Nonexistent Objects [1 ed.] 0300024045, 9780300024043

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Nonexistent Objects

Nonexistent Objects

Terence Parsons

Tale University Press New Haven and London

5Dc2/t - r3 /

Copyright © ig8o by Tale University. All rights reserved. This book may not be reproduced, in whole or in part, in any form (beyond that copying permitted by Sections ioj and 108 of the U.S. Copyright Law and except by reviewers for the public press), without written permission from the publishers.

Designed by James J. Johnson and set in Monotype Baskerville type. Printed in the United States of America by Murray Printing Company, Westford, Mass.

Library of Congress Cataloging in Publication Data

Parsons, Terence. Nonexistent objects. Bibliography: p. Includes index. i.

Nonexistent objects (Philosophy)

BD219.P37

hi

ISBN 0-300-02404-5 10 98765432 1

79-21682

I.

Title.

TO MY PARENTS

without whom I might have been one

Contents

Preface Introduction

1

1. HISTORICAL DEVELOPMENT

2

2. THE CURRENT SCENE

5

3.

9

METHODOLOGICAL PRELIMINARIES

I: Initial Exposition 1. Initial Sketch of the Theory

2.

3.

17

1. objects

*7

2. EXTRANUCLEAR PREDICATES

22

3. IDENTITY

27

Meinong and Motivation

3°

1. meinong’s motivation

3°

2. EVIDENCE FOR THE THEORY

32

3.

russell’s arguments against meinong

38

4.

intentionality

44

A Sketch of a Theory of Fictional Objects 1.

LITERARY THEORY

49 49

2. IMMIGRANT AND NATIVE OBJECTS

51

3. THE THEORY

52

4. SURROGATE OBJECTS

57

5.

59

RELATIONAL PROPERTIES

vii

CONTENTS

viii

11: Formal Development 4. The Language G 1.

63

THE SYMBOLISM OF

G

64

2. RULES AND AXIOMS 3. THE SEMANTICS OF

70

G

78

4.

THEOREMHOOD EQUALS VALIDITY

84

5.

AN ORTHODOX THEORY

85

6. MODELING

G

WITHIN

88

7. USES OF THE PICTURING

5. Further Developments of the Language G 1.

92

98 98

MODALITIES

2. ABSTRACTS AND COMPLEX PROPERTIES

IO3

3.

PROPOSITIONS AND PROPOSITIONAL ATTITUDES

I08

4.

SINGULAR TERMS

III

123

5. FORMALIZATION appendix: a semantics for a fragment of ENGLISH

134

III: Applications and Discussion 6. Summary of the Formal Development and More on Nuclear and Extranuclear 1. SUMMARY OF CHAPTER

133

\

I33

2. COMPARISON WITH ORTHODOX SYSTEMS

160

3. SUMMARY OF CHAPTER 3

l6l

4.

166

MORE ON NUCLEAR AND EXTRANUCLEAR

5. MODIFYING THE DISTINCTION

7. Fictional Objects, Dream Objects, and Others 1.

“in the story .

.

170

173 173

2. WHAT ARE THEY LIKE?

182

3. DIGRESSION concerning the author

187

4.

UNCLARITIES IN THE THEORY

l88

5.

INDISCERNIBLES: CROWDS AND SIBLINGS

190

6.

RELATIONS TO UNREAL OBJECTS

194

7- EXTRANUCLEAR PREDICATIONS; STORIES WITHIN STORIES

jgy

CONTENTS

IX

8. ALTERNATIVE THEORIES

202

9. FANTASY, MYTH, AND LEGEND

206

10. OBJECTS IN DREAMS

207

11. VISUAL OBJECTS

210

8. Traditional Issues from the Present Perspective

212

1. ONTOLOGICAL ARGUMENTS; WHY SHOULD ANYONE CARE WHETHER GOD EXISTS?

212

2. EPISTEMOLOGY: MIGHT I BE A NONEXISTENT

3.

OBJECT?

2I7

leibniz’s monads and possible worlds

219

4. ESSENTIALISM

224

5.

227

PLATONIC FORMS AND COMPLEX PROPERTIES

6. THEORETICAL ENTITIES IN SCIENCE

9. Global Issues

228

233

1. ARE THERE TOO MANY OBJECTS?

233

2. ARE THERE TOO FEW OBJECTS?

24O

3. SOME CONCLUDING REMARKS

245

Selected Bibliography

2 47

Index

255

Preface

Alexius Meinong was an Austrian philosopher and psychologist who did most of his work around the turn of the century. He believed that he had discovered a whole realm of objects which had not been studied previously by philosophers or by scientists. These are the objects that don’t exist. As examples he cited the golden mountain—it doesn’t exist, and it has certainly not been extensively

scrutinized

by

serious

scholars—and

the

round

square, which not only does not exist but also has the interesting property of being impossible. I first became acquainted with Meinong’s views when I was slated to teach a course on metaphysics at the University of Illinois at Chicago Circle during the fall of 1966. My intent was to impart to the class the wisdom I had recently gained as a graduate student, and a nice vehicle for this was to be W. V. Quine’s essay, “On What There Is.” I feared, however, that the students would find the discussion there too abstract unless they were already familiar with the views that Quine was opposing in the first few pages of his essay: they would appreciate Quine’s applications of Occam’s Razor more if they were already familiar with the engaging but obscure theory against which it was being wielded. I had been told that Quine’s character “Wyman” was based on the historical Meinong, and so I selected Meinong s “The Theory of Objects” as an initial reading. Meinong’s views had a profound impact on me. At first, I was convinced by the criticisms leveled against him by Russell and Quine; in fact, I first thought of these “refutations” as Xi

PREFACE

xii

constituting one of the clearest examples of philosophical pro¬ gress that we have. Clear progress is rare in philosophy, and I was pleased to have an example to cite. But as I thought about it more, I became increasingly dissatisfied. I found the criticisms intellectually compelling, but I kept thinking that there was something very true in Meinong’s views that was being missed. And eventually I began working out a similar kind of theory, a theory that I thought preserved most of Meinong’s radical and exciting ontological views—such as the belief in nonexistent objects, even in impossible objects—but a theory that is immune to the standard criticisms. That theory was developed gradually in a series of papers and talks, and the present book represents its most recent form. This is not an exposition of Meinong. Although I have gained much in inspiration and ideas from reading his work, I am not well enough acquainted with his voluminous writings to qualify as an expert on them. From time to time I will discuss gross similarities and differences between Meinong’s views and those presented here, but for the most part I will simply treat Meinong as an ally who had many of the ideas first. I was most influenced in the early stages of my work by a manuscript by Richard Routley entitled “Exploring Meinong’s Jungle,” a work that is, I suspect, closer to Meinong’s views than is my own. I have not tried to draw detailed comparisons be¬ tween Routley’s work and my own, and the same goes for many other contemporary writers on related topics. Such comparisons would have required too much work and would probably have been out of date by the time this is published. Likewise, I have not tried to catalogue the ways in which the present work coheres with or departs from my own earlier work. I intend this book to be an independent work, readable on its own. My goal has been to put forth a certain kind of theory of nonexistent objects. I realize that both the theory and its ex¬ position are somewhat crude. If the theory is of any value, it will doubtless be developed by others in ways that I do not at present envisage, and it seems to me time to place it in their hands. As for the exposition, I ask the reader to try to see past any poor choices of terminology and minor blunders. This

PREFACE

xiii

burden will fall heaviest on those who are not in sympathy with the idioms and presumptions of current professional “analytic” philosophy. I’ve tried to make the main ideas of the book ac¬ cessible to a broader audience, especially in the introduction and part I. I have benefited enormously from numerous discussions with students and colleagues and with people outside academia altogether. In addition to those persons mentioned in the text, I have received special support and help from Kit Fine, Edmund Gettier, Gael Janofsky, Kathryn Pyne Parsons, Barbara Partee, Robert Sleigh, David Woodruff Smith, John Vickers, and, most of all, from Karel Lambert. They helped in various ways, mostly by keeping me honest by one means or another. I am grateful for a grant from the National Endowment for the Humanities which, together with a sabbatical leave from the University of Massachusetts (Amherst), gave me a year’s free time in which to write this book, and I wish to thank the Phi¬ losophy Department at the University of California at Irvine for providing office facilities and hospitality during that period. University of Massachusetts Amherst, Massachusetts December rgy8

'

Introduction

Are there objects that don’t exist? The orthodox, mainstream answer (in Anglo-American philosophy, anyway) is a resounding “No I.—there’s

no such thing as a thing that doesn’t exist. Though

there may be kinds of things that are nowhere exemplified (e.g., being a winged horse) there is no particular thing that fails to exist.” Or, put in positive terms: “everything exists.” This is a central tenet of contemporary philosophy. I’m inclined to call it the “Russellian rut”: “Russellian” because it stems principally from Russell, and a “rut” because it s a view in which most of us are so entrenched that it’s hard to see over the edges. The view is defended (though obliquely) in Russell s classic paper, “On Denoting”;1 published in I9°5> 1^11S PaPer also contains Russell’s most terse and unsympathetic treatment of Meinong. (It is unfortunate that most people are acquainted with Meinong only as the bad guy in this paper of Russell’s, for Russell published several reviews of Meinong’s work which were much more sympathetic, some even containing lavish praise).2 1. All references are to the bibliography at the end of the book. Most references will be given in the text by means of the author’s last name followed by an abbreviation of the title of the work in square brackets; for example, a reference to Russell’s article “On Denoting” would be given as [0Z>],” possibly followed by page references. The author’s

“Russell

name will be

omitted if it is clear from the context. 2. For example, “Before entering upon details, I wish to emphasize the admirable method of Meinong’s researches” ([1904 Review] p. 205)

and

“Meinong’s present position appears to me clear and consistent and fruitful of valuable results for philosophy” ([1905 Review] p. 538). 1

2

INTRODUCTION

‘Rut’ has an unfavorable connotation; the same point can be put more favorably. I believe that, until recently, at least, philosophy has been in a state that Kuhn ([£57?]) calls “normal science.” We have a set of paradigm beliefs and techniques which we work with, and work with very fruitfully, but that we nor¬ mally do not seriously question. One of these key beliefs is that everything exists, and one of the paradigm techniques, in meta¬ physics, if not in the philosophy of language so much anymore, is Russell’s famous theory of descriptions (which was first pre¬ sented in the paper mentioned above). In this introduction I want to discuss how such a situation arose, and then I want to examine the current scene in more detail. This should set the stage for the departure from orthodoxy envisaged in the body of the book. i. Historical Development In 1900 Bertrand Russell believed in nonexistent objects, a view he says he got from G. E. Moore (Russell [POM] p. xviii). And indeed, superficially, it’s quite a plausible view. If we forget or inhibit our philosophical training for the moment, we are all prepared to cite examples of nonexistent objects: Pegasus, Sher¬ lock Holmes, unicorns, centaurs, .... Those are all possible objects, but we can find examples of impossible ones, too; Quine’s example of the round square cupola on Berkeley Col¬ lege will do. It is an impossible object, and it certainly doesn’t exist, so it seems to be an example of an impossible nonexistent object. With so many examples at hand, what is more natural than to conclude that there are nonexistent objects—lots of them! Well, by 1919 at least, Russell had changed his mind. Non¬ existent objects offend against our “robust sense of reality,” and the main task of the metaphysician seems to be to explain away the apparent examples without committing himself to objects that don t exist [[IMP] p. 170). And the theory of descriptions, as all philosophers learn in graduate school, if not sooner, pro¬ vides a means for doing that.3 3. The theory of descriptions is essentially a method for paraphrasing

INTRODUCTION

3

Most of Western philosophy has agreed with Russell ever since. Why? The question has a certain poignancy. For in adopt¬ ing the theory of descriptions (at least as Russell originally pre¬ sented it in “On Denoting”), we paid a rather high price for avoiding nonexistent entities. Formerly, we could think of a statement such as ‘Pegasus is winged’ as a simple predication, true if the object named is winged and false otherwise. To use the theory of descriptions to eliminate the “apparent” reference to Pegasus, we first assume that ‘Pegasus’ is, logically speaking, not a name at all, but rather a kind of code for ‘the winged horse of Greek mythology’ (or perhaps just ‘the Pegasizer’ as in Quine [OWTI]); then we say that this description, which logically underlies the apparent name, is not itself a constituent of the proposition at all, but that the entire sentence really means something like ‘Some existing thing is a winged horse, and is the only existing winged horse, and is winged’. This is hardly an intuitive result, and it doesn’t even accord well with the apparent data. For one thing, it makes all simple sentences containing

certain English locutions into the terminology of symbolic logic (or into literal English renderings of that terminology). Its most famous application involves the word ‘the’. A sentence involving this word gets paraphrased, roughly, by means of the format: ‘. . . the A . .. . ’ => ‘Something is such that it is an A, and nothing else is an A, and . . . it . . .’. For example, ‘The king of France is bald’ would be paraphrased as ‘Something is such that it is a king of France, and nothing else is a king of France, and it is bald’ (where ‘is bald’ occupies the position of the ellipses in the format). On its orthodox construal, you are to read the ‘some¬ thing’ as ‘some existing thing’ and the ‘nothing else’ as ‘no other existing thing’, though this construal is really independent of the paraphrase method. The main advantage of the theory is supposed to be that it allows us to replace a sentence that contains a term, ‘the A,’ which apparently refers to something, by a sentence which does not contain such a term. The latter sentence can then be denied without the denier having to (apparently, anyway) refer to ‘the A’. Thus someone who does not believe in the king of France can comfortably avoid the apparent commitment to such a king that is suggested by ‘The king of France is not bald’ by saying instead: ‘It is not the case that something is such that it is a king of France, and nothing else is, and it is bald . Russell also held that English proper names are disguised definite descriptions, to which the paraphrase should be applied (see below in the text for an example); he and others hoped to extend this treatment to all sorts of other linguistic construc¬ tions (see Urmson [PA] chaps. 3, 4, 10).

4

INTRODUCTION

names of nonexistents false, a matter that has been controversial ever since it was proposed. And, worse, it seems not to work at all for one of Russell’s own paradigm tests: the sentence ‘George IV wished to know whether Scott was the author of Waverley’ is said to mean ‘George IV wished to know whether one and only one man wrote Waverley and Scott was that man’, a result that hardly anyone finds plausible.4 So why did Anglo-American philosophy follow Russell instead of Meinong? I do not believe that it was because of our “robust sense of reality.” For one thing, the issue doesn’t concern reality, but rather unreality; it is not what exists that is in ques¬ tion, but rather whether there is something more, something outside the realm of existence. And, for another, I think that our intuitions are genuinely in conflict on this matter. We do tend to focus on what exists, if this is what a robust sense of reality comes to. But we also have a contrary tendency to believe in particular examples of nonexistent objects, such as Pegasus and Sherlock Holmes. No, I think we had much better reasons for agreeing with Russell—at least two. The first is that the contrary view—a Meinongian bloated ontology—seemed inevitably plagued with difficulties, absurdities, and outright inconsistencies. I’ve men¬ tioned Russell’s attacks on Meinong’s theories. Well, Russell argued very effectively against Meinong. And Meinong did not provide a persuasive reply. (I believe that Meinong’s reply was correct in part, but his reply was not persuasive).5 Thus we inherited the belief that, whatever its initial plausibility, an en¬ dorsement of nonexistent entities is untenable. The second reason for following Russell was this: Russell took the view that everything exists, plus his theory of descrip¬ tions, and on this foundation he erected one of the most impres¬ sive philosophical systems ever known. He made great strides in 4. See Linsky [it] chap. V for a discussion, and chapter 5, section 4, of this book. The reading in question is the de diclo one (see chapter 2, section 4). 5. The initial objections were raised in Russell [1905 Review], Meinong’s replies were in [f/SGW] sec. 3, and Russell’s final comments are in Russell [1907 Review], A brief synopsis of the exchange is in Chisholm [RST] pp. io-ii. The arguments will be discussed in chapter 2, section 3.

5

INTRODUCTION

the development of modern logic, he provided a kind of founda¬ tion for mathematics, and he articulated very powerful and inter¬ esting metaphysical and epistemological views. More than that, the techniques he employed—principally modern logic supple¬ mented by the theory of descriptions—turned out to have wide¬ spread application far beyond Russell’s own theories. No wonder, then, that we inherited many of his ontological views along with the rest. 2. The Current Scene Let me repeat my view of the current scene. Metaphysically, we are just beginning to emerge from a state of

normal science.

Normal science is characterized by the existence of certain para¬ digm views which are simply taken for granted—and taken for granted in such a way that it is hard to see what it would be like to deny them. I’ve identified the view that everything exists as one of these. Now that may sound presumptuous. After all, people have published books and articles in which they raise the question whether there might be things that don’t exist. They usually con¬ clude that the answer is no, of course; but they do raise the question. Well, that’s not my point; my point is that in the nor¬ mal everyday functioning of philosophy it is taken as a truism that there are no nonexistent objects. Let me illustrate this with a very simple example. In a recent article, Keith Donnellan discusses a certain principle about names, and he speaks in favor of this principle as follows: “it does not involve our theory of reference in any difficulties: ... it has no Meinongian implications, no overpopulation with entities whose existence is being denied” ([SN] p. 26). In other words, Donnellan takes for granted that Meinongian theories are bad, and that nonexistent objects are bad. And this is not a rhetorical error of his—quite the opposite. You can’t defend everything you say, and he is aware that he’s addressing an audience that agrees with him in taking those things for granted. (The literature abounds with other examples.) Here is a different illustration of the same point. It is rela-

6

INTRODUCTION

tively common to teach elementary logic in a manner that pre¬ supposes the orthodox view. In particular, when students are asked to symbolize these sentences: (a) Tables exist. (b) There are tables. the instructor expects the same symbolization, namely: (c) (3x)Tx. And this expectation is not presented as embodying a metaphys¬ ical view that might be wrong; instead it is treated as a matter of pure logic. But it is not pure logic. Symbolizing both (a) and (b) in the same way amounts to equating the quantifier ‘there is’ with the quantifier ‘there exists’, an equation which makes sense only if what exists exhausts what there is; and that is the meta¬ physical view I am now questioning.6 This example from logic also illustrates another point: why, from the orthodox point of view, it is hard to see as sensible the question whether there are things that don’t exist. If you sym¬ bolize this in the customary fashion, it comes out synonymous with there exist things that don’t exist’, and that is inconsistent on anybody’s view. But, of course, such a symbolization begs the question at issue. The matter is actually a bit more complicated than I have indicated, for variations in word usage also enter in. In particu¬ lar, I think that we sometimes use ‘there are’ to mean ‘there exist ; when this is done, the symbolization discussed does not beg the question in any overt sense. But we also use ‘there are’ in a broader sense, a sense roughly equivalent to that of the word some , or at least one’, and this usage cannot be appropriately symbolized in the same way as ‘there exist’.^ For example, we are inclined to say both: . Quantifiers are locutions from symbolic logic. There are usually two,

6

the universal quantifier “(*)’, which means ‘everything is such that . . .’or for any object x, . .

and the existential quantifier ‘(3*)’, which means

something is such that . . or ‘for at least one thing x,

or ‘there is at least one thing such that . . .’,

. . . ’.

- The literature now contains numerous references to this distinction

7

INTRODUCTION

7

(d) There are winged horses—Pegasus, for example. and: (e) There are no winged horses. When we truly utter (d), we are using ‘there are’ in the broad sense. When we say (e), we mean that there are no real winged horses, and (e) is appropriately symbolized using a quantifier that is read ‘there eixst’. To avoid ambiguity, I will try always to use ‘there are’ in the unrestricted sense, the sense of ‘at least one’; when I want to as¬ sert existence, I will use ‘there exist’ or some similar locution. During certain periods of history (e.g., the Middle Ages) the view that everything exists would have been regarded as abso¬ lutely outrageous. But since the early 1900s it has become the re¬ ceived view, very firmly entrenched and almost impossible to refute. There are several reasons why it is almost immune to ref¬ utation. First, as the received view, it has authority on its side; it is endorsed or presupposed by those of our contemporaries whom we most respect. Also, as the received view, it is intuitively obvious (to many philosophers, anyway), our intuitions having been shaped by years of experience with theories that embody this view. These factors tend to throw the burden of proof on those who might want to challenge the received view. But that is almost impossible to do, for reasons that Kuhn and many others have made clear: the view in question is a high-level theoretical claim in our metaphysical scheme. And high-level theoretical claims don’t confront the data directly; they can be tested against data only as interpreted by some method. And the orthodox view contains within it a methodology that interprets the data so as to preserve and protect the claim that everything exists. I’ve given

between ‘there is’ and ‘there exists’ (although different terminology is sometimes used), with about half the authors pointing out the importance of the distinc¬ tion (e.g., Russell himself in [EIP]) and the other half saying that they can’t see any difference. Some seem to resolutely see no distinction, and I have no hope of convincing them; as for others, I hope that acquaintance with the theory described in the body of the text will provide an explanatory illustra¬ tion.

8

INTRODUCTION

one example above, the manner in which we use logic to sym¬ bolize claims so as to presuppose that everything exists. More important, we’ve all learned to use Russell’s theory of descriptions to analyze away apparent reference to nonexistent objects; those beliefs that seem to require nonexistent objects for their truth we instinctively paraphrase into other beliefs that do not. And we retain our conviction that apparent reference to the unreal must be capable of being paraphrased away even when we don’t see how to do it. It may now come as a surprise that I have hardly any objec¬ tion to this situation whatsoever. I think the orthodox view is a fine view; it has been extremely useful. I don’t object to its taking things for granted, nor to its defending some of its central claims by means of a methodology that biases the data. I don’t object because I think that any fruitful philosophical theory is going to do just that. But I do think it’s a rut, and I’d like to look over the edge and see how things might be different. To do this, we need to encounter an actual theory about nonexistent objects. That will be the task of the present work. The way has been paved by a recent mood in logic according to which logic ought not to rule out nonexistent objects (see Scott [AML\). But much of the moti¬ vation here has stemmed from the desire to preserve the neu¬ trality of logic, and this very neutrality has prescribed silence about what nonexistent objects are substantively like. The same also holds for much work in “free logic”: Free logic validates certain reasoning containing words such as ‘Pegasus’. But it does not follow from this fact that it is committed to a realm of entities among which is included a flying horse. To be sure, one could develop a philosophical semantics for free logic that does recognize a realm of non¬ actual but possible beings. . . . But one need not develop the semantics that way. ... In our development, talk about non-existents is just that—“talk” is what is stressed. “Non¬ existent” object, for us, is just a picturesque way of speaking devoid of any ontological commitment.8 8. Lambert and van Fraassen

[EA&P]

pt. X, and Marcus [Q6?0].

[D&C]

pp. 199-200. See also Leonard

INTRODUCTION

9

My intent is to describe in some detail the ontological commit¬ ment that these and other authors wish to avoid. 3. Methodological Preliminaries I have had certain goals in mind when working on this project, and it will aid the reader’s understanding to be aware of them. For they have often influenced what I have said in ways that would not be apparent from my words alone. One goal I have had is to try to develop a theory that is understandable to those who, like myself, approach this topic from what I have called the orthodox tradition. My techniques will be familiar to those in that tradition, and my terminology has been kept as familiar as possible; I have made efforts to clarify the nonorthodox terminology that I found it important to use (principal examples are the notions of nuclear and extranuclear properties, and impossible and incomplete objects). This goal has also guided me in producing a theory that is, in certain re¬ spects, as detailed and specific as possible. I have avoided many alternative theories and many variants of the chosen theory—not because they seemed to me to be wrong, but because I couldn’t see how to develop them in sufficient detail to grasp clearly how they would go. I can’t emphasize this point too much; although I have often taken a given path in order to avoid error that I saw elsewhere, I have much more often taken a particular approach just because it was the only one I could develop to the point where I felt comfortable with it. The reader who tries to find objections to alternatives lurking behind my choices will often be frustrated (though I do think it is often much more difficult to develop an alternative approach than it seems at first glance, and that “objection” to alternatives is often relevant). I don’t mean to suggest, of course, that I have completely avoided vague¬ ness and unclarity myself; these are matters of degree, and I have had as one of my goals to minimize them. A second goal that I have had is to produce a theory that is inconsistent with the orthodox view. One popular style in philos¬ ophy is to take a position that initially appears outrageous, and then to “interpret” it in such a manner that it turns into some¬ thing that we already believed. This is not what I am trying to do

10

INTRODUCTION

here. If I am successful in my enterprise, some people who begin with orthodox opinions will end up agreeing with the theory presented here, but only because they have changed their minds, not because the theory is “really” one they originally held. There is a danger that the question of whether there are objects that don’t exist should turn out to be a semantic quibble rather than a substantive matter of disagreement between Meinongians and the orthodoxy. There are at least two ways in which this might happen. First, we could define ‘exists’ to mean some¬ thing like ‘has spatio-temporal location’, and then defend the claim that some things don’t exist by pointing to numbers, classes, ideas, or similar things. I want to avoid such a move. I am not sure how to define ‘exists’, but I may be able to say enough about my intended use of the word to forestall such a trivialization of the issues. First, I want to follow Meinong in separating abstract things (e.g., numbers, properties, relations, propositions) from concrete things (tables, unicorns, people). Meinong held that abstract things never exist (they are the wrong sort of thing to exist); instead, some of them have a kind of being called subsistence. I want to avoid this issue entirely. When discussing problems of existence and nonexistence, I’ll limit myself entirely to a discussion of concrete objects. So when I say that some objects don’t exist, I mean that some concrete objects don’t exist—I don’t have in mind propositions, or numbers, or sets. With regard to concrete objects, Meinong held that some of them exist and some of them don’t, and the ones that don’t do not have some other kind of being—for example, subsistence (see Meinong [TO] sec. 4, where he considers and rejects an argument that purports to establish a kind of being that all objects have). Russell objected that if there are objects that do not exist, they have to have some other kind of being (see [OZ)], [T/P]). I have never been able to find more than a terminological issue here. If there is an issue about whether nonexistent objects have some kind of being, I intend to remain neutral on the issue. This also goes for a view (which may be the same one) that I have often heard expressed in conversation; it is that “everything has its own special mode of existence.” For example, Pegasus

11

INTRODUCTION

exists in mythology, Sherlock Holmes exists in fiction, .... Some would even emphasize that these sorts of existence can be more important than the everyday sort of existence that I share with my house and my automobile. Well perhaps, but that is not the issue that I will be discussing in this book. There is a perfectly ordinary sense of the word ‘exists’ in which Sherlock Holmes does not exist, and that is the sense that I intend when I call Holmes a nonexistent object. This is also the sense in which orthodox philosophers claim that there is nothing except what exists. (This does not commit them to the unimportance of literature; they need only hold that the importance of literature does not depend on the existence of its characters.) Even given these provisos, there is still room for disagree¬ ment concerning exactly what concrete objects exist—for ex¬ ample, concerning whether there exist any living beings on other planets. I am not concerned with these issues and so I will, as a matter of policy, agree (or at least not disagree) with others on these issues. Specifically, I intend to use the word exists so that it encompasses exactly those objects that orthodox philosophers hold to exist. In particular, it includes all the ordinary physical objects that we normally take to exist, and it does not include unicorns, gold mountains, winged horses, round squares (round square things), Pegasus, or Sherlock Holmes. The theory given below will say that there are unicorns, there is such a thing as Pegasus, etc., but that none of these exist. For reasons of simplicity, I have avoided entirely dealing with tensed properties in the theory. When I give examples like ‘being blue’, it would have been better to give examples like ‘being blue at time t’ or ‘being blue sometime’. My ‘exists’ is always meant tenselessly, so I take it to be true that Socrates exists (i.c., Socrates is not an example of a nonexistent object), even though it is perfectly correct English to say,

Socrates once existed, but

he no longer does’. For those who prefer tenses here, read my ‘exists’ as short for ‘existed or exists or will exist’. A second way that the ontological issues might be trivialized would be if I were to reveal in the last chapter that my quantifiers are merely “substitutional,” that ‘There are winged horses

is

true only because the sentence ‘Pegasus is a winged horse is true,

12

INTRODUCTION

and the latter sentence is true in spite of the fact that ‘Pegasus’ doesn’t refer at all. Don’t bother skipping ahead; I won’t do this. Whenever there is a choice, my quantifiers are always intended to be interpreted objectually.9 A third goal of mine is that the theory described be con¬ sistent with the data. This is too vague to be of much help, but it can be formulated more precisely in terms of the relation be¬ tween the proposed theory and the orthodox view. This is that the only point of disagreement between these views should be ex¬ plainable in terms of what some call a “robust sense of reality,” and what Meinong called the “prejudice in favor of the actual.” Namely, the views should agree on any issue which concerns only existing objects. More specifically, there should be no disagree¬ ment between them concerning the truth value of any sentence whose quantifiers are all restricted to existing objects and whose singular terms all name real objects. (The sentence ‘some things do not exist’ is not one of these.) Then the orthodox view can be seen to be a kind of special case of the more libertine one devel¬ oped here; it is the libertine view with blinders on, blinders that prohibit vision of the unreal. Another way of putting this is that the more libertine view should “reduce to” the orthodox view when applied to old and familiar (i.e., real) objects in much the same way that relativity theory and quantum physics reduce to classical physics when applied only to slow-moving middle-sized physical objects. This will be made clearer in chapter 6, section 2.

9. Quantifiers can be read in different ways. The usual reading is the

objectual reading; here a sentence of the form ‘There is an A’ is supposed to be true if, and only if, there is an object which is an A. The substitutional reading treats There is an A as being true if, and only if, there is some true sentence of the form N is an A’, where ‘N’ is a name. In case every object has a name and no names fail to refer, then the objectual and substitutional readings are equivalent; otherwise, they need not be equivalent. For example, some pro¬ ponents of substitutional quantification assume that there are names which fail to refer but which nonetheless appear in true sentences of the form ‘N is an A’, and they then hold that some sentences of the form ‘There is an A’ are true even though no object is an A. For example, Leonard (in [EA&P] pt. IX) suggests that ‘For some *, x is fictitious’ is true, on the grounds that ‘Santa Claus is fictitious’ is true, even though the name ‘Santa Claus’ does not refer to anything, and no object (e.g., no person) is fictitious. See also Marcus [Q. *1/ I > *k—1> x, xv, . . . , xny e ext(r)}; and likewise for extranuclear relations (i.e., with JVn and Wn+1 replaced by En and En+1). (8) The eighth member is a one-place function W which is such that for any R e En, W(R) e JVn, and ext(fT(/?)) = ext(R) fl EX". (g) The ninth member is a function, A, defined on the terms of (?. A is called the assignment function. A should assign the right sorts of things to the terms of G, namely: (9.1) If x is a constant singular term, then A(t) e OB. (9.2) If a is a primitive n-place nuclear predicate constant, then A (a) € Nn.

FORMAL DEVELOPMENT

80

(9.3) If a is a primitive rc-place extranuclear predicate constant, then A (a) £ En. (10) Last, a global requirement: the members of I must be such that the axioms OBJ and AB(E) of the last section are true in I. This requirement presupposes a definition of ‘true in I’, which is given below. Truth in an Interpretation As a preliminary to defining truth in an interpretation, we char¬ acterize what is meant by an “extended assignment.” An ex¬ tended assignment is a function g, defined on all the terms of 0, and satisfying (i)-(vi): (i) g(a) = A (a) for any primitive constant term of (9. (ii) If x is a singular term variable, g(z) £ OB. (iii) If a is an n-place nuclear predicate variable, then g(a)eJV„. (iv) If a is an rc-place extranuclear predicate variable, then g(a) e En. (v) If a is of the form /3rk,

then g(a) = PLUG(g(/3),

g(v), k). (vi) If a is of the form w([3), then g(a) = W(g(/3)). Now we can define the notion ‘ is truex ’ (‘^ is true in inter¬ pretation I with respect to assignment g’) by the following re¬ cursive definition: (Di) If a is a one-place nuclear predicate term and if z is a singular term, then azl is truej g if and only if g(a) £

f(g(r))(D2) If a is a one-place extranuclear predicate term and if z is a singular term, then or1 is truet

if and only if

g(z) £ ext(g(a)). (D3) a = j3 is truet g if and only if g(a) = g(fi). (D4)

(j) is true! g if and only if (j> is not truej g.

(D5) {(j> & (p) is trueI>g if and only if both ^ and (Jj are truei.g-

(D6) ( d! = £§)•

WD

(£)(*i) • • • •

PLUG(N)

•

• *n“ =

0)(*l) •

•

• • • *i =

QP\

& ... & £!*„ =>

W(Q.)*11

•

-

- *£“))•

’ OnX^ &

& £!*j_l &

E\xj+i & ... & is!.*,, 3

. . . Ar^n & E\xj =

^ • • • *Pr1*j?x‘1 • • • Cn))-15 III. Third, we have the axioms governing objects (chapter 4, section 2): mi OBJ

OiX^XOXO1*! = qlx2) => = *2)(3xn) (g1) (qlxn = (ji), where Xi = X2contain ^

VI. Last, there are the rules and axioms governing modal¬ ities (section 1 above): NECC

If (j) appears on a line of a derivation with the empty set of premise numbers, then \2 may be written on a later line, also with the empty set of premise num¬ bers.

15. In PLUG(E)* and PLUG(N) the

k's

and Wj’s must be related as

described in conjunction with the presentation of PLUG(N) in chapter 4, section 2.

FURTHER DEVELOPMENTS OF THE LANGUAGE 0

DROP

BF

□

S-5

n

n

DISTR

□

0 = U => D( 0 => no. = nw^.16

DEF

127

As far as consistency is concerned, these rules and axioms are pretty safe. For we can regard all the new notation of chapter 5 as abbreviations of notation that is already present in the system of chapter 4. This is not the intended interpretation, of course, but unintended interpretations are relevant where questions of simple consistency are concerned. In particular, wre may suppose that: (1) If cj) ([/Ukl . . . *kn0]) is an atomic wff, it is an abbre¬ viation of (3Pn)((xkl) . . . (xkn) (Pn*kl • • • *kn = ). Similarly for the other sorts of quantifiers: faq”), faXi¥’ and (17) Finally, we require that X be so related to the other elements of M that every instance of the set abstraction axiom ABSTR be true in

M with respect to every

assignment g (see below for the truth definition). This completes the definition of a modal structure.

FORMAL DEVELOPMENT

134

Given the above characterization of a modal structure we

“ is true in world w of modal structure M with re¬ g” as “extw(Ag( is valid =A((j) is true in every modal structure with re¬ spect to every assignment g. and:

(j> is a valid consequence of the set of wffs, Z1 =df for any M and assignment g, if every wff of 71 is true in M with respect to g, so is . modal structure

I believe that all the theorems of this system are valid wffs, and that any wff that is derivable from a set of wffs is a valid conse¬ quence of that set. I also suspect that the theorems constitute all of the valid wffs, and that any valid consequence of a set of wffs is derivable from that set. But I haven’t proved any of this. One natural alteration of the semantics would be to require

En be the set of all functions from 0Bn to P, and that X be the set of all subsets of and that S be the set of all functions from N± (J to P, and similarly for En, Nn, that in a modal structure

C, P, and B. Then the “structure” part (clauses (i)—(13)) could be defined independently, as constituting the basic ontology of objects and meanings; clause (14) could be an additional clause imposed on the first (13), and it would constitute a view about what possible worlds there are, and what they are like. Then clauses (15) and (16) would be independent of one another; (15) would say which world was the actual one, and (16) would be a purely linguistic stipulation concerning how to interpret our language. The requirements on the “structure” that appear in various subclauses of (16) would be redundant, and so would clause (17)- The additional strength of the new requirements on the early clauses would, however, make the theory not completely axiomatizable. Appendix :

A Semantics for a Fragment of English

Throughout chapters 4 and 5 I have made various remarks about

FURTHER DEVELOPMENTS OF THE LANGUAGE n) e Nom, and

who(m) 0'(a>n) G Nom, and a which

a

G Nom,

where (f>\a>n) comes from 0(a>n) by deleting the first pronoun that replaced itn in dx°)

-body

(x) (E!x & Px Z) xLxs)

7

3

it loves it

3

x,Lx

P

(I am beginning to omit case markings on pronouns for simplic¬ ity.)

(RC9)

woman who loves everybody

[Lv#( Wx3

& (x) (E\x & Px ID xsLx))]

The rules that we have so far can interact in reasonably intricate and interesting ways. Here is a partial analysis tree as an ex¬ ample :

FORMAL DEVELOPMENT

146

man

it, dates it,

(E)

The reader might want to check that the semantic rules provide the following as one translation of the sentence (the letters refer to the constituents of the analysis tree): (A)

x2Kx3.

(B)

(*)(£!* & Px zd xKx3).

(C)

[A*3(Wx3 & (x)(-E!* & Px z> */fx3))].

(D)

& Wy & (x)(fi!A; & Px id xKy) & Jy°).

FURTHER DEVELOPMENTS OF THE LANGUAGE &

147

(Here y was selected in order to avoid a clash of bound variables.)

6

(E)

x Dx 4.

(F)

[A x6(M*6&*6Z)*4)].

(G)

(z)(E\z & Mz & £-0*4

(H)

x5Lx±.

(I)

(z) (Elz & Mz &

zk:0). zLx4).

and finally: (J)

(3\y)(E\y & Wy & (x)(E!x & Px => xKy) & (z) (Elz & Mz & zDy zd zLy)). Once we have relative clauses we can play with them:

(Rg)

WD: If a who is in ft e Nom, or if a which is in /3 e Nom, then a in ft e Nom.

(Rio) WDP: If a who is /3 e Nom, or if a which is ft e Nom, then, if ft e Adj, then /3 a e Nom (provided that a A f~ thing or pbody). (Sg)

and (Sio): There is no change of translation when (Rg) or (Rio) is applied.

:1

Examples

(WD)

man in the doorway

man who is in the doorway

(WDP)

happy man

/ man who is happy

(WDP)

(RC497)

happy man who dates Agatha

man who dates Agatha who is happy

man who dates Agatha

1.

it497 is happy

Guided by these examples, the reader should now be in a position to

generate A certain fictional detective is more famous than every real

FORMAL DEVELOPMENT

148

Incidentally, there is no way in this fragment to have a relative clause modify a proper noun (so that who is happy above can¬ not modify Agatha). This is because proper names can only be modified by nonrestrictive relative clauses, and the only relative clauses that are dealt with in this fragment are restrictive ones. (Ri i) Adv-S: If a e Advs and (f> e S, then a, eS. (Si i) Example:

(Adv-S)

Necessarily, everything exists

Necessarily

□

everything exists

The translation of this sentence depends crucially on the choice of the category word in the translation of everything. If exists* is chosen, then the resulting translation is: □ (*) (is !.*: & Tx =5 E\x), but if object* is chosen, it comes out saying: □ (*)(0x & Tx zd E\x) a sentence I can only agree with if thing means something fairly special. (R12) Prop-Att: If a e Ts and ^ e S, then a(j> e VP.2 (S12) (a)* = a*{0*}. detective. The generation will presume that is more famous than is to be treated exactly like a transitive verb; this is probably incorrect (see chapter 6, section 4), but it is perhaps an approximation of the truth. A similar treat¬

ment of knows more about chemical analysis than would also let us generate sentences like Every good modern chemist knows more about chemical analysis than Sherlock Holmes.

We can straightforwardly

generate Pegasus is the mythological winged horse; to get Pegasus is the winged horse of Greek mythology we would have to add some way to generate of Greek mythology. 2.

I don’t think that this is the best way to generate propositional attitude

constructions. I have followed Montague

[PTQ_~\

here for simplicity. However,

amalgamating the that to the believes as we have done in the vocabulary makes it very difficult to handle other constructions in which the that is absent: for example, Mary believes everything that John believes. For a discus¬ sion of what I take to be a better treatment, see Parsons [ TT&0L\.

FURTHER DEVELOPMENTS OF THE LANGUAGE 0

149

Examples :

(Pro-VP)

it3

it3 believes that somebody is a spy

(Prop-Att)

believes that somebody is a spy

\

believes that

(Quant5)

somebody is a spy

it3 believes that somebody is a spy

somebody

(Pro-VP)

it3

it3 believes that it5 is a spy

(Prop-Att)

believes that

\

believes that it5 is a spy

it5 is a spy

The first of these examples exhibits the analysis tree for the S in question that yields the de dicto reading; its translation will be x3P{(3x)(E\x & Px & Sx)}. The second example exhibits the analysis tree for the very same S which yields the de re reading; its translation will be (3x)(2s!x & Px & x3P{»Sx}). (R13) Neg: If (p e S and (j> isn’t already negative, then the nega¬ tive form of (j) e S (provided that a certain doesn’t occur in ). (Si3)

(negative form of (j>)* —

Examples:

(Neg)

(Quant4)

The king of France doesn’t exist

The king of France exists

FORMAL DEVELOPMENT

150

The king of France doesn’t exist

(Quant4)

The king of France

(Neg)

it4 doesn’t exist

it4 exists

The

translation

of the

former will

be ~ (lx) {E\x

&

Kx)

and that of the latter (ix)(E\x & Kx)[Xx4 ~ E\x^\. Clearly, if there exists no king of France, then the former will be true and the latter false. (R14) Pass: If a e TV and if a isn’t a passive or a comparative or is in, then is aen by e TV, where aen is the past participle form of a(S14)

(is aen by)* = [^c1^(x2a*Jf1)]-

Example:

(Quant3)

Gladstone is seen by Holmes

Gladstone

(Quant4)

Holmes

(Pro-VP)

it3

(Pass)

(TV-Pro)

is seen by

sees Finally, one last rule:

it3 is seen by Holmes

it3 is seen by it4

is seen by it4

FURTHER DEVELOPMENTS OF THE LANGUAGE 0

151

(R15) Non: If a: is a simple Adj or simple common noun, then so is non a, unless a already started with a prefix (some¬ times non should be spelled un or im). (Si5)

(non a)* = [A(N)x ~ a*x\, where “jV” is chosen or not depending on whether a is nuclear or extranuclear.

Example: (Quant,)

(DP)

Thec nongolden mountain is nongolden

(Pro-VP)

the,,, nongolden mountain

it,

(is-Adj)

(Non)

them

(WDP)

it, is nongolden

is nongolden

nongolden

nongolden mountain

golden

(RC2)

moui

mountain which is nongolden

Ill Applications and Discussion

6 Summary of the Formal Development and More on Nuclear and Extranuclear

The purpose of this chapter is to summarize the formal de¬ velopment of the theory from part II and, given the formal development, to discuss in greater detail the distinction between nuclear and extranuclear properties. i. Summary of Chapter 4 Chapter 4 was devoted to a basic development of the theory that was sketched in part I. The technique used was to develop a

0, within which to make explicit various theoretical assumptions about objects. The system 0 has a dis¬

formal system, called

tinctive syntax, semantics, and axiomatic development. For¬ tunately, most of it bears a strong resemblance to the secondorder predicate calculus with identity (‘second-order’ here means that predicates as well as individual terms are quantifiable). There are three main ways—all discussed in part I—in which

0

differs from the predicate calculus. First, there is a distinction made between nuclear and ex¬ tranuclear properties and relations, and certain assumptions are made about how they are interrelated. In particular, for every extranuclear predicate P, there is a nuclear predicate wP which is the “watered-down” version of P that was discussed in chapter 2; among real objects, P and wP are required to be coextensive. Second, it is explicitly assumed that variables may range over all objects, not just those that exist. There is an extranuclear 155

APPLICATIONS AND DISCUSSION

156

predicate of existence, written E\, and there are axioms which entail that there are objects that don’t exist: (9x) ~ E\x. Third, the system incorporates a special treatment of rela¬ tions. In chapter 3 it was suggested that where nonexistent objects are concerned, a relational statement that is superficially of the form xRy may be ambiguous between x[Ry\, which says that x has the property got by plugging up the second place of R by y, and [xP]jy, which says that y has the property got by plugging up the first place of R by x. These two readings are dis¬ tinguished within

0.

I will now give a more detailed sketch of 0, beginning with its symbolism and a simultaneous commentary on the intended semantics. The notation used here differs in minor ways from the symbolism of chapter 4, which was developed with an eye on logical generality and on having a system easy to prove metathe¬ orems about. The present notation should be a bit handier to use. The symbolism of & contains, first of all, variables which range over (all) objects: x,y, z, xh x2, x3, .... It also contains variables and constants for nuclear properties: Pj^, P. . . , and nuclear relations: Pf, R$, .... (Although the official sym¬ bolism allows for 72-place relations, for any n, I will only discuss two-place relations in this chapter.) The symbolism also contains variables and constants for extranuclear properties: Pf, Pf, . . . , and extranuclear relations: Rf, Pf, .... One of the one-place extranuclear predicates is singled out for the special role of stand¬ ing for existence; it is written E\. The identity sign is also present, and it may go between any two terms of the same kind (e.g., we may have Xj = _y4, Pf = Rf7); such a wff is true if and only if the two terms stand for the same thing. In addition to identity for¬ mulas, atomic formulas may be formed in two other ways. First, any one-place predicate, nuclear or extranuclear, may be com¬ bined with an object term—for example, P3%, orPfx^. A formula of this form is true if and only if the object has the property in question. Second, there are relational statements. If R is a twoplace relation term, nuclear or extranuclear, then both x[Py] and [xP]j are atomic wffs. The former is true if the object denoted by x has the property got by plugging up the second place of the

SUMMARY OF THE FORMAL DEVELOPMENT

157

relation denoted by R with the object denoted byy, and the latter is true if the object denoted byy has the property got by plugging up the first place of the relation denoted by R with the object denoted by x. This explanation presupposes that [/?jy] and [*/?] themselves behave just like one-place predicates which denote properties, and that is exactly the way they are treated. So wffs of this relational form are really just special cases of the Px form (except that [.fry] has its argument written in front of it instead of after it). These complex predicates may also flank indentities, so we may write PN = [P1^], for example, which is true just in case each side denotes the same property. We sometimes want to say that a relation R holds between x andy regardless of the order of plugging up. This is written as the simple form xRy; this is defined notation, and its definition is simply: xRy =df x[Ry] & \xK\y. We have one more way of making complex predicates. As noted above, if Q is any extranuclear predicate, then wQ_ is a nuclear predicate of the same number of places as Q_. wQ_ may appear in formulas in any place that any other nuclear predicate can. Last, we can make complex wffs by combining simpler ones with connectives and quantifiers. This is just like the predicate calculus, with the understanding that the range of the quantifiers that bind object variables includes all objects, not just the existing ones. The symbolism may be made clearer at this point by a few examples. (3*)£!x & (3*) ~ E\x says that some objects exist, and some don’t. (3PN) (*)(£!* zd PNx) says that there is a nuclear property which all real objects have. (PN)(3x)(~P!x & PNx) says that every nuclear property is had by some nonexistent.

APPLICATIONS AND DISCUSSION

158

(3PE)(x)(~E\x => PEx) says that there is an extranuclear property which all unreal objects have. (/?N)(3x)(3jy)(x[.fiNjf] & ~ [xtfN]j>;) says that for any nuclear relation there is a pair of objects such that the first has the property got by plugging up the relation (in its second place) by the second, but the second does not have the property got by plugging up the relation (in its first place) by the first. (PN) (3PE) (x) (PNx = PEx) says that for any nuclear property there is a coextensive extranuclear property. Incidentally, all these sample sentences except the first are theorems of &. (The first isn’t a theorem of 0 because its first conjunct isn’t; (9 does not assume that it is a necessary truth that any objects exist. But the second conjunct is a theorem.) The theorems are whatever wffs can be proved from the axioms and rules, and these will be illustrated now. They come in four groups. I. First, there are some “ordinary” rules and axioms for the predicate calculus with identity. These include the rule of modus ponens, universal specification, substitutivity of identicals, etc. This first set of rules does not contain any abstraction principles; these are included in the second set. II. Second, there are axioms which make assumptions about what properties and relations there are. For extranuclear prop¬ erties we have an “ordinary” abstraction schema; it says that, for any wff (f> containing one free variable x, there is an extranu¬ clear property which is had by all and only those objects which satisfy (j>\ (3 PE)(x)(PEx = ). There are similar axioms for extranuclear relations as well as properties, and (PEx = w(PE)x)). This axiom, together with the abstraction axiom for extranuclear properties, yields the following weak abstraction principle for nuclear properties: (3PN) (*)(£!*

3

(PN* = if,)).

III. Third, there are axioms that deal specifically with objects. These are the axiomatic versions of principles (i) and (2) of chapter

1.

The first is the axiom of the identity of nuclear

indiscernibles: (*) (y) ((PN) (PNx = P^) => x = y). This states simply that if x and y have the same nuclear proper¬ ties, then they are the same object. The second axiom guarantees that, for any set of nuclear properties that is expressible in the language, there is an object that has exactly those nuclear prop¬ erties. For any wff we have: (3 x)(PN){PNx = ). This axiom is called the axiom for objects, and I will refer to it as axiom OBJ. This is the axiom that lets us prove, for example, that there is such an object as the gold mountain; just substitute (PN = Gn V PN = MN) for (j) in OBJ, getting: (3x)(PN)(PNx = (PN = GN V PN = MN)). The round square is obtained similarly. IV. Finally, there are some axioms that govern the behavior of relations. First, there is an axiom which says that, for extranu¬ clear relations, the order of plugging up is always irrelevant: (*)(jy)(PE)(*[PE/| = [xPE]jy). Second, there is an axiom schema for nuclear relations which, in its two-place form, is equivalent to two claims. The first claim is: (RN)(x)(y)(E\x & E\y

=3

(*[PN.X] =

APPLICATIONS AND DISCUSSION

160

So, for existing objects, the order of plugging up is always ir¬ relevant. But this is not always true when one or more of the objects is unreal; in fact, for mixed cases we have the second claim: (RN)(x)(y)(E\x

~E\y zd (~x[/P^] & ~ [>KN»).

Consequently, a nuclear relation may hoM between existents and existents, and between nonexistents and nonexistents, but never between existents and nonexistents (recall that a relation is said simply to “hold” between x and y just in case it holds no matter which end is plugged up first). In its precise formulation the system of axioms can be shown to be consistent, and when the semantics is formulated settheoretically, a completeness theorem is provable. The reader is referred to chapter 2.

4

for details and discussion.

Comparison with Orthodox Systems

The assumption about objects made in axiom OBJ depends essentially on the nuclear/extranuclear distinction. For if this distinction is eliminated from the syntax (by erasing all super¬ scripts), the system becomes inconsistent. (The abstraction axiom for extranuclear properties already allows us to prove that there is an extranuclear property—e.g., nonself-identity—which no object has. With the nuclear/extranuclear distinction eliminated, axiom OBJ would tell us that some object has this property.) On the other hand, the nuclear/extranuclear distinction together with axiom OBJ are what gives the system its import. For if these are both dropped, and if we add the assumption that at least one object exists, then the system of axioms becomes equivalent to a version of the second-order predicate calculus (to which has been added a single extension-preserving predicate operator w). The order of plugging up relations becomes provably irrelevant in all cases, and it becomes a theorem that every¬ thing exists: (— (x)E\x. As it stands, the system 0 says a great deal (consistently) about objects that transcends the orthodox view, but it also

SUMMARY OF THE FORMAL DEVELOPMENT

161

“contains” the “neutral” part of the orthodox metaphysics within it. Suppose we say that a neutral formula is any closed wff all of whose object quantifiers are restricted to existents; in other words, a closed wff ^ is neutral just in case every existen¬ tial quantifier (3*k) of (j> occurs in cj> only in contexts of the form (3A:k) (£■ !Ark & (/)), and every universal quantifier (*k) of occurs in (j> only in contexts of the form (xk) {E\xk => (f>). Intuitively, neutral wffs are those that explicitly refuse to discuss nonexistents. Because their quantifiers are restricted to existents, the order of plugging up a relation within a neutral wff is provably irrelevant, and so we may ignore this idiosyncrasy and compare neutral wffs directly to the wffs of a version of a two-sorted second-order predicate calculus (to which a single extension¬ preserving predicate operator w has been added). This predicate calculus will be peculiar in that it will have two styles of predi¬ cates (the ones with superscript E and the ones with superscript JV), so it will be a two-sorted theory. But within neutral wffs there will be no difference in the logical behavior of these two sorts of predicates, so the peculiarity has no special import. That is, when all talk is explicitly limited to what exists, the nuclear/ extranuclear distinction has no logical significance; this is true both within the ordinary predicate calculus and within 0. It now turns out that the neutral theorems of 0 correspond exactly to the neutral theorems of this predicate calculus. (For this fact to obtain, it makes no difference whether or not the predicate calculus in question contains the special axiom (x)E\x.) So any neutral truth of the orthodox conceptual scheme can be preserved within & just by making explicit that it is ex¬ istents that are being discussed. Other comparisons with orthodox systems can be made; the reader is referred here to chapter 3.

Summary of Chapter

In chapter

5

4,

sections

5-7.

5

the system 0 was expanded so as to include modali¬

ties, abstracts, verbs of propositional attitude, names, and definite descriptions. These additions will be discussed briefly here. An

APPLICATIONS AND DISCUSSION

162 appendix to chapter

5

contains a formal procedure for translat¬

ing a certain fragment of English into this expanded version of system 0; that procedure will not be discussed here. The modal operators □ (‘necessarily’) and 0 (‘possibly’) can be added to 0 and given a semantics similar to a possible worlds treatment. The result is a system of quantified S5 in which the Barcan formulas hold; that is, □ commutes with the uni¬ versal quantifier and

0

with the existential quantifier. The

standard objection to the Barcan formulas are that they lead from a certain truth, ‘necessarily, everything exists’, to a certain falsehood, ‘everything necessarily exists’, or from □(x)£'!x to (x) □£'!*. But this objection depends on the orthodox assumption that (necessarily) everything exists, an assumption that is re¬ jected within 0. In the system 0, both □ (*).£: !x and (^□E'lx are provably false. With the addition of modal operators, it is natural to place necessity signs in front of all the axioms discussed previously. It is also natural to adopt certain de re variants of some of the axioms, and this is also done. For example, we now have not only:

□ (3PE) (*)(/>% = 0), but also:

(3PE)n(*)(i>E* = ). For example, not only is it true in every world that there is a property which (in that world) applies to all and only purple unicorns (of that world), but there is a property which does this uniformly in all worlds. The addition of abstracts is an enormous convenience. Given a formula (f>, we write 0,”

for “the property of being

and we add the axiom of abstract elimination (also called

the axiom of abstract introduction):

□

= 0O»))-

For example, if TN represents being purple, and UN being a unicorn, then [Ax(PNx & £/Nx)] will represent the property of being a purple unicorn. This is a property that, in every world,

SUMMARY OF THE FORMAL DEVELOPMENT

163

is possessed by all and only those objects that are both purple and a unicorn; that follows from the axiom of abstract elimina¬ tion: □ OOttX**1** & UNx)]y ee (PNy & U*y)). Such abstracts always denote extranuclear properties, and we are often interested instead in nuclear ones. So the symbol AN is introduced for the nuclear abstraction operator, and it is de¬ fined as: =df w[Xx(j>]. This, together with previous axioms, yields a weak axiom of elimination / introduction of nuclear abstracts:

□ 0)iE'y => (UN*^(*)]j>> = y))Abstracts are convenient when discussing “complex” nuclear properties. For example, the (nuclear) negation of a nuclear property P may be defined as [ANx ~ Px], the nuclear property of not being P. This is not a property possessed by all and only those objects which lack P; as was pointed out in chapter i, there is no such nuclear property (though there is an extranu¬ clear one: [Ax ~ P*]). But it is a property that is possessed by all and only those real objects that lack P. Verbs of propositional attitude, such as ‘believes’, are in¬ corporated into 0 as symbols which precede wffs to form oneplace nuclear predicates. For example, ‘believes’ (or ‘believes that’) combines with ‘some objects exist’ to form ‘believes that some objects exist’; and this combines with subjects to form sentences just as a simple predicate like ‘runs’ does. Within (9 these verbs are represented by the symbols B^, B%, B%, . . . ; they combine with wffs which, for reasons of punctuation, are enclosed in braces. So, for example, the de dicto reading of ‘y believes that someone is a spy’ would be written: yB{(3x){Px 8c Sx)}, where P represents ‘is a person’ and S represents ‘is a spy’. The de re reading of that sentence (the reading which might be par¬ aphrased ‘y believes of someone that they are a spy’) is written:

164

APPLICA TIONS AND DISCUSSION

(3x){Px ScyB{Sx}). Except for the law of substitutivity of identity, no logical principles at all are adopted for the behavior of items within the braces. For example, although ‘x is a villager’ and lx is a vil¬ lager who does not shave all and only those villagers who do not shave themselves’ can be proved to be necessarily equivalent, it is not assumed that these phrases are automatically interchange¬ able within propositional attitude contexts. That is, it is not a theorem that ‘y believes x is a villager if and only ify believes x is a villager who does not shave all and only those villagers who do not shave themselves’. The laws of identity do hold even where propositional at¬ titude verbs are concerned, so that from P = Q, and xB{Py) we can infer xB{Q_y}. Although it’s hard to find interesting versions of that inference, a contrapositive version of it is often useful: from xB{Py} and ~xB{Q_y} we infer P ^ Q. For example, from ‘x believes y has a heart’ and ‘x doesn’t believe y has a kidney’, one may infer that having a heart / having a kidney. Propositional attitude constructions are often thought to provide contexts within which singular terms may violate the law of substitutivity of identicals. For example, from ‘Pegasus is the winged horse of Greek mythology’ and ‘x believes that the winged horse of Greek mythology is winged’, we cannot (on the

de dicto reading, anyway) infer that ‘x believes that Pegasus is winged’. In fact, the treatment of singular terms within 0 avoids this problem. That will be explained below, after a sketch of how singular terms are treated. First, definite descriptions. They are written in the normal way; that is, if you have a formula , then you can put an ?x in front of it, (?x)^, and you read it ‘the thing such that (f>\ or words to this effect. For example, you read:

()x)(Wx & Hx) as the thing such that it’s winged and it’s a horse’, or just ‘the winged horse’. And the semantical account is that (;x)0 refers to the unique object that satisfies (f), if there is one, and otherwise (ix)(j> just doesn’t refer at all.

SUMMARY OF THE FORMAL DEVELOPMENT

165

Definite descriptions are used to make sentences in a manner that is just slightly unorthodox: they go in front of the predicates they combine with (there is no logical significance to this). In other words, any definite description may be placed in front of any one-place predicate to form a wff. So if we want to write, say, ‘The man in the doorway is clever’, we write something like this: (;*)(MN* & /N*)CN. I say “something like this,” for although what has been written is perfectly well formed, it probably doesn’t accurately symbolize most normal uses of that English sentence. For if you recall how varied our ontology is, you will realize that there are lots of men in the doorway (this was pointed out in chapter i), but most of them are just not relevant to what I am saying. Generally, I’ll be referring to (or at least attempting to refer to) a real man. And so the best way to symbolize most natural uses of the sentence is: (ix)(MNx & INx & E\x)CN. That is, ‘The existing man in the doorway is clever’; I don’t say ‘existing’, but the context makes it clear that this is what I mean. When are such sentences true or false? The account pro¬ posed in chapter

5

was that a sentence of the form (ix)P is true

when (ix) / £ & x hasjy & x has z)]. Then it would seem that there are two distinct children, each of which m has:

APPLICA TIONS AND DISCUSSION

194

(3y)(3z)(y / £ & m has y & m has z). No, this does not follow. The latter statement is true in the story, but we cannot in general infer that whatever is true in the story is actually true. We can export certain nuclear predications, so that we can infer that m has the nuclear property listed above, but the latter statement does not follow from this. This was the sort of mistake discussed near the end of section 2. 6. Relations to Unreal Objects According to the story, Holmes talked to Watson. So, according to the story, Holmes has the property of having talked to Watson, and Watson has the property of having been talked to by Holmes. Then, by the theory, each of them has those properties: h[Tw] & [hT]w. Neither Holmes nor Watson exists, and neither is identical to the other, so: h # w & ~E\h & ~E\w & h[Tw] & [hT]w, which entails: (3x)(3jy)(3f?N)(x # jy & ~ E\x & ~£fy &

& [x/?]j).

Recall that x\Ry\ & [xK]y is the theoretical analysis of ‘x stands in relation R toy’, so the above may be summed up as: Some distinct nonexistent objects stand in nuclear relations to one another. This is interesting because it is not a theorem of the basic theory, and because it has consequences for our view of what nonexistent objects can be like. It is an extension of the basic theory, got by combining that theory with its application to fictional objects. One consequence of this version of the theory is that it is not plausible to maintain a certain kind of constructivist view of non¬ existent objects. Here is the view I have in mind. Suppose that we start with an initial stock of objects, the existent ones, EX, and an initial stock of nuclear properties P0, which does not include any relational properties got by plugging up nuclear relations with nonexistent objects. In other words, we start with materials to-

FICTIONAL OBJECTS, DREAM OBJECTS, AND OTHERS

195

tally acceptable to the orthodoxy. Then we “make” some non¬ existent objects by making arbitrary sets of nuclear properties. We can either suppose that the objects so constructed are the sets produced, or that producing such a set somehow produces an object corresponding to it. Call the set of such objects, including those in EX, OBj. Now, using the objects in 0B±, we can extend our original set of properties P0 to a new set P\ by adding those relational properties that are “made” by plugging up nuclear relations with arbitrary members of 0BX. Then we again make objects out of sets of members of Pl9 yielding a new set of objects,

0B2. Some members of 0B2 are already in OBbecause some members of Pi were already in P0> but some are new. We then continue the process, getting P2, 0B2, P3, .... Maybe we even extend the process into the transfinite, in an attempt to ensure that we have enough objects for our needs. (If we assume that every time we plug up a nuclear relation with a new object we get a new property, then the process never terminates. The result is a theory reminiscent of Zermelo-Fraenkel set theory. We never get, for example, a “universal” object, an object which has all nuclear properties; so if we need such an object, it will be im¬ possible to go far enough to meet our needs.) This particular theory is not a version of the basic theory; it is incompatible with axiom OBJ (which, e.g., yields a universal object). But if we liked it enough, we might be willing to modify the basic theory in its direction. One trouble with it would be that it is incompatible with the theory of fictional objects under discussion. Here is why. On the constructivist theory, for every nonexistent object there is an earliest stage at which it is con¬ structed. Then suppose that Holmes is first made at stage aSince Holmes has the property of having talked to Watson, that property must have been made before stage a. So Watson must have been made even earlier; that is, Watson must have been constructed before Holmes. But a similar argument shows that Holmes must have been constructed before Watson, and both of these cannot be true. Fictional objects created in the same story are on a par; constructively, they must be made simultaneously, if made at all. But then they cannot be made out of things (relational properties)

APPLICA TIONS AND DISCUSSION

196

which are made out of their compatriots. So fictional objects provide an impediment for a joint constructivist view of non¬ existent objects and relational properties. There is, however, a quasi-constructivist view which may be compatible both with the basic theory and its application to fictional objects. The idea is to maintain a constructivist view of objects, while ignoring, insofar as possible, relational properties got by plugging up nuclear relations with unreal objects. We cannot deny that there are such properties without significant alteration of the basic theory, but we can “trivialize” them to get much the same effect. We are already assuming that it is impos¬ sible for any real object to have such a property. Suppose, then, that we identify all such properties with some particular impos¬ sible nuclear property (some nuclear property such that it’s impossible for any real object to have it). We pick some such property, call it p0) and we add the axiom:

(*)(*N)(~£!* = ([^N] = Po & [*N*] = />„))• In terms of the constructivist view sketched earlier, this amounts to giving up the assumption that we can initially distinguish re¬ lational properties got by plugging up nuclear relations with non¬ existent objects from other properties; in particular, we assume that all such properties are already in P0, since they are all identi¬ cal to p0, which is in P0. Then OB^ turns out to contain all objects, since Px contains nothing that is not already in P0, and so 0B2 contributes no new objects;

Po = Pi

=

P2 =

•

•

•

0BX = 0BZ = 0B3 = . . .

and

-11

Is this view at all viable? There are at least two sorts of problems with it. The first has to do with the central issue of sections 5-7: if so many relational properties are identical with one another, we may not have enough nuclear properties to distin¬ guish different fictional objects. For example, suppose that I rewrite the Conan Doyle novels by interchanging certain charac¬ ters in certain episodes; say that Holmes occasionally discovers that Watson, instead of Moriarty, has committed the crime. My Holmes would be a different fictional object than Doyle’s, but 11. This quasi-constructivist view guided much of my early work on this

theory; I am now quite doubtful that it is the best approach.

FICTIONAL OBJECTS, DREAM OBJECTS, AND OTHERS

197

mightn’t the theory identify them? For example, we cannot now distinguish my Holmes from Doyle’s by claiming that mine has “attributed a crime to Watson” and Doyle’s does not, for Doyle’s has “attributed a crime to Moriarty,” and that is the same nuclear property as “attributed a crime to Watson.” But, of course, my Holmes and Doyle’s will differ in other respects. Mine will have “attributed a crime to someone he lived with,” which Doyle’s will not, and we have not proposed identifying these properties with one another. (See Parsons [AL4F0] for more discussion of this point.) Perhaps the view in question is immune to the first objection, but there is another. Let us use w for Watson, m for Moriarty, and L for lived with. Then we seem to have the following truths (where w and m are understood to occur de re): (a) According to the story, Holmes has [Lw]. (b)

~ according to the story, Holmes has [Lm].

(c)

[I«j] = [Lm],

But according to the logic employed in the formal theory, the property identity in (c) permits intersubstitutivity in (a) and (b), so (a)-(c) are inconsistent. And this is one of the reasons that I have for not liking the quasi-constructivist approach; it seems to me that the logic is right in not permitting (c) to be true in the face of (a) and (b). However, this is a fairly abstract issue on which there is plenty of room for disagreement,12 so others may not regard this as seriously undermining the approach. 7. Extranuclear Predications; Stories within Stories Typically,

stories

attribute

to

their characters extranuclear

properties as well as nuclear ones. The theory in question says that these characters have the nuclear properties so attributed, but does not say this for the extranuclear ones. In many cases this is essential. According to the story, Holmes exists; but we would not want to attribute existence to him on that account, 12.

One might, for example, argue that it is not true that according to the

story Holmes has

\Lw\;

it is only true that he has

\JPxW[\y(xLy)]\, where W is

the proper name ‘Watson’; recall the discussion of names in chapter 5,section 4.

APPLICATIONS AND DISCUSSION

198

for he does not exist. There are cases, of course, in which a fic¬ tional object does have some of the extranuclear properties attributed to it in the story. Holmes has the extranuclear property of having been thought about by criminals, but that is because they have read the novels, not because it says so there; had Doyle not published his work, Holmes would have lacked this property. These facts lead to some possible difficulties with the theory; these difficulties form the subject matter of this section. To begin, suppose that a character in a story is given only extranuclear properties in that story. Then the theory may say either that there is no such character, or that the character is the null object, both of which sound suspicious. Are there such characters? Suppose that this is the story: Story. “Jay exists. The end.” No, this won’t do, for two reasons. First, the story is too meager to be plausible; pretheoretically, it is unclear that this is a story, or that it has a character. And second, if we were to insist on the example, then the theory in fact would identify the hero of the story as a certain nonnull object; it would be an object which has at least watered-down existence, and the property of being named “Jay.” Let us try avoiding such properties by omitting the name and changing existence to nonexistence: Story. “An object doesn’t exist. The end.” But now we pretty clearly have a “story” without a main char¬ acter, so the theory does not apply incorrectly here. The moral of these examples seems to be that if we want to make trouble for the theory, we’re going to have to produce stories which have fairly detailed and well-delineated characters; extremely brief and abstract examples just aren’t convincing. And since real objects have the watered-down versions of all the extranuclear properties that they have, we will probably have to have recourse to characters which, according to the stories in which they occur, are not real. All this is quite difficult to do in a convincing manner (the reader is invited to try), but there is a closely re¬ lated strategy which seems more promising. Try to falsify the

FICTIONAL OBJECTS, DREAM OBJECTS, AND OTHERS

199

theory by producing examples of pairs of fictional objects, objects which we would distinguish pretheoretically, but which are alike in all of their nuclear properties. This allows us to attribute to each object a large number of nuclear properties, which makes the example realistic, without automatically defeating the strat¬ egy designed to produce a counterexample. Here is an illustrative example:13 Story: “On my way home from work I encountered a thug who attempted to hold me up. I said to him, ‘In a moment a policeman will come around the corner and capture you.’ A moment later a policeman came around the corner and captured him. The end.” The difficulty is supposed to be this: that there are two police¬ men in the story, the “made-up” one />M, and the “real” one pT. But they differ only with respect to extranuclear properties, such as existence, having been mentioned by the narrator, etc. There are various weaknesses in the objection. First, we might maintain that in the story the policeman who came around the corner was the policeman described to the thug, so that there would in fact only be one policeman in the story. But this isn’t very convincing; I don’t think that it is the right way to interpret the given story, and if it were, we could probably alter the story in such a manner as to avoid this interpretation. Second, and more interesting, one might maintain that pu is not a char¬ acter of the story (so again there is only one policeman in the story). The narrator said, “In a moment a policeman will . . . ,” but this just reports what he said, it does not introduce a new character into the story. I think that this is the right way to inter¬ pret this story. However, this way out could be avoided by embellishing the example somewhat. For example, the narrator could have told the thug a fairly lengthy story about a policeman, and the story could then have “come true.” So let me suppose that the story has been sufficiently embellished so that it is clear that according to the story there are two policeman, that pM ^ pr. This supposition is needed if the story is to provide a counter¬ example. 13. This example originated with Robert M. Adams.

200

APPLICATIONS AND DISCUSSION

But now the theory does distinguish the two policemen. We know that according to the story, pu ^ pT. So according to the story:

U*(Al

* *)]Pr-

We also know that according to the story pr exists, so, in the story, pr also has the watered-down version of the above property; it has:

HMAm # *)]• But then this is a nuclear property that pT has in the story, and it is a property that there is no reason at all to attribute to pu in the story. So the two policemen do have different nuclear prop¬ erties in the story, and the theory does distinguish them from one another. One might, of course, attack the above reasoning, for there are limits to the inferences that one can make within stories (see section i above). But normal inferences can be made, so long as they are not unduly complex, and so long as they contribute to, rather than detract from, the surface coherence of the story. Our inferring that pT has [ANx(/)M ^ *)] is a case of such a normal inference. This sort of reasoning will suffice to avoid most realistic counterexamples based on characters which are distinguished within a story “only” by the fact that one is real and the other is not. But there is one more type of possible counterexample (the last that I’ll discuss) which is not so easy to avoid. The idea is to have two stories, each of which contains subsidiary stories (or dreams, or legends) about objects which, according to the main story, do not exist. Then if the subsidiary stories are sufficiently similar, perhaps the theory will be unable to distinguish char¬ acters of the subsidiary stories when they should be so distin¬ guished. But before discussing this sort of objection, we need to see how the theory applies to stories within stories. Suppose that a story occurs within another story, such as the famous case of the play-within-a-play in Hamlet. How does the theory apply to the characters of the subsidiary story? Well, it identifies such a character as the object which has all and only

FICTIONAL OBJECTS, DREAM OBJECTS, AND OTHERS

201

those nuclear properties attributed to it in the story—that is, in the main story. These properties are determined by the reader in two different ways: (i) often the main story tells us some things about the plot of the subsidiary story, and we can judge for ourselves some of the nuclear properties possessed by the char¬ acters of the subsidiary story—roughly by imagining ourselves to be characters of the main story who are reading or hearing the subsidiary story; and (2) sometimes we discover things about the characters of the subsidiary story by things that the characters of the main story (or possibly the author) say about them. Occasionally, we get the entire subsidiary story verbatim, but, typically, we learn a great deal about it by means (2). For exam¬ ple, in Hamlet we discover from Hamlet, not from the reported acting out of the play-within-the-play, that Gonzago’s murder took place in a garden, and that the motive was economic. Characters of stories-within-stories, then, will be relatively ordinary fictional objects, with ordinary nuclear properties. They will typically be “isolated” from the characters of the main stories in that they will not be related to them by ordinary nu¬ clear relations. Nor will they stand in watered-down versions of typical extranuclear relations to them. For example, in Hamlet Gonzago has the extranuclear property of being thought about by Hamlet, but, being unreal (in Hamlet), he does not inherit the watered-down version of this property. Now what would a counterexample to the theory (of the sort under discussion) be like? Well, it would consist of two stories, each containing subsidiary stories, such that: (1) the subsidiary stories are given to us, by one means or another, with enough detail so that we would judge them to give rise to genuine characters, and (2) it is clear, pretheoretically, that the stories contain different characters, but (3) the theory identifies them as the same characters. The power of the theory here is that it will only identify the characters as the same if the same nuclear things are true of them in the two stories, and that makes it difficult to satisfy (1) and (2). In fact, I have been unable to construct a clear and compel-

APPLICA TIONS AND DISCUSSION

202

ling counterexample along these lines. However, this could be because of a feebleness of motivation; perhaps others will have better luck. 8. Alternative Theories Most theories of fiction take the orthodox position regarding fic¬ tional objects: there aren’t any. Many writers have commented on the implausibility of this view, but hardly any have offered a theory that is developed in any detail. (Plantinga [7S0V] proposes a possible worlds account, but he proposes it only as an example of how not to develop such a theory.) One exception to this is an article by Peter van Inwagen ([COF]). Here is a liberal para¬ phrase of that theory: (a) fictional objects are theoretical entities of literary criti¬ cism; (b) fictional objects exist; (c) typically, a fictional object does not have the properties attributed to it in stories; and (d) for any property p which is ascribed to a fictional object x in a story s, x has the property of having-/>-ascribed-toit-in-.r. The notion of “ascribed-to” is a technical one for van Inwagen; in terms of my discussion above, we can equate ‘p is ascribed to x in s’ roughly with ‘in j, x has />’ (see [COF] for discussion). Van Inwagen does not discuss the native/immigrant distinction in detail, and the theory could take many different forms, depend¬ ing on how this is treated. I’ll try to avoid this multiplicity of versions by avoiding the issue; I’ll limit my discussion to those fictional objects which are native to a story and which do not appear as immigrants in any other stories. Suppose that we temporarily ignore (a) and (b). Then we are left with the outline of a theory of fictional objects which can be formulated within the ontology of parts I and II of this book. Instead of: Sherlock Holmes = the object which has exactly those nu¬ clear properties attributed to Holmes in the Conan Doyle novels,

FICTIONAL OBJECTS, DREAMOBJECTS, AND OTHERS 203

we have: Sherlock Holmes = the object which has exactly those nuclear properties of the form “having/) in s,” where p is a (nuclear or extranuclear) property attributed to Holmes in the Conan Doyle novels, and s is the account determined by those novels. Let me call the former theory ‘Mod i’ and the latter ‘Mod 2’. Then Mod 2 has at least one possible theoretical advantage over Mod 1 : it seems to bypass at least some of the worries about ex¬ tranuclear predications within stories that were raised in section 7. For if one character has P attributed to it in s, and another character has P' attributed to it in s' (where P and P' are dis¬ tinct), then the former (but not the latter) has [JNx(x has P in $)], and the latter (but not the former) has [JNx(x has P' in /)], and so the theory automatically distinguishes them. (Actually it does so only if [JNx(x has P in j)] and [ANx(x has P' in s')] are different nuclear properties. This could fail to happen, for it is not in general true that distinct extranuclear properties have dis¬ tinct watered-down versions.14 But this could probably be main14. We can prove that for some P and Q, P / Q. and wP = wQ_, by the following adaptation of Cantor’s theorem. By axiom OBJ there is some object x0, such that:

(0

(P)(px0 = (P)(p

=

wP

=> (jv){Py

=>

~py))).

By axiom AB(E) there is some Cfsuch that: (2)

(y)(Q.y = y =

*o)-

Substituting wQ_ for p in (1) yields:

(3) wQ_x0 = (P)(wQ = wP zd (y){Py

=3

~wQ_y)).

Now we can show that ~ wQ_x0. For assume otherwise. Then by (3) we have:

(4) (P)(wQ_= wP 3 (y)(Py

=>

~wQ_y)).

Substituting Q. for P in (4) and using the law of identity yields:

(5) (y)(Q.y => -^CbOAnd so:

(6) Q_x0 => ~wQx0.

APPLICATIONS AND DISCUSSION

204

tained for typical cases of extranuclear predications in stories.) With regard to other problems discussed above, Mod 2 seems to be pretty much on a par with Mod i, provided that immigrant objects are treated appropriately. Does Mod 2 have any additional difficulties? All that I have discovered amount to niceties. For example, consider the sen¬ tence : The fictional detective who lived at 22 iB Baker Street lived with a doctor. To make this come out true on Mod 2, we need somewhere in the semantical account to replace ‘is a detective’, ‘lived at 22iB Baker Street’, etc., by ‘is a detective in a story’, ‘lived at 22iB Baker Street in a story’, etc.—or something like this. A little bit messy, but not too bad (see discussion of a similar point in [COF] p. 305). Notice that these paraphrases do not eliminate commit¬ ment to fictional objects, so they are not the sought-after para¬ phrases of chapter 2. Let us return now to claims (a) and (b). In (a), van Inwagen says that fictional objects are theoretical entities of literary criti¬ cism. Well, the intent of both Mods 1 and 2 is that the fictional objects described therein should form part of the subject matter of literary criticism, so in this respect all theories may agree. More may be meant by calling them “theoretical entities” than this, But this contradicts the conjunction of (2) and the assumption that

wQx0. (7)

So we have shown:

~wQx0.

This, together with (3), yields: (8) (3P)(wQ=

wP

That is, for some

P,

(9)

WQ. = u>P

& ~(jy)(Py => we have:

and (3\y)(Py &

It suffices then to show that

P

~wQy)).

uiQ_y). P y

and this is easy. For assuming

= (Hn (9) yields:

(10) (3>')(Q.J’ &

wQy),

which contradicts the conjunction of (2) and (7).

FICTIONAL OBJECTS, DREAM OBJECTS, AND OTHERS

205

but to pursue this topic in any detail here would take me far beyond my present task (but see chapter 8, section 6). In (b), van Inwagen says that fictional objects exist. This is a little tricky to evaluate, since he also insists that ‘there exists’ means the same as ‘there is’, a view which I do not accept. From the perspective of the present work there are two ways to inter¬ pret this claim. First, we may take his ‘there is/exists’ to mean just ‘there is’; on this interpretation his theory may be consistent with Mod 2. (It lacks any detailed ontological development, but so does Mod 2 if taken in isolation from the rest of the book.) Second, we may take his ‘there is/exists’ to mean ‘there exists’. Then there are two issues to face. First, a superficial difficulty: Sherlock Holmes doesn’t exist, but van Inwagen says he does. However, van Inwagen can explain this: when we say that Holmes doesn’t exist, we don’t say literally what we mean. We mean something like ‘Holmes is not a man’ (‘There exists no man who is Holmes’) or ‘Holmes does not have the properties com¬ monly attributed to him’ ([COF] p. 308). I don’t think this is right, but I have no argument against it that doesn’t beg the question. This is a twist on the paraphrase approach to non¬ existent objects: instead of paraphrasing away the apparent ref¬ erences to the alleged nonexistent objects, we paraphrase away the allegation that they don’t exist. (However, van Inwagen explicitly limits this technique to fictional objects.) If we assume with van Inwagen that fictional objects exist, Mod 2 cannot be the same as his theory, since according to Mod 2 fictional objects are incomplete, and so they do not exist. Van Inwagen’s objects must be complete, and so they must have lots of nuclear properties that they do not get by means of attribution in a story. To say more about the details of his theory here would be to go beyond his statement of it; let me just suppose that it has been filled in in some appropriate manner. Then we could com¬ pare this enterprise with Mods 1 and 2 as follows: both recognize the need for fictional objects, including objects which are said not to exist, and both add them to our ontology. One approach is to bloat the realm of existence and the other the realm of nonexis¬ tence. As theories of fictional objects alone, it is hard to assess ei-

APPL1CA TIONS AND DISCUSSION

206

ther of them against the other. Conceivably, the only important difference between them might turn out to be a fruitless debate about whether such objects really exist. 9. Fantasy, Myth, and Legend Although I have explicitly limited myself to realistic narrative fiction, departures from this style of story do not typically lead to new problems; they only enhance old ones. In fantasy writing, for example, it may be much more difficult to be clear about what is to go into the account of the story. Sometimes fantasy can be so coherently done that this problem is no worse than in typical realistic writing; Tolkien’s Lord of the Rings is an example of this. In this work there are lots of things left undetermined, and some of them are left undetermined because it is fantasy—for example, the extent to which magic can influence natural events, and how and by whom it can be practiced—but this is no different in principle than the underdetermination of the furnishings in Holmes’s sitting room. Other examples can be harder. Suppose a story specifies that in the year 4000, civilization is about to be destroyed by a disease that is caused by a bacterium that was produced by mutation in an experiment in the year 2000. A time traveler is sent back into the past to interfere with the experiment, and does so successfully. Civilization is saved. But wait a minute. What did happen (according to the story) in 4000? Was a time traveler sent back into the past? Why? Because civilization was about to be wiped out? Not according to the end of the story; there we are told that the mutation was prevented in 2000, and so no disease threatened the civilization of 4000. I suggest that this is simply another case of an impossible story. Its main character will have the watered-down version of having traveled back into the past, and will also have the (nu¬ clear) negation of this property as well. It’s more poignant, per¬ haps, but no different in principle than realistic fiction. The hardest issues in fiction arise wheil authors intentionally depart from “traditional” forms, say by mixing themselves in with their characters. This can make the theory quite difficult to

FICTIONAL OBJECTS, DREAM OBJECTS, AND OTHERS 207 apply in given cases, but again the difficulty seems appropriate to the intent of the work. Myths are “traditional stories serving to explain some phe¬ nomenon, custom, etc.” They make vivid at least two problems. First, in a myth there will typically be an unclarity regarding what happens in the story, because there will be no definitive text; instead there will be a long tradition of tellings of stories which will diverge from one another in various ways. Here we probably need to appeal to what is most common and most im¬ portant to the various tellings. As above, I think that unclarity in the identity of mythical objects within the theory sketched meshes with a real unclarity in our pretheoretic conceptions of such objects. Second, there is often an early time at which the myth is generally believed to be a true account. At such a stage in history, apparent references to the participants of the recounted happen¬ ings should be treated as genuine failures of reference to real objects rather than as successful references to unreal ones. When the situation is in flux, so that some people believe the story and some don’t, there may be unresolvable difficulties regarding which line to take. Legends raise a slightly different problem. Suppose that we know or suspect that a given legend is based on the activities of a real person, but that we assume that most of the feats recounted in the legend were not in fact performed by that person. When we use the name from the legend (e.g., ‘Noah’ or ‘Homer’), do we refer to the real person on whom the legend is based, or to a non¬ existent “fictional” object who is native to the story? (This prob¬ lem has been discussed recently within the context of the causal theory of names, where it is usually formulated as the issue of whether or not a name from a legend is “empty.”) There is probably no simple general answer to this question. io. Objects in Dreams At a pretheoretical level, no one is puzzled to hear someone say, “The unicorn 1 dreamed about last night resembled my depart¬ ment chairman.” But unicorns don’t exist, and so dreams ap-

208

APPLICATIONS AND DISCUSSION

parently provide us with more examples of objects that don’t exist. I propose that dream objects be treated, theoretically, al¬ most exactly the same as fictional objects. In particular, we may employ the schema: The (f> of dream d = the object which has exactly those nuclear properties which the (j) has in d. There are many parallels between stories and dreams which make this plausible. We use the locutions ‘in the dream’ and ‘according to the dream’ in much the same way that we use ‘in the story’ and ‘according to the story’. The immigrant/native distinction also seems to be relevant. I wake up and report: “I had a dream about my dog last night; she was tearing up the living room.” Here both my dog and the living room are immigrant objects. But if I report: “Last night I had a dream about a big black dog that was tearing up a living room,” then I am probably describing a native of the dream. As with fiction, the distinction is not always un¬ problematic. Suppose that I dream about a purple dragon, and my psychiatrist tells me that it is really about my first-grade teacher. It may be hard to tell whether this is correct. At one end of the spectrum are those cases in which I respond by exclaiming, “My God, you’re right; I didn’t realize it!”; then I would say, ceteris paribus, that the dragon was my first-grade teacher. At the opposite end of the spectrum are those cases in which the psychia¬ trist was making a shot in the dark, and there’s no evidence at all in favor of the proposal. The problem cases come in between. But none of this should obscure the fact that the distinction is usually clear. A major difference between dreams and fiction is this: in fiction (at least in unillustrated fiction) the account of what happens in the story comes to us primarily in propositional form—we construct the account from a series of sentences— whereas in dreams the account of what happens in the dream comes to us by gestalt; it must be constructed by interpreting a continuum of global impressions, images, feelings, etc. In this respect, dreams are a kind of thought that does not consist of inner speech. It is not clear to me whether it’s ever possible for

FICTIONAL OBJECTS, DREAM OBJECTS, AND OTHERS 209 an account originating in a story to be identical to an account originating in a dream. The principles of interpretation differ also. In the case of fiction, literary tradition is relevant, whereas this is not the case with dreams. (At least, I don’t think that there are traditions in dreaming; there may be traditions in opinion concerning the proper methods of interpreting dreams, but this is another mat¬ ter.) And dreams, of course, present a special problem with re¬ spect to availability of data. In a novel, the story is in a sense com¬ pletely present to the reader, whereas dreams seem to proceed in part at a subconscious level; their availability to the conscious¬ ness of the dreamer is a problematic issue. But this is a problem of evidence, not one of ontology. An object may be native to a series of dreams, as when some¬ one is plagued by a recurring nightmare; this is like a fictional object which is native to a series of novels. The problems of de¬ termining when this happens don’t seem to be different in prin¬ ciple. In the case of dreams the incompleteness and occasional im¬ possibility of their objects is vivid. It is typically very difficult to describe a dream, even to oneself, without imposing details on the characters and happenings in a way that distorts the dream. This is because dream objects tend to be highly incomplete and, more important, they tend to be indeterminate with respect to those properties in terms of which we normally “identify” things. I dream about a person with a face, but with no particular face, a person who is either-male-or-female but whose sex is completely undetermined. In conceptualizing dream objects, we instinctively try to treat them as existing objects; we expect them to be deter¬ minate in every detail, and we try to fill in the details as we are accustomed to do with existing objects. But it doesn’t work, and this is one of the things that is so distinctive about them. Dream objects provide some of the nicest examples of im¬ possible objects. I dream that I am in a room; the ceiling is above me but you get to it by going down those stairs in the corner. The tiles on the floor keep passing through one another, yet with absolutely no change in their relative geometrical relationships. A horse shows up; it is also a person, yet clearly not a person.

APPLICATIONS AND DISCUSSION

210

Fortunately, all this is compatible with the theory under dis¬ cussion. 11. Visual Objects In addition to fiction, the visual arts provide another source of nonexistent objects. One of the clearest cases is that of realistic illusionistic painting. The unicorn in the picture (if native to the picture) is a unicorn, and has the other nuclear properties attrib¬ uted to it there. (For an attempt to explicate what is true ac¬ cording to a picture, see Howell [LSPi?].) The native/immigrant distinction appears here also. The main figures in portraits are always immigrants, no matter how untrue to life, and immigrants appear in other paintings as well. For example, in Rubens’s painting The Judgment of Paris, Paris is an immigrant from the Greek legend, but the women in Chardin’s Back from the Alarket is native to that painting. Paintings, like dreams, operate by gestalt; except for their titles, their content is not propositionally presented. But unlike dreams, a knowledge of the tradition within which they are painted is relevant to their interpretation; this tradition influences the question of immigrancy, and also more mundane issues, such as the way in which three-dimensional volumes are represented two-dimensionally. Comic strips with accompanying text (e.g., Prince Valiant) form a medium midway between pure fiction and painting; their content is conveyed by an interaction between propositional and gestalt information. It is traditional to make a distinction between form and con¬ tent that applies to most of visual art. It is mainly the content of a work of art which provides nonexistent objects, for it is the con¬ tent which determines what is true in the work (in the sense of ‘true in’ used above; this probably has very little to do with “artistic truth”). In those areas of art, such as modern abstract painting, in which there is an attempt to depict form without separate content, it is doubtful that nonexistent objects are rel¬ evant. Realistic sculpture provides another source of nonexistent objects. Statues provide both native and immigrant objects in

FICTIONAL OBJECTS, DREAM OBJECTS, AND OTHERS 211 much the same way that paintings do. Rodin’s The Thinker de¬ fines a native object, whereas Michelangelo’s Bacchus yields an immigrant one. Objects native to works of visual arts are always incomplete, and, as with Escher’s prints, occasionally impossible as well. Plays are peculiar in that we have both scripts (which are often read as stories in their own right) and performances. The information in a script is presented propositionally; that in a per¬ formance (except for program notes) is presented by gestalt. It is probably impossible for any performance to present exactly the same information as is contained in a script, and that suggests that we will have to distinguish the characters of a performance from the characters of the script. This is initially surprising, but in fact we do seem to talk in this way. For example, we compare “Barrymore’s Hamlet” with “Burton’s Hamlet” as if we are comparing two different things; they can’t both be Hamlet, then, and it is plausible to suggest that neither of them is. (This is not to deny that they both play Hamlet, where this Hamlet is the one from the script; this is like two different actors both playing Lyndon Johnson, in McBird).

8 Traditional Issues jrom the Present Perspective

The point of this chapter is to ask: what would certain traditional issues look like if the present theory of objects were taken to be correct? I will not be concerned here to defend the theory of objects. i. Ontological Arguments; Exists?

Why Should Anyone Care Whether God

The present system is so rich in objects that one might suspect that God would be found among them. That depends on what is meant by ‘God’. (i) If ‘God’ means, say, ‘the main deity described in the Bible’, and if this is treated as an object native to the Bible story, then there is such a god as God, though he will definitely not exist (since he will be incomplete). (ii) If ‘God’ means, say, ‘the existing deity of the Bible’, then there may or may not be such an object, and the quoted definite description may or may not refer. In short, the system provides for lots of gods, with lots of inter¬ esting characteristics, some worthy of veneration and some not. But nothing in the system alone can be used a priori to show that any deity exists. This is a relatively trivial logical point, for the system allows of models in which nothing exists. It won’t help to add words like ‘perfect’ or ‘omnipotent’ to a description in hopes that some ingenious argument will yield an existent god.

212

TRADITIONAL ISSUES

213

For either the description will be purely nuclear in character, and we will not be able to show that the objects which satisfy it exist, or it will be partially extranuclear, and we will not be able to show that any object satisfies it. Descartes had a version of the ontological argument which illustrates this point: Whenever it pleases me to imagine a first and supreme being, and as it were to bring down an idea of him from my mind’s treasury, it is necessary that I should attribute to him all perfections, even though I neither then enumerate them all nor attend to each one: and this necessity is plainly sufficient that afterwards, when I notice that existence is a perfection, I rightly conclude that a first and supreme being really exists. (Barnes [OA] p. 16) Clearly, Descartes assumes that there is an object which satisfies

‘x is perfect’. If perfection does not entail existence, then this assumption might be justified, but then he cannot conclude with necessity that existence is a perfection, and that such a being exists; if perfection does entail existence, then he is not justified in assuming that there is a perfect being to begin with. The most he can show is that there is no nonexistent perfect being, but maybe that is because there is no perfect being at all. Anselm’s argument has always seemed more persuasive than Descartes’s because he first argues, in a seductive manner, that there is a perfect being, and then argues that it exists. Most reconstructions of Anselm’s argument fail to do justice to the persuasiveness of his presentation. Here is Barnes’s translation: Even the fool is bound to agree that there is at least in the understanding something than which nothing greater can be imagined, because when he hears this he understands it, and whatever is understood is in the understanding. And certainly that than which a greater cannot be imagined cannot be in the understanding alone. For if it is at least in the understanding alone, it can be imagined to be in reality too, which is greater. Therefore if that than which a greater cannot be imagined is in the understanding alone, that very thing than which a greater cannot be imagined is something

APPLICATIONS AND DISCUSSION

214

than which a greater can be imagined. But certainly this cannot be. There exists, therefore, beyond doubt something than which a greater cannot be imagined,

both in the

understanding and in reality. (Barnes [OT] p. 3) I think that the persuasiveness of this argument hinges on a double ambiguity regarding ‘imagines’. This is an intentional verb which takes two kinds of direct objects: propositional ones, as in ‘Jones can imagine that we will soon land on Mars’, or ‘Jones can imagine us landing on Mars soon’, and ordinary denoting phrases, as in ‘Jones can imagine a purple unicorn’. And whichever it takes as object, it may do so in either a de re or a de dicto sense (recall the discussion in chapter 2, section 4).1

1. Barnes

[OA]

pp. 88-89 actually offers a formalization of Anselm’s

argument which encapsulates these ambiguities by using the same notation (though with two different definitions) to symbolize both and

F’ (with no de re readings).

imagines something

de dicto

tween the

and

‘x

imagines that

P’

notational distinction being made be¬ This turns out not to be important,

however, since other of Anselm’s rules and assumptions do all the real work in the proof. In fact, although Barnes does show how to derive ‘God exists’ from five of Anselm’s

assumptions,

it is possible using his Anselmian

rules

to

derive anything at all from no assumptions. Here is a sketch of the argument. First we give two definitions: (Dr) (D2)

Ax = d[Bx v ~Bx. a =df (jx)~Ax.

(These definitions are patterned after ones given by Barnes.) Now let any sentence at all not containing the name

a.

C

be

The proof, using Barnes’s

notation and rules, is:

.

A 1 1 1 1

1 A A

(1) ~C

assumption

C 3 Ba v (3) Ba v ~ Ba (4) Aa (5) {x)Ax (6) Aa (7 )A[{ix)~Ax] (2) ~

(8) ~ ~C (9)

C

~

Ba

tautology (1), (2) MPP

(3) , D, (4) , UI (5) , UE

(6) , D2 (1), (7), RAAAns (8), DN

The work is all done by treating definite descriptions as terms subject to quanti¬ fication, as in

(6), and simultaneously using rule RAAAns (“reductio-ad-

absurdum-Anselm”) in step (8); this latter rule essentially assumes the falsity

TRADITIONAL ISSUES

215

Anselm’s argument begins by establishing that the fool “imagines that than which nothing greater can be imagined” in its de dicto sense (for the justification is merely that the fool understands the words). But then he begins referring back to the alleged referent of the denoting phrase by means of singular pronouns, as if it had been established that there is such an object imagined by the fool (de re), a natural and reasonably subtle transition—but a question-begging one. Then later, he implicitly switches to the usage of ‘imagines’ in which it takes a propositional object; he judges that such an object’s being in reality is greater than such an object’s not being in reality. But in the crucial phrase ‘that than which nothing greater can be imagined’ it is the thing that is said to be greater, not some proposition or state of affairs in which it figures. This makes the argument, as literally stated, so patently invalid that virtually everyone who comments on it rephrases the argument in some way, either by turning the first use of ‘imagine’ into one which takes a that clause as its object (as in Adams [LSAA\), or by turning the second use into one which takes a denoting phrase as object (as in Barnes [OA]). Anselm’s statement of the argument gives no clear guidelines for how either of these is to be done, and I suspect that one of the reasons the argument has never been fully disposed of is the thoroughgoing unclarity about just what the argument is (plus, of course, the importance of its subject matter). But however the argument is construed, I suspect that it will either rely on fallacious reasoning, as in the first transition from a de dicto to a de re reading of ‘imagines’, or it will employ assumptions

about

the

relationships

between

these

readings

which are not viable. The only support it receives from the theory of objects is the vindication of the coherence of reasoning about a thing without prejudice as to whether or not that thing exists. It has often been thought that the crucial fallacy in onto-

of any sentence of the form D[(;x) ~Z>x]. (In Barnes’s formalization of Anselm’s argument, these rules are employed in his steps (8) and (27).) The theory of objects as I have formulated it would sanction rule RAAAns, but would not allow the use of universal specification (Barnes’s rule UE) for arbitrary definite descriptions since the theory assumes that some definite descriptions do not refer to anything.

APPLICA TIONS AND DISCUSSION

216

logical arguments is treating existence as a property. There are (at least) three main versions of this thesis. (i) According to Frege, existence isn’t a property of indi¬ viduals, but rather a property of concepts ([FA\ sec. 53); ex¬ istence is not properly represented in language by a predicate (‘exists’) but rather by a quantifier (‘there exists’).

However,

there certainly is a property of individuals represented by the complex predicate ‘being something such that there exists such a thing’

(‘[A*(3y) (x — _>>)]’), and the arguments can all be re¬

phrased (though perhaps clumsily) in terms of this predicate. (ii) According to others (e.g., Kant), existence isn’t a prop¬ erty because it is trivial (it adds nothing) to say of something that it exists. This view would appear to identify ‘there is some¬ thing such that . . . ’ with ‘there exists something such that . . .’. If this identification were correct, and if we could es¬ tablish that there is a god, then we would automatically have established that a god exists. This would actually vindicate part of the ontological argument. Unfortunately, no historical version of the argument successfully establishes that there is a god. The theory of objects does assert this, but it can’t be combined with the view in question to show that a god exists, for it rejects the triviality of existence statements. (iii) There seems to be an undercurrent in a lot of discussion that existence, although a property, is not a property on a par with others—it can’t be treated like ordinary properties, especially with regard to “defining” objects. This may be part of what lies behind the issue of whether or not existence can ever be a part of the “essence” of a thing. Sometimes existence is called a “tran¬ scendental” property. This is, in fact, the view taken in the theory of objects; existence is an extranuclear property, not an “ordi¬ nary”

nuclear

one.

We

can

“define”

objects

using

nuclear

predicates—that is, using nuclear predicates we can specify an object and be sure that there is such an object; there is no a

priori guarantee that we can do this using extranuclear predi¬ cates, such as ‘exists’. Who cares? Why is it important whether or not God exists? There are two questions to be distinguished here: first, why is it

TRADITIONAL ISSUES

217

important to people that there be a god, and second, if there is one, why is it important that it exist? Presumably the answer to the first question is that religious activity typically involves worship and veneration, and that such activities are inappro¬ priate without something to worship and venerate. Of course, the phenomenological side of such activities may be present even in the absence of an object, but such isolated mental states are presumably just as undesirable to their agents as are beliefs that are false. But supposing there to be a god—for example, a fictional one determined by a biblical myth—why would it be devastating for it not to exist? In one sense the answer is clear: it’s something that people do care about. You can’t always provide reasons for attitudes, and this may be such a case. On the other hand, it ought to be equally possible for someone to simply not care whether God exists. Many people would find it inappropriate to worship or venerate such a being, but I think that this is an attitude of theirs which not everyone needs to share. As to its feasibility, well, there are people who venerate Jesus without believing him to be divine, and prima facie, divinity seems to be just as important in a religious object as existence.

2.

Epistemology: Might I Be a Nonexistent Object?

In the Meditations Descartes opposed reason to skepticism. Reason was declared the winner,

but later generations have almost

unanimously agreed that this was mainly due to the home-court advantage, and that an unbiased referee would have declared skepticism the victor. Reason should have lost in the first round, when Descartes was overly impressed with the catchy “cogito”. The evidence was supposed to be, roughly, the phenomenologi¬ cal side of doubt occurring. Somehow this got analyzed into an activity with an agent, and the conclusion was then drawn that the agent exists. It wasn’t even fair to analyze the doubt into an activity plus an agent.2 But supposing that there is an agent, how 2. Cf. Nietzsche

cogito

\BG&E~\

pt. I sec. 6. I am not attempting to discuss the

exactly as Descartes articulates it. As I see it, the relevant structure should

have been:

APPLICATIONS AND DISCUSSION

218

do we get the further conclusion that it exists? Descartes can hardly presuppose the equivalence of being something with being something existent, for the ground rules were established in col¬ laboration with skepticism, and the skeptic doesn’t need a theory so elaborate as the theory of objects to demand a justification for the step from being to existing (especially when the data are so “mental” to begin with, and the conclusion is that the agent is not just an object of thought). As with the standard Cartesian approach (“How do

1

know that I’m not just dreaming?”), there are homier applica¬ tions of this issue. Even if I don’t doubt that I am something, how can I know, say, that I am not (merely) a (native) object of a very detailed and cleverly designed story? What can I learn about myself which would ensure my reality? I am human, male, brunette, etc., but none of that helps. I see people, talk to them, etc., but so did Sherlock Holmes.1 2 3 4 Instead of fearing that I am dreaming, and everything around me is unreal, why shouldn’t I be equally afraid that someone else is dreaming, and / am unreal? This question was faced by Alice in Through the Looking-Glass, chap. 4, and as Tweedledum

and

Tweedledee

mercilessly

pointed

out,

her

efforts to gather evidence in favor of her reality met with no success whatsoever. It seems to me that this is a philosophical

(1) Doubt is occurring. (2) I (the doubter) am thinking. (3) 1 am(4) I exist. The criticism is for

presuming

(2) instead of (1), not for explicitly inferring (2)

from (1). My next criticism (below in the text) is for ignoring the difference between (3) and (4), not for explicitly announcing that (4) follows from (3). (Note that (2) should not be confused with Descartes’s later argument that thinking is part of his essence.) 3. Hintikka [CTS] suggests in this connection that the inference from ‘Hamlet thinks’ to ‘Hamlet exists’ is not a valid one. But his point is that the former might be true even though the name ‘Hamlet’ fails to designate any¬ thing. My point here is the different one, made by Meinong in [TO], that there might

\DOA\

be

a thing that thinks without that thing existing. See Kenny

for further discussion of this point within the setting of Descartes’s

ontological argument.

TRADITIONAL ISSUES

219

problem that deserves to be treated seriously on a par with issues like the reality of the external world and the existence of other minds. (I don’t know how to solve it.) 3. Leibniz’s Monads and Possible Worlds Certain aspects of the theory of objects look somewhat Leibnizian. For example, all relational statements are analyzable into conjunctions of property statements: ‘x bears R toy’ is shorthand for ‘x has [Ry] and y has [xi?]’. These properties, of course, “encode” the relations out of which they are made. This encod¬ ing can be exploited so that certain objects “mirror” the pos¬ sible worlds in which those objects “appear”; that is, whole possible worlds can be encoded into the properties of single ob¬ jects, if those objects are of certain special sorts. One sort I will call monads', these include all existing objects, and there will be others as well. Here is how it goes. Suppose that we are working with a fully interpreted version of &, as developed in chapter 5. Sentences of

6 will have truth

values relative to various possible worlds. Call the actual world ‘w0’. Then, following Castaneda {TSW] sec. 11, we can define: x is a monad =df in wQ, x is both complete and possible. Then if x is a monad, we define: x appears in w =df there is an object which exists in w and which has, in w, exactly those nuclear properties which x has in w0. Notice that to say that x appears in w does not mean that x itself exists in w, but rather that some “surrogate” for x exists there. This surrogate might be x itself; this will happen when w is wa, and might happen in other cases as well. But, in general, the surrogate of an object in a different world may be a different object. Now various metatheorems may be proved about the se¬ mantical structure of the modalized version of & that was develPortions of this section resemble material that appeared originally in Parsons [N&EPM&L].

220

APPLICA TIONS AND DISCUSSION

oped in chapter 5, metatheorems which reveal some of its Leibnizian aspects. The key fact, on which all the rest are based, is: Metatheorem o: If object jy exists in world w, and if 0 is a wff that does not contain x free, then

is true in w (with respect

to an assignment g of values to the variables) if and only ify has, in w, the property that w[Xxcf)] stands for in w (with respect to assignment g). This metatheorem tells us that facts about a world (of the sort that are expressible in 0) are reflected in the nuclear prop¬ erties that the objects that exist in that world have in that world. The metatheorem depends

crucially on the watering-down

principle (axiom WD), which might appropriately be renamed the “principle of preestablished harmony”—objects that exist in a world are, insofar as their nuclear properties are concerned,' in harmony with each other and the rest of the world. (The “preestablished” part is that the system was designed so as to satisfy this principle.) A proof of the metatheorem goes somewhat as follows :4 4. This is a very informal sketch of a proof technique. It contains a certain amount of use-mention confusion (e.g., it talks about an object’s having a

predicate

instead of a

property)

and it ignores the complications of assignments

to the variables. Other proof sketches below share some of this informality. The official proofs all utilize the technical apparatus developed in chapter 5, section 5. Since metatheorem 0 is so important for what follows I’ll give a somewhat more accurate description of its proof here. Suppose thaty exists in

w

does not contain * free. Recall that in Ag such that ‘.4g(a)’ denotes what¬ ever thing a stands for in the model with respect to the assignment g to the variables of 0. When y exists in w, ‘y has the property r in w' is formulated as ‘y e extw(r)’. And ‘ is true in w with respect to g’ is formulated as ‘extw(.4g(^)) = T’. A formal statement of the metatheorem then is: for any objecty, and any wff not containing x free, and any assignment g, y e extw(.45(ii>[2x^])) if and only if extw(.4g(^4)) = T. The proof then goes as follows: and that

chapter 5, section 5, we defined a function

j, and so (by axiom AB(E)**) objects have

if and only if (f> is true. Putting these facts

together we have:

y has w\Xx(h~\ in w if and only if 0 is true in w, which is what we want. We can now establish:

Metatheorem i: If x is a monad, x appears in exactly one world.

Sketch of proof: First we show that x appears in at least one world. Let ^ be the set of nuclear properties that x has in wQ. Since x is a monad, x is possible, and so there is an object £ and world w such that £ exists in w and z has (in w) all the properties in Since x is complete, z cannot have any nuclear properties that are not already in % without being impossible (in w), and so not existing in w. Therefore, z exists in w and has (in w) exactly the nuclear properties that x has in wa, and so, by definition, x ap¬ pears in w. Second, we show that x appears in at most one world. As¬ sume not; that is, assume that there are objects y and z and worlds wl and w2 such thatjy exists in wx and has, in wx, exactly the nuclear properties in

and z exists in w2 and has, in w2,

exactly the nuclear properties in

Since wx ^ w2, there must be

a difference between wx and w2 that affects the truth value of some wff (f) (which does not contain x free) with respect to some assignment to the variables (see below). Suppose that is true in wx and false in w2 with respect to g. Then, by metatheorem o,

y has, in wh the property denoted by w[Xxcf>] with respect to g,

iff

extw(A(j>)) = T

iff

extw(Agy()) =

iff

extw(ffg

=

by condition (14.3)

T T

by above characterization of since

does not contain

x

h

free

(Strictly, the last step involves the customary but complicated proof that the truth value of a formula relative to an assignment to the variables is not affected when the assignment is changed for a variable that is not free in the formula.)

222

APPLICATIONS AND DISCUSSION

and z lacks that property in w2, contrary to the assumption that bothjy and z have (in those respective worlds) exactly the nuclear properties in The dirty work in spelling out this proof lies in showing that if Wi # w2, then there is some wff 0, not containing x free, and some assignment g, such that (j) is true in

with respect to g

and false in w2 with respect to g. You find such a and g as follows. First, as worlds are constituted in chapter 5, section 5, they cannot differ at all unless they differ with respect to: (i) which objects exist in them, or (ii) which objects have which nuclear properties in them, or (iii) which extensions are possessed by which extranuclear properties, propositions, etc. In case (i), if u exists in

but not in w2, pick (j) to be E\v, and

let g be any assignment that assigns u to v. In case (ii), if u has p in Wi but not in w2, let cf) be qlvl and let g assign/? to ql and u to v. Case (iii) has several subcases which are dealt with similarly. It is now natural to define compossibility as follows: x is compossible withy =df there is a world in which x and y both appear. Because of metatheorem 1 it is now easy to prove: Metatheorem 2: Compossibility is an equivalence relation on the class of monads. (See Mates [LPW].) Furthermore, compossibility is the “right” equivalence relation. To show this we first define, for any monad x: M — df the class of monads that are compossible with x, and: PW(\x\) =df the world in which any member of |x| ap¬ pears. Then we have: Metatheorem 3: P IT is a one-one function from the set of equivalence classes of monads (with respect to compossibil¬ ity) onto the set of “nonempty” worlds.

TRADITIONAL ISSUES

223

(A “nonempty” world is any world in which at least one object exists.) So the monads fall into realms (equivalence classes of cornpossible monads), and the realms correspond one-one with the nonempty possible worlds. All the monads in the same realm appear in the same world—the world to which the realm cor¬ responds—and each of the monads in the realm “represents” an object that exists in that world (namely, the object which, in that world, has exactly the nuclear properties that are had by the representing monad in the actual world). And each such monad mirrors the corresponding world, in the sense that every fact true in that world is encoded in the nuclear properties possessed by the monad in the actual world; in other words, we have: Metatheorem 4: Ifjy is a monad, then for any wff (f> not con¬ taining x free, and for any assignment g, (f> is true in the world in which y appears if and only ifjy has [/U not containing x or y free:

0(j) = (ly)(y is possible Scy is complete & w[hc]y). (Recall that ‘is a monad’ is defined as ‘is both complete and pos¬ sible’.) This is not a reduction of the modal to the nonmodal, of course, and in my articulation of the theory it is arguably not a

224

APPLICATIONS AND DISCUSSION

“reduction” at all, since the modal predicate ‘is possible’ was defined in terms of the modal operator. The point is rather that, if we had taken the predicate as primitive instead of the operator, we could have reversed the order of definition—assuming that no worlds are empty. Actually, in one version of the theory we can effect a similar reduction without making the assumption that all worlds are nonempty. This is the version in which we assume that we are working with a modal structure in which our set variables range over all sets of nuclear properties.5 Then we can use pure reflectors to get a reduction of 0 . Let x be any object, and define: x is a pure reflector — df for some world w, the following holds: for any proposition s, s is true in w if and only if x has (in wQ) the nuclear property denoted by w[fas] in w0 with re¬ spect to any assignment g that assigns s to .y. Then the following holds for any wff (j) which does not contain x orjy free (with respect to any assignment g):

0 (j> = (3jv) (y is a pure reflector & w\Xxf]y). 4. Essentialism I have described 0 as quite neutral with regard to de re modali¬ ties, and this means that it is also quite neutral with respect to essentialism. It is clear how it is consistent with essentialism, even of the strongest kind. For example, we can suppose that every object has all its nuclear properties essentially; just take a modal structure in which the extension of r is the same in every world, for every nuclear relation r. This does not rule out a diversity of possible worlds, for objects could still differ extranuclearly from world to world; for example, different objects might exist in dif¬ ferent worlds. (In such a model a monad would appear in a world if and only if it existed in that world.) For the strongest kind of essentialism, in which every object has every property essentially, 5- This is discussed briefly in chapter 5> section 5- Making this an condition on

all

a priori

modal structures would make the theory nonaxiomatizable;

see a discussion of a similar point in chapter 4, note 8, and in Henkin [CTT].

TRADITIONAL ISSUES

225

if at all, including the extranuclear ones, just take a modal struc¬ ture in which there is only the actual world. How consistent is the system with antiessentialism? Well, clearly, any object will have certain properties essentially, say, the property of self-identity. This isn’t ordinarily considered to be a particularly bad kind of essentialism. But objects will also have certain other extranuclear properties essentially, properties that not all objects share. For example, in any modal structure the following will be true for any object (a) (3x)(3y)(Dx =

z & ~ Djv = z).

Therefore, the following will also be true: (b) (3x)(3jf)(DUm(m =

z)]x &~

=

z)~\y),

from which, by existential generalization we get: (c) (3P)(3x)(3j;)(DPx & That is, there is a property P which some object has as an essence, and which some other object does not. In case £ is Socrates, this parallels Plantinga’s argument (in [JVJV]) that Socrateity is an essence of Socrates, an essence which is not shared by other objects. Now there is something peculiar about such properties. We are inclined to view them as concocted. There seems to be a natu¬ ral sense in which Socrateity is not a property at all. Perhaps this is captured by the fact that Socrateity is not a nuclear property. (The same holds for properties like being blue in world w; such a property cannot be nuclear and hold in every world of exactly those objects which are blue in world w—unless the same objects are blue in all worlds.) With respect to nuclear properties, is it possible to be completely antiessentialist? That depends on what you mean by antiessentialism. For example, it will always be the case that for any object x there is some nuclear property p which x has in every world in which x exists,6 It x is Socrates, the watereddown version of Socrateity will be an example. And sometimes ‘essentialism’ is defined in these terms; it has to do with an ob¬ ject’s having a property in every world in which that object ex6. I am indebted here to Thomas Ryckman.

APPLICATIONS AND DISCUSSION

226

ists. But the clause ‘in every world in which x exists’ has a dif¬ ferent import in the (orthodox) theories within which it is usually invoked than it has here. For in those theories, existing in a world is usually tantamount to falling within the range of the quanti¬ fiers in that world, and in the present theory those conditions are not equivalent. In short, there is another version of essentialism: must there always be at least one object that has at least one nuclear property necessarily? The answer is no, but this answer may not be of any great significance (see below). Let me call a modal structure an antiessentialist structure if, in that structure, for any object x and any nuclear property p, there is a world in which x does not have p. Then it is relatively easy to describe antiessentialist structures in which no object ex¬ ists in any world.7 This may be regarded as not very interesting. The difficulty with showing that there are more natural anties¬ sentialist structures—ones in which lots of worlds (say, two or more) contain lots of existing objects (say, two or more) is that such structures are so big and complicated that it is difficult to verify that they satisfy the conditions for being modal structures; this is due mainly to verifying that the watering-down and plug¬ ging-up conditions hold. I haven’t been able to show that there are any antiessentialist structures of this sort, though my con¬ fidence has been strengthened by my inability to show that there are no such structures. 7. Such a structure may be constructed as follows: Let same cardinality as

8P(N x),

Let the set of possible worlds one functions from which

w

OB

to be

W

s(w).

W,

onto ^(jV,). If oie

EXW = A. W into {T, F).

3P(N^).

let /w be the function with

(For extw, see below.) If

we W

Let P = the

and if j e P, define extw(r)

These conditions then force certain other conditions, and leave

certain others open. For example, if

k)

have the

be paired one-one with the set of all one-

is paired, and let

set of all functions from

OB

that is, as the power set of Nv and let X =

must be the unique

r'( are inconceivable. (Perhaps a similar line can be taken with respect to Russell’s problem about propositions as well.) There are at least two sources of doubt regarding this de¬ fense. The first is a logical one: is it even consistent to suppose that if x # y and

= [Ry], then at least one of x and y is

inconceivable? The second is philosophical: if it is consistent, is it plausible? I don’t know the answer to either of these. But the first can be given a fairly clear formulation, so I’ll leave it as an exercise. Exercise for the reader: Is there a version of the language 0 (from chapter

4)

and an interpretation for it in which:

(1) There are lots of existing objects. (2) Every existing object has a name in the language. (3) Lots of properties and relations have names. (4) For any instance of axiom AB(E) of the form: (3QJ(x) {Q.x = (j>), in which cf> contains no free variables except x, there is a constant predicate P such that (x) (Px = is actually of the form (x)(E\x 3 f), and every subformula of the form (3x)$/> is actually of the form (3x)(Zs!x & %). 3. One unpleasant consequence of the proposal is that it would probably

de re belief. For suppose de re of x that b has the property got by plugging up the second place of R with x, but that this is a case in whichy is inconceivable and [ifa] = \Ry]. Then it seems likely that a has no de re beliefs about_y at all. But if we adopt the method of symbolizing de re belief that was adopted in chapter 5, section 3, then we symbolize the belief that a has by aB [b\Rx]}, and the belief that a lacks by aB {b\Ry]}. But if [/?*] = [Ry], the latter follows from the former by require a reassessment of the analysis I have given of that

a

believes

substitutivity of identicals. The obvious way to save the proposal in the face of this problem is to require something

more

along the lines of Kaplan’s proposals in [Q/].

for

de re

belief, say, something

APPLICATIONS AND DISCUSSION

240

Axiom OBJE is designed to do much of the work of our earlier OBJ while impeding the derivation of the theorem dis¬ cussed above. It easily allows all the simple applications that OBJ allowed; for example, the proof that “the gold mountain” is an object is unaffected; it is: ('lx)(P)(P* = P = g V p = m), which is just as much an instance of OBJE as of OBJ. The viability of this restricted theory depends on positive answers to the following two questions, a logical one and a philosophical one: Exercises for the reader: (1) Is the revised version of 0 consistent with (x)(y)(x ^ y => [Rx] # [i?y])? (2) Does the amended version of 0 support the important applications of the theory as well as 0 does? 2.

Are There Too Few Objects?

As developed, 0 is a type theory: what can be predicated of entities of one type—objects, properties, propositions—cannot meaningfully be predicated of entities of another type. So, for example, we can say of the proposition s that Agatha wonders (whether) s: aW{s}, but it is not even well formed to say that Agatha wonders (whether) Sherlock Holmes: aW{h). This case does not seem particularly troublesome, but others give rise to greater uneasiness. Suppose I have a dream in which there is a proposition which Agatha believes, and which (in the dream) is chartreuse (i.e., the proposition is chartreuse). Some¬ how a chartreuse proposition seems like the sort of thing you can dream about; yet it isn’t allowed within 0.

GLOBAL ISSUES

241

There are two problems here. First, it at least seems mean¬ ingful to say that Agatha believes something which is chartreuse: (3j)(a5{^} & Cs); yet this is not well-formed in 0. And second, we might want to hold that such an entity is a character in Agatha’s dream, and that there is something (something unreal, maybe impossible, maybe even in some sense incoherent) which is dreamed about by Agatha and is chartreuse. Crudely put, why admit round squares and then stop short of chartreuse propositions? The first problem is easily solved, probably in many different ways. We could expand our symbolism so as to allow any type of variable to occur in any position in a sentence, but that would make the syntax hard to read. Instead, let me adopt a somewhat rough approach that will do equally well. I will just relax the well-formedness constraint on identities, so that terms of different types may flank the same identity sign. Then we can write things like ‘Agatha is goldenness’, symbolizing it as: a = g; or ‘Bill is the proposition that every round square is round’: b = (x)(Rx & Sx

Rx).

And then we can write meaningfully that there is something chartreuse that Agatha believes, by writing: (3x)(3j)(x = s & aB{s} & Cx). The second problem is much harder to deal with. Here are various options. Option i: No cross-category identity statements are true. All characters of dreams and stories are objects. Such characters may, according to the dream, be propositions or properties, etc., and they may (again according to the dream) have proper¬ ties that are appropriate only to propositions or properties, but they do not have these properties simpliciter. Such properties, like extranuclear properties, should simply be ignored when identifying the characters of dreams or stories (recall the discus¬ sion of chapter

7,

section 7. In the present case as well, watered-

APPLICATIONS AND DISCUSSION

242

down properties may serve to make the theory more plausible. For example, if an object has “being a property” attributed to it in a dream, then the dream attributes to it: [>(3P)(* = P)]. Then there will be a watered-down version of this property, namely: [AN*(3 P)(x = P)], and this will normally also be attributed to the object, so the object will have a property that might be written ‘the property of being a property’.) Option i is consistent with the official position taken in this book. But some may find it implausible, and in any case others are worth exploring. So, in the following discussion, I will sup¬ pose, at least for the sake of exposition, that it is inadequate. Option

2:

All properties, relations, propositions, etc., are in

fact objects, and can be treated as such in the applications of the theory. In addition to the other axioms of 0 we also have: (P)(3x)(x = P); (s)(3x)(x = s); etc. Unfortunately this won’t work, for it leads to inconsistency. It could be carried out in part, for it would be consistent to identify all one-place nuclear properties with objects. For example, we could identify each property p with the object which has p and no other nuclear properties (recall the discussion of Plato’s theory of forms in chapter 8). But in at least some other cases the view is inconsistent. In particular, if extranuclear properties are identified with objects, then, no matter which objects they are identified with, the theory becomes inconsistent. The argu¬ ment is a short one, patterned after Russell’s objection to Frege’s theory of the Grundgesetze der Arithmetik. If all extranuclear prop¬ erties are objects, then the extranuclear property of “not being identical with any extranuclear property that you possess” is an object; call it x0. That is: *o =dr [/U~(3P)(x = P & />#)].

GLOBAL ISSUES

243

Now we ask whether x0 “has itself.” Begin by assuming that it does: [Ax~(3P)(x = P & Px)]x0. Then, by abstract elimination: ~(3P)(*0 = P&Px o). That is, (P)(x0 = P =>

Px0). But plugging in x0 (i.e., [Ax~

(3P)(x = P & Px)]) for P yields ~ [Ax~ (3P)(x = P & Px)]x0, which contradicts our assumption. So x0 doesn’t have itself; that is: ~[Ax~(3P)(x = P & Px)]x0. But then, by abstract elimination and double negation: (3P)(x0 = P & Pxo). But the Pin question must be x0, that is, [Ax~ (3P)(x = P & Px)], and so x0 does have itself after all, contradicting the above proof that it doesn’t. So option 2 is not viable. Option j: We might try to make all objects, properties, prop¬ ositions, etc., be species of a “neutral” sort of entity, and expand the theory so that analogues of axiom OBJ hold for this sort of entity. This is actually a vague sort of suggestion, which could probably be developed in many different ways. I think that al¬ most any way would lead to the same sort of inconsistency that infects option 2. Option 4:4 The idea here is that, when we have a dream in which some character is “a property,” we are really dreaming about an object—an object which is not a property. Because, when we dream that that object “is a property” we are not really dreaming that it is a property, but rather dreaming something else which it is easy to misreport as dreaming that the object is a property. We are dreaming that the object has a certain prop4. For purposes of discussing this option, please ignore the cross-category identity statements introduced above. To include them at this point would complicate the discussion. (This does not mean that they should obviously be prohibited from the theory.)

244

APPLICA TIONS AND DISCUSSION

erty, a property which is appropriate to objects, and which is therefore not the property of being a property. It is a different property—let me call it the property of being a property*. This is reminiscent of Frege’s view in \C&0~\. When we try to attribute properties to properties in the same manner in which we attribute properties to objects we fail, and instead attribute (different) properties to objects. The properties that we attribute are proxies for the properties that we appear to be attributing. Thus when I dream of a “chartreuse property,” I am really dreaming of an object which has, in the dream, the properties of being chartreuse and of being a property*—but not of being a property, for this would make no sense. But then there is the following objection: now that we un¬ derstand the difference between being a property* and being a property, we can have a dream in which we clearly do not confuse one with the other, and in which we attribute the latter, not the former, to an object—an object which is also, in the dream, chartreuse. The only viable rejoinder that I know of to this is to deny that we understand ‘being a property’ as opposed to ‘being a property*’, at least to deny that we understand it in such a man¬ ner that we can attribute it to an object. Perhaps dreaming (or believing or surmising) that something chartreuse is a property is like

wondering whether Sherlock Holmes”; you can say the

words to yourself, and doing so may give rise to a host of images and thoughts, but that doesn’t mean that you are succeeding in believing a proposition that is expressed by those words. Perhaps what happens is that we then have before our mind part of a model of a theory of objects and properties, a model in which certain objects play the role of objects, and certain others play the role of properties. We are actually thinking about object representatives and property representatives. (Again, this was Frege s view in [C

Incomplete objects

Complex predicates, 103-05, 157,

162-63

163, 185-86, 227-28

‘According to the story . . .

53-54,

Compossibility, 222 Concrete objects, 10-11

56, 60, 175-82 Account, maximal, 175-211

Conjunction, nuclear, 2 in, 105

‘Actual’, 13

Consistency of the theory, 90-92

Anselm, 213-15

Constructivist theory of fictional ob¬

Authors, utterances by, 187-88

jects, 194-97 Contradiction, 31; law of, 38, 42, 171

Axioms: listed, 70-77, 124-27, 158-60; axioms for objects, 74,

Contradictory objects, 42

»59> 235.239-40

Correlation of objects with sets of properties, 17-18, 73, 79, 81, 92-97, 171

Barcan formulas, 100-01, 162

Counterfactual properties, 186-87

Barnes, J., 21411 Being, 10, 42; vs. so-being, 42.

also

See

“Creating” (objects in stories), 51, 188

Sein/sosein

Brentano, F., 48 Bundles of properties, i8n, 93

De dictolde re:

distinctions explained,

46-48; readings contrasted, 111, Castaneda, H-N., 171, 172

ii2n, 117-18, 122, 149, 163-64,

Categories, 2on, 231

166, 2 14-15. See also

Characters: of stories, 180-211; of scientific myths, 229-30; of dreams, 240-44.

See also

Dream

objects; Fictional objects

Cogito,

217-18n

de re

Definite descriptions, 30-32, 43, 111-20, 164-65; Meinongian, 118-20.

See also

Russell, theory of

descriptions

De re,

2 in, 35, 55, 58, 224; reading of

Comparatives, 24, 168-70

‘in the story’, 175, 181, 183. See

Completeness theorem, 83-85, 22411

also

De dictolde re 255

Index

256

Descartes, R., 213, 217-18

Ideal entities, 232

Disjunction, nuclear, 2 in

Identity, 27-29; of indiscernibles,

Donnellan, K., 5, 121

28-29, 74, 159; conditions, 81,

Dream objects, 207-10, 243

110; statements, 142, 156, 166, 241-43.

See also

Substitutivity of

identicals

Essence, 186, 224-26

Immigrant objects, 51-60, 175,

Essentialism, 224-26 ‘Exist’, 10-11, 22-24

182-85, 189, 202, 204; in dreams,

Existence, 213-17; kinds of, 11;

208—09; in visual art, 210-11; in

extranuclear, 25; watered-down, 42-44; possible, 186; fictional, 188; and passim

25, 31, 42; in fiction, 184; in

Existent gold mountain, the, 42-44.

See also

scientific myth, 229 Impossible objects, xi, xii, 2, 21-22,

dreams, 209; in visual arts, 211.

See also

Gold mountain

Existential generalization, 33, 35

Possible objects

Incompleteness: in maximal ac¬

‘Exist in’, 50

count, 182; of characters, 183—84;

Extranuclear predicates, 22-26; es¬

of fictional objects, 205; of objects

sentially extranuclear, 167-68; in

in dreams, 209; of objects in visual

stories, 197-202, 203; and passim.

arts, 211; of God, 212; of neutri¬

See also

nos, 230-31; radical and

Nuclear/extranuclear dis¬

tinction

nonradical, 183-84.

See also

In¬

complete objects ‘Fictional’: as an extranuclear predi¬ cate, 23, 26

Incomplete objects, 19-21, 56, 77-78.

Fictional objects, 32, 49-60, 172,

See also

Complete objects;

Incompleteness

>73- >75-211 Free logic, 8

Inconceivable objects, 40, 236 Indiscernibles: identity of, 28-29,

Frege, G., 18, 24, 45, 216, 244-45

74, 159; in fiction, 190-94 Intentionality, 30-31, 44-48

Gestalt, 208, 211

Intentional predicates and proper¬

God, 212-17

ties, 23-24, 44-48, 186, 214

Gold mountain, the, xi, 11, 18, 20, 23> 3°. 93. 94; as referent of

Kant, I., 40, 216

Meinongian definite description,

King of France, 2n, 112, 115-16

30, 118-20; yielded by axioms, 74, 159; not a set of properties, 93.

also

See

Existent gold mountain

Leibniz, G., 219-20 Logical constructions, 92 Logically closed objects, 19-22,

Hamlet, 201, 211

Hamlet,

106-07; defined, 106

200-01

Holmes, Sherlock, 2, 4, 32, 34; ex¬ isting in fiction, 11; as a paradigm fictional object, 49-60, 170, 172, 180-90, 202-05; not a set °f prop¬

Man in the doorway, the, 27-28, 114-15, 165 Meinong, A., xi, xii, 1-24 passim, 30-48, 118, 2i8n

erties, 93; reference to, 121; hav¬

Mirroring worlds, 219, 223-24

ing relational properties, 194-97

Modalities, 98-103, 162; reduction

Index

257

of operators to predicates, 223-24. See also Possible objects; Impossi¬ ble objects Modal moment, 44 Monads, 219-23 Myths, 207

Plantinga, A., 202, 225 Platonic forms, 227 “Plugging up” relations, 26-27,

Names, 271, 111, 120-23, 165-66; bearing a name, 192; causal theory of, 121, 192; as rigid designators, 122 Native objects, 51-60, 175, 182-85, 189, 202-06; in dreams, 208-09;

Possible objects, 2, 21-25, 28;

in visual arts, 210-11; in scientific legends, 229 Negation: of nuclear properties, 19-20, 4211, 105-06, 227-28; within categories, 231 Neutrinos, 230 Nonextensional contexts, 33-35, 47-48. See also Intentionality “Normal science,” 2, 5, 36-37 Nuclear/extranuclear distinction, 22-26, 42-44, 52-54, 64, 155, 160-61, 166—74, 216, 227-28 Nuclear abstracts, 163 Nuclear negations, 183, 206 Nuclear predicates/properties,

19-29>74 Nuclear relations, 59-60, 194-97 Null object, 22, 198 Objectives, 45

59-60, 64-69 passim, 75-77, 156-61 passim, 234-40. See also Relations and Relational properties defined, 21, 101. See also Impossi¬ ble objects Possible worlds, 98-103, 219-24; and fiction, 56, 182, 202 “Prejudice in favor of the actual,” 12, 18, 1 14 Properties, 17-29 and passim Propositional attitudes, 45, 108-1 1, 163-64 Propositional functions, 1 10 Propositions, 10, 45-46, 108-10, 180, 233-34, 240-41 Pure reflectors, 224 Quantifiers, 6, 11-12, 35, 38; substi¬ tutional vs. objectual, 1 1-12, 36 Quine, W., xi, 3, 18, 27, 37 ‘Real’, 13, 50 Reference: to objects, 3, 8, 30, 37, 52, 111-22; failure of, 37, 43, 56, 112-16, 170-74, 207, 212,228-29 Relations and relational properties, 26-27, 59-60, 75~77> 156-60 pas¬ sim, 194-97, 234-39 passim; rela¬

Ontological arguments, 212-17 Ontological commitment, 32-38, 204

tions encoded in relational prop¬ erties, 219 Relativity theory, 12, 41

Orthodox theory, 85-97; compari¬ son with, 92-97 Orthodox view (of nonexistent ob¬

“Robust sense of reality,” 2, 4, 12 Round square, xi, 2, 11, 21, 38-42, 46; as referent of definite descrip¬

jects), 1, 6-12, 33-38, ii2n, 162, 202, 246; comparison with,

tions, 30, 118-20; not a set of prop¬ erties, 93; yielded by axioms, 159

160-61. See also Orthodox theory Paradoxes, 234-40 Pegasus, 2-11 passim, 35, 37; refer¬ ence to, 112, 121

Routley, R., xii, 119, 172 Russell, B., 1-8, 18, 24, 27n, 30; ob¬ jections to Meinong’s theory, xi, 1, 10, 23n, 27, 30-32, 38-44, 171, 172; theory of descriptions, 2-5, 8,

Index

258 Russell, B. (continued) 37; objections to Frege’s theory, 242; paradox concerning proposi¬

Substitutivity of identicals, 33-35, 110-11, 164, 166 Surrogate objects, 52, 57-59, 183

tions, 233-34

Scope distinctions, 117 Sein/sosein, 23M. See also Being

Tensed properties, 11, 2 8n Theoretical entities: of literary criti¬ cism, 202-05, of science, 228—32 ‘There is (are)’, 6n, 6—7, 205

Sets, 31, 93, 101, 190, 195, 233 Sherlock Holmes. See Holmes,

Van Inwagen, P., 202-06

Satisfaction principle, 30-32

Sherlock Stories, 175-82; inconsistency in, 177-78, 182, 184, 206; within other stories, 200-02; with us as native characters, 218-19. See also ‘According to the story . . . ’; Fic¬ tional objects Subsistence, 10, 45«

Vulcan, 228-30 “Watered-down” properties, 44, 65, 68, 155, 220, 225; axioms concern¬ ing, 73, 159; used to define nu¬ clear abstracts, 104; used in fiction, 184, 186, 192, 200, 201, 206

t

Date Due

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tftr

IN Q |

0 L

%P' m'

97

BD 219 .P37

Parsons, Terence. Nonexistent objects / Terence

010101 000

163 0 82887 1

TRENT UNIVERSITY

BD21S

*T37

Parsons, Terence. Nonexistent ob3