessity of identities between ordinary names were incorrect, that the natural intuition that the names of ordinary language are rigid designators can in fact be upheld. Part of the effort to make this clear involved the distinction between using a description to give a meaning and using it to fix a reference. Thus at this stage [in 1963-64] I rejected the conventional description theory as an account of meaning .... Let me not pay inadequate tribute to the power of the then prevailing complex of ideas, emanating from Frege and from Russell, that I then [in 1963-64] abandoned .... Although I, with others, always felt some strain in this edifice ["the description theory of proper names"], it took some time to get free of its seductive power". [1980: 3-5]. Over fifteen years later (see Holt, 1996: 36] Kripke seems to recollect that he was already in grasp of Marcus' "direct reference" theory of rigidity before Marcus' February 1962 talk: "Ruth [Marcus] said in her 1962 talk that proper names were not synonymous with descriptions. A subset of the ideas I later developed were present there in a sketchy way, but there was a real paucity of argumentation on natural language. Almost everything she was saying was already familiar to me at the time. I knew about Mill's theory of names and Russell's theory of logically proper names, and I hope that, having worked on the semantics of modal logic, I could have seen the consequences of such a position for modal logic myself". As Kripke acknowledges, it is hard to remember exactly what beliefs one held thirty years ago, and I think is safer to rely on textual evidence. I have argued that the 1980 recollection (in which Kripke says he first realized the Millian consequences of modal logic for ordinary names in 1963-64) is confirmed by the 1962 text I quoted and thus that an historical account of this period should accord with the 1980 recollection in this respect. If Kripke's 1980 recollection is correct and my interpretation of the 1962 discussion among him, Quine, F0llesdal and Marcus is correct, then Marcus' (eds.),

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later interpretation [1993: 226-27] of Kripke's 1962 remarks is mistaken. We should instead conclude that in 1962 Kripke held the theory that names are descriptionally rigid. In at least one respect, this reverses the standard history of the New Theory of Reference; the standard history attributes the origin of the descriptionally rigid theory of names to Plantinga and the origin of the argument for the nonequivalence of the necessary/contingent and a priori/a posteriori distinction to Kripke. In fact, Kripke originated (at least in a sketchy form) the theory of names as descriptionally rigid and Plantinga originated the argument for the nonequivalence of the necessary/contingent and a priori/a posteriori distinction (see section 9). But there are still more ways in which the standard histories of contemporary philosophy need to be re-examined. 7. METAPHYSICAL POSSIBILITY IN HINTIKKA: 1957-63

The New Theory of Reference is a theory of natural language that includes the ideas that expressions in natural languages are informal analogues to certain terms in a semantics for quantified modal logic. The ideas of a rigid designator, of a statement that is true in all possible worlds, and of the distinction between logical and metaphysical possibility, belong to the New Theory of Reference and are analogues of certain notions in modal logic. What is metaphysical possibility? In this section, I understand this notion to include two ideas, one being the idea of what really might have been the case and the second being the idea of a material or nonformal component that belongs to the possibility operator (; in modal logic. The first idea involved in the notion of metaphysical possibility or necessity is that what might exist or what must exist is a distinct notion from what is logically possible or logically necessary. The primitive metaphysical notions of what might have been or could have existed (de re possibility) or what might have been true (de dicto possibility) are distinct notions from the notion of what does not involve a logical contradiction. Likewise, the ideas of what must be or what must be true are distinct ideas from the idea of something whose negation or denial involves a logical contradiction. If "real possibility", possibility in the sense of what might have been the case, is divorced from logical possibility, how are we to reason about it? What theory of axioms, rules of inference, etc., will capture its patterns of reasoning? The answer that many New Theorists of Reference adopt is that we employ the semantics for metaphysical necessity in one of the systems S5, S4, M, etc., of modal logic. This metaphysical semantics is based on the idea that the necessity and possibility operators in modal logic have a material or nonformal content, and in this respect differ from the formal modal operators in the semantics for logical necessity and possibility. There is an essential connection between the semantics of metaphysical necessity and the theory of rigid designators in natural language. A crucial question for the New Theory of Reference is: what sort of semantics for modal (eds.),

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logic is "the right one" for the individual constants that are the formal counterparts of rigid names in natural language? This semantics cannot be a semantics for logical necessity, such as Carnap's [1946; 1947]; the semantics of logical modalities cannot accomodate the notion that some singular terms are rigid designators. Suppose for purposes of reductio that a name is the natural language counterpart of an individual constant in a semantics for logical modalities. Consider the use of "Socrates" as a name of the Greek philosopher, Socrates; we may consider "Socrates" in this usage as a hononym. If names are counterparts of individual constants in a semantics for logical modalities, then the hononym "Socrates" would refer to Socrates as he exists in all logically possible worlds, and in many of these worlds he is a typewriter or a number or the color red, and such worlds are not the right sort of worlds for rigid designators in natural languages. For example, the sentence "Socrates might have been the color red" is inconsistent with the rules of use of names in natural languages (given that "Socrates" is the hononym I mentioned). If "Socrates" is a different hononym and is used by fabric sellers as a name of a special shade of red, then the sentence is consistent with the rules of use of names in natural languages. Names in natural languages are related to metaphysically possible worlds. The reason is that rigid designators go hand in hand with the notion of non-trivial essences (even if the designators are directly referential). When we refer to the Greek philosopher Socrates by the rigid name "Socrates", we refer to Socrates in each possible world in which he exists, but this means each metaphysically possible world, for we restrict the worlds at which "Socrates" has a referent to the worlds in which Socrates has his non-trivial essences, such as being human. A rule of use of "Socrates" and each other ordinary name is that it is used to refer to an object only insofar as it exists in metaphysically possible worlds. Hintikka's [1957a; 1957b; 1961; 1963] first offered the conceptual materials to formulate (but he himself did not formulate) this rule of use of names in terms of a semantics for modal logic, for he introduced metaphysically possible worlds as the relevant worlds for rigid designators. Hintikka introduced the idea that the possibility and necessity operators have a nonformal content in the semantics for modal logic, but did not explicitly relate this content to nontrivial essences. (It is worth emphasizing that the theory of rigid ordinary names, metaphysically necessary worlds, non-trivial essences, the necessity of identity, and other ideas that constitute the New Theory of Reference is different than the theory that Hintikka concentrated on developing, especially in his later writings. For references and a criticism of the Marcus~Kripke version of the New Theory of Reference, see Hintikka and Sandu [1995]. I shall here concentrate on Hintikka's 1957~1963 writings on the semantics for metaphysically possibility and necessity.) It is now known by some logicians that Kanger's [1957] is the first publication introducing into modal logic the idea that features of the alternativeness relation (also called the "accessibility" or "relative possibility" rei a(eds.),

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tion), features such as reflexivity, symmetry and transitivity, can give us semantics for different modal logics, e.g., S4, S5 and Fey's calculus T [Kanger, 1957: 40; the relevant discussion begins on page 33]. Montague [1960] also gave an early and independent presentation of some partly similar ideas about S5. Montague presented his ideas in a May, 1955 conference at the University of California at Los Angeles [Montague, 1974: 71] and Kanger presented his ideas in Spring 1955 in a course on logic at the University of Stockholm (see [F011esdal, 1994: 886]). Hintikka independently introduced the accessibility or alternativeness relation in the same year as Kanger's publication (Hintikka, 1957a; 1957b]; Hintikka first introduced the idea of metaphysical necessity in [1957a; 1957b] and Hintikka was the first to develop (in a manuscript written prior to his 1957 articles; see [Hintikka, 1957a: 10] and the first to publish (in [1961]) a metaphysical semantics for modal logic in terms of the reflexive, transitive, etc., features of the alternativeness relation. The metaphysical alternativeness relation was introduced in Hintikka's [1957a; 1957b] and its features of reflexivity, transitivity, etc., were used to develop semantics for the systems M, S4, S5, etc., in [1961]. In his 1957 essay on "Quantifiers in Deontic Logic", which is the earliest system of quantified deontic logic, Hintikka writes: "My treatment [of deontic logic] derives from an earlier treatment of quantification theory along the same lines as well as from a similar (unpublished) theory of modal logic. Most of the formal considerations will turn out to be special cases of this new general theory of modal logic I have developed'. [1957a: 10]. (Presumably, Hintikka's unpublished theory of modal logic is the theory published in his [1961; 1963.) Hintikka first introduces in [1957a] the modal metaphysical notion of alternativeness and its deontic counterpart, copermissability. The metaphysical notion of alternativeness involves the idea that states of affairs or possible worlds are not possible absolutely (as Carnap [1946] and others assumed) but are possible relative to a certain world W, such that Wand the worlds possible relative to W constitute a subset of the set of all logically possible worlds. Necessary truth is not truth in all logically possible worlds (as Carnap [1946] held), but is truth in a world Wand in all the alternatives to W, such that Wand the alternative worlds are members of a subset of the set of all logically possible worlds. 2 (The subset may be an improper subset, in which case it would be the set of all logically possible worlds; but this is not required by the meaning of the possibility and necessity operators.) This introduces content into the (otherwise formal) interpretations of the box and diamond. The content enables a subset of the set of all the formally (logically) possible worlds to be demarcated from other subsets of the set of all formally possible worlds. What is necessarily true is not determined by what is true by virtue of its form, but what is true by virtue of a certain content. Other logicians had discussed relevantly similar nonlogical necessities, such as physical necessity, but they did not develop a semantics for these nonlogical necessities but characterized them in terms of logical necessity (eds.),

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and a conjunction of physical laws or (laws of some other sort). The characterization of "metaphysical necessity" in terms of logical necessity and a conjunction of laws of some sort is (at least implicitly) the sense in which Moore [1903] and Wittgenstein [1922] had the concept of "metaphysical necessity". Hintikka's second 1957 article, "Modality as Referential Modality", outlines the second system presented of quantified epistemic logic (later more fully given in [Hintikka, 1962]), the first being Von Wright's [1951]). But this article is also in large part about non-epistemic modal logic. One way the idea of a semantics for metaphysical modalities appears in Hintikka's [1957b] involves his explanation of how proofs can be carried out in modal logic. In the following passages, he makes some suggestions about the alternativeness relation in (non-epistemic) modal logic. He has indicated [Hintikka, 1955] how the notion of a model can be replaced by the notion of a model set of logical formulae, and Hintikka adds the idea: "It turns out that an intuitive and powerful theory of modal logic can be based on these notions [of a model or a model set of logical formulae]. The main novelty is that we have to consider several interrelated models (or model sets). They correspond to the different situations we want to consider in modal logic, and they are interconnected, in the first place, by a rule saying (roughly) that whatever is necessarily true in the actual state of affairs must be (simply) true in all the alternative states of affairs. It turns out that it suffices, for the interpretation of each given proof carried out by means of modal logic, to consider only a finite number of alternative models (model sets). Of course, no finite number wiJI suffice for the interpretation ofal1 the proofs" [1957b: 61-62].

Let us see exactly how this notion of metaphysical necessity differs from the notion of logical necessity given in Kanger's [1957] and Carnap [1946; 1947]. Kanger discusses models rather than model sets or state descriptions. In general terms, a model consists of a domain D of individuals and an interpretation of a language L in terms of that domain. Individual variables in L are assigned to individuals in D and predicates in L are assigned to n-tuples of individuals in D. By contrast, a model set is a set of logical formulae that partially describe a possible world; in this respect, model sets are somewhat analogous to Carnap's [1946; 1947] state descriptions, which Carnap says are complete descriptions of a possible world. In Kanger's version of a model-theoretic semantics for logical modalities, < D, V> is a system where D is a domain of individuals and V a primary valuation for a language L of quantified modal logic. V is a function which for every domain D' assigns an extension in D' to each individual variable, individual constant and predicate constant in the language L. Logical necessity is characterized as follows: Dp is true in the system S if and only if p is true in every system S' (where each system is an alternative to each other system). (See [Lindstrom, 1998] for a more detailed discussion of Kanger's theory.) This differs from Carnap's [1946; 1947] theory of logical necessity in that Carnap discussed state descriptions rather than models and said a statement is logically necessary if and only if it is true in all state descriptions; Carnap did not have (eds.),

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the notion of accessibility or alternativeness and thus did not specify that logical necessity requires each state description to be an alternative to each other state description. It is easy to see how Hintikka's metaphysical theory differs from Kanger's and Carnap's theories of logical necessity. For Hintikka in [1957a; 1957b], a model set is a set of logical formulae that partially describe a possible world. Necessity is truth in a model set, such that Op is true in the model set M if and only if p is true in M and in every model set that is a real alternative to M. But not every model set need be a real alternative to M and thus 0 is not required to quantify over all model sets. Op requires merely that p is true in a subset of the set of all logically possible model sets. This imports material content into 0 and thus 0 now means a non formal, metaphysical necessity. The second appearance of metaphysical necessity is in Kripke's [1959a], where Kripke uses models rather than model sets. Kripke uses a metaphysical semantics to provide a completeness proof for quantified S5 and this proof requires a metaphysical rather than logical semantics. (This requirement was first demonstrated by Cocchiarella [1975b]; in this work Cocchiarella also first demonstrated that the logical ["primary"] semantics for quantified modal logic is incomplete ~ an issue left unresolved in Carnap [1946].) Kanger [1957] introduced models into theories of modal logic but Kripke [1959a] is the first to use metaphysical models. In Kripke's [1959a], he mentions a complete assignment for any formula A in a domain D of individuals. A is any formula that contains free individual variables, propositional variables and n-adic predicate variables. A model of A in the domain D is a pair (G, K), where G is a complete assignment for A in D and K is a set of complete assignments for A in D, such that G is a member of K and all members of K differ from G only in the assignments for the propositional and predicate variables in A. In Kripke's semantics for necessity, necessity is characterized in terms of some set K of complete assignments, where K is not required to be the one and only set C of all complete assignments. This implies that necessary truth does not mean truth in all logically possible worlds, but truth in all the members of some subset of the set of all logically possible worlds. (The subset may be an improper subset of the set C of all complete assignments, i.e., C itself, but the characterization of necessity does not require that the subset be this improper subset.) The first step in the metaphysical semantics for modal logic occurred in 1957 with Hintikka's [1957a; 1957b] and the second in Kripke's [1959a]. The next significant step is Hintikka's 1961 article on "Modality and Quantification". This 1961 article was the first article to present a metaphysical theory of possible worlds characterized in terms of the reflexive, transitive, symmetrical, equivalence and connected features that can be possessed by the alternativeness relation. Tn other words, Hintikka [1961] provided the first metaphysical semantics for standard systems of modal logic, e.g., the systems M, S4 and S5, that used the reflexive, transitive or symmetrical properties that can be (eds.),

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possessed by the alternativeness relation. (Kanger's [1957] semantics for several systems was a logical semantics and Kripke's metaphysical semantics for these and other systems appeared in [1963b], but with a [l959b] abstract.) Hintikka proceeds by "saying that a model set is the formal counterpart to a partial description of a possible state of affairs (of a 'possible world'). It is, however, large enough a description to make sure that the state of affairs in question is really possible. For it is natural to say that a set of sentences is satisfiable if and only if it can be imbedded in a (partial or exhaustive) description of a possible state of affairs; and this is just what we demonstrated if model sets are interpreted as such descriptions" [1961: 122]. In modal logic, we do not consider just one model set at a time (e.g., one partially describing the actual world), but a set of model sets. Hintikka calls such sets of sets model systems. More fully, a model system < U, R > is a couple where U is a set of model sets each of which satisfies a condition (stated informally) that if necessarily p is true in a model set (partial description of a possible world), then p is true in that model set. The relation R of alternativeness satisfies the condition that if possibly p is true in a model set U that belongs to a model system S, there is an alternative set v in S in which p is true. The relation of alternativeness also satisfies the condition that if necessarily p is true in a model set u that belongs to the model system S, then p is true in every model set in S that is an alternative to u. (These last two conditions are also satisfied by the model system S.) But not every model set in the model system S to which u belongs need be an alternative to u. Given these conditions, we have a metaphysical modal semantics for the Von Wright system of modal logic M. If we add that the relation of alternativeness is transitive, we have a metaphysical modal semantics for S4, and if symmetry is also added, we have a semantics for S5. But in each of these cases the model system, in which is included each alternative to a given model set, is not required to include all logically possible model sets. The necessity of a formula p is p's truth in all the alternative model sets in a model system, and thus necessity is not characterized as a logical necessity. Further or different conditions need to be used to characterize the necessity of a formula if we adopt a varying domain semantics. In this case, if an individual exists in the actual world and necessarily has a property F, it does not follow that the individual exists in every alternative world and has F in these worlds. Rather, it follows that if the individual exists in some alternative world, then the individual possesses F in that world. This requires the following condition be added to the characterization of metaphysical necessity. In Hintikka's logic, the presence of a free variable in a formula p that belongs to a model set u is the formal counterpart to the existence of its value in the possible world partially described by u. Accordingly, if Dp, it does not follow that p is true in every model set that is an alternative to u. We cannot transfer a formula p from a model set u to an alternative model set v unless the values of the variables in p exist in the possible world partially described by v. If Dp, (eds.),

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then p is true only in alternative model sets where the free individual variables in p are contained in formulae in these alternative model sets. See {CN. *} in Hintikka [1961: 125]. How does this notion of metaphysical necessity connect with the notion of a rigid designator? The theory of nonrigid singular terms (typically, contingent definite descriptions) and rigid individual constants or names is developed in Hintikka's most well-known early article on modal logic, his "The Modes of Modality" [1963] presented at an August 1962 conference in Helsinki in which Marcus, Kripke, Montague, Prior and Geach participated (see Marcus [1993: 89]). It is worth quoting the passage in which the "rigid individual constant or name versus nonrigid definition description" distinction is made, since this is the most explicit appearance of this distinction after Marcus' February, 1962 talk. This distinction appears in Hintikka's example of the contingent description "the number of planets" as contrasted with the modally stable name "9". Hintikka refers to his [1962: 138-158], F011esdal [1961] and Quine's many writings on the topic as background material. Hintikka writes: "Why do some terms fail in modal contexts to have the kind of unique reference which is a prerequisite for being a substitution-value of a bound variable? An answer is implicit in our method of dealing with modal logic. Why does the term "the number of planets" in (i) ["the number of planets is nine but it is possible that it should be larger than ten"] fail to specify a well-defined individual? Obviously, because in the different states of affairs which we consider possible when we assert (i) it will refer to different numbers. (In the actual state of affairs it refers to 9, but we are also implicitly considering other states of affairs in which it refers to larger numbers.) This at once suggests an answer to the question as to when a singular term (say a) really specifies a well-defined individual and therefore qualifies as an admissable substitution-value of the bound variables. It does so ifand only ifit refers to one and the same individual not only in the actual world (or, more generally, in whatever possible worlds we are considering) but also in all the alternative worlds which could have been realized instead of it; in other words, if and only if there is an individual to which it refers in all the alternative worlds as well. But referring to it in all these alternatives is tantamount to referring to it necessarily. Hence (Ex)N(x = a) formulates a necessary and sufficient condition for the term a to refer to a well-defined individual in the sense that critics of quantified modal logic have been driving at, exactly as I suggested."

(Ex)N(x = a) is the material mode definition of a rigid designator. Note the two ways of using "a". In "the term a" it refers to a rigid designator and in "(Ex)N(x = a)" it refers to the individual that is the rigid designatum of the term. This dual usage has become standard in discussions of modal logic. Well-defined reference is a stable reference. It is a broader category than (non-epistemic) modally stable reference, for Hintikka notes that well-defined reference breaks down for "even proper names" [1963: 73] in epistemic contexts. (Unlike Marcus' [1961] and F011esdal's [1961] theories, Hintikka's theory rejects the universal intersubstitutivity thesis.) Hintikka's point is that an individual constant or proper name may have a stable reference in modal contexts (and thus be a "rigid designator") but fail to have a stable reference in epistemic contexts. Contingent definite descriptions, by contrast, are always unstable in modal contexts. The above history of the metaphysical semantics for modal logic ill accords (eds.),

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with the standard history of metaphysical semantics and some defence is needed. According to the standard history, a modal semantics for logical necessity was originally developed by Carnap in 1946 and 1946 (which is true), and the modal semantics for metaphysical necessity was first developed in Kripke's 1963 work on modal logic (which is false). One of the most precise and best statements of the standard history of metaphysical necessity appears in Joseph Almog's [1986]. He writes: "But where did metaphysical possibility and necessity come from? It came from Kripke's 1963 paper" [1986: 217]. Almog's argument for this is that in Kripke's [1963a: 69], he characterizes worlds as primitive "points" that "may include a world, a time, an agent, a spatial location, or what have you" [Almog, 1986: 218], and does not characterize them in terms of complete noncontradictory assignments of extensions to a given language. (According to Almog, Kripke [1963b] introduced into modal logic the idea of varying domains; but varying domains are present in Hintikka [1957a; 1957b; 1961; 1963] and Kanger [1957].) Almog writes about Carnap's "... logically possible worlds. Really, they were 'state descriptions' or, later, models, but still language-bound, i.e., complete assignments of extensions to a given language. On this conception, possibility obeys a maximum principle: any noncontradictory assignment is possible. This view was not confined to Carnap. It was also the view of Stig Kanger, Jaakko Hintikka, Richard Montague (of that period) - and the 1959 Kripke. Indeed, Kripke had at that time nothing more than 'complete assignments' and the modality he worked with was definitely logical possibility". [Almog, 1986: 217]. I shall confine myself to some of the mis-interpretations of Hintikka and Kripke that appear in this passage. First, Hintikka was the first person to introduce, in [1957a; 1957b; 1961; 1963], the idea that possibility does not obey a maximum principle, i.e., it is not the case that any noncontradictory assignment is possible. Hintikka's notion of possibility requires merely that, for any given world, only some noncontradictory assignments are possible (relative to that world). More precisely (and using Hintikka's terminology), a model system is a set of model sets and a model system need not include all model sets. If a formula is possibly true in a model set U, this requires only that the formula is true in another model set v that both belongs to the same model system as U and that is an alternative to u. For example, if we suppose u partially describes the actual world, we (as members of the actual world) may say that tnere are many noncontradictory formulae that are not possible, since these formulae either are not (i) elements in any maximal model set in which u is embedded and that maximally describes the actual world, or are not (ii) elements. of a, model set that is an alternative to u and that belongs to the same modef system as u. This characterization of possibility is based on Hintikka's condition (C.M.*) in [1961: 123] and [1963: 67]. As Hintikka intuitively puts it, "we have assumed that not every possible world (say P) is really an alternative to a given possible world (say Q) in the sense that P could have been realized instead of Q". [1963: 67]. Thus, Hintikka (eds.),

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rejects the Carnapian idea that possibility obeys a maximum principle. A second respect in which Almog's interpretation of Hintikka is mistaken is that Almog thinks that Hintikka's possible worlds are linguistic items, i.e., are descriptions. This is not so. Hintikka's linguistic items are descriptions of a possible world, they are not the possible worlds themselves. A model set (m.s.) is a description: a "m. s. may be thought of as a partial description of a possible state of affairs or a possible course of events (,possible world'). Although partial, these descriptions are large enough to show that the described state of affairs are really possible ..." [1963: 66]. Also see [1961: 122]. Each model set can be embedded in a maximal model set and "each maximal model set is an extended state-description" [1961: 121]; it is not the possible world described by the extended state-description. A third respect in which Almog's interpretation is inaccurate is that Hintikka does not work with models, but with model sets. A fourth respect in which Almog's theory is problematic is that the definition of a world as a "primitive point", rather than as a model (or as what is described by a maximal model set), is a sufficient but unnecessary condition for the possibility and necessary operators to have nonformal, metaphysical content. Another sufficient condition for this nonformal content is that the box or necessity operator be interpreted in terms of all the members of a set of logically possible worlds, rather in terms of all the members of the one and only set of all logically possible worlds. In the specifics of Hintikka's logic, this nonformal content appears (among other places) in the condition (C.N+) [1961: 123; 1963: 67], which says that if a formula is necessarily true in a model set U, then the formula is true in each model set that is an alternative to U in a model system to which u belongs. Kripke first published the notion of metaphysical necessity in [1959a], not (as Almog maintains) in 1963. In the specifics of Kripke's semantics [1959a], the necessity operator is interpreted in terms of a set K of complete assignments, not the one and only set C of all complete assignments. Kripke [1959a] gave a metaphysical semantics for Lewis' quantified S5 but not based on the alternativeness relation. Kripke's metaphysical semantics that was based on features of the alternativeness relation appeared in Kripke [1963a; 1963b]. Kripke had developed the basic ideas of his 1963 semantics at least as early as Spring 1961 (see [F011esdal, 1966: vD. He also developed a metaphysical semantics for S2 and S3 at least as early as 1961 (see Hintikka, 1961: 124). Kripke's [1959b] abstract for his [1963b] may plausibly be read as implying the metaphysical alternativeness relation with its reflexive, etc., features, but it is too brief to draw definite conclusions about its implications. Kripke says in the first footnote to his [1963b] that Hintikka's and Kanger's theories have the closest points of contact with his own theory and that his treatment of quantification draws some inspiration from Hintikka's and Prior's methods. But Kripke's idea of a metaphysical alternativeness relation plausibly seems to have been formulated independently. F011esdal mentioned to Kripke in 1961 that Hintik(eds.),

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ka [1957a; 1957b] and Kanger [1957] contained the notion of the a1ternativeness relation (private communication from F011esda1, April 23, 1997). Kripke read [Kanger, 1957], which contained the notion of a logical alternativeness relation, after January 1958 and before the end of 1960; there is a letter from Kripke to Kanger, dated January 24, 1958, in which Kripke asks Kanger for a copy of his [1957] (see [F011esdal, 1994: 887-888, n. 61], and Kripke reported to F011esdal in 1960 that he studied Kanger but that his study of Kanger was not "thorough" (see [F011esdal, 1994: 888, n. 7]). The alternativeness relation does not appear in Kripke's paper [1959a], but may plausibly be read as implied by his abstract [1959b]. The paper [1959a] was received by The Journal of Symbolic Logic in August, 1958 and the abstract [1959b] was received by this journal in October, 1959. This may suggest that in August, 1958 Kripke did not have the notion of the alternativeness relation, but in October 1959, almost two years after his letter requesting Kanger's [1957], Kripke was in possession of this notion. In his abstract [1959b] Kripke does not mention Kanger but does mention similar work by Hintikka: "(For systems based on 84, 85, and M, similar work has been done independently and at an earlier date by K.J.J. Hintikka.)" [Kripke, 1958b: 324]. Given all of the above-mentioned facts, it may be conjectured that Kripke acquired the notion of the alternativeness relation some time after the summer of 1958 (when he submitted his [1959a]) and before the fall of 1959 (when he submitted his [1959b]). If Kripke's notion of the alternativeness relation was acquired from earlier work, it seems more likely it was acquired from Hintikka's than Kanger's work. This is suggested by the fact that neither Hintikka nor Kanger are mentioned in [Kripke, 1959a] and only Hintikka is mentioned in [1959b] and is said to have done similar work. However, there is no good reason to think that Kripke did not acquire this notion independently. F011esdal, who had extensive discussions with his fellow student Kripke in 1960-1961, is in a position to reliably report that "Saul Kripke got the idea [of the alternativeness relation] independently [of Kanger and Hintikka] and extended it (in 1959) so as to make it applicable to the Lewis systems S2 and S3. (Cf. his "8emantical analysis of modal logic (abstract) [1959] ..." [F011esdal, 1966: 43, n. 1]. Given all of this evidence, the most probable hypothesis is that Kripke and Hintikka came up with the idea of a metaphysical alternativeness relation independently, but that Hintikka developed the theory first (prior to his 1957 publications) and published it first [Hintikka 1957a; 1957b]. Kanger [1957] and Montague [1960], independently of each other, came up with the idea of a logical, but not metaphysical, alternativeness relation, which they originated in 1955. 8. COCCHIARELLA AND THE SECONDARY SEMANTICS FOR LOGICAL NECESSITY

The notion of metaphysical necessity includes two ideas, the primitive idea of what must be and the idea that the necessity operator is nonformal or includes (eds.),

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a material content. The idea of a nonformal necessity and possibility that is present in Kripke's writings on modal logic was first demonstrated to be different from the notion of logical necessity and possibility in Nino Cocchiarella's 1973 talk at the University of North Carolina at Chapel Hill (published as [1975a]). 3 Especially see Cocchiarella [1975b], and also see Hintikka's 1977 talk in Rome [Hintikka, 1980] and Hintikka's [1982]. This demonstration was made in terms of models, rather than model sets, and involved showing the equivalence of some early writings on modal logic to a primary semantics for logical necessity and the equivalence of some other writings to a secondary semantics for logical necessity. Note that it is not requisite to demonstrate this difference within one's modal logic in order to present a metaphysical or logical semantics. Some authors in the 1940s, 1950s and 1960s worked with logical modalities (e.g., Carnap [1946], Kanger [1957], Montague [1960], Beth [1960], Kaplan [1964]; but Montague [1963] and Kaplan [1978a; 1978b; 1989a] later used metaphysical modalities). Other writings on modal logic worked instead with metaphysical modalities (Hintikka [1957a; 1957b; 1961; 1963] and Kripke [1959a; 1963a; 1963b]; but in [Hintikka, 1980; 1982] and later works Hintikka discusses logical modalities). As I indicated, Nino Cocchiarella [1975a; 1975b] was the first to show that metaphysically possible worlds defined in terms of models relate to the distinction between the secondary semantics for logical necessity and the primary semantics for logical necessity. Cocchiarella argued this distinction involves the notion of a model (e.g., as in Kripke's [1959a)) and Cocchiarella did not discuss model sets or model systems (the notions Hintikka used). (Hintikka also discussed his related distinction, between standard and nonstandard logics, in terms of models rather than model sets [Hintikka, 1980; 1982].) Cocchiarella showed that Kripke's [1959a] is equivalent to a secondary semantics for logical necessity and thereby is a semantics for metaphysical necessity. Roughly speaking, this means that "all possible worlds" in Kripke's semantics are a subset of the set of all logically possible worlds and thus that we permit "modal operators to range (in their semantic clauses) over arbitrary non-empty subsets of the set of all the possible worlds (models) based upon the given universe of objects and the set of predicates in question ... the exclusion of some of the worlds (models) ofa logical space, imports material conditions into the semantics of modal operators". [Cocchiarella, 1975b: 13]. Cocchiarella points out that Carnap [1946], Kanger [1957] and Montague [1960] developed a primary semantics for logical necessity, but that since the early 1960s most modal logicians concentrated on the secondary semantics. (But this is not to say these logicians were aware of this primary/secondary distinction; Cocchiarella was the first to note this distinction in 1973 and this distinction is not often noted today.) Cocchiarella does not say that there is a primitive idea of what must be that is included in the notion of metaphysical necessity and in this respect (among others) his account differs from the one T am presenting. One significant (eds.),

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difference is that Cocchiarella made his metaphysical/logical distinction in terms of models and thus his distinction does not correspond to the metaphysical/logical distinction I made, where it is indifferent whether models or model sets are used. A model set is a set of logical formulae but a model is a structure such as < D, R >, where D is a non-empty set (a domain of objects) and R an interpretation of the relevant terms in the language with respect to D. This difference can be explained more exactly in Cocchiarella's terms. Cocchiarella's primary semantics includes a satisfaction clause for necessity that covers all the models for a domain D. Cocchiarella calls them L-models in [1984: 311], where L = the set of predicate constants that are provided an interpretation for the language in question. An L-model is a structure of the form < D, R >, where the domain D is a set of objects and R is an interpretation of the predicate constants in the language. For each predicate F in L, R(F) is a set of n-tuples of members of D. Accordingly, the clause for the necessity operator interprets this operator as ranging over all the L-models having D as their domain, such that the predicates in the language are assigned all possible reinterpretations (extensions) drawn from the domain D. (See clause 6 in Cocchiarella's [1984: 312] for a more technical formulation. His primary semantics can also be applied to a varying domain [1984: 321-323]. Cocchiarella's secondary semantics includes a satisfaction clause for necessity that is "cut-down" so as to cover, not all the L-models having D as their domain, but all the L-models in a set K of L-models having D as their domain, where K need not include all the L-models based on the domain D. Since the meaning of the satisfaction clause for necessity does not include all the Lmodels for D, the necessity is not a logical necessity but a necessity with some nonformal content, a metaphysical necessity. (The satisfaction clause is stated in [1984: 315]). Cocchiarella argues that this secondary semantics is equivalent to the semantics in Kripke [1959a]. Hintikka's notion of a model set does not allow the contrast Cocchiarella made between the primary and secondary semantics for logical necessity. This contrast is most naturally seen in a theory of models, and for this reason Hintikka's later discussion [1980; 1982] of Kripke's and others' metaphysical semantics in terms of the primary/secondary semantics distinction used the notion ofa model. However, I believe Hintikka's early semantics (1957-1963) was a secondary semantics and that one may formulate the primary/secondary distinction using only the concepts in Hintikka's early writings. Each model set can be embedded in a maximal model set and a maximal model set is an extended state description [1961: 121]. Although Hintikka does not say this, I think we can take all the maximal model sets with respect to a language Land characterize logical necessity in terms of the set of all the maximal model sets with respect to L. This would pertain to the primary semantics for logical necessity and the secondary semantics for logical necessity would be a "cut down" in the sense that necessity is instead analyzed in terms of all the members of a subset of the set of all the maximal model sets with respect to L. (eds.),

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But we must not think that the distinction between the primary and secondary semantics must be formulated within Hintikka's modal logic in order for it to be the case that his semantics for modal logic is a secondary semantics. Even if Hintikka's early modal logic (1957-1963) does not permit the formulation of a primary semantics for logical necessity, it is still the case that his early modal logic is a secondary semantics. More generally, we must not think that his semantics must be a secondary semantics (if a secondary semantics is held to essentially involve models) in order for his semantics to be a metaphysical semantics. It suffices that the necessary operator in his modal logic is not analyzed in terms of the one and only set of all logical possibilities, and we have seen in our above discussion that the necessary operator in his semantics does not quantify over all logical possibilities but a subset of them. Modal logicians in the 1950s and 1960s were not aware of such metaphysical/logical distinctions. At this time, neither Hintikka nor Kripke noted this distinction (even though their semantics were metaphysical rather than logical semantics). The main element in this distinction (insofar as it pertains to a primary and secondary semantics involving models) was first noted by Cocchiarella in 1973, as I indicated above. Cocchiarella's dissertation [1966], which was finished in 1965, discussed the problem of the nature of the material content in secondary semantics. In his dissertation, he showed how this content can be explained if we adopt a temporal interpretation of modality, where the alternativeness relation is interpreted in terms of temporal relations, such as a causal signalling relation between different local times (as part of Einstein's Special Theory of Relativity). (A.N. Prior discussed a temporal interpretation of modal notions, but not in terms of the primary/secondary semantics distinction.) Cocchiarella subsequently developed a logic of natural kinds with the view in mind of interpreting the material content in terms of essences (see Cocchiarella [1987] for references). Hintikka first discussed the primary/secondary semantics distinction (or rather, a relevantly similar "standard/nonstandard" distinction) in a 1977 talk in Rome, later published as his [1980]. (For the reference to the Rome talk, see Hintikka's [1982: 89]. Note that the "early Hintikka semantics" I analyzed is different than Hintikka's later semantics. In Hintikka's later writings on modal logic, e.g., his [1980; 1982; 1986], one of his aims is to show that the secondary or "nonstandard" semantics for logical modalities is not the proper semantics for logical modalities. Hintikka has also raised serious doubts about whether an adequate semantics for logical modalities can be developed (e.g., [Hintikka, 1982]). Furthermore, Hintikka now rejects the notion of a metaphysical necessity inasmuch as this is understood as something narrower than logical necessity and broader than physical necessity [Hintikka and Sandu, 1995]. Contrary to what many writers say, Kripke has evinced no awareness of a logical/metaphysical distinction in his writings. Even Cocchiarella [1984: 317] is not strictly accurate when he writes: "Kripke himself, it should be noted, (eds.),

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speaks of the necessity of his semantics not as a formal or logical necessity, but as a metaphysical necessity (cp. Kripke [1971: ISO]". It is true that Kripke speaks of his necessity as a metaphysical necessity. However, Kripke explicitly and emphatically identified logical with metaphysical necessity, as I demonstrated at length in my [1998a] with extensive quotations from Kripke's [1971] and [1972]. I think Cocchiarella's demonstration that Kripke's semantics is not a semantics for logical necessity is sound, but Kripke at no time has expressed an awareness of the distinction or an affirmation that his semantics is a secondary semantics for logical necessity. I have suggested that the nonformal element in the interpretation of the box and diamond should be understood in terms of the non-trivial essences of objects. Many New Theorists of Reference, however, are in a position similar to Kripke in not taking a stance about (or mentioning) the primary and secondary semantics for logical necessity and its relation to non-trivial essentialism. Marcus [1961; 1967; 1971] has argued that neither a Carnapian semantics nor a Kripkean semantics for modal logic includes any non-trivial essential attributions among its theorems (but without mentioning a primary/ secondary semantics distinction). At the opposite end, Plantinga [1974: 241-S1] has argued that the semantics for modal logic (what Plantinga calls "applied semantics") that Marcus considers as well as Kripke's semantics include nontrivial essential attributions among their theorems (but without mentioning a primary/secondary semantics distinction). Notwithstanding this difference, both Marcus [1961; 1967; 1971] and Plantinga [1967; 1969; 1970; 1974] believe objects have non-trivial essences. What this goes to show is the fundamental importance of Cocchiarella's [197Sa; 1975b] for the New Theory of Reference, for in these publications we see for the first time the recognition and argument that systems of modal logic that include non-trivial essentialism (or more precisely, a nonformal content in the systems using models) in their semantic characterizations of possibility and necessity are secondary semantics oflogical necessity. It also shows that we can interpret the New Theorists of Reference in this way but this does not imply that this is how all (or even most) New Theorists of Reference interpret their own work. It is not requisite for New Theorists to interpret their own work in this way in order for this interpretation to be true. (The evaluation of Marcus' theory that neither Carnapian nor Kripkean semantics include non-trivial essential attributions as theorems, and the evaluation of Plantinga's theory that the "applied semantics" of both Marcusian and Kripkean semantics include non-trivial essential attributions, is too large a task to undertake here. It suffices to note that there is no uniform agreement of New Theorists of Reference about the relation of non-trivial essentialism to modal logic.) Cocchiarella himself writes of the secondary semantics for logical necessity that there is a difficulty or unsolved problem with its "objective, as opposed to its merely formal, significance" [1984: 310]. This is tantamount to the problem of the meaning or truth of non-trivial essentialism. (eds.),

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Cocchiarella [1984] believes that the introduction of a secondary semantics for logical necessity, which he believes was first made in Kripke's 1[959a], provided the semantical framework for the later theory that some "logical necessities" (in the sense of the secondary semantics) are knowable a posteriori. Cocchiarella shares with others the belief that the theory of a posteriori necessities was first published in [Kripke, 1971; 1972]. I shall now leave the issue of the primary/secondary semantics distinction, a topic in modal logic, and turn to the issue of the distinction between necessity and a prioricity, which is a topic in the disciplines of "epistemology" and "metaphysics". 9. PLANTINGA'S DISTINCTION BETWEEN THE EPISTEMIC NOTIONS OF A PRIORI/A POSTERIORI AND THE METAPHYSICAL NOTIONS OF NECESSITY ICONTINGENCY

Who first made (in the context of the New Theory of Reference) the explicit distinction between the epistemic notion of a priori and the metaphysical notion of necessity? (This distinction is logically implied by Marcus [1961; 1963], as I argue in [Smith 1995a; 1995b; 1998a] but we are here interested in the first explicit statement of this distinction.) It is a "commonplace" that this explicit distinction was first published in Kripke's [1971] and [1972]. This distinction is now even called "Kripke's Thesis" by some and an a posteriori necessity is called by some a "Kripkean necessity". For example, D.M. Armstrong talks as follows about a question involving a necessary a posteriori truth: "it may be a question to be decided a posteriori to the extent that it can be decided. But it is not a contingent matter. It is what might be called a Kripkean necessity". [Armstrong, 1989: 67]. Are these commonplaces about the history of contemporary analytic philosophy accurate? Would it be more accurate to call an a posteriori necessity a Plantingean necessity, and the relevant thesis Plantinga's Thesis, if one is interested in attributing an idea to its originator? (This concerns the context of the New Theory of Reference; the theory is already present in Moore [1899] and can be traced back to Aristotle and Plato. Perhaps we should call the thesis "Moore's thesis" or "Plato's thesis".) First let us quote from Kripke's [1971]; Kripke said we should "distinguish between the notions of a posteriori and a priori truth on the one hand, and contingent and necessary truth on the other hand" [1971: 152-53]. Kripke wrote in a well-known passage that "Hesperus is Phosphorus" is both empirical and necessary: "I thus agree with Quine, that 'Hesperus is Phosphorus' is (or can be) an empirical discovery; with Marcus, that it is necessary. Both Quine and Marcus, according to the present standpoint, err in identifying the epistemological and metaphysical issues" (1971: 154, n. 13). Kripke's [1971] and [1972] are held by some to have "astonished" the philosophical community with the discovery of this distinction, but what is astonishing, however, is not this alleged discovery but the pervasiveness of the (eds.),

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oversight that Plantinga earlier published this same distinction in an article that was hard to miss ("World and Essence", in the October, 1970 issue of The Philosophical Review).

Kripke presented his lectures on "Naming and Necessity" at Princeton University in January 1970 and Plantinga presented his paper (in final draft form) on "World and Essence" in October 1969 at Cornell University. The ideas in the final draft were worked out by Plantinga in 1968~69, when he was a fellow in the Center for Advanced Study in the Behavioral Sciences in Palo Alto.4 Here is Plantinga's statement (the third sentence, "And hence ..." states the traditional view he is refuting): "Consider the well-known facts that Cicero is identical with Tully and that Hesperus is the very same thing as Phosphorus. Do not these facts respectively represent (for many of us, at least) historical and astronomical discoveries? And hence are not the counterfactuals Hesperus and Phosphorus are entities distinct and Tully is diverse from Cicero, though counterfacts indeed, contingently counterfactual? [Plantinga says the answer to this last question should be NO; they are necessarily false. He says the traditional thesis that they are contingently counterfactual is false, for the following reason (in this passage, "Kronos" is the name of the actual world):] "The argument here implicit [that if a truth is a posteriori, it is contingent] takes for granted that the discovery of necessary truth is not the proper business of the historian and astronomer. But this is at best dubious. I discover that Ephialtes was a traiter; I know that it is Kronos that is actual; accordingly, I also discover that Kronos includes the state of affairs consisting in Ephialtes' being a traitor. This last, of course, is necessarily true; but couldn't a historian (qua, as they say, historian) discover it, too? It is hard to believe that historians and astronomers are subject to a general prohibition against the discovery of necessary truth. Their views, if properly come by, are a posteriori; that they are also contingent does not follow." ]1970: 480-481].

Plantinga proceeds to discuss a posteriori necessary identities, such as Hesperus is Phosphorus. "Exactly what was it that the ancient Babylonians discovered? Was it that the planet Hesperus has the property of being identical with Phosphorus? ... [Before the discovery] the Babylonians probably believed what can be expressed by pointing in the evening to the western sky, to Venus, and saying 'This is not identical with' (long pause) 'that' (pointing to the eastern sky, to Venus, the following morning). If so, then they believed of Hesperus and Phosphorus-identity that the latter does not characterize the former; since Phosphorus-identity is the same property as Hesperus-identity, they believed of Hesperus-identity that it does not characterize Hesperus. ... The quality of their intellectual life was improved by the Discovery in that they no longer believed of Hesperus that it lacked the property of Hesperus-identity.... Still, this is at best a partial account of what they discovered. For they also believed that there is a heavenly body that appears first in the evening, and another, distinct from the first, that disappears last in the morning. This is a contingent proposition; and part of what they discovered is that it is false .... And of course this is a contingent fact; there are possible worlds in which the thing [Venus] that in fact has the distinction of satisfying both sets of criteria [appearing first in the evening and disappearing last in the morning] satisifes only one or neither." [1970: 481-482].

Plantinga includes identities as well as nontrivial essential attributions to be among the necessities that are a posteriori. It is perhaps symbolic of the neglect of Plantinga's original contributions to the New Theory of Reference that his own later [1974: 81~87l account of a (eds.),

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posteriori necessities is widely regarded as a restatement and defense of "Kripke's Thesis" (e.g., Wong [1996: 53]. "Kripke's Thesis" is that identity statements such as "Hesperus is Phosphorus" are necessary a posteriori. Wong notes "Plantinga makes the same claim as Kripke about the modal status of 'Hesperus is Phosphorus' " [1996: n. 24]. But Wong is not aware that Plantinga made this claim prior to Kripke in Plantinga's "World and Essence"; Wong regards Plantinga's claim (later stated in [Plantinga, 1974: 81-87] as a defence of Kripke's statement of this Thesis [Kripke, 1972], which is supposed to be where Plantinga and everybody else got the Thesis. Thus Wong says "I will now outline a fairly common way of defending Kripke's [sic] Thesis, as suggested by Alvin Plantinga [1974: 81-87]" [Wong, 1996: see his discussion of his sentence numbered (6)]. Plantinga's [1970] appears nowhere in Wong's very extensive bibliography. The virtually universal belief that Plantinga's statement of the Thesis in [1970] does not exist and that the Thesis was first stated in Kripke [1971, 1972] is one of the main beliefs that needs to be changed if an accurate account of the genesis of the ideas associated with the New Theory of Reference is to replace the "standard account" that remains prevalent in some quarters. Plantinga's original presentation of the theory of a posteriori necessities takes place in the context of a theory of metaphysical necessity. Plantinga has in mind metaphysically necessary truth when he says that in some cases people can make an empirical "discovery of necessary truth. Their views, if properly come by, are a posteriori; that they are also contingent does not follow". [1970: 481]. To see this, note first of all Plantinga's discussion of nontrivial essential properties. Plantinga writes: "Are there any nontrivial essential properties? Certainly; the number six has the properties of being an integer, being a number, and being an abundant number". [1970: 465]. Socrates "also has essentially some properties not had by everything: being a non-number and being possibly conscious are examples". [1970: 473]. Further, the correct way of explaining Socrates' trivial and nontrivial essences' is "to explain Socrates' essence and essential properties by means of properties he has in every world in which he exists" [1970: 477]. Plantinga is here talking about metaphysically possible worlds ("metaphysical possibility" is here used interchangeably with "broadly logical possibility"; by the time of his [1974], Plantinga uses almost exclusively the latter phrase). Here is the first mention of metaphysical possibilities in the articles or books published in the 1970s: "Recall that a possible world is a state of affairs that could have obtained if it does not. Here 'could have' expresses, broadly speaking, logical or metaphysical possibility.... If a state of affairs S is possible in at least one world W, then S is possible in every world. This principle may be false where it is causal or natural possibility that is at stake; for logical or metaphysical possibility, it seems clearly true." [1970: 475).

There is another and related feature of Plantinga's philosophy of language (eds.),

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and metaphysics that is worth noting; Plantinga's [1967] was the first publication after Marcus' [1961] and [Marcus et aI., 1962] to argue that ordinary names are rigid designators and (contingent) definite descriptions are nonrigid designators. (Hintikka [1963] and F0llesdal [1961; 1967] were talking only tangentially about ordinary names.) In "De Re Et De Dicto", Plantinga says [1969: 257]: "Perhaps the notion ofa proper name itself involves essentialism; perhaps an analysis or philosophical account of the nature of proper names essentially involves essentialist ideas". What Plantinga means here appears on pages 176ff. of his God and Other Minds, published in 1967; the relevant section of this book was written in 1965 and the ideas were presented in seminars at Wayne State University between 1963 and 1967 (after Planting a left Wayne State University for Calvin College).4 Planting a asks us to consider: "( 1) An object x has a property P essentially if and only if x has P and the statement x lacks P is necessarily false." [1967: 176].

Plantinga notes problems will arise if we substitute definite descriptions for the individual variable, but will not arise in the case of names: "Difficulties arise if we generalize to (1); but the instantiation of (1) for Socrates may seem harmless enough, as it will in any case where a proper name replaces the variable 'x' in (1)." [1967: 177]. Plantinga adds that we need rigid designators of properties (e.g., "whiteness") and not non-rigid designators of properties (e.g., "the property I am thinking of') if (1) is to be satisfactory. (Here again I am using the terminology, "rigid/nonrigid' that has become an established part of philosophical vocabulary, and whose meaning is not tied to the details of anyone philosopher's theory. I think a more accurate phrase is "modally stable signifier" but it facilitates communication to stay with established terminology.) Plantinga notes an analogy between rigid/nonrigid designators of properties and rigid/nonrigid designators of individuals: "Still, expressions like 'whiteness', 'masculinity', 'mean temperedness', and the like, differ from expressions like 'Socrates' least important property', 'the property I am thinking of, 'the property mentioned on page 37', and so on, in pretty much the way that proper names of individuals differ from definite descriptions of them". [1967: 178]. P1antinga already holds at this time the theory of nontrivial essences and he uses his theory of essences to indicate how names are rigid designators but definite descriptions are not. Given the rigidity of names for individuals and properties, then (1) is satisfactory. This requirement is embodied in Plantinga's conditions involving rigid names and nonrigid descriptions: "(3) x has P necessarily if and only if x has P and the proposition x lacks P is necessarily false (where the domain of the variable 'x' is unlimited but its substituend set contains only proper names, and

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where the domain of the variable 'P' is the set of properties and its substituend set contains no definite descriptions or expressions definitionally equivalent to definite descriptions)" [1967: 179].

The idea is that (to use my example) "Scott lacks rationality" is necessarily false since the reference of the name "Scott" is rigid in modal contexts. But the definite description, "the biped discussed most frequently by Russell" is nonrigid in modal contexts. Thus, we cannot substitute the definite description of Scott for the variable x in (3) if we want to determine whether Scott has rationality necessarily; it is possible that the biped discussed most frequently by Russell is not Scott. Plantinga extends his criticism of the traditional descriptivist theory of names in his October 1969 talk at Cornell University, "World and Essence". This talk, published as [1970], contains a lengthy criticism of the modal thesis that belongs to the descriptivist theory of names, in particular, Searle's cluster theory, which is also the main target of Kripke's attack in Kripke's January 1970 talk, "Naming and Necessity", published as [1972]. Plantinga argued at length that it is false that "if x exists, x has most of the properties commonly attributed to it". Kripke quotes Searle on page 287 of [Kripke, 1972]: "it is a necessary fact that Aristotle has the logical sum, inclusive disjunction, of properties commonly attributed to him". Kripke comments: "This is what is not so. It just is not, in any intuitive sense of necessity, a necessary truth that Aristotle had the properties commonly attributed to him". [1972: 287]. Plantinga's earlier criticism of Searle's theory is similar. For instance, Plantinga writes such things as: "Searle is wrong, I believe, in thinking the disjunction of the Sj [the properties commonly attributed to Socrates, is] essential to Socrates". [1970: 473]. "Socrates could have been born ten years earlier and in Thebas, let us say, instead of Athens. Furthermore, he could have been a carpenter all his life instead of a philosopher. He could have lived in Macedonia and never even visited Athens." [1970: 473]. In this paper, Plantinga distinguishes two uses of proper names, one in which they are rigid and one in which they are not; he here differs from his [1967], which suggests that names only have a rigid use. Plantinga made several other early contributions to the New Theory of Reference that are not included in the standard history, e.g., there is an explicitly descriptional theory of rigidity Inonrigidity in Plantinga's 1969 article "De Re Et De Dicto"; this paper which was given in a seminar at the University of Michigan in Fall, 1967 and later in a summer 1968 conference that was mentioned in Quine's brief autobiographical sketch in Schilpp's [1986: 37]. The ideas were worked out in a series of seminars given at Wayne State University in 1963-67. 4 By a descriptional theory of rigidity I do not mean a theory that simply notes that some definite descriptions, such as "the number that immediately follows number two" are rigid designators. Rather, Plantinga developed a theory of rigid descriptions that (arguably) could account for all cases of rigidity, even proper names, so that an appeal to direct reference is otiose. In Plantinga's 1969 article, he makes a distinction between definite (eds.),

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descriptions that are used de re or de dicto. Plantinga considers the definite description (using his numbering): (32) It is possible that the number of apostles should have been prime.

Plantinga writes: "Now (32) can be read de dicto, in which case we may put it more explicitly as (32a) The proposition, the number of apostles is prime, is possible;

It may also be read de re, that is, as (32b) The number that numbers the apostles (that is, the number that as things in fact stand numbers the apostles) could have been prime." [1969: 244]

Plantinga's "de re reading" of the description involves the description designating rigidly by virtue of its descriptive conditions. Plantinga uses the phrase "as things in fact stand" to express a rigid descriptive condition that belongs to the "de re reading" of the description "the number of apostles'. This descriptive condition is that "the number of apostles" refers to whatever number is the number of the apostles in the actual world. The description condition is a world-indexed condition that picks out a certain possible world, the actual world. The standard history of the New Theory of Reference has Plantinga making an appearance merely in his [1978], as a "co-originator" of the rigid descriptional theory of names, along with Linsky [1977]. I mistakenly endorsed this part of the standard history in my [1995a] and [l995b]. As I briefly suggested earlier, the standard history has some of the contributions of Kripke and Plantinga reversed. The theory of rigid descriptional names is first sketched in part by Kripke in 1962, but Plantinga had published before Kripke's [1971] and [1972] the distinction between rigid names and nonrigid descriptions, the extensive modal argument against Searle's "cluster of descriptions" theory of reference, and the theory that the necessary/contingent distinction is a metaphysical distinction and is nonequivalent to the epistemological distinction between the a priori and the a posteriori. 10. GEACH, DONNELLAN, KRIPKE AND THE "HISTORICAL CHAIN" THEORY OF REFERENCE

The reason why Peter Geach [1969] is not recognized or credited for originally publishing the "historical chain" theory of reference is one of the most perplexing mysteries of the standard history of contemporary analytic philosophy. A review of the literature suggests the nearly universal consensus of opinion is that Donnellan [1970] or Kripke [1972] developed the theory and that Geach's presentation of the theory does not exist. There is no debatable question about textual interpretation, since Geach's presentation of the theory [1969] is virtually identical with Kripke's presentation [1972] and to a slightly lesser extent with Donnellan's presentation [1970]. Both Kripke [1972: 769] and (eds.),

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Donnellan [1970: 357] refer to each other's presentation of the theory, but neither refer to Geach's presentation and Geach is absent from subsequent discussions of the theory and accounts of its origin. (Kripke added a sentence to footnote 2 of his [1972] in [1980: 23, n. 2], reading: "I also recall the influence of early conversations with Albritton and with Peter Geach on the essentiality of origins". The "essentiality of origins" is a different topic than the historical chain theory of reference.) In this section, I need only quote the parallel presentations. Geach writes: [1969: 288-89] "I do indeed think that for the use of a word as a proper name there must be in the first instance be someone acquainted with the object named. But language is an institution, a tradition; and the use of a given name for a given object, like other features of language, can be handed on from one generation to another; the acquaintance required for the use of a proper name may be mediate, not immediate. Plato knew Socrates, and Aristotle knew Plato, and Theophrastus knew Aristotle, and so on in apostolic succession down to our own times; that is why we can legitimately use 'Socrates' as a name the way we do. It is not our knowledge of this chain that validates our use, but the existence of such a chain; just as according to Catholic doctrine a man is a true bishop if there is in fact a chain of consecrations going back to the Apostles, not if we know that there is. When a serious doubt arises (as happens for a well-known use of the word 'Arthur') whether the chain does reach right up to the object named, our right to use the name is questionable, just on that account. But a right may obtain even when it is open to question .... I introduced the use of the proper name 'Pauline' by way of the definite description 'the one and only girl Geach dreamed of on N-Night'; this might give rise to the idea that the name is an abbreviation for the description. This would be wrong."

Geach's theses can be compared with Kripke's [1972: 298-300]: "Someone, let's say, a baby, is born; his parents call him by a certain name. They talk about him to their friends. Other people meet him. Through various sorts of talk the name is spread from link to link as ifby a chain .... A certain passage of communication reaching ultimately to the man himself [Richard Feynman] does reach the speaker. He is then referring to Feynman even though he can't identify him uniquely.... So he doesn't have to know these things [descriptions]. but, instead a chain of communication going back to Feynman himself has been established, by virtue of his membership in a community which passed the name on from link to link .... On our view, it is not how the speaker thinks he got the reference, but the actual chain of communication, which is relevant. ... Obviously the name is passed on from link to link. But of course not every sort of causal chain reaching from me to a certain man will do for me to make a reference. There may be a causal chain from our use of the term 'Santa Claus' to a certain historical saint. but still the children, when they use this, by this time probably do not refer to that saint."

Kripke's theory is more similar to Geach's than is Donnellan's, but the basic ideas are also present in Donnellan [1970]. Donnellan writes [1970: 352-353] "In general, our use of proper names for persons in history (and also those we are not personally acquainted with) is parasitic on uses of the names of other people - in conversation, written records, etc.... The history behind the use of a name may not be known to the individual using it. ... Yet, in such cases the history is of central importance to the question of whether a name in a particular use has a referent and, if so, what it is. The words of others, in conversations, books and documents can ... distort our view of what we are naming. But at the same time it can, to one who knows the facts, provide the means of uncovering the referent, if there is one.

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The role of this history leading up to a present use of a name has almost always been neglected by those who accept the principle of identifying descriptions . ... That is, if we neglect the fact that there is a history behind our use of the name 'Thales' or 'Aristotle' and concentrate only upon the descriptions we would supply about their life, their works and deeds, it is possible that our descriptions are substantially wrong without the consequence being that we have not been referring to any existent person."

Despite these virtually identical passages, the historical chain theory of names has been attributed almost universally to Donnellan and Kripke for the past 25 years or so, with Geach being eclipsed from the scene. I I. CONCLUSION

The basic ideas of the New Theory of Reference had been published or presented in lectures before 1970, mainly by Marcus, F0llesdal, Hintikka, Plantinga and Geach. What remained was to develop and extend the concepts formulated by these five thinkers. The development had two waves: the first involving Kaplan (who extended the ideas to indexicals, among other contributions), Kripke and Putnam (who extended the ideas to natural kind terms, among other contributions), and Donnellan (who concentrated mostly on the causal theory of reference, but also made other contributions). Kaplan, Kripke, Donnellan and Putnam (who appear in the standard history as the four main originators of the New Theory of Reference) are in fact four of the main figures in the first wave of developers of this theory. There is a fifth figure in the first wave of developers who does not appear in the standard history, namely, Nino Cocchiarella, whose explanation of the distinction between metaphysical and logical necessity in terms of primary/secondary semantics is crucial to understanding the New Theory of Reference but has gone unrecognized by most New Theorists. The second wave of developers, headed by such philosophers as Michael Devitt and Nathan Salmon, covers a large number, if not most, of contemporary philosophers. What is know by the referentially used description, "The New Theory of Reference", has already become one of the major movements in the history of analytic philosophy, comparable to logical positivism and ordinary language philosophy. Given the extent and importance of this movement, it is not unreasonable to think that the time is ripe for more philosophers to engage in the research necessary to construct a complete history of the origins and development of this movement. 5 Philosophy Department Western Michigan University

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NOTES My mis-interpretation appears in [Smith, 1995b]. My mistake lay in not realizing that Smullyan was talking about an artificial language and in not realizing that his first solution to Quine's paradox involved using a Russellian theory of logically proper names. I am not aware of any other recent publications in which Smullyan's theory is interpreted accurately. 2 I am aware of the problems with the idea that there is a set of all possible worlds, but will continue to talk of sets since this is the language used in the 1950s and 1960s. 3 I thank Nino Cocchiarella for providing me with the information about the origin of his ~1975a].

I am grateful to Alvin Plantinga for answering my questions about the background of some of his publications. Plantinga indicates that (according to his best recollection) some of these ideas were circulating around Wayne State University before he left in 1963 (in discussions that included, besides Plantinga, Robert Sleigh, Ed Gettier, Richard Cartwright, Hector-Neri Castaneda, George Nakhnikan and [a bit later] Keith Lehrer) and Plantinga emphasized that these other named philosophers deserve as much credit as he for the general gist of the ideas I am attributing to Plantinga. 5 I thank two referees for their helpful criticisms of an earlier draft of this paper, which enabled improvements to be made. My main intellectual debt is to the writings by, and private communications with, Nino Cocchiarella, whose responses to my questions about his theory of the primary/secondary semantics for logical necessity has proved helpful in my account of the history of modal logic. My interpretation of Kripke's [1959a] derives from Cocchiarella's interpretation and is similar on most points. I have also been influenced by Lindstrom's [1998] and Hintikka's [1980; 1982]. I differ from these three authors on a number of points but my main difference from them is my interpretation of Hintikka's 1957-1963 writings and the particular way in which I have formulated the metaphysicalliogical distinction (but my basic idea of a nonformallformal interpretation of the box and diamond comes from Cocchiarella). I thank Alvin Plantinga for providing me with background information about the genesis and dates of origin of some of his publications (see footnote 4). I also thank Dagfinn F0llesdal for clarifying some of his ideas for me, but he is not aware of all the particulars of my interpretation of his ideas and I am not sure if he would agree with all of them. REFERENCES

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(eds.),

NAME INDEX

Albritton, Rogers 143-4, 250, 277 Almog, Joseph 3, 4, 11, 51, 141, 169, 235-6, 249,264-5 Aquinas, St Thomas 239 Aristotle 145, 199,239,241,271 Armstrong, David 144,271 Augustine 174 Ayer, Alfred Jules 149, 152 Bacon, John 95, 102 Bayart, 186 Bemays, Paul 189 Beth, E.w. 267 Black, Max 90 Boolos, George 232 Bradley, F.H. 237 Braun, David 4 Brouwer, L.E.J. 184,200,201 Burge, Tyler 138, 141, 142, 146, 174 Burgess, John x, 65, 85-87, 144, 149, 150,151, 153-155, 157-163, 173-175 Cantor, G. 226 Camap, Rudolf 98, 106, 107, 110, 165, 167, 168,175,181,182,184,186,187,194,2045, 209-11, 215, 231, 240, 242-4, 249, 251, 258-61, 264-5, 267, 270 Cartwright, Richard 175,279 Casteneda, Hector-Neri 175, 279 Chastain, Charles 250 Church, Alonzo 15, 17, 19, 39, 69, 100, 196, 243-4 Cocchiarella, Nino 97, 105, 175,236, 261, 26771,278-9 Cohen, Robert S. ix, xii Craig, William Lane 56 Creswell, Max 232 De Finetti, Bruno 38 Devitt, Michael 141-42, 148-49, 153, 175,236, 278 Donnellan, Keith xii, 3-5, 8,11,14,41,90,137145, 147-48, 158, 160, 174, 175,236,250, 277-8

285

Dretske, Fred 144 Etchemendy, John 215 Falk, Arthur 60 Feys, 182,201,259 Fitch, Frederick 15, 17, 19,21, 23, 28, 38-40, 42,45, 60, 67-73, 75, 77, 81, 82, 100, 126, 132, 174, 191, 194,201,244-6,250-1 Fitzgerald, Paul 40, 174 Fogelin, Robert xii, 60-61 Follesdal, Dagfinn x, xii, xiii, 89, 97, 99, 122, 138, 146, 175, 203, 236, 245, 246-52, 254-7, 263,266,274,278-9 Forbes, Graeme 236 Fraenkel, A.A. 201 Frege, Gottlob 4, 5, 90, 92-94, 102, 105, 107, 137, 140, 147, 148, 187, 195,235,239,2524,256 Garson, James W. 86, 232 Geach, Peter 90, 93, 137, 138, 142-146, 174, 236,248,250,263,277-8 Gentzen, G. 203 Gettier, Edmund 175,279 Godel, Kurt 182, 184, 185, 199,203 Grice, H. Paul 143-4 Gurlank, David 156 Herodotus 145 Hilbert, David 189 Hintikka, Jaakko x, xii, 146, 148, 153, 167,203, 207, 210-11, 213, 236, 245, 249-50, 254, 258-69,274,278-9 Holt, James 250, 256 Hughes, G.E. 232 Hume, David 57, 239 Jonsson, B. 207, 231 Kanger, Stig x-xi, 47, 165, 203-233, 245, 25962, 264, 266-7 Kant, Immanuel 237-8 Kaplan, David 3-5, 11, 14, 16,87, 89, 90, 137, 138, 141-43, 146-49, 149, 153, 158, 160, 165,168-73,175,224,235-6,267,278 Kneale, William 90, 93

286

NAME INDEX

Kreisel, Georg 229,232 Kripke, Saul passim, but see especially vii-xiii, 3-12,13-35,37-61,66,72,73,76,77,80,82, 89-123, 125-135, 137, 138, 140-78,203-233, 236,238,247-50,252-7,261-79 Langford, C.H. 201, 240 Lehrer, Keith 279 Leibniz, Gottfried Wilhelm 47, 95, 100, 153, 166,192,194,204-5,240 Lewis, David 232 Lewis, Clarence Irving 7, 98, 107, 110, 152, 165,182,201,240,265 Lindstrom, Sten x-xi, 279 Linsky, Leonard 7,8,40,43,44, 50, 86, 99, 252, 276 Locke, John 239 MacCarthy, Desmond 236 Malebranche, 57 Marcus, Ruth Barcanpassim, but see especially vii-xiii, 3-12, 13-35, 37-61, 65-87, 89-123, 125-135,137-39,141,144,146-78,186,191, 194, 197,201,204,224,235-6,240,244-7, 249-57,263,270-2,274,278 McCracken, C.l 57 McDowell, John 11 McGee, Van 231 Mill, John Stuart 28, 40, 50, 67, 90, 92-95, 97, 104, 108, 118, 126, 129, 132, 158, 160, 163, 169,174,239,243,245,251,256 Montague, Richard x, 146, 203, 207-11, 231, 259,263-4,266-7 Moore, George Edward 236-8,241,260,271 Nagel, Ernest 90 Nakhnikan, George 279 Nerlich, Graham 170 Ockham, William 174, 239 Parmenides 239 Parsons, Terence 247 Pears, David 90 Peirce, Charles Saunders 174 Perry, John 3, 4, 5, 235-6 Plantinga, Alvin 7, 8,40, 43, 44, 50, 138, 146, 153,156,157,161,175,236,238,252,257, 270-6, 278-9 Plato 174,239,271 P10tinus 5 Prior, Arthur 67,69,96,97, 100, 112, 127, 146, 243,255,263,266,269

Putnam, Hilary xii, 3,4,5,52,53,90, 104, 141, 158,236,238,250,278 Quine, Willard van Orman viii-xiii, 3, 14, 15, 17,18,23,38,39,45,56,67-73,75,85,86, 89,90,97-102,105, 107-1l0, 114, 116, 1l9122, 132, 134, 164, 165, 187, 191, 197-199, 201,221,240-9,251-7,263,271,276 Ramsey, Frank Plumpton 38, 96, 97, 127 Recanati, F. 4 Richard, Mark 16 Russell, Bertrand 5, 67, 72, 79, 86, 90, 95-97, 99,101-103,105,107,112,114, 1l8, 126, 127, 131, 137, 140, 148, 158-160, 163, 184, 188,190,235,238-9,242-5,252-4,256 Salmon, Nathan 3, 4, 6, 9,11,41,44,141,142, 145, 160, 235, 236, 278 Sandu, Gabriel 148, 153,258,270 Schopenhauer, Arthur 129 Searle, John 90, 94, 97, 275-6 Shapiro, S. 99 Sidelle, Alan 170 Sleigh, Robert 175, 279 Siote, Michael 250 Smith, Quentin vii-xiii, 13-35,48,51,56,65-87, 123, 125-135, 137 Smullyan, Arthur 15, 17-19,21,23,28,38-40, 42,45,60,67-73,77,81,82,85,86,97,99, 100, Ill, 118, 126, 132, 160, 174, 191-94, 241-2,243-6,249-51,255,279 Soames, Scott vii-xiii, 3, 4, 37-61, 90,106, 123, 125, 129, 132, 150, 151, 153-155, 157, 163, 174,175 Strawson, Peter 90, 94 Tarski, Alfred 204,206,207-9,231 Thales 145 Tooley, Michael 144 Vallicella, William 60 Von Wright, Georg Henrik 260, 262 Wedberg, Anders 203 Wettstein, Howard 3, 4, 5, 11, 141, 160, 235-6 Whitehead, Alfred North 160 Wilson, Neil x, 191, 192,201 Wittgenstein, Ludwig 60, 96, 97, 174,205, 239, 260 Wong, Kai-Yee 273 Yablo, Stephen 236, 238 Zabludowski, A. 85 Ziff, Paul 90, 94, 126, 132, 174

SUBJECT INDEX

a posteriori 7, 49-50, 51, 131-2, 155-7,235, 239. See also necessity a posteriori a priori 7, 8, 26, 27, 49, 52, 101, 109, 111-2, 127,130-2,134,153-7,160-2,235,237,239, 253, 271. See also contingent a priori absolutely infinite 226 abstracts 187 accessibility relation 206-8,211-12,217,225, 259. See also alternativeness relation accidental vs essential. See essential properties acquaintance 142 aliases, problem of 98 alternativeness relation 259-60, 262, 265-6, 269. See also accessibility relation American Philosophical Association vii, xi analytic truth 8, 18,25,52,72,79,81,86,95, 98, 101, 109, 110, 127, 130-2, 134, 152-3, 213-5,217,220 anonymity, problem of 98 arbitrariness, problem of 98 assignment 212, 216-8,222,225,228 assignment operator, constant 223-4 Barcan formula 30, 87, 205, 209-10, 213 belief statements, see knowledge statements Brouwer's axiom 184,201 capitalization 94 Carnap frame 210 causal theory ofreference vii, 6, 9, 20, 103-4, 115, 125, 127, 137-8, 141-5, 173-4,235,248, 277-8 Church's theorem 206 classes, identity condition for 184 class abstracts 39, 184, 186, 188-90, 193 closed formula 98 coextensiveness 197-8, 200 coincidence relation 219, 221 common nouns 103-4 completeness theorem, Godel's 203, 206 completeness theorems for modal logics 181, 195,211,228 concept 237

concept, individual 168, 187,219-21,244 congruent 6, 39,42,240 constant, individua147, 86, 89, 143, 155, 166-7, 169,258 constant domain (in model theory) 97, 170 context 6, 107-8, 111-2, 127. See also modal context contingent. See necessity, necessary truth contingent a priori vii, 28, 105 contingent vs empirica125, 49,51 counterfactual argument (against descriptive theory) 93,103,104-7. See also modal argument Cornell University 157, 272, 275 counterfactual contexts 77, 108 counterfactual situation 154 counterfactual stability 105-7. See also necessity, metaphysical definition 93 definition, contextual 187-8 demonstrative pronouns 103, 239 descriptions passim, but see especially 7, 38, 90, 94,96,99, 100, 101, 106, 122, 130-2, 138, 142, 144, 181, 182, 184, 186, 189-91, 199-200 description, attributively used 8,41, 137-41 description, contingent 8, 43, 44, 46, 80, 156, 236 descriptions, disguised 3,5,6,38-40,67, 189 description, empirical 10 description, Fregean 16 description, identifying 4 description, modally stable 8 description, necessary 7 description, reference-fixing 6, 41,52, 143-4 description, referentially used 8, 41, 137-41 description, rigidified 86 description, rigid 122, 276 descriptions, Russell's theory of 99, 184, 191, 242-3 description, singular 5, 45, 150-1 description, unique 5, 40 descriptive meaning 92

287

288

SUBJECT INDEX

descriptive sense, contingent (of names) 6 descriptive theory of names 92, 93, 95,101, 102, 103,275 designator, non-rigid 8, 48, 105,274 designator, rigid. See rigid designator dictionary. See also lexicon, encyclopedia 10, 19,54-5,92,110,115-7,119-20,133-4,1557, 175,253 dictionary, biographical 10 direct reference vii, xii, 3-12, 19,35,38-9,42, 43,50,68,81,92,115,121,126-7,137,139, 141,143,168,173,235,237-9,245,256 discovery, non-empirical 112 domain 47,206-8,208-9,214,216,217-8,222-6 empirical, see a priori encyclopedia, encyclopedic dictionary entry. See also dictionary, lexicon 10, 92, 110, 113, 115-7,132-3,135 epistemic contexts, see knowledge statement, context epistemological argument (against descriptive theory) 7, 24, 27-8, 37,43-4,48-50,93, 1034, 146 equivalence, strict 6-7 essence 162-4, 258, 270 essential properties 10, 98,121-2,153,163-4, 254-5, 270, 273 essentialism vii, x, 3-4,10,14,17,34,119-21, 143,153, 199,247,253-5,270-71 equivalence relation 6 existential generalization 73-5, 86, 191-2,221 extensional opacity 246 extensional vs intensional, see intensional extensions 187,206,212,228 fact. See state of affairs fact, empirical 7-8, 24, 25, 26, 49-50, 56,96, 100, 109 fact, contingent 25, 49, 51 Gentzen's Haupstatz 203 genus 8, 129-30, 139-40 historical chain theory. See causal theory of reference identity vii, 6-7, 48, 58, 70,100,106,111-3, 131, 134, 152, 181-2, 190-1, 194-5,200,213, 219-221,223,253 identity, necessity of 3,7,9, 10, 11, 13, 14, 17, 18,19,22-23,28,29-31,38,43-6,54,59,60, 69,70,72,73-77,78-9,80,87,95,105,116,

126-7,156,163-4,213,224,243,250,256, 272-3 identity of extension 186, 194 identity of intension 184 identity statement 99,101,102,105-7,110, 118-20, 152, 158-9, 160 identity, transworld 3 incompleteness, semantic 195 indexicals 8, 44,146-7,188 indiscernibility 6, 13 Indiscernibility ofIdenticals 95, 100, 192,213, 220,223 intensional entities 187, 197,204 intensional 18, 39, 74-5, 112, 197,204. See also context intensional arithmetic 99 interpretation 207-9, 216-8, 225, 228-9 interpretation, metalinguistic 214 interpretational semantics 215 inventory 91, 102 K-validity 212 Kanger model 217, 223-6 Kanger semantics 204,208,214-15,218,223-6, 230. See also semantics, set domain; semantics, class domain Kanger-Kripke semantics 203 knowledge statement 18, 66, 107, 108, 111-4, 251,264 Kripke models 207, 212 Kripke semantics 203, 230, 232 language, formal with modalities 105 language, ordinary vs artificial 14, 150-1, 2425, 248, 250-1, 279 Leibniz' Law. See Indiscernibility of Identicals lexicography 92 lexicon, lexical dictionary entry, see also dictionary, encyclopedia 91, 92, 110,113, 1167, 132-3, 135, 155-6 linguistic vs empirical. See analytic truth, a priori logical atomism 95,96,97, 114 logical consequence 204, 215, 217, 225 logical truth 72, 98, 101, 152, 154, 161,204-6, 208-11,214-15,217,219-20,227-8,230 logicaUy proper names 14-15, 17,27,67,69,72, 97, 101-2, 107, 112, 118, 158-60,242-3. See also tag, names in an ideal sense, proper name Lowenheim-Skolem theorem 203, 231 meaning postulates 135

SUBJECT INDEX modal argument 6-7, 21-22, 28, 33, 37,42-4, 46,57-80,77-81, 146,276. See also counterfactual argument modal context 3, 6, 8, 16, 17, 18,23,38,40,42, 44,59,66,77,107, 111, 114, 147, 159, 196-8, 210,218,224,255 modal distinctions, collapse of 182, 184-6, 199200

modal logic x, 9, 38, 89, 91, 95, 97, 109, 118, 203-4, 206-7 modal logic, quantified 13, 17, 152, 158, 181, 195-8,200,203-4,206,211-13,216,221-2, 240, 242-3, 246 modal logic, semantically complete 181 modal operator 47-8,75, 166,205-7,210,2137,225, 227-8, 267-8 modal paradoxes 39 modal system, Godel's 182, 184-5 modal system, QS5= 213, 227-9 modal system SI 182 modal system S2 70,186-7,266 modal systems S4, QS4 7, 13,22,29,70,87, 152,158,160,182,184-5,204,207 modal system S5 152, 181, 182, 184-5, 194,204 modal test 7 modalities, iterated 187, 201 modality, de dicto 34, 98, 120-2, 164, 257 modality, de re 34,51-2,98,99, 120-2, 164, 257 modality, epistemic 190 modality, logical 190, 255 modality, metaphysicaL See necessity, metaphysical model 47, 105, 154, 159, 166-7,209,211-12, 217,231,260-1,265,267-8 model sets 211, 260-5, 267-9 model structures 211-12, 228 model theory 23,47,97, 105-6, 166,203 Morning Star paradox 220, 223. See also identity, substitutivity names, naming passim, but see especially xi, 311, 13-35,37-61,73-137, 155, 159, 165-6, 181, 189-90,195,199,239 names, coreferential 157 names, in an ideal sense 91, 1l0, 126, 128. See also tag, logically proper names names, logically proper. See logically proper names names, proxy 148 name-relation method 241 natural kind 3, 8, 9 natural kind terms vii necessary truth 9, 109, 110, 159, 161,204,214, 259

289

necessity 98-99,101,106-7,110,112,130-1, 152,154,205,214,235,239,271 necessity, a posteriori 3, 8, 11,24-8,50-56, 1056,113,130,157,162,164,235,236-9,271-3 necessity, analytic 213,215,217,220-1 necessity, de dicto. See modality, de dicto necessity, de reo See modality, de re necessity, logical xi, 72, 75, 107, 152-3, 161-3, 204-9,214-17,224,229-30,257-8,260-1, 264,267-70 necessity, metaphysical, see also counterfactual stability xi, 72, 75, 81,107,130,161-3,213, 215,227,229-30,232,235,238,257-63,26470,273-4 necessity, metaphysical feature of facts 109 necessity, senses of (metaphysical vs other) 107, III, 127, 158,238 necessity, synthetic 9, 11 necessity of origins thesis 9, 162 New York University 172 New Theory of Reference passim but see especially 3-11,14-15,37-61,90,92,103-4,1256,137,148,160,235-283 nonlexical, see dictionary ontological operator 216-7, 225 ontology, intensionaL See intensional entities opaque construction 15-17 open formulas or sentences 98 ostension 93, 144, 155 possibilia 204, 212,215,227-8 possibility. See necessity possible world 8, 47-8,153-4,159,164; 166-7, 181,193-4,203-5,211-13,215-6,227-8,240, 259,265 primary valuation 206, 214, 216, 224-5 Princeton University vii, 146-7,272 procedure, empirical 19, 55-6 procedure, linguistic 55-6 proper name x, 3-8, 14, 16, 17, 18, 19,38-9,43, 45,46-7,59-60,66,68,76,81,82,137,139, 142, 147, 149-50, 163, 182, 187,200,201, 242-3, 247-9, 253. See also logically proper name; tag; names, in an ideal sense property, modally indexed 44 proposition 112-3,217 proposition, de re 237 proposition, general 170, 239 propositional attitude 66 purely designative occurrence 15-16 quantification theory 182,191,199-200,208, 218-19,222 quantifier, general 226

290

SUBJECT INDEX

quantifiers, substitutional interpretation of 96, 255 quantifying in. See modal context quantification, objectual16, 23, 31, 255 reference, causal theory of or historical chain theory. See causal theory of reference referential transparency 246 reflection principle 214 regimentation 102 representation theorems 207 representational semantics 215 rigid designation, complete concept 165 rigid designation, direct reference definition 137,168,171-3 rigid designation, world definition 137, 170-3 rigid designator vi, x, 3-4, 8, 10, 17,22,23,28, 33,43,47-8,60,68,75, 105, 115, 122, 137-8, 146-9,163,167-70,212,235,239,248,252, 254,258,263,274,276 rigid designator, obstinate 168 rigid designator, strong 47,171-3,247 rigid designator, weak 47, 171-3,247 rigid names, descriptionally 252, 257, 276 rigid singular terms 170, 255, 263 rigidity 4,35, 104-6, 108, 154, 165, 168,249, 256 rigidity argument 106 scope (of description) 188, 191-3 semantic argument (for direct reference) 28, 44, 145-6 semantic content 7, 77-8, 81, 141,145 semantic value 207 semantics 4, 41, 140-1 semantics, class domain 224, 226-7. See also Kanger semantics semantics, modal x-xi, 166-7,218,240,259 semantics, model-theoretic 48, 203-4, 206-7, 230,260 semantics, possible world 9,204,210-11,215, 230 semantics, primary 261, 267-9 semantics, secondary 267-71 semantics, set domain 224-7. See also Kanger semantics sense 7, 143, 169, 187 sense, descriptive 3, 7 sense, Fregean 4 sense, modally stable 7-8, 26, 43, 50 singular proposition 3-4, 169-70, 237-8

singular term 16, 45, 60, 181, 188, 190-1, 193, 196-200,246-8,252 singular term, purely designative 16, 17 species vs genus, see genus speech act 140 standard interpretation (of modal logic) 211 Stanford University 138, 146-7 state descriptions 204-5,209-11,215,231,240, 260 state of affairs I 08-II 0, 112-3 substitutability salva veritate, universal intersubstitutability of co-referential names 6-8, 14,17,18,22,26,28,38,43-4,48,54,59,66, 70-71,73,78-80,100,106,107,111-2,114, 118,122,127,134,152,158,168,185,190-1, 194-6, 199,241-2,244-5,247,251,263 substitutivity of concretion 184, 186 substitutivity, of description for description 189 substitutivity, of description for singular term 189 supervalidity 229 synonymy, of names 17,40,42,66,68,80,86 synthetic vs analytic. See analytic truth synthetic a posteriori 9, 131 system 206-8,211,216-9,225 tag, identifying 5, 6,10,19,21,32,54,58-9,69, 79-80,82-83,90,94,96, 101, 110, 119-22, 130,133,139,148-51,154,163,169-70,2535. See also logically proper name, names, in an ideal sense tautology, tautological truth 18, 25, 52, 72, 789,81,95,96, 107, 109, 114, 118, 127, 130-1, 152, 158, 160-1 truncated description. See descriptive theory of names truth, analytic. See analytic truth truth in a mode1204, 207-8 truth, in various senses 203-233 truth, logically necessary. See logical truth universal substitutivity thesis. See substitutivity universal instantiation 73-4, 189, 191, 220 universal truth 211 University of Michigan 276 use vs mention 108-9 validity 98,109,114,152,217,225-6,229 variable, individual 16, 23, 28, 46, 47, 95 Wayne State University 146, 175,276 well-formedness (of sentences) 189-90 world-indexed sense 40