The Logic of Epistemology and the Epistemology of Logic: Selected Essays (Synthese Library, 200)

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THE LOGIC OF EPISTEMOLOGY AND THE EPISTEMOLOGY OF LOGIC Selected Essays

JAAKKO HINTIKKA Florida State University, Tallahassee

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MERRILL B. HINTIKKA t

KLUWER ACADEMIC PUBLISHERS DORDRECHT / BOSTON / LONDON

Library of Congress Cataloging in Publication Data Hlntlkka, ~aakko, 1929The logic of eplsteeology and the eplsteeology of logic selected essays I by ~aakko Hlntlkka, Herrlll B. Hlntlkka. p. ce. -- (Sy~thes8 library) ISBN 0-7923-0040-9. ISBN 0-7923-0041-6 (pbk.) 1. Knowledge, Theory of. 2. LogiC. 3. Eplsteelcs. I. Hlntlkka. Herrlll B., 1939n. Title. Ill. Series. BD161.H535 1988 121--dc19 88-39953

ISBN 0-7923-0040-8 ISBN 0-7923-0041-6 (pbk.)

Published by Kluwer Academic Publishers, P.O. Box 17, 3300 AA Dordrecht, The Netherlands. Kluwer Academic Publishers incorporates the publishing programmes of D. Reidel, Martinus Nijhoff, Or W. Junk and MTP Press. Sold and distributed in the U.S.A. and Canada by Kluwer Academic Publishers, 101 Philip Drive, Norwell, MA 02061, U.S.A. In all other countries, sold and distributed by Kluwer Academic Publishers Group, P.O. Box 322,3300 AH Dordrecht, The Netherlands.

Also published in 1989 in hardbound edition in the series Synthese Library. Volume 200

All Rights Reserved © 1989 by Kluwer Academic Publishers No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical induding photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner. Printed in The Netherlands

To Patrick Suppes

a mentor and a friend

TABLE OF CONTENTS Origin of the Essays

ix

Errata

xi

Introduction

xiii

Essay 1. Is Alethic Modal Logic Possible? Essay 2. Reasoning About Knowledge in Philosophy: The Paradigm of Epistemic Logic

17

Essay 3. Are There Nonexistent Objects? Why Not?But WhereAre They?

37

Essay 4. On Sense, Reference, and the Objects of Knowledge

45

Essay 5. Impossible Possible Worlds Vindicated

63

Essay 6. Towards a General Theory of Individuation and Identification

73

Essay 7. On the Proper Treatment of Quantifiers in Montague Semantics

97

Essay 8. The Cartesian cogito, Epistemic Logic and Neuroscience: Some Surprising Interrelations

113

Essay 9. Quine on Who's Who

137

Essay 10. How Can Language Be Sexist?

155

Essay 11. On Denoting What?

165

Essay 12. Degrees and Dimensions of Intentionality

183

Essay 13. Situations, Possible Worlds and Attitudes

205

Essay 14. Questioning as a Philosophical Method

215

Index of Subjects

235

Index of Names

243

ORIGIN OF TIIE ESSAYS

The author is Jaakko Hintikka unless otherwise indicated. Essay 1. Is Alethic Modal Logic Possible?, by 1. Niiniluoto and E. Saarinen, eds., I ntensional Logic: Theory and Applications, Acta Philosophical Fennica, vol. 35, Societas Philosophica Fennica, Helsinki, 1982, pp. 89-105. Essay 2. Reasoning About Knowledge in Philosophy: The Paradigm ofEpistemic Logic, in Joseph Y. Halpem, ed. Reasoning About Knowledge: Proceedings of the 1986 Conference, Morgan Kaufmann Publishers, Los Altos, CA, 1986, pp. 63-80. Essay 3. Are There Nonexistent Objects? Why Not? But Where Are They?, Synthese vol. 60 (1984), pp. 451-458. Essay 4. On Sense, Reference and the Objects of Knowledge, Epistemolo gia vol. 3 (1980), pp. 143-162. Essay 5. Impossible Possible Worlds Vindicated, Journal of Philosophical Logic, vol. 4 (1975), pp. 475-484; reprinted in a revised and expanded form in Esa Saarinen, ed., Game-theoretical Semantics, D. Reidel, Dordrecht, 1979, pp. 367-379. (This revised version is what is reprinted here.) Essay 6. (with Merrill B. Hintikka) Towards a General Theory ofIndividuation and Identification, in Wemer Leinfellner et. aI., eds., Language and Ontology, Proceedings of the Sixth International Wittgenstein Symposium, HOlder-Pichler-Tempsky, Vienna, 1982, pp. 137-150. Essay 7. On the Proper Treatment of Quantifiers in Montague Semantics, in S. Stenlund, ed., Logical Theory and Scientific Analysis, D. Reidel, Dordrecht, 1974, pp. 45-60. Essay 8. The Cartesian cogito, Epistemic Logic and Neuroscience: Some Surprising Interrelations. Unpublished, but scheduled to appear also in Synthese.

ix

x

ORIGIN OF THE ESSA YS

Essay 9. Quine on Who's Who, in L.E. Hahn and P.A. Schilpp, eds., The Philosophy ofW.V. Quine, Library of Living Philosophers vol. 18, Open Court, La Salle, Illinois, 1986, pp. 209-226. Essay 10. (with Merrill B. Hintikka), How Can Language Be Sexist?, in Sandra Harding and Merrill B. Hintikka, eds., Discovering Reality: Feminist Perspectives on Epistemology, Metaphysics, Methodology, and Philosophy of Science, D. Reidel, Dordrecht, 1983, pp. 139-148. Essay 11. On Denoting What? Synthese vol. 46 (1981), pp. 167-183. Essay 12. Degrees and Dimensions of Intentionality, in R. HaIler and R. Grassl, eds., Language, Logic, and Philosophy, Proceedings of the Fourth International Wittgenstein Symposium, Holder-Pichler-Tempsky, Vienna, 1980, pp. 69-82. Essay 13. Situations, Possible Worlds and Attitudes, Synthese vol. 54 (1983), pp. 153-162. Essay 14. Questioning as a Philosophical Method, in James H. Fetzer, ed., Principles of Philosophical Reasoning, Rowan & Allanheld, Totowa, NJ., 1984, pp. 25-43. All previously published papers are reproduced here with the permission of the copyright owners, which is hereby gratefully acknowledged.

ERRATA The following are corrections for typographical errors that appear in these collected essays.

Introduction P. xvi, line 7 from bottom, "intentional" should read "intensional". Essay 2 P. 19, title to section 2 should read "Indirect Wh-Questions". P. 29, line 22, after "steps of deduction" add "and steps of reasoning". P. 29, lines 23-24, "purposes" should read "purpose". Essay 3 P. 42, line 8 from bottom, omit the word "not". Essay 4 P. 49, line 7, italicize the book titles Begriffsschrift and Grundgesetze. Essay 5 P. 63, line 5 from bottom, "imcompatibility" should read" incompatibility". Essay 6 P. 82, line 4 of section 5, "cross-identity" should read "cross-identify". P. 84, line 1, "one solution" should read "two solutions". P. 93, note 30 (line 8), after "basket" add "known". Essay 7 P. 105, line 14, "contradiction" should read "construction". Essay 8 P. 129, line 14, "contrast" should read "contrasting". P. 133, note 4, add quotation marks to "existentially self-verifying". Essay 9 P. 146, lines 18-19, "cross-reference" should read "cross-identification". Essay 10 P. 162, line 11, change "as" to "or". Essay 11 P. 178, lines 7-8, "individualization (non-identification)" should read "individuation (cross-identification)". Essay 12 P. 196, line 4, "splitting" should read "merging". P. 197, line 9, after "dimensions" add "of'.

xi

INTRODUCTION I almost gave this collection of essays the title "Seven Theories in Search of an Author" or "Seven Ideas in Search of a Theory". In each of the central essays reproduced here, one major new idea is proposed and outlined. Each such idea appears eminently capable of sustaining the weight of a full-fledged logicophilosophical theory (of the same order, say, as the so-called situation semantics) and also interesting enough to merit such a development. We saved for years some of these ideas and some of these papers, in the sense of not having them reprinted, in the hope of later having an opportunity of letting them grow into the theory each of them potentially is. Alas, for a variety of reasons these hopes have not yet been realized. There have been dramatic changes in my life, including Merrill's death on January I, 1987. I have also got interested and involved in a number of new projects, some of them outgrowths of the ideas represented in the present volume. All these developments have left our ideas still searching for an author of a full-fledged theory. One of the reasons why I am putting together the present volume is that I have changed my mind. I now hope that this republication would prompt authors other than myself to develop these brave new theories, for there does not seem to be any realistic prospect that I would find the time to do the job alone. These incipient theories are, by and large, aspects or further developments of the complex of ideas usually but misleadingly called "possible-worlds semantics". It started its career in the late fifties and eariy sixties as the semantical (model-theoretical) basis for the then existing syntactical (axiomatic and deductive) systems of modal logics, especially perhaps the Lewis systems. These were intended in the first place as logics of logical modalities, that is, of logical necessity and logical possibility, sometimes also known under the alias "alethic modalities". In the first essay of this volume, entitled "Is Alethic Modal Logic Possible?", it is shown that the most common type of semantics for modal logics, the one ahistorically known as Kripke semantics, is not, and cannot be, a viable model theory of logical modalities. This observation opens the door to the first of our Pirandello-like theories-in-spe. Can we develop a better logic of logical modalities? It turns out that the right logic cannot be axiomatized. It would nevertheless be highly interesting to develop a theory of how this true alethic logic could somehow be approximated. This idea is made espccially intriguing by a possibility also pointed out in the first essay. It is the possibility of interpreting Kripke semantics as a kind of nonstandard semantics in a sense xiii

xiv

INTRODUCTION

somewhat like Hcnkin's nonstandard interpretation of higher-order logics, while the right scmantics for logical modalities is an analogue to the standard interpretation of type theory in Henkin's sense. Another possibility would be to follow W.V. Quine's advice to give up logical modalities as being beyond repair. Or we could also try to develop a logic of conceptual possibility, restricting the range of our "possible worlds" to those compatible with the transcendental presuppositions of our own conceptual system. This looks in fact like one of the most interesting possible theories I have dreamt of developing but undoubtedly never will. Its kinship with Kant's way of thinking should be obvious. Besides putting the entire enterprise of possible-worlds semantics into a perspective, we can also see that the actual history of possible-worlds semantics is more complicated than it might fIrst appear to be. For the standard interpretation of modal logics has reared its beautiful head repeatedly in the writings of Stig Kanger, Richard Montague the pre-Montague-semantics theorist, and Nino Cocchiarella. The possibility of a logic of logical modalities is an example of what I mean by the locution "epistemology of logic" in the title of this book. The other half of the title is exemplifIed by the second essay, which is simply a survey of those approaches to the logie of epistemology (logic of knowledge) which take off from possible-worlds semantics. It was originally written for a meeting on artifIcial intelligence. Not surprisingly, computer scientists working on AI, intelligent systems and database theory have discovered the importance of knowledge representation and reasoning about knowledge. Here we also have virtually unlimited possibilities of further theorizing. The third essay was originally written as a comment on a paper by Terence Parsons (a former fellow student of one of us and a former student of the other). It is included here because we try to discuss there the general methodological ideas which have given rise to epistemic logic as an application of semantical (possible-worlds) tcchniques. Some of the main applications of the semantics of epistemic logic to classical problems are outlined in the essay "On Sense, Reference, and the Objects of Knowledge". It is argued there that if we really understand the semantics ("possible-worlds semantics") of the concept of knowledge we can bury for good the problems of identity and indirect contexts which occupied Frege and which prompted his stopgap theory of sense and reference. Admittedly, this may not be the last word on the subjcct. We will undoubtedly be led to new problcms, such as the problems of cross-identifIcation, by the possible-worlds analysis of Frcge's problems (cf. below). However, the restructuring of the problcm situation which the possible-worlds approach

INTRODUCTION

xv

yields provides several useful clues to the ultimate understanding of the remaining difficulties. Furthermore, it is suggested that in this way we can also approach one of the central epistemological problems, to wit: What are the objects of knowledge? Needless to say, there is plenty of room here for another as yet undeveloped logico-epistemological theory. One of the main difficulties which many people have found in an attempted model-theoretical treatment of the concept of knowledge is that it seems to lead inevitably to what is commonly known as the "paradox oflogical omniscience". It seems to lead to the unacceptable consequence that everybody who ever knows anything knows all the logical consequences of what he or she knows, and also knows that others know that, etc. Among others, Chomsky has adduced this alleged paradox as a reason against any model-theoretical semantics of propositional attitudes. Yet Chomsky's problem was solved quite some time ago. This solution is presented in Essay 5. It is hoped that its reappearance here helps to raise the consciousness of linguists and philosophers alike, helping them to stop worrying and to begin to love epistemic logic. Once again, a tremendous amount of further research remains to be done in the theory of non-omniscient epistemic logic and in its applications. For instance, a parallel reformulation of probability calculus, with an essentially similar semantics, would provide a solution to the probabilistic version of the problem of logical omniscience which LJ. Savage pointed out a long time ago and which haunts every adherent of a subjectivistic interpretation of probability. One crucial problem arises as naturally, not to say as inevitably, both in the epistemology of logic as in the logic of epistemology. It is the problem of crossidentification. It is endemic in the very idea of possible-worlds semantics. If we countenance logic with several possible "scenarios" (states of affairs or courses of events), we have to have a way identifying our individuals across the boundaries of such scenarios or "worlds". This problem is addressed in the essay "Towards a General Theory of Individuation and Identification" which in some ways is the central part of this volume. It is argued there that the problem of cross-identification of physical objects between possible worlds can be handled, at least partly, by tracing them in their respective worlds to the common ground which the two worlds share. In short, the cross-identification of physical objects reduces in paradigmatic cases to their re-identification between different time-slices of the same course of events. It is also suggested that such re-identification is essentially a matter of continuity. In diagnosing the nature of this continuity we are led to consider it essentially as a problem which belongs to the stability theory of sets of differential equations -- a next-

xvi

INTRODUCTION

door neighbor, in other words, to the famous or infamous "catastrophe theory" of Rene Thorn's. The opportunities for further theorizing in this direction are truly mind-boggling. And even before these opportunities have been made use of, the very possibility of a precise, mathematically interesting treatment of a paradigm case of cross-identification carries an important philosophical moral. We do not have to dismiss the re-identification and cross-identification problems as a hopeless mess, as Quine advises, nor cheat and simply take the re-identification of persistent physical objects for granted, as Kripke has proposed. Instead of either of these counsels of despair, we can try to develop a genuine theory of re-identification and thereby a theory of cross-identification. The next few essays deal with the further problems, solutions, and applications prompted by the task of cross-identification, which we somehow have tacitly solved in our actual conceptual system. Two phenomena are especially important here. One concerns the extendibility of the imaginary "world lines" which connect the roles of one and the same individuals in different worlds with one another. It is argued briefly in more than one essay that we must allow, not only a nonexistence of some individuals in some worlds, but also a more radical failure of world lines. When this radical failure takes place in some possible world, it does not even make sense to ask whether the relevant individual exists in that world. In other words, an individual may not only fail to exist in certain worlds, but it may fail to be as much as defined there. The latter contingency is not allowed for in the usual logics of knowledge and belief, which must therefore be modified. Here, too, plenty of further work is possible and indeed badly needed. The other vista on cross-identification which is opened here concerns the possibility of drawing world lines in different ways. There is, first of all, a sharp contrast between two types of world lines, viz. those utilizing object-centered considerations and those utilizing agent-centered coordinate systems, as it were. In Essay 8, this contrast is shown to correspond to a distinction between two cognitive systems which have been distinguished from each other by psychologists and neuroscientists. Some differences between various ways of drawing world lines are obviously psychologically and sociologically conditioned. In Essay 10, it is argued that certain differences may be sex-linked, which lends a subtle new dimension to the notion of "sexist language". One form in which the contrast between the two main modes of cross-identification has surfaced in twentieth-century philosophy is Bertrand Russell's distinction between objects of acquaintance and objects of description. The contrast can therefore be used to put Russell's philosophical ideas into a shar-

INTRODUCTION

xvii

per relief. This is attempted in Essay 11 ("On Denoting What?"), which in some ways continues the story of the hidden role of epistemic logic in contemporary philosophy from Essay 4. On an earlier occasion (in the title essay of my 1975 book The Intentions of Intentionality) I had suggested that the gist of phenomenologists' famous phenomenon of intentionality lies in a kind of multi-world character. A concept is intentional if and only if its semantical explication involves several "scenarios" considered in relation to each other. In short, intentionality is (very nearly) intensionality. This idea is developed further in Essay 12 by turning intentionality into a matter of more or less. This reveals a multiplicity of different kinds (dimensions) of intentionality, which are not all equally important. They correspond to the different ways in which alternative "possible worlds" can differ from the actual one. One kind of difference is the variability of certain alternative worlds involved in coping with the failure of logical omniscience in Essay 5 above. These ideas arc tested by applying them to various arguably intentional concepts and also to what philosophers like Roderick Chisholm have said of the symptoms of intentionality in the logical behavior of different concepts. Once again, the logical behavior of epistemic concepts ("the logic of epistemology") looms large in these applications. Sometimes possible-worlds semantics is presented as an older rival of the theory developed by Jon Barwise and John Perry and labelled by them "situation semantics". The relation of the two is discussed briefly in Essay 13. It turns out that they arc rivals to a lesser extent than the misleading popular view assumes. Part of the confusion is due to the term "possible-worlds semantics." Anyone who has ever tried to build a realistic analysis of epistemic concepts on the basis of a model-theoretic approach knows that the models or "possible worlds" involved are not worlds in any literal sense of the word. They are merely courses of events in some relatively small nook or corner of the universe. What it required is merely that outside influences can be disregarded for the relevant purposes. In short, the "possible worlds" we are talking about in this book are what a physicist would call systems. As such, they are not very far removed from Barwise's and Perry's so-called "situations". Possible-worlds semantics of, say, epistemic concepts is "situation semantics". In both, we are studying relations between scenarios, nee "situations". What is different is that the "possible-worlds" approach concentrates mainlyon one dimension of relations between scenarios, viz. to the relation of a scenario to its possible but unrealized alternatives, while "situation semantics" concentrates on certain other relations between situations, mostly those obtaining within one and the same world. Whatever the achievements of situation semantics are or will be, I do not see any reason to think that it can dispense

xviii

INTRODUCTION

with the possibility-dimension which possible-worlds semantics is calculated to handle. Hence it is not in reality a serious rival to possible-worlds semantics. In Essay 13, this overall judgment is also supported by examining the muchvaunted solution to a special case of the paradox of logical omniscience which situation-semantics theorists have offered. This partial solution neither contradicts anything in the general solution offered in Essay 5 nor makes my solution dispensable. The last essay, Essay 14, is unique among the essays in this volume in that it is being actually developed so as to become the foundation of an extensive theory, in the first place my theory of questions and answers and in the second place the theory of interrogative "games" of inquiry. Suffice it here to point out the link of these theories and epistcmic logic. One of the absolutely crucial tasks of any theory of questions and answers ought to be to offer a satisfactory analysis of the relation of a question to its (full, conclusive) answers. In traditional expositions of the "logic of questions" or "erotetic logic", no such analysis is offered. It turns out, however, that a solution to this "answerhood problem" is obtained from the kind of epistemic logic studied here, explicitly for the simplest cases and in principle for all of them. Since epistemic logic offers a handy framework for the study of questions and answers in general, we are justified in thinking of the entire study of questions and answers as a further development of epistemic logic. Thus there is in reality much more unity in this volume than might appear at first sight. The different essays are related to each other and support one another. Sometimes the theme of an essay has grown out of that of a predecessor. A concluding general comment may be in order. Many of the discussions that have been carried out within the possible-worlds framework and that are found in the literature are unsystematic and ad hoc, without any overarching theoretical vision. Many of them have for this reason failed to yield any significant general results. As a consequence, expressions of frustration and criticisms have been levelled at the entire enterprise of possible-worlds semantics. One of the reasons I have for a long time had for writing a systematic book on the semantics of intentional logic and on its applications is to show that the critics have not said the last word and that a highly interesting general theory can be developed of the subject. Unfortunately that book is not likely ever to be written. Instead, this collection of essays will have to serve as a substitute. In particular, I hope that the multiple interrelations between the different essays reprinted here will show some of the hidden unity of the problem situation in the different parts of the ill-named "possible-worlds semantics".

INTRODUCTION

xix

A more personal explanation may also be needed in order to put this book into a historical perspective. Merrill Bristow Hintikka is listed as the co-author of this volume even though she has been dead for a year and half and even though she was originally by-lined only in two of the essays. The reason for giving her the status of a co-author is not a sense of piety, however, but her very real share in the development of many of the ideas figuring in this book. In the preface to our joint book, Investigating Wittgenstein, we tried to describe the joys of our scholarly cooperation. Many of the same remarks apply to several of the papers in this volume. It is especially important for me that Merrill Hintikka's share in the development of the kinds of ideas discussed in the essays of this book be recognized. She took an early interest in the different developments that are sometimes pidgeonholed together as "possible-worlds semantics". Merrill read my bookKnowledgeandBelieJsoon after it appeared, years before we got together and found it not only congenial but suggestive of further developments. She also knew Richard Montague and several of his students, among them Nino Cocchiarella, and discussed with them the developments that eventually resulted in Montague semantics. She anticipated some of the developments reported here, and contributed substantially to others through the informal discussions we were constantly having, probably much more substantially than I am myself aware of. (Among other things we had a sequel to the essay "Towards a Geneml Theory of Individuation and Identification" all planned. Alas, this sequel was never written by either of us.) It is therefore more than proper for her to be listed as a co-author; it is eminently fitting. It is likewise both proper and fitting that a book which represents our joint work be dedicated to PaLrick Suppes. He played an important part in the early career of both of us. He has not only been a close friend and an incredibly generous mentor and adviser. Merrill was, and I continue to bc, especially fond of him. PaLrick was one of the first friends who came to know our relationship in 1976, and he reacted to the news with a delight and enthusiasm rare even for him. Later he was my best man at our wedding in 1978. I cannot think of a more obvious person to dedicate this volume to. In editing this volume for publication and in preparing the camera-ready text, I have been helped in various way by several persons, including Alan Mabe, Erkki Kilpinen, Steve Harris, Margaret Dancy, Cathy Butler and Florene Ball. My warmest thanks are due to all of them. I am also gmteful to Kluwer Academic Publishers. Not only have they accepted this for publication; they have made it the two hundredth volume to be published in Synthese Library, an honor which I deeply appreciate, and which Merrill would have appreciated.

x. x.

INTRODUCTION

Some of the essays have been reproduced from the originals; others have been revised and rcformatcd. I have made an attempt to maximize stylistic uniformity, but in many instances it has unfortunately been impossible to reach complete consistency.

Jaakko Hintikka Helsinki, July 1988

IS ALETlllC MODAL LOGIC POSSIBLE? The title of my paper may appear paradoxical, misplaced, or even worse, out of date. The possibility of a reasonable modal logic was denied by Quine on philosophical grounds, but his objections have been dead for a while, even though they have not yet been completely buried. 1 What has made a crucial difference is the development of what has generally been taken to be a viable semantics (model theory) for modal logic? This semantics has provided a basis from which Quine's objections can apparently be answered satisfactorily and which yields a solid foundation for the different axiom systems for modal logic. Thus the question of the possibility of modal logic has apparently been disposed of for good, and my title question accordingly may seem pointless. Yet there remains a king -size skeleton in the cupboard of the semanticists of modal logics. It may be related to Quine's doubts, even though Quine himself has (surprisingly enough) failed to spell it out? It was pointed out by Nino Cocchiarella in 1975 and independently by myself in my 1977 Rome paper. It throws new light on most of the recent discussions of the philosophical problems connected with modal logic. This difficulty affects mainly what is usually known as alethic modal logic, that is, the logic of logical modalities, the logic of logical necessity and logical possibility. To what extent it applies also to the logic of analytic modalities, that is, to the logic of conceptual or analytic necessity and conceptual possibility needs a separate discussion. I shall return to this matter later in this paper. The difficulty I have in mind is not a marginal phenomenon, either. It stems directly from the basic ideas of the currently fashionable model-theoretical treatment of modal logic, often known misleadingly as Kripke semantics. What does this treatment amount to? In it, we are supposed to envisage a frame F = SFft. that is to say, a set SF of models or worlds on which a two-place relation R is defined. This relation is intuitively speaking a kind of alternativeness relation, and we shall call it that. The worlds Wl which from the vantage point of a world Wo are at the receiving end of this relation (i.e., for which we have R(Wo,Wl)), are called alternatives to wo. Roughly. they are to be thought of as the worlds that are legitimate alternatives to Wo in the sense that they are the worlds that could be realized instead of wo. Initially, no restrictions (except possibly for the requirement of reflexivity) are to be placed on the alternativeness relation. On the basis of these intuitive ideas we can formulate the truthconditions for modal sentences:

ESSAY I

2

(T.N) Given a frame F, Np (read "necessarily p") is true in Wo E SF iff P is true in each alternative Wj E SF to Wo (i.e., in each member Wj of SF such that R(wo.wj». (T.M) Given a frame F, Mp (read "possibly p") is true in Wo true in at least one alternative Wj of SF such that R(wo, Wj).

E

SF iff P is

What was noticed by Kanger, Guillaume and (Hintikka and later by Kripke) is that by imposing suitable relation-theoretical properties (reflexivity, transitivity, symmetry, etc.) on R we can obtain a model theory for the best known Lewis-type axiom systems for propositional modal logic. However, completely independently of the relation-theoretical behavior of R, this treatment is in trouble if our modal operators N,P are thought of as expressing logical modalities. For there is a sense in which the truth-conditions (T.N) and (T.P) are obviously inadequate. What is needed for the logical necessity of a sentence p in a world Wo is more than its truth in each one of the arbitrary selected set of alternatives to wo. What is needed is its truth in each logically possible world. However, in Kripke semantics it is not required that all such worlds are among the alternatives to a given one. Conversely, for the logical possibility of p in Wo it suffices that p be true in some logically possible world. However, in Kripke semantics there is nothing to guarantee that that world is among the alternatives to wo. Hence Kripke semantics is inadequate in its present form as a logic of logical modalities. And of course this was the primary application of modal logic historically. It is the purpose for which the Lewis systems were originally developed. Hence there is not only a skeleton in the closet of Kripke semanticists; the skeleton threatens to overturn the whole house. Notice that this observation is completely independent of the relationtheoretical properties of R. If we require, as has been suggested, that for logical modalities the alternativeness relation is reflexive, symmetric, and transitive i.e., an equivalence relation, then this has merely the consequence that each world WoE SF has as its alternatives in F all the members of the same equivalence class of worlds. This does not guarantee in the least that all logically possible worlds are among the alternatives to wo. The basic problem with the latter is that the appropriate worlds may not be in SF in the fIrst place. The requirements of transitivity, symmetry, and reflexivity (plus, possibly, connectedness) can only guarantee that Wo has a maximal number of sets as its alternatives among the worlds that so to speak are already in SF. This paper is an attempt to discuss the consequences and ramifIcations of the basic observation just made concerning the inadequacy of Kripke seman-

IS ALETHIC MODAL LOGIC POSSIBLE?

3

tics for alethic modal logic. Some of these consequences have been examined in an earlier paper of mine. 4 Here I shall concentrate mostly on matters which were not explicitly treated in the earlier paper. It is my observation concerning the failure of Kripke semantics that lends a point to the title of this paper. If an alethic modal logic based on Kripke semantics is inadequate, can we find an adequate one elsewhere? Is an alethic modal logic possible at all in the sense of there existing a viable semantics for it? If the answer to this question is yes, is there a complete axiomatic and deductive codification of such a semantically defined alethic modal logic? One possible reaction here is to reply to me: Your observation does not really show that there is anything wrong with Kripke semantics. What you point out is merely the need of amplifying the usual Kripke semantics. Surely we can keep all the ingredients of Kripke semantics intact and simply add the requirement that, given Wo E SF, all the logically possible structures that can be formed from the given individuals and from the given predicates are exemplified among the alternatives to Wo -- or so it seems. This is certainly a viable course to take technically. Nino Cocchiarella, who seems to have been the first to call attention publicly to the possibility I just mentioned, formulates the new semantics essentially by requiring that all models (in the usual first-order sense) with the same domain do(wo) of individuals as Wo occur among the alternatives to wo. As was already said, this is of course technically possible to do. Asking whether alethic modal logic is possible then largely becomes the question as to how manageable the new logic is. What remains to be examined are therefore primarily the consequences of the new modal semantics and the philosophical status of these consequences. For the purpose, a brief glimpse of the "new" semantics is in order. The only difference between the "old" (i.e., Kripke) and the new semantics is in the defini tion of a frame. A Kripke frame is any F = SF, R as defined above with a reflexiveR. A frame in the new sense must satisfy the additional condition that for each WO SF, the alternatives to Wo in F must include all models with the same domain do(wo) of well-defined individuals as wo. A word on the treatment of individuals is nevertheless needed. Usually, a fixed domain D of individuals is given and it is assumed that each individual is well defined everywhere in the sense that an answer can always be given to the question: Does a given individual exist in a given world (i.e., member of a frame)? The domain of individuals dO(Wl) of each different member Wl of SF is then some subset of D. If so, life would be easy, and among other things the main argument to be given later in this paper would be strengthened and simplified. (Cf. (vi) below.) Unfortunately, as I have argued on several dif-

4

ESSAY I

ferent occasions earlier, this is unrealistic interpretationally. Hence the flexible approach is to allow an individual to be ill defined in some members of the frame. Then it does not make sense to ask whether that individual exists or doesn't exist in them. Moreover, in the most flexible semantics we must allow individuals to merge or to split when we move from one world to another. Then an individual goes together with a world line which normally is not defined everyWhere, and a proper name of such an individual is a singular term which picks out the nodes of such a world line whenever it is defined. (Note that a world line can connect non-existent embodiments of individuals as long as they are well defined for each of the worlds in which a node of the world line is to be located.) It turns out that truth-definitions can easily be given for such a semantics in the usual way. For instance, (3x) p(x) is true in w iff there is an individual, say with the proper name z, such thatp(z) is true in w. Several observations are possible concerning the semantics so defined. (i) As is pointed out in my earlier paper, the contrast between the "new" semantics and Kripke semantics can be taken to be the same as the contrast between standard and (a certain kind of) nonstandard semantics for higher-order logics, in something like the sense first spelled out by Henkin. Hence we shall call the "new" modal semantics simply standard semantics and label Kripke semantics as (one possible kind of) nonstandard or nonclassical semantics. The analogy on which this terminology is based should be obvious. In the same way as we obtain standard semantics for higher-order logics by requiring that higher-order quantifiers range over all extensionally possible entities of the appropriate higher logical type (higher type than that of individuals), in the same way we obtain standard semantics for modal logics by letting the quantifiers which modal operators in effect are to range over all extensionally possible worlds. This parallelism will be turned into something stronger than a mere analogy below. In the course of an argument to show that the decision problem for second-order logic reduces to that for standard first-order modal logic, it turns out that standardness in the latter sense can do precisely the same job as standardness in the former sense. (ii) Historically speaking, there is nothing really new about standard semantics for modal logics. Indeed, the recent history of the semantics of modal logics is much more many-faceted than has been pointed out in the literature. The first explicit semantics for modal logics was constructed by Kanger in 1957, and it was a standard semantics. Kanger has apparently held quite consistent-

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ly that this is in his mind the right approach to the semantics of modal logics. In contrast, the semantics envisaged in Hintikka's 1957 paper is a nonstandard one ("Kripke semantics" five years before Kripke). Likewise, Guillaume's semantics of 1958 is a nonstandard one. In his early (i.e., pre-1964) papers, Richard Montague was defining a standard semantics, but later he switched over to a nonstandard one, without (as far as I know) ever explaining his reasons for doing so. Some of Montague's followers seem to have overlooked completely standard models. For instance, in Gallin's monograph on higher-order modal logic both the standard semantics for modal logics and the standard semantics for higher-order logics is completely overlooked. It appears from these observations alone that the recent developments in the semantics of modal logics and its philosophical implications need a closer analysis than it has been given by logicians, philosophers, or historians. On the systematic side, it is Kripke models that have been studied in great detail in recent years. There are very few detailed studies of standard semantics for modal logics. Indeed, Cocchiarella's papers plus mine seem to be the only ones. (iii) One reason for this neglect may lie in the problems one faces in standard semantics for modal logics. This semantics seems to be in order, and hence to belie the title of this paper. However, not everything is sweetness and light here. One important problem is the following. In the definition of standard semantics above, it was required that among the alternatives to Wo ina given frame F there are all those models that can be built up from one's basic concepts (predicates) and of the individuals in the domain of wo. What this amounts to requiring is that the individuals quantified over in the alternatives to Wo are well defined in Wo (i.e., connected by a world line to some well-defined individual, not necessarily an existing one) in the initial world wo. This means assuming that there cannot (logically cannot) be other well-defined individuals in other relevant possible worlds than what there already is (at least well defined) in the ac tual world. As someone once jokingl y illustrated this im plication of the definition of standard semantics given above, birth control is a logical impossibility. In brief, this seems an absolutely intolerable consequence. How can we possibly set limits to what there could be in the sense of the "could" of logical possibility? Yet there is something to be said for the other side, too. We clearly must somehow delimit the domains of the alternatives to any given Wo. If we allow domains of arbitrary cardinality, we will run into mutatis mutandis versions of set-theoretical paradoxes.

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I cannot study these paradoxes in any detail. It is relevant to point out, however, that we have here an opening for an interesting new branch of logical studies. You are all familiar with set-theoretical paradoxes (antinomies), that is, contradictions generated by too strong set-theoretical assumptions. Since strong set-theoretical assumptions can easily be seen to have (a least rough) parallels in modal logic with standard interpretation (cf. my Rome paper, note 4 above), too strong set-theoretical assumptions are likely to be matched by too strong modal assumptions. The resulting paradoxes may, it seems to me, throw light on the set-theoretical ones, both by similarity and by contrast. One direction in which paradoxes can arise is the following. Allowing arbitrary high cardinalities in the domains of the alternatives to a given Wo amounts to considering the class of all cardinalities as a set, and hence is bound to lead to paradoxes. (iv) The only natural way of avoiding this catastrophe seems to be to limit the domains of the alternatives to the same individuals as are well-defined in wo. (Various philosophical motivations have been presented for this particular restriction, but not for any others.) But this was seen to be open to the charge of arbitrariness. I strongly suspect that something like the paradoxes we saw threatening has been instrumental in leading some logicians like Richard Montague to postulate a fixed given domain of individuals for all the members of a given frame F. If so, there is an awkwardness in the underlying line of thought of such logicians. For they have typically been working on the basis of Kripke semantics (or other nonstandard semantics) whereas the problems that motivate the limitation of the domains stem from standard semantics. It may very well be that there has been a confusion present in many logicians' thinking, due to an insufficiently sharp distinction between standard and nonstandard semantics. Or perhaps it is more charitable to interpret the logicians in question as trying to make it possible for their nonstandard (Kripke) modal frames to become standard modal frames by adding worlds to them, i.e., for the standard modal logic to be a special case of nonstandard modal logic in this sense. Be this as it may, it does seem hard to avoid restricting the domains of individuals of alternatives to a given world Wo to individuals well defined in wo. We shall work on this assumption in the next few sections. Yet its unnaturalness is so great that we are forced here very close to a negative answer to the question: Is alethic modal logic possible? (v) There may also be a historical explanation, if not an excuse, for the relative neglect of standard semantics for modal logics. It is found by asking: What

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difference, if any, does the step from Kripke semantics to standard semantics entail? Answering this question in full is of course a matter of detailed investigation, which is more than one can undertake in one paper. Here I shall only make a few observations which are calculated to give my readers an overview of what is involved in the step from Kripke semantics to standard semantics. By and large, this step is much longer than one might perhaps expect prima facie. Little of interest seems to happen in propositionallogic. However, Cocchiarella showed that already in the simplest quantificational case, monadic predicate logic, standard logics differ radically from their Kripkean cousins. Cocchiarella shows that standard monadic predicate logic is decidable. This result is in sharp contrast to Kripke's earlier result to the effect that monadic predicate logic based on Kripke semantics is undecidable. Hence the distinction between standard and nonstandard modal semantics makes a big difference. This does not yet take us beyond what can be handled by the conventional logical, that is, axiomatic and deductive, methods. On the contrary, decidability implies axiomatizability. However, as soon as we go beyond monadic predicate logic, we are dealing with a semantics of a tremendous power, complexity, and consequent intractability. Sharpening the observations offered in my earlier paper, I shall indicate how one can prove that standard quantified first-order modal logic is in a certain sense as strong as second-order logic (with standard semantics). The latter is of course immensely strong, so strong indeed that several of the most difficult unsolved logical and set-theoretical problems can be expressed in the forms of questions of the logical truth (or satisfiability) of certain second-order formulas. The sense in which "as strong" is to be taken here is that of having an equally difficult decision problem. It can be shown that the decision problem for standard second-order logic can be reduced to the decision problem for standard quantified rlIst-order modal logic. Even though this reduction is weaker than translatability, it is interesting because of the importance of the decision problem for standard second-order logic -- and even for suitable fragments thereof. (vi) The basic ideas of the argument which can be used to carry out the reduction was already indicated in my earlier paper. I shall outline the argument in a somewhat different form from that given in my Rome contribution. First, I showed in 1955 that the decision problem for satisfiability of standard secondorder logic reduces to the decision problem for sentences which have one initial universal quantifier whose variable is a one-place monadic predicate

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variable, over and above free predicate variables and first-order quantifiers. These sentences can thus be taken to be of the form (1) (VX) M(X, yl •... ,yk)

where M contains no second-order quantifiers, only first-order ones, and X is a one-place second-order (predicate) variable. The basic idea needed to carry out the reduction further is to let quantification over alternative worlds do the job of the second-order quantifier" (V X )." This can be accomplished (given certain assumptions) as follows. (a) We shall assume that the domains of worlds alternative to Wo are restricted to those in the domain do(wo). More explicitly, each individual well-defmed in an alternative Wj to Wo is well-defined in wo. (b) The converse requirement (on individuals existing in wo) can be imposed by the sentence (2) (Vx)(3 z)( x = z & N(z = z )).

Whenever (2) is true in a member Wo of a frame F, each well-defined and existing individual in the domain do (wo) is also well-defined in each alternative to wo. (c) Existence can be required to be transferable from Wo to its alternatives and back by the following sentences (3) (Vx)(Vy)« x = y) :::> N (3 z)( z = y)) (4) ('Ix )(P(3 z)( z =x) :::> (3z )(z = x))

(d) The branching and merging of world lines between Wo and its alternatives can be ruled out in the usual way. (e) The total effect of (a)-(d) is to ensure that there is a one-to-one correspondence between individuals existing in Wo and its alternatives. Each individual existing in Wo has one and only one counterpart in each Wl such thatR(wo,Wl), and that counterpart exists; and vice versa.

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Now we can require very simply that each predicate YI, ... ,Yk occurring in (1) holds of the same individual in Wo and its alternatives. This can be done by means of the following sentences, where I am assuming by way of example that Yi is aj-place predicate, and where i = l, ... ,k. (5) (VXI) .. , ('VXj) [Yi (xl, ... , xj) H NYi (Xl, ..• , xj)] (6) (VXl) •.. ('VXj) [Yi (xl, ... , Xj) H PYi (Xl, ... , Xj)]

(t) Now it is immediately seen that (1) is satisfiable in standard second-order logic iff the conjunction of (2)-(6) and (7) N M(X, YI, ... , Yk)

is satisfiable in standard quantified first-order modallogic.5 For the standardness of this modal logic requires that X be chosen in all the different extensionally possible ways, all yielding a true model (if the conjunction of (2)-(7) be true). And this is precisely what (1) requires for its truth in the first place. (vii) What this amounts to is that standard first-order quantified modal logic is an extremely strong theory, comparable in force with second-order logic. It immediately follows that it is not axiomatizable. In a sense, this answers the question: Is alethic modal logic possible? It shows that there cannot be a logical system, that is to say, an axiomatic and deductive treatment, of the quantified logic of logical modalities. In another sense, too, we thus have to conclude that alethic modal logic is not possible. Neither any of the Lewis systems nor Kripke semantics is capable of serving as a viable modal logic of logical modalities. Jointly, these observations answer the question as to how long the step is from Kripke semantics to standard semantics. It is a very long step indeed. A note on procedure may be helpful here. In the Rome paper, I showed how the presence of the so-called backwards-looking operators makes standard quantified modal logic extremely strong. In the present paper, I am arguing that, even apart from backwards-looking operators, there are reasons for assuming in standard modal logic one uniform domain and hence ending up with an extremely powerful and hence unmanageable logic. The two lines of argument reinforce each other. It can be maintained that the absence of backwards-looking operators is merely an accidental consequence of the peculiarities of the received syntax of modal logic. Hence they

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should be incorporated in any satisfactory treatment of modalities. And if this is done, we can prove the same reductions result as was indicated by my earlier proof. In this way, too, we can see the enormous power of standard firstorder quantified modal logic. (viii) An important ramification of our problem must be noted here. So far, I have been writing as if there were just one standard logic and just one nonstandard one. The former impression is true, but the latter is false. This is of course a direct consequence of the definition of the standard-nonstandard distinction. For instance, suppose that a higher-order quantifier is not required to range over the set L of all extensionally possible entities of a certain type, but may range over some subset (j of L Then it still remains possible to impose all sorts of further requirements on (j. The common (but frequently unacknowledged) motivation of these further requirements is to bring (j closer and closer to L without losing some of the advantages of operating with (j rather than L, such as complete axiomatizability. In brief, one attempts to have at least a good approximation of having one's standard cake (strong conditions on (j) and eating (i.e. axiomatizing) it, too. The question as to what the best ways of doing so are is an important problem which comes up in several different parts of logic. There is a sense in which the problem of finding stronger and stronger (but in some sense true) set-theoretical assumptions can be considered a case in point. In different parts of logic, the preferred conditions of this sort are apparently quite different. In modal logic, it has been customary to impose no further restrictions on (j. In contrast, in second-order logic it has been almost universally assumed that er be closed with respect to Boolean operations and with respect to projective operators (applications of quantifiers). These are obviously most important restrictions whose upshot is to cause the behavior of (j visa-vis deductive methods to resemble that of L. (The same sorts of explicit inferences are then by and large valid in both.) Henkin showed that in spite of the extra restriction on (j we can still have semantically complete axiomatizability. The highly interesting question can be raised here as to what would happen if similar conditions were imposed on nonstandard models of modal logics. This question remains completely open, as far as I know. The standard-nonstandard contrast can be extended to first-order logic also, as I indicated in my Rome paper. This extension is accomplished by means of game-theoretical semantics, which effects a translation of first-order logic into a fragment of higher-order logic. In this area, the main temptation is not so much to make sure that er is large enough by imposing on it various closure

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conditions, but to restrict er so as to include only recursive or otherwise manageable functions, for these functions will represent strategies in accordance with which someone will have to play a semantical game. Comparisons between these different kinds of nonstandard models and the restrictions one puts on them may be hoped to yield insights into the best strategies of handling the problem mentioned earlier. This is the problem of (as it were) approximating standard models by nonstandard ones. Virtually all work remains to be done here, however, in spite of the interest and promise of this line of thought. (ix) Why hasn't the need of standard models in modal logics caused more consternation among logicians and philosophers? One partial reason why not is that there seems to be no such need in other branches of modal logics (in the wider sense that covers all intensionallogics.) For instance, in the semantics of epistemic logic the alternatives to a given world Wo (with respect to a person b and a time t ) are now all the worlds compatible with everything b knows in Wo at t. There is normally a tremendously large variety of such worlds, but there is no need whatsoever to require that all the different kinds of models with the same domain as Wo should be among the alternatives to Wo. In brief, epistcmic logic and many other intensionallogics -- including the "logics" of all propositional attitudes -- clearly have a nonstandard semantics. Hence it seems that a modal logician need not fear unemployment even ifhe or she concentrates on deductive and axiomatic methods, for these methods seem reasonably adequate for intensional logics in the narrower sense which excludes logical modalities. There are further problems here, however. I indicated above that there are reasons, at least prima facie reasons to restrict the domains of all the members of a frame to the same domain in standard semantics for modal logics. Since intensionallogics use nonstandard semantics, there is no reason to impose this requirement on their frames. Such a restriction would be obviously inappropriate for other reasons as well. For instance, in epistemic logic it would mean that everybody knows the identity of all individuals in the world. In general, the requirement would amount to a kind of omniscience with respect to knowing who and knowing what questions that is completely unrealistic. But if so, the ensuing situation becomes curiouser and curiouser. If the restriction mentioned earlier is enforced in the semantics of logical modalities but not in (say) epistemic logic, this means that there must often be epistemic alternatives to a given world Wo which are not alethic (logical) alternatives to Wo. This contradicts sharply the eminently natural idea that logically possible worlds constitute the widest class of alternatives to a given onc.

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It is not clear how we should view this situation. One possibility is to take it to constitute a strong objection to the assumption of restricted domains mentioned above. Since this assumption seems very difficult to avoid in standard alethic modal logic, we obtain in this way a new argument against the possibility of alethic modal logic. There is another possibility here, however. It is to acknowledge frankly the idea that epistemically and doxastically possible worlds need not all be logically possible. I believe that it can be shown on independent grounds that such "impossible possible worlds" are needed in order to overcome another paradox of omniscience, viz. that of so-called "logical omniscience" which is often put forward as an objection to epistemic logic and its semantics. It would be interesting to know to what extent Montague's move from standard to nonstandard semantics was connected with the partial switch of his interests from alethic and deontic modalities to other ones, especially to various intensional concepts. The observations made above prompt further criticisms of the two best known semanticists of modal logics, Richard Montague and Saul Kripke. Even though Montague's interests extended to intensional notions other than logical modalities, his main ambition was to construct a framework for general meaning analysis. For this purpose, he would need in his frames F all the worlds that are linguistically (semantically, analytically) possible. It would have required much stronger arguments than the ones ever given by Montague to restrict these so as to be fewer in the relevant respects than logically possible worlds. Hence Montague's use of nonstandard rather than standard semantics in his mature works is very strange. What is needed here is perhaps some notion of transcendental possibility which limits the range of worlds in our frames to those that conform to the general presuppositions of our conceptual system. Neither Montague nor anyone else has recently tried to delineate such a range of conceptual possibilities, however. Kripke has eschewed epistemic logic and the logic of other propositional attitudes and has stuck to pure modalities. It is hence most surprising that he should have not only used nonstandard semantics but the most liberal version thereof (i.e., the version which imposes no restrictions on the set of alternatives to a given member of a frame). Kripke seems to have realized, however dimly, that such nonstandard semantics does not work for logical modalities. Accordingly, he has sought to interpret the modalities he is dealing with as metaphysical rather than purely logical modalities. However, he has failed to provide more than the most rudimentary explanations of what these mysterious metaphysical modalities are. What is even worse, Kripke has not presented the

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slightest reason for thinking that his metaphysical modalities are so restrictive of the worlds in one's frame that he can use the most liberal nonstandard semantics imaginable. I do not see that his semantics for alethic (metaphysical) modalities has anything like a satisfactory interpretational foundation. All told, the question which constitutes the title of my paper is still very much open. Insofar as I have found grounds for an answer, they all point towards a negative one. The best we seem to be able to do is to replace logical (or metaphysical) modalities with some suitable version of transcendental modalities. But that still remains to be done almost completely. NOTES 1 Besides Quine's writings, see also Hintikka 'Quine on Quantifying In'and the further references listed there, as well as Follesdal, 'Interpretation of Quantifiers' . 2 This semantics was originally discovered independently by Kanger, Hintikka, Guillaume, and Montague and possibly by still other logicians. Latcr, it was indepcndcntly discovercd also by Kripke and E.W. Beth. 3 One connection with Quine's idcas is the following. Quine has occasionally hintcd that modal logic amounts to illegitimately running togcther logical and mctalogical considerations. Pressed on the point, he has nevertheless retreated and admitted that these need not be anything per se self-defeating abut building modalities into our object language. It is now beginning to seem that this retreat was premature and that there are serious problems in the very direction which Quine was pointing to, viz., in trying to incorporate essentially metalogical concepts (logical modalities) in one's object language. We shall find plenty of examples of such difficulties in this paper. In general, it is hard to avoid a strong impression that Quine's objections to quantified modal logic have been discussed by many philosophcrs on far too Iowa levcl of logical sophistication. One of the purposes of this papcr is to point out connections betwecn thc direct criticisms of alcthic modal logic and sevcral important logical and foundational issues. 4 See my paper, 'Standard vs. Nonstandard Logics'. 5 Notice here how a standardly interpreted necessity-operator does literally the samc job (evcn syntactically) as a standardly interpreted higher-order universal quantifier.

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REFERENCES Beth, E.W. and Nieland, J.J. E, 1961:'Rapports 1,2,3,6,8,10,13' in Compte rendu des travaux effectues par l' Universite d' Amsterdam dans le cadre du contrat Euratom, Contrat no. 010-60-12, Rapport CETIS 26, Logique Euratom-C.C.R. Ispra. Beth, E. W. and Nieland, J. J. E: 1965,'Semantic Construction of Lewis's Systems' in J. W. Addison,Leon Henkin, and Alfred Tarski (eds.), The Theory of Models, North-Holland, Amsterdam, 17-24. Cocchiarella, Nino B.: 1975, 'Logical Atomism, Nominalism, and Modal Logic', Synthese 31, 23-62. Follesdal, Dagfinn: 1968, 'Interpretation of Quantifiers' in B. van Rootselaar and J. E Staal (eds.), Logic, Methodology and Philosophy of Science IIl, North-Holland, Amsterdam, 271-281. Gallin, Daniel: 1975, Intensional and Higher-Order Modal Logic, North-Holland, Amsterdam. Guillaume, Marcel: 1958, Rapports entre caIculs propositions modaux et topologie implique par certaines extensions de la mcthode des tableaux semantiques. Systeme de Feys-von Wright, Systeme S4 de Lewis, Comptes Rendues des Seances de [' Academic des Sciences (Paris), 246,1140-1142, 2207-2210; Systeme SS de Lewis, ibid., 247,1282-1283. Henkin, Leon: 1950, 'Completeness in the Theory of Types' ,Journal of Symbolic Logic, 15, 81-91. (For a correction, see Peter Andrews: 1972, 'General Models and Extensionality', ibid. 37, 395-97.) Hintikka, Jaakko: 1955, Reductions in the Theory of Types,Acta Philosophica Fennica, 8, 57-115. Hintikka, Jaakko: Quantifiers in Deontic Logic, Societas Scientiarum Fennica, Commentationes Ilumanarum Litterarum 23, no. 4). Hintikka, Jaakko: 1957, 'Modality as Referential Muiliplicity', Ajatus 20, 4964. Hintikka, Jaakko: 1961, 'Modality and Quantification', Theoria, 27, 119-28. Hintikka, Jaakko: 1953, 'The Modes of Modality', Acta Philosophica Fennica 16,65-81. Hintikka, Jaakko: 1975, 'Quine on Quantifying In', in Jaakko Hintikka, The I ntentions of Intentionality and Other New Modelsfor Modalities, D. Reidcl, Dordrecht, 102-36. Hintikka, Jaakko: 1981, 'Standard vs. Nonstandard Logic: Higher-Order, Modal, and First-Order Logics' , in E. Agazzi (ed.), Modern Lo gic (Proceedings of the 1977 Rome Symposium), D. ReideI, Dordrecht, 283-96.

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Kanger, Stig: 1957, Provability in Logic (Stockholm Studies in Philosophy, vol. 1), Almqvist & Wiksell, Stockholm. Kripke, Saul A: 1963, 'Semantical Considerations on Modal Logic', Acta Philosophica Fennica, 16, 83-94. Kripke, Saul A.: 1965, 'Semantical Analysis of Modal Logic 1', Zeitschriftfur mathematische Logik und Grundlagen der Mathematik 9,67-96. Kripke, Saul A: 1965, Semantical Analysis of Modal Logic II', in J. W. Addison, Leon Henkin, and Alfred Tarski (eds.), The Theory of Models, NorthHolland, Amsterdam, 206-20. Kripke, Saul A: 1971, 'Identity and Necessity', in Milton K. Munitz (cd.), Identity and Individuation, New York University Press, N.Y., 135-64. Kripke, Saul A: 1972, 'Naming and Necessity', in Donald Davidson and Gilbert Harman (eds.), Semantics of Natural Language, D. Reidc1, Dordrecht, 253-355. Montague, Richard: 1960, 'Logical Necessity, Physical Necessity, Ethics, and Quantifiers', Inquiry, 4, 259-69 (reprinted in Thomason 1974). Montague, Richard and Kalish, Donald: 1959, 'That', Philosophical Studies 10,54-61 (reprinted in Thomason 1974). Quine, W. V.: 1960, The Ways of Paradox, Random House, New York. Quine, W. v.: 1960, Word and Object, MlT Press, Cambridge, Mass .. Quine, W. V.: 1969, Ontological Relativity, Columbia University Press, New York. Thomason, Richmond (cd.): 1974, Formal Philosophy: Selected Papers of Richard Montague, Yale University Press, New Haven.

REASONING ABOUT KNOWLEDGE IN PHILOSOPHY: THE PARADIGM OF EPISTEMIC LOGIC 1. EPIS1EMIC LOGIC AS A VEHICLE OF KNOWLEDGE REPRESENTATION The main vehicle of speaking and reasoning about knowledge in philosophy has recently been epistemic logic. l Even though epistemic logic is not the only relevant language-game in town, it offers a useful perspective here, for certain other approaches can be thought of as improvements on epistemic logic. In its axiomatic-deductive forms, epistemic logic is normally considered a branch of modal logic, and its semantics is usually subsumed under the misleading heading of "possible-worlds semantics". I will not attempt here a survey of the existing literature on epistemic logic? Most of this literature is focused on syntactical (e.g., deductive and axiomatic) methods of dealing with knowledge representation and reasoning about knowledge. This is in my view a serious defect in much of the current work on epistemic logic. For typicalJy the most interesting problems and solutions are found by considering the model-theoretical (semantical) situation. For this reason, I will not attempt here a survey of existing literature, but a review of some of the central conceptual problems arising in epistemic logic. The basic laws of epistemic logic are in fact easily obtained on a basis of a simple semanlical idea. It is that all talk about what a knower b knows is spelled out by reference to the subset Wl of the space W of all the relevant scenarios (worlds, situation) which consists of all those scenarios that are compatible with everything b knows. In brief, knowlege is what enables b to restrict her or his attention to Wl. Since Wl is relative not only to b but also to the scenario Wo E W in which b's knowledge is being considered, the obvious implementation of this intuitive idea, which of course is but a form of the old adage "information is elimination of uncertainty", is to assume that a two-place relation R is defined on W for each b. The members of Wl arc the worlds compatible with what b knows knows in wo. Then Wl is the set of all scenarios to which Wo bears this relation. The rclation will be called an epistemic alternativeness rclation, and the members of Wl arc called the epistemic b-alternatives to wo. Thus "b knows that S" is true in Wo i[f S is true in all the epistemie b-alternatives to wo. Each such alternativeness relation must be assumed to be rellexive (what is known is true) and transitive. (If b is in a position to rule out alJ scenarios in W-Wl, b is ipso facto in a position to rule out the claim that he or she is not in 17

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such a position.) These definitions and stipulations (combined with a suitable semantics for the usual quantification theory) specify the semantics of a system of epistemic logic, and hence its deductive-axiomatic treatment, subject to the qualifications to be discussed below. The resulting logic turns out not to be devoid of interest. Its propositional part (restricted to one knower) is the logic of the topological closure operation. Hence epistemic logic is related to the logic of topology. Its laws are in effect those of intuitionistic logic. There are also close relations between the semantics of epistemic logic and the technique of forcing? However, in order to reach this connection, the semantics of negation and conditional have to be modified somewhat. Many of the further developments in epistemic logic can be thought of as solutions to problems concerning the epistemic logic so far set up. One of the first problems is to represent the other kinds of knowledge, those expressed by knows + an indirect wh-question and by knows + a direct grammatical object, respectively, by starting from the knows that construction. This basic construction (b knows that S) is in the notation used here expressed by " {b } K S". Two comments are in order here. (a) The propositional alternatives I have called "scenarios" or "models" can be states of affairs, situations, courses of events, or entire world histories. The last of these applications is highlighted by philosophers' misleading term "Possible-worlds semantics". This term is misleading, because applications to entire universe are scarcely found outside philosophers' speculations.5 The primary intended applications are to scenarios covering relatively small pieces of space-time. Thus the label "situation semantics" ,6 which has recently been applied to a study of additional relations between what I have called scenarios, does not mark any sharp contrast to rightly understood possible-worlds semantics. (b) The most im;ortant application of epistemic logic is to the theory of questions and answers. No separate treatment is needed, however, for a direct question like (1.1) Who's living here?

can be construed as a request of infonnation which might as well be expressed by (1.2) Bring it about that I know who is living here.

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Here the subordinate clause is an indirect question with "knows" as its main verb. I have called it the desideratum of the question (1.1). It fells within the purview of epistemic logic (sec. 2 below). And obviously the logical study of direct questions like (1.1) reduces largely to the study of their desiderata. The first and foremost problem is the theory of questions and answers concerns the relation of a question of its (conclusive) answers. When does a reply, say "d" to a wh-question like (1.1) do its job? Obviously when it makes the desideratum (1.3) I know who lives here true. But what does the reply "d" in fact accomplish? Obviously, the truth of (lA) I know that d lives here. Hence the problem of answerhood is the question as to when (lA) implies (1.3). Now the logical forms of (1.3) and (lA) are, fairly obviously (but see sec. 4 below), (1.5) (3x)(I) K (x lives here) and (1.6) {I} K (d lives here). Hence the operative problem is when (1.6) implies (1.5). This. is a question concerning the interplay of quantifiers and epistemic operators. This interplay will be discussed in section 2 below. s

2. QUANTIFIERS IN EPISTEMIG LOGIC. KNOWING + INIRECT WH-QUESTIONS The first conceptual problem I shall analyze is the representation of other kinds of knowledge that knowing Ihat. 9 They include the kind of knowledge expressed linguistically by the constructions knows + an indircct wh-question and knows + a direct grammatical object objcct. Here philosophers' preoccupation with the surface phcnomena of ordinary usage has seriously hampered their thcorizing. In fact, the right treatment is nevertheless not hard 10 find. It can be presented as a succession of steps.

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(i) In order to use quantifiers in context which, like epistemic contexts, involve a multitude of scenarios, it must be assumed that criteria of identity for individuals across worlds have been given. In order to have a vivid vocabularly, I shall speak of the imaginary lines connecting the counterparts of the same individual in different model of scenarios as "world lines". Once a warp of world lines connecting the members of W is given (for each relevant knower), truth conditions for quantified sentences in a (first order) epistemic language. Such truth-conditions solve all the conceptual problems Quine and others have raised or, rather, transform them into problems concerning the way world lines are drawn. (ii) It cannot be assumed that the same individuals exist in all models. Then the basic laws of quantification theory have to be revised by changing some of the instantion rules. For instance, the law of universal instantiation might be changed so as to read: (UI) If "x" occurs in S[x] outside the scopes of all epistemic operators. (2.1) «(\fx)S[x] & (3y)(z= y»

=>

S[z]

In other words, when we speak of z as a member of the actual world, we have to assume that it exists in that world in order for it to be a bona fide value of quantifiers pertaining inter alia to the actual world. 1O (iii) The obvious formal counterpart to knows + an indirect wh-question, e.g., to (2.2) b knows who (say, x) is such that S[x]

is (2.3) (3x)(b}K S[x].

This paraphrase amounts to saying that b knows who (x) is such that S[x] is there to be a world line which in all of b's knowledge worlds picks out an individual x satisfying in that world the condition S[x]. The best proof of the aptness of this rational reconstruction of "knowing + wh-construction" sentences is that it leads into an elegant and powerful analysis of the relation of a (direct) wh-question to its (conclusive) answers.

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(iv) In order for this idea to work, we nevertheless must allow world lines to break down in a more radical sense than the failure of an individual to exist in a given "world". We must allow a world line of x to break down in a world W1 in the strong sense that it does not even make sense to ask whether x exists in W1 or not 11 For otherwise (if all world lines could be extended ad libitum) everybody would know the identity of every individual (under some guise or other, so to speak), on the basis of the paraphrase of constructions of the form knowing + indirect wh-question agreed on in (iii). In other words, the natural model-theoretical counterpart of b's knowing the identity of x is that some world line passing through x (considered as a member of the actual world) spans all of b's knowledge worlds. How is the well-definedness of x in a world W1 (i.e., the extendibility of the world line of x to W1) to be expressed in a fonnallanguage? The obvious candidate is the truth of "x=x" in W1. This simple idea yields the first fully satisfactory treatment of quantification in epistemic contexts. This simple idea yields the first fully satisfactory treatment of quantification in epistemic contexts. This treatment has not been worked out in the literature, but the main points are nevertheless clear. Since the truth of (3z)(x=z) implies that of x=x, no changes are needed in the quantifier rules. Instead, we need a three-value logic with different kinds of negations, forced on us by the idea that if x is undefined in a world W1, any atomic sentence containing "x" does not have either of the two usual truth-values "true" and "false" in W1, (v) Essentially the same treatment can be extended to higher-order logic. (Such a treatment is needed, among other purposes, for applications of epistemic logic to the theory of questions and answers.) There is one difference, however. In the case of higher-order entities, existence is not needed as a condition of being a value of a quantified variable. (It is not clear what existence might mean here.) But well-definedness is still required. Hence valid the counterpart to (UI) for, e.g., one-place second-order quantifiers is (UI)* (\Ix) S [X]

&

(Y = Y)

S[y]

where (Y = Y) is to be taken to as (2.4) (\Ix)(Y(x) H

Y(x))

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(vi) There is another crucially important feature of the conceptual situation here which has been obscured by the surface phenomena of ordinary language and therefore neglected by philosophers. This is in fact that that in certain situations there are two systems of world lines in operation. 12 A knower's (say, b's) cognitive relations to his or her environment (including past situations in which b was directly involved) span a framework which can be used for the purpose of drawing world lines. Such a world line connects such (scenario-bound) individuals as play the same role in these first-hand cognitive relations to b. For instance, in the case of visual perception these world lines connect the objects that occupy the same location in b's visual space. (If b does not see who or what they are, they are not the same absolutely or descriptively identified entities.) In other words, b's pcrspcctively identified objects are in this case his or her visual objects. This can be extended to other kinds of knowledge in a fairly straightforward way. Because of the presence of two systems of world lines, we must have two pairs of quantifiers corresponding to (relying on) them. Success in the perspectival cross-identification will then be expressed in the same way as with the other (public, descriptive) mode of identification, but with a different kind of quantifiers, say (Ax) and (Ex), instead of ('
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23

manifested as the contrast between what are called semantical and eRisodic memory I 4 as well as a distinction between two kinds of visual systems. IS

3. THE PROBLEM OF "LOGICAL OMNISCIENCE" The model-theoretical treatment of epistemic logic so far outlined leads to a paradoxical result. Suppose that (SI:J S2), Le., that all models of SI are models of S2. Then all the epistemic alternatives in which SI are true are also alternatives in which S2 is true. From this it follows that the following will be true for any b and in any scenario:

(3.1) {b)KSI

::J

{b)KS2

In brief, everybody always knows all the logical consequences of what he or-she knows. This is obviously an unacceptable result, and in ccrtain quarters it is still considered a sufficient reason for rejecting a model-theoretic analysis of epistemic concepts. I6 This follows only if the paradox, known naturally as the paradox of logical omniscience, is unavoidable. And it has been known for quite a while that it is not. In fact, we have had one of the several unmistakable but unheralded triumphs of epistemic logic. There are in fact two equivalent ways of delineating the subclass oflogical consequences (SI ::J S2) for which (3.1) holds. (i) This set can be defined by putting syntactical restrictions on the deductive argument which leads from SI to S2. This argument can of course be of many different kinds. It turns out, however, that for all the half-way natural ones, the same heuristic idea works and gives the same result. In an easily appreciated sense, the number of free individuals symbols together with the number of layers of quantifiers determine how many individuals are considered in a given sentence S (or in a given argument). The natural restriction on the argument from SI to S2 now is that this parameter should never be larger at any stage of the argument than it is in SI or S2. Even though this basic idea is thus easy to understand and to implement, no simple axiomatic-deductive system codifying it has been presentcd in the literature. This way of defining knowledge-preserving logical inferences is connected, via the idea of so many individuals considered in their relation to each other in an argument with a wealth of traditional philosophical issues in the philosophy

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oflogic and mathematics. 17 The same idea also promises connections with the psychology of deductive reasoning. IS (ii) This syntactical (deductive-axiomatic) restriction on "logical omniscience yields the same result as a different and apparently completely unlike line of thought. This line begins with an interesting generalization of the concept of model (world, scenario). Unlike its rivals as a candidate for the role of a logically nonstandard world (semantical basis of so-called paraconsistent logics),19 this generalization is completely realistic. Indeed, this generalization but a variant of the notion or urn model in probability theory, and is referred to by the same term?O In an obvious sense, nested quantifiers can be thought of as representing successive "draws" of individuals from the model. The concept of urn model is obtained by letting the set of available individuals change between successive "draws". (The world, in other words, is run by a malicious demon who can restrict the set of available individuals in tandem with our examination of the world (via successive searches or "draws"). Actually, not all and sundry urn models are natural candidates for the role of epistemically possible but (classically speaking) logically impossible worlds which are the model-theoretical codification of the failure of logical omniscience. For that role, only those urn models (changing models) are acceptable which vary so subtly that they cannot be told apart from the invariant (classical) models by means of sequences of draws as long as those envisaged in (SI ~ Sz). It turns out that the sentences which are true in all such "almost invariant" urn models (at the length of sequence of draws envisaged in the conditional) are precisely the same as those for which the step from I- (SI ~ Sz) to (3.1) is authorized by the syntactical restriction. 4. EPIS1EMIC LOGIC AND INFORMATIONAL INDEPENDENCE One of the most characteristic features of epistemic logic has barely been mentioned in the existing literature?l In order to see what is involved, let us consider the familiar distinction between (4.1) b knows that there is an individual x such thatS[x]

and (4.2) b knows of some individual x that S[x].

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25

Usually, it is said that these two are to be represented in the language of epistemic logic by (4.3) {b} K (3x)S[x]

and (4.4) (3x)(b}KS[x],

respectively. Here the latter has roughly the force (4.5) b knows who (what), say x, is such that S[x].

Hence the contrast in question is roughly that between "knowing that there is" and "knowing who or what". I am not questioning the status of (4.4) as being logically equivalent with (4.2), i.e., as a possible translation of (4.2). What I am asking is how this translation comes about, i.e., what the mechanism is that leads us from (4.2) to (4.4). It is usually assumed, as the rendering (4.4) of (4.2) shows, that the mechanism in question is the relative order (relative scopes) of K and (3x). The linguistic evidence for this idea is unconvincing, however. It is much more natural to assume that in epistemic contexts like (4.2), the choice of the individual we are talking about is independent of epistemic considerations, i.e., that the quantifier somehow ranges over just the actually existing individuals. The independence can be captured by the two-dimensional expression (4.6)

(3x)

............. S[x] {b} K / ' Even though the meaning of (4.6) is intuitively obvious, further explanations are needed here to incorporate expressions like (4.6) in our formal language. In order to spell out the semantics of expressions like (4.6) we must combine possible-worlds analysis of epistemic concepts (as sketched ever so briefly in section 1 above) with what has been called game-theoretical semantics (GTS).22 Very briefly, in GTS the truth of a sentence S in a model M is explicated as the existence of a winning strategy in a certain verification game (semantical game G(S)) played with S on M for one of the players, called Myself (or the Verifier), against an opponent called Nature (or the Falsifier). Most of

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the rules of these games can be anticipated on the basis of the verification idea. The following are cases in point: (G.E) If the game has reached the sentence (3x)S[x] and M, Myself chooses an individual, say b, from the domain do(M) of M. Then the game is continued with respect to S[b] and M. (G.U) Similarly, except that Nature chooses b. ,

(G.v) G(Sl v Sz) (played on M) begins with Myself's choice of Si (i = 1 or 2) The rest of the game is G(Si) (played on the same model M). (G. &) Similarly, except that Nature chooses Si. (G.-) G(-S) is like G(S) except that the roles of the two players are reversed. (G.K) If the game has reached the sentence {b}KS and the model (world) Mo, Nature chooses an epistemic b-altemative Ml to Mo. The game is continued with respect to S and Ml. By means of GTS the semantics of branching formulas like (4.6) can be dealt with explicitly?1 What they instantiate is the well-known game-theoretical phenomenon of informational independence. In (4.6), the moves connected with "(3x)" and "{b}K" are each made without knowledge of the other move. More generally, each move is associated with an information set which includes those other moves that are known to the player making the move. Hence the operator structure of a sentence need not always. be even partially ordered. We can linearize the branching notation used in (4.6) by attaching to each quantifier an indication which shows which of the earlier epistemic operators (if any) it is informationally independent of. Thus (4.6) can be written, in a self-explanatory notation, as (4.7) {b}K «:Jx/{b}K) S[x]

which is of course logically equivalent with (4.6) and (4.4). It is a most important general fact about the logic of epistemic concepts that when they mix with quantifiers, these quantifiers frequently have to be taken to be independent of some of the epistemic operators present. For instance, the so-called de re reading of quantifiers is in reality precisely the reading obtained

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27

by taking the quantifiers in question to be infonnationally independent of an epistemic (or other intentional) operator. GTS shows that (and how) other primitives of one's language, not just the quantifiers, can be independent of epistemic operators. For instance, an atomic predicate A(x) or a proper name a may be evaluated in M independently of an epistemic operator, say "(b}K. "Since the epistemic operator governs the choice of an alternative world Ml, this means evaluating these primitive in the pre-epistemic-move-model Mo. And since in the winning strategy they clearly have to be evaluated so as to assign to them their actual references, such expressions as A(x/ (b } K) and a/ ( b} K in effect pick out the actual references in

Mo. As the equivalence of (4.6) and (4.4) illustrates, in the simplest cases sentences containing informationally independent quantifiers have non-independent equivalent. But even in such cases, a notation which spells out the independence can bring out the intended logical fonn of our epistemic statements more clearly than the dependent (linear) notation. For instance, naturallanguage statements of the form (4.8) b knows who (say, x) is such that A (x)

(whereA is an atomic predicate) have normally two readings, which in the linear traditional notation are expressed as follows: (4.9) (3x)(b}KA(x)

(4.10) (Vx)(A(x)::J (3z)(y=z & (b}KA(x»).

The parallelism of the two is not obvious in (4.9)-(4.10) but is brought out much more clearly in an independence-friendly notation as follows: (4.11) (b}K(3x/(b}K) (A(x/(b}K) &A(x» (4.12) (b}K(Vx/(b}K) (A(x/(b}K)

::J

A(x».

However, in other cases the independence notation can be indispensable?4 For instance, (4.13) b knows whom everybody adores

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cannot be expressed (on the reading according to which different persons may have different idols) by (4.14) (Vx)(3y)(3z)(x = z & {b) K(z admires y)),

for (4.14) implies (as you can easily see) that b knows the identity of each person and of his or her admireree. In fact, the normally intended force of (4.13) can only be expressed (unless we resort to higher-order quantifiers) by something like (4.14) (b}K(Vx)(3y/{b}K) (x admires y).

Indeed, (4.15) (unlike (4.14)) is logically equivalent with (4.16) (3j){b}K(Vx) (xadmiresf(x))

which neatly bring out the obviously intended force of (4.13). For what (4.13) says is, obviously, that b knows how to find, for a given x, whom x admires, i.e., knows a function which takes us from any person to someone she or he admires. And this is precisely what (4.16) says. Notice that the informational dependence of the different operators {b } K, (\Ix) and (:ly) in (4.15) is not even partially ordered, but exhibit a loop structure: (4.17)

{b}K

J'

~

(x admires y)

(3y)", (Vx)

This is logically equivalent with (4.15). Asemantical game connected with (4.17) is hard to implement in the usual move-by -move form. It is easy to "play" in what game theorists call the normal form of a game: Both players choose a strategy, which jointly determine the course of the game, including its outcome. This observation is connected with the equivalence of (4.16) with (4.17). Ithas some general interest as an illustration of what different kinds of games (in the sense of game theory) can be like. Thus the independence notation sometimes lends added power to epistemic logic. How much more? It is known that the force of quantification theory with branching quantifiers is extremely strong, coming close to that of the entire second-order logic?5 Hence no complete axiomatization of quantified epistemic logic with unlimited independence is possible. However, for a

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29

variety of simpler cases, for instance, when all the cases of independence pertain to ignorance of a move connected with a single unnegated epistemic operator {b} K, an explicit formal treatment may very well be possible, even though it has not been presented in the literature.

5. KNOWLEDGE ACQUISITION BY QUESTIONING So far, I have been concerned with problems of knowledge representation and only indirectly with reasoning about knowledge. Of course, the representation problem has to be solved before problems about reasoning are tackled. But what is represented is already acquired and already available knowledge, whereas much of the actual reasoning about knowledge is also concerned with the step-by-step processes of knowledge acquisition. For instance, in the wellknown puzzle variously known as the case of cheating husbands or of the wise men,z6 the reasoning of the participants depends essentially on their knowing what the others knew or did not know at the preceding stage of their synchronized reasoning processes. One way of modelling knowledge acquisition is to conceptualize itas a series of questions a reasoner, here termed the Inquirer, addresses to a source of informationj to be called the Oracle (in some applications, more naturally called Nature)? The answers, when available, may be used by the Inquirer as premises of deriving a given conclusion C (or, in an alternative version of the model) for the purpose of answering the question "C or not-C"? In the process, steps of deduction may alternate with each other, and the Inquirer may have a fixed initial premise T (called the theoretical premise) available for the purposes?8 The deductive rules to be used are restricted to those that satisfy the subformula principle. Before a question may be asked by the Inquirer, its presupposition must have been established?9 In this way we obtain what I have called the interrogative game or the interrogative model of inquiry. Since the logic of questions and answers is in effect (as was pointed out in section 1 above, part (b)) a branch of epistemic logic, the interrogative model can also be thought of as another outgrowth of epistemic logic. One of the main advantages of the interrogative model is that it enables us to discuss cognitive strategies and not only static cognitive situations. This possibility can be realized in many different ways. The Oracle can be literally nature, and nature's answers can then be scientific experiments. In a simpler case, the source of information is one's environment, and the answers the Inquirer can hope to obtain are perceptual observations. But in other cases, the available answers can be items of information stored in the database of a computer, which will then play the role of the Oracle. In still other applications,

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the computer is the Inquirer's own brain, and the totality of available answers define's the Inquirer's tacit knowledge. The most natural application is undoubtedly one in which the answerer (the Oracle) is another human being, with whom the Inquirer is symmetrical n-person game in which at each interrogative mode each player can address a question to each of the other players. Some of the most intriguing types of reasoning about knowledge can be dealt with by means of such games, for instance, the "case of the cheating husbands". Such applications and extensions can be thought of as belonging to the logical theory of dialogues (discourse)?O I shall not discuss the details of any of these applications detail. It is in order, however, to locate some of the crucial parameters which play a role in these different interrogative games and distinguish them from each other. (i) In different applications, different kinds of questions are answered by the Oracle. The most clear-cut restraints here are those that depend on the logical complexity, especially the quantifier prefix structure of the available answers. For instance, sense-perception can only answer yes-or-no questions concerning particular matters of fact in one's environment. For a logician, these are yes-or-no questions concerning atomic sentences. (b) In contrast, controlled experiments can yield answers which codify functional dependencies. Such answers must have an AE quantifier prefix (i.e., a prefix of the form (\fx)(:ly ))?1 (c) Again the information stored in the memory of a human being or of a computer can logically speaking be of arbitrarily high complexity. These are of course but special cases of a long spectrum of different kinds of interrogative procedures, distinguished from each other by the quantificational complexity available answers. This spectrum ranges from case (a) via the different AEA. .. prefixes to the unlimited case (c). This hierarchy turns out to be highly important for many purposes, especially in the philosophy of science. These of course are normally other kinds oflimitations on available answers. In all these cases, it obviously makes a difference to the strategy selection of the Inquirer what (partial or total) knowledge he or she has of the limitations on available answers. This is illustrated by the knowledge which the user of a database may have as to what information is or is not stored in it.

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(ii) In many applications of the interrogative model and indeed in many applications of epistemic logic, it makes a crucial difference what kind of knowledge we are dealing with. For instance, tacit knowledge must fairly obviously be modelled by a sub-oracle. The list of propositions stored in the "memory" of this sub-oracle defines the extent of the Inquirer's tacit knowledge. At the other extreme there is the completely activated knowledge the Inquirer has. This is naturally modelled by the set ofthose sentences which have been put forward by the Inquirer as outcomes of interrogative or deductive moves (or which have the status of explicit initial premises of the interrogative process). This might be called the Inquirer's active knowledge. Active knowledge, unlike tacit knowledge, is relative to a stage of the interrogative game. Dealing with such distinction is vital for reasoning about knowledge, for it is a speaker's active knowledge that he or she is aware of and can report to others. But neither tacit knowledge nor active knowledge obeys the laws of epistemic logic. For instance, neither is closed with respect to logical consequence, not even if relations of logical consequence are restrained as indicated in section 3 above. In order to be able to develop satisfactory ways of reasoning about knowledge, we have to consider other kinds of knowledge. Among the most important ones there are the following: The Inquirer's potential knowledge consists of all the conclusions C the Inquirer can establish by means of the interrogative process. The Inquirer's virtual knowledge consists of all the conclusions C the Inquirer can establish by means of the interrogative process without introducing new "auxiliary" individuals into the argument in the sense of sec. 3 (i). By limiting the Inquirer's moves to deductive ones we can similarly define potential deductive knowledge and virtual deductive knowledge. (iii) The purely logical properties of the interrogative games are also of considerable interest. Let us denote the interrogative derivability of C from T in a model M by M:T 1- C. This relation depends of course on whatever restrictions there may be on available answers. It turns out that this relation depends also on the set RA of available tautological premises of the form

(5.1) (Si v -Si)

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where i Era. The reason is that in interrogative processes one cannot always restrict one's methods to those satisfying the sub formula principle?2 In other words, metalogical results analogous to Gentzen's fIrst Hauptsatz, which implies the eliminability of premises of the form (5.1), of the cut rule, of unrestricted modus ponens, etc., are not available in the theory of interrogative deri vability. There is a sense in which the notion of interrogative derivability is between the relations of logical consequence T I- C and the truth of C in M. For if no questions are allowed, M:T 1- C obviously reduces to T I- C. On the other hand, if no restrictions are imposed on available answers or on available tautological premises RA, it can be shown that M: cl> I- C iff C is true in M (cl> = the empty set). The set RA has an intuitive interpretation which is worth noting here. What the set RA codifIes is essentially the totality of yes-or-no questions which the Inquirer is prepared to ask (independently of the initial premise T). A restriction on RA is therefore very much like a restriction on the range of questions the Inquirer is prepared to raise, secondarily in the sense of a restriction on the items of tacit knowledge the Inquirer an activate. This is because the activation of such knowledge can only happen by means of questions whose presuppositions have to be available to the Inquirer. Thus the concept of range of attention is not purely subjective and psychological but has an objective logical and epistemological counterpart. This is but an example of the many possibilities of analyzing -- and synthesizing -- interesting epistemic concepts by means of the interrogative model. Most of the work in utilizing these possibilities still remains to be done. NOTES 1 The idea of epistemic logic goes back at least to G .H. von Wright: 1951, An Essay in Modal Logic, North-Holland, Amsterdam. The first book-length treatment was my: 1962, Knowledge and Belief" An Introduction to the Logic of the Two Notions, Comell U.P., Ithaca. 2 For a partial survey of earlier work, see Wolfgang Lenzen: 1978, Recent Work in Epistemic Logic (Acta Philosophica Fennica 30, no. I), Societas Philosophic a Fennica, Helsinki. 3 See here, e.g., Melvin Fitting: 1969,Intuitionistic Logic. Model Theory. and Forcing, North-Holland, Amsterdam; Kenneth A. Bowen: 1979, Model Theory for Modal Logic, D. Reidel, Dordrecht. These treatises are not addressed to the specific problems of epistemic logic, however.

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4 In the earlier literature, the knower used to be indicated by a subscript. This is misleading, however, for the term referring to the knower is not within the scope of the epistemic operator. 5 Some philosophers have tried to find a difference in principle between the two kinds of applications. It is nevertheless clearer in epistemic logic than in some of the parallel theories that the intended applications have always been to "small worlds", to use LJ. Savage's phrase. 6 See Jon Barwise and John Perry: 1983, Situations and Attitudes, MIT Press, Cambridge, Mass .. 7 See here Jaakko Hintikka: 1976, The Semantics of Questions and the Questions of Semantics (Acta Philosophica Fennica, 28, no. 4), Societas Philosophic a Fennica, Helsinki. 8 The question here is under what conditions existential generalization is valid in epistemic logic. The conditions are of course the same as the conditions on valid universal instantiation dealt with in sec. 2, part ii, below. 9 Cf. here chapter 1 of my book: 1974, The Intentions of Intentionality, D. Reidel, Dordrecht. 10 I am assuming that a distinction is made between those name-like free singular terms which pick out the same individual from different worlds and those that might refer to different individuals in different worlds. Here "z" is assumed to be of the former kind. 11 This matter will be dealt with in a greater detail in a projected monograph of mine. 12 See here chapters 3-4 of my book: 1974, The Intentions ofIntentionality, D. Reidel, Dordrecht. 13 Bertrand Russell: 1917, 'Knowledge by Acquaintance and Knowledge by Description', in Mysticism and Logic, George Allen & Unwin, London; chapter 5 of: 1912, The Problems of Philosophy, Home University Library, London, and cf. Jaakko Hintikka, Knowledge by Acquaintance - Individuation by Acquaintance, in D.E Pears (ed.): 1972, Bertrand Russell (Modem Studies in Philosophy), Doubleday, Garden City, NJ., 52-79. 14 See Endel Tulving: 1983, Elements of Episodic Memory, Clarendon Press, Oxford. 15 See Lucia Vaina, From Vision to Cognition: A Computational Theory of Higher-Level Visual Functions, Kluwer, Dordrecht, forthcoming. 16 Cf., e.g., Noam Chomsky: 1982, The Generative Enterprise, Foris, Dordrecht. From what is reported in the rest of this section, this objection against possible-worlds analysis of knowledge was effectively disposed of more than ten years ago.

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17 See Jaakko Hintikka: 1973, Logic, Language-Games, and Information, Clarendon Press, Oxford. 18 See Jaakko Hintikka: 1986, 'Mental Models, Semantical Games, and Varieties of Intelligence', in Lucia Vaina, ed., Varieties of Intelligence, D. Reidel, Dordrecht. 19 The so-called paraconsistent logics have never been given any realistic model-theoretical and pragmatic interpretation, and hence have in their present fonn little interest. Cf. here Nicholas Rescher and Robert Brandom: 1979, The Logic ofInconsistency, Basil Blackwell, Oxford. 20 See Veikko Rantala: 1975, 'Urn Models: A New Kind of Non-Standard Model for First-Order Logic', Journal of Philosophical Logic, 4, 455-474, reprinted in Esa Saarinen (ed): 1979, Game-Theoretical Semantics, D. Reidel, Dordrecht. 21 The first time this interesting phenomenon was pointed out in the literature is in Lauri Carlson and Alice ter Meulen: 1972, 'Informational Independence in Intensional Context', in Esa Saarinen et aI., (eds.): 1979, Essays in Honour o{ Jaakko Hintikka, D. Reidel, Dordrecht, 61-72. 2 See here Esa Saarinen (ed.), Game-Theoretical Semantics, and Jaakko Hintikka and Jack Kulas: 1983, The Game of Language, D. Reidcl, Dordrecht. 23 For branching quantifier structures, there exists a growing body of studies. For references, see the bibliography of Jaakko Hintikka and Jack Kulas: op. cit. Independences between other kinds of concepts have scarcely been studied, except for the papers referred to here. 24 See here Jaakko Hintikka: 1982, 'Questions with Outside Quantifiers', in R. Schneider, K. Tuite and R. Chametzky (eds.), Papers from the Parasession on Nondeclaratives, Chicago Linguistic Society, Chicago, 83-92. 25 See here Jaakko Hintikka: 1974, 'Quantifiers vs. Quantification Theory', Linguistic Inquiry,S, 153-77, reprinted in Esa Saarinen (ed).:1979, GameTheoretical Semantics, D. Reidel, Dordrecht, 367-379. 26 See, e.g., Danny Dolev, Joseph Y. Halpern and Yoram Moses: 1985, 'Cheating Husbands and Other Stories: A Case Study of Knowledge, Action and Communication', preprint. 27 The model sketched here has been studied in a number of papers of mine. See, e.g., Jaakko Hintikka and Merrill B. Hintikka: 1982, 'Sherlock Holmes Encounters Modem Logic: Towards a Theory of Information-Seeking by Questioning', in E.M. Barth and J.L. Martens, Argumentation: Approaches to Theory Formation, Benjamins, Amsterdam, 55-76; 'The Logic of Science as a Modcl-OrientedLogic', in P.D. Asquith andP. Kitcher (eds.): 1984,PSA 1984, 1, Philosophy of Science Association, East Lansing, MI, 177-85.

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28 As a book-keeping device we can use a Beth-type semantical tableau. (For

them, see W. Beth: 1955, 'Semantic Entailment and Formal DerivabiIity', Mededelingen van de Koninklijke Nederlandse Akademie van Wetenschappen, Afd. Letterkunde, N.R. 18, no. 13, Amsterdam, 309-42.) Then we can use all the usual terminology of the tableau method, and the deductive "moves" will be simply tableau-building rules. (We shall minimize movements between the left and the right column, however, and restrict the rules to those in keeping with the subformula principle.) Each application of the game rules is then relative to a given stage of some one subtableau. As is well known, the tableau method is simply the mirror image of a Gentzen-type sequent calculus. The only novelty here is that Nature's answers are centered into the left column of a subtableau as additional premises. 29 For the concept of presupposition presupposed here, see Jaakko Hintikka: 1976, The Semantics of Questions and the Questions of Semantics (Acta Philosophica Fennica, 28, no. 4), Societas Philosophica Fennica, Helsinki. 30 An excellent example of what can be done in this direction is Lauri Carlson: 1982, Dialogue Games, D. Reidel, Dordrecht. 31 This observation has important consequences for the contemporary philosophy of science, where it has generally been assumed that only questions concerning the truth of falsity of atomic sentences are answered by Nature. In reality, the logic of experimental inquiry is an AE logic, not the logic of the atomistic case. 32 The notions of subformula principle, cut elimination, Gentzen's Hauptsatz, etc. are explained in any decent introduction to proof theory. For Gentzen's classical papers, see M.E. Szabo (ed.): 1969, The Collected Paper of Gerhard Gentzen, North-Holland, Amsterdam.

ARE THERE NONEXISTENT OBJECTS? WHY NOT? BUT WHERE ARE THEY?* Our title question is important, but to my mind it is not nearly as intriguing as two responses it easily prompts. The first response is, Why not? The second is, But where are they? The main overall answer to the question, Are there nonexistent objects? is so obvious that it is much more interesting to ask: Why not? Why have many philosophers been moved to doubt and even to deny that there are nonexistent objects? I believe that by understanding and by removing these counter-reasons we can provide important further arguments for the same affirmative answer that Parsons gives to our theme question. It seems to me as obvious as anything in philosophy that there are unrealized possibilia: that our life is - as I once expressed it intrinsically and inevitably transacted against the backdrop of possibilities (possible states of affairs and possible causes of events), most of which will never be realized. And it seems eminently plausible that there are unrealized and hence nonexistent objects in some of these unrealized possibilities. If I had to present direct arguments for these conclusions, admittedly I would be more than a little puzzled; I don't know what kinds of arguments to present. But then I am not sure whether I could produce more impressive arguments for existent objects. I am reminded here of the question (undoubtedly apocryphal) I have heard attributed to Mencken: "Is there life before death in the Midwest?" A positive answer to this question may seem in suitable circumstances as unconvincing as an affirmative answer to its more common variant. It is nevertheless highly interesting to ask why philosophers have denied the (to my mind) obviously affirmative answer to our title question. The most conspicuous reason is undoubtedly that they have been thinking in syntactical (inference-theoretical) rather than semantical (model-theoretical) terms. Parsons's paper offers examples, both homemade and imported, of this phenomenon. Parsons argues that Ryle's own paraphrase test fails in the case of such sentences as "Mr. Pickwick is a fiction." However, the relevance of the criterion itself is 37

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highly dubious. Why should the possibility of paraphrasing sentences about Mr. Pickwick in this or that way prove a point about his ontological status, e.g., that he is or isn't Pickwickian? I don't see any force in the type of philosophical argument that relies on verbal paraphrase for any ontological question. It is only when we begin to ask serious model-theoretical questions that we can hope to find viable reasons for (or against) nonexistent objects. I don't think that anyone who takes these questions seriously can hope to dispense with nonexistent beings. Instead of boring you with model-theoretical technicalities, I will present an analogous but nontechnical case. In the possible world of Verdi's Tosca, the riveting question is whether there really are bullets in the soldiers' muskets in the execution scene. Is the execution a mock one or will the hero die in a hail of bullets? But even if there are bullets in the muskets, they are nonexistent ones, for the world of Tosca is not the world of existing objects. Hence a question as to whether there are certain specific nonexistent objects can be very burning indeed. The same goes for many other questions concerning the being of nonexistent individuals, once the plot or, more generally, the model-theoretic structures involved in our language understanding is taken seriously. The main weakness of Parsons's paper is that he is relying far too much on syntactic argumentation, that is, on what we would say, on what so-called "intuitions" we have about different sentences, on what inferences we feel like drawing, and suchlike. There is no future in such arguments. The very concepts they rely on, such as intuitions, acceptability of sentences, acceptability of inferences, etc., all cry out for a real semantical (model-theoretical) foundation. Admittedly, Parsons speaks occasionally of the entities we are committed to. But he quickly moves to questions of what we would say, or can correctly say, e.g., what inference we would draw, and apparently treats the two questions as equivalent. For instance, on p. 7 he writes at a crucial juncture: "I propose that a use of a sentence involving a grammatically correct singular term commits the user to a referent for that term just in case it commits the user to the existential generalization of the original claim." Here a commitment to a referent - presumably, an object - is explicated in terms of a commitment to an inference. Which is the basic kind of commitment here? Admittedly, a number of leading philosophers have rejected modeltheoretic argumentation completely. Frege, early Russell, Wittgenstein, and Quine are cases in point. However, these philosophers have had

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what their followers don't have, to wit, a deep theoretical reason for their position. As unlike as the four philosophers just mentioned are, they share what undoubtedly is the most important undiagnosed assumption in contemporary philosophy of language. Or, rather, they exemplify one half of an important undiagnosed dichotomy. I have called this dichotomy a contrast between the view of language as the universal medium and the view of language as calculus. Roughly, on the former view, we cannot as it were get outside our own language and look at it from the outside. We cannot speak in language of the semanticallinks that tie our language to the world. In brief, semantics is ineffable on the view of language as the universal medium. We cannot think of these semantical relations as being varied, either. Hence systematic model theory is impossible on this view, for it relies essentially on experimentation with different representative relations between language and reality. In particular, we cannot change at will the ranges of our quantifiers. Each of them should be thought of as ranging over the domain of the correct logical type. Parsons treats this kind of absolutist view of quantifiers literally as a bad joke. In reality, it is one of the most serious and consequential ideas in the philosophy of language of Frege, early Russell, Wittgenstein, and Quine. (The case of Rudolf Carnap, to whom Parsons refers, remains to be investigated.) Even though I personally reject the view of language as a universal medium, it (and ipso facto its consequences) should be taken much more seriously than Parsons apparently does. The contrary view, that of language as calculus, maintains that we can perform all these neat tricks. It is clear that all serious model theory presupposes the view of language as calculus. But notice that a believer in language as the universal medium is not barred from having all sorts of sharp views on semantical matters. All he (or she) has to do is to admit that these views cannot be expressed in language and hence cannot be built into any real theory. It seems to me that far too many contemporary philosophers have adopted certain consequences of the view of language as the universal medium without realizing where they come from. One of these consequences is the denial of nonexistent individuals. This was certainly one of the reasons why the Wittgenstein of the Tractatus postulated his "objects" which form the substance of every possible state of affairs but which are transcendental in the sense that we cannot say that they exist or don't exist. It seems to me that a systematic discussion and systematic criticism of

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the view of language as the universal medium is the best strategy for arguing that there are nonexistent objects. A refutation of this view would remove some of the reasons for denying that there are nonexistent objects, and at the same time it would provide, in legitimizing model theory, forceful constructive lines of thought for the purpose of arguing for nonexistent objects. The rejection of language as the universal medium and the consequent model-theoretical treatment also thrust the second of my teasing questions to the forefront of our attention. If there is not one big predetermined domain of objects for our individual quantifiers to range over, we have to ask, with a new urgency, Where are the nonexistent individuals? It will not do just to argue that natural language quantifiers like "some" "every" and "no" occasionally range over nonexistent objects. One has to try to say what the particular domain is that they range over. This is illustrated by the strange fate of my favorite nonexistent individuals, everybody's lover and nobody's beloved. They are both conspicuously possible, even though the first one is perhaps unlikely to exist. They have a much better claim to subsistence than, e.g., Meinong's round squares. (If I change the example slightly, both characters can come even closer to existence, e.g., "the envier of everybody" and "the one envied by no one.") The only remarkable thing about them is that they are incompatible: the former must love the latter, but the latter cannot be loved by the former. And it will not do to deny that "everybody" and "nobody" in the characterizations of these two unforgettable characters range over existing individuals only. It is precisely to allow them to range also over nonexisting individuals that Parsons and his great predecessor Meinong marshalled their arguments. The general point illustrated by this story is that in the presence of relations and relational predicates, objectively understood, we are forced to give a specific, precise answer to my second initial question. If you start with nonexistent objects, you have to partition them into several sets of possible objects, which might as well be called possible worlds. If you ask, Where are the nonexistent objects? the answer is, Each one in its possible world. The only trouble with that notorious thicket, Meinong's jungle, is that it has not been zoned, plotted and divided into manageable lots, better known as possible worlds. Observations of the same sort as mine led Leibniz and before him

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Duns Scotus, to divide the ill-structured mass of nonexistent individuals into neatly compartmentalized possible worlds. To do anything else after the great Gottfried Wilhelm appears to me basically as very poor logical taste. Furthermore, other arguments can be given against pooling all nonexistent objects into one and the same big pool. For instance, I have recently argued in effect that the totality of all nonexistent individuals is an ill-formed totality. It has to be divided into smaller totalities in some way or other in any case. All this highlights further my second question: Where are the nonexistent objects? I am suggesting this answer: Each on its own possible world. In other words, each individual is located in some local possible world which it does not make sense to pool together. But doesn't this radically misrepresent the intentions of the defenders of nonexistent objects? Isn't their real point that there really are nonexistent objects in this world of ours, albeit some remote Platonic part of it? Of course they cannot all be there, according to what I have been arguing. But perhaps some of them are located in our world? It may seem that the possible-worlds treatment I favor is committed to a negative answer to this question. Isn't it the point of the whole exercise that nonexistent individuals are interpreted as merely possible individuals? Maybe it is, but the fact remains that when the possible-worlds approach is developed far enough, nonexistent individuals make their appearance once again in this real world of ours. How so? Let's begin at the beginning. I used to say (and to some extent still say) that possible-worlds semantics shows the triviality of questions of existence, including the question whether there are nonexistent objects. Bona fide individuals can exist in one world but fail to exist in another one. What more is there to be said of the matter except that the world in which one of them fails to exist may very well be the actual one? Existence is a much less important issue than the drawing of world lines, i.e., the notional lines which connect the embodiments of the same individual in different worlds and which help to constitute our concept of individual (very same individual). And the problem of world lines is a very real one indeed, for unless we believe in the extreme parochial theory of Leibniz and claim that no two individuals in different worlds are ever identical, it is clear that denizens of different worlds can be identical. Hence the question: When are they identical?

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All this is true, and has some bite. For one thing, it shows that Parsons's use of the viability of existential generalization as a criterion of ontological commitment is misguided. For existential generalization

can fail for reasons that have nothing to do with the failure of existence. Let me demonstrate this point by means of an example. From (1)

Queen Victoria knew that Lewis Carroll is Lewis Carroll

it cannot be inferred, even though Lewis Carroll existed and was known by the good Queen to do so, that (2)

(3x) Queen Victoria knew that Lewis Carroll is x;

or that for that matter, (3)

Someone is such that Queen Victoria knows that Lewis Carroll is him (or her).

Indeed, (2)-(3) obviously say the same as (4)

Queen Victoria knew who Lewis Carroll is,

which obviously is not entailed by (1). I cannot argue fully here for the equivalence of (2)-(3) and (4) even though I believe it is completely unassailable, nor do I have time to qualify it in certain requisite ways. The main point is nevertheless patent. The equivalence of (2)-(3) and (4) is completely independent of the question whether the quantifiers are construed as ranging over existing individuals only or whether they also take nonexisting ones as their values. The reason for this failure of existential generalization is not a failure of uniqueness: in different situations compatible with what the Queen, who had been amused by Alice in Wonderland, actually knew, the name Lewis Carroll applied to different persons. Hence there is no single one who could serve as the value of "x" in (2). Hence existential quantification does not apply to "Lewis Carroll" in (1), and yet it can be taken to commit its utterer to the existence of Lewis Carroll. In other words, Parsons's criterion fails. In spite of the failure of Parsons's test, there is more to be said here.

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My emphasis on cross-identification (the drawing of world lines) rather than existence leads to interesting conclusions when pushed to the bitter (or sweet) end. I said earlier that each nonexistent individual is located in its own possible world. We have already seen that this is an oversimplification. If I am not Leibniz, I have to consider my individuals as denizens of more than one possible world. This is what the Lewis Carroll examples were predicated on. (The reason why individuals can do this is that in different worlds one and the same individual can have different relations and hence be compatible with a different selection of other individuals.) Now how do we do this? How do we draw the imaginary world lines that connect the embodiments of one and the same individual in different worlds? All I have time to say here is: this is a highly nontrivial and complex task, so complex indeed that we may fail in it in many cases. It just is the case, I have argued at length elsewhere, that the principles that govern it fail in some cases. Sometimes we just cannot tell what the counterpart (to use David Lewis's term) to a given individual in one world would be in another. This natural observation enforces a surprising distinction. We have to distinguish from each other two kinds of failure of a world line. Case (1): Sometimes our criteria of cross-identification work and tell what a given individual, say i, would be like a given world w, while the application of those criteria to w leads to the conclusion that i does not exist in w. Case (2): However, world lines may fail in a more radical way. They may fail to tell us what i would be like in w to a degree that would not even enable us to decide in principle whether or not i exists in w. The former is a failure of existence; the second may be called failure of well-definedness. Now well-defined but nonexistent objects are in some natural sense in the world in question. They are the best rational reconstructions of nonexistent individuals which don't merely exist in some other possible world but which enjoy some reasonable status in our real one, viz., when w happens to be the actual world. Thus, possible-worlds semantics vindicates in the end merely possible individuals even as members (albeit by courtesy) of the actual world. An attempt to dispense with them is bound to misrepresent thoroughly the true semantical and logical situation. And hence I have to conclude that, even though I reject most of Parsons's argumentation, I find myself agreeing with most of his conclusions.

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NOTE

* This paper was originally written as a response to Terence Parsons's paper, 'Are There Nonexistent Objects?' which was presented at the American Philosophical Association, Pacific Division Meetings, in March 1982. Parsons's paper appeared in American Philosophical Quarterly 19 (\982), 365-371. Department of Philosophy The Florida State University Tallahassee, Florida 32306 U.S.A.

ON SENSE, REFERENCE, AND THE OBJECTS OF KNOWLEDGE The problems which are discussed by Frege in "On Sense and Reference" and to which he proposes a solution in that famous paper might seem to be of interest primarily to philosophers of language and to logicians. l It is not hard to see, however, that they are also of an intensive interest to epistemologists. They are highly relevant to a problem which has not (it seems to me) received its fair share of epistemologists' attention. This is the problem of the objects of knowledge. Moreover, both Frege's discussion and my criticism of it can be extended to other epistemologically important concepts, including belief, memory, and thinking. In general, epistemologists have been preoccupied far too much recently with the problems of evidence, justification, and certainty at the expense of what to my mind are more fundamental problems concerning the logical structure of knowledge and its objects. The way in which the problem of the objects of knowledge enters into Frege's discussion is well known. Frege is in effect asking what entities we have to assume in order to account for the logical behavior of our language in contexts in which someone's knowledge is being spoken of. This question is to all practical purposes the same as the question concerning the objects of knowledge. The fact that Frege is apparently dealing with questions of linguistic meaning only does not invalidate this point. As Husserl in effect did later, Fregean questions can be generalized beyond linguistic meaning so as to pertain to all mental acts and the entities involved in them. But in what sense are the objects involved (according to Frege or someone else) in our use of epistemic concepts really the objects of knowledge? Several comments are relevant here. First, what I am primarily interested in here are the entities (individuals) involved in epistemic contexts. It is only a secondary question for me how natural it is to label these entities "the objects of knowledge". Secondly, it can be shown that both the intensional entities Frege introduced and certain other, parallel entities other philosophers have postulated have in fact been cast into the role of the objects of certain propositional attitudel by some philosophers? The main purpose ofthis paper is to compare Frege's (partly implicit) theory of the objects of knowledge with the competing solution offered by so-called possible-worlds semantics and to argue for the superiority of the latter. I am taking the general nature of possible-worlds semantics as being familiar to my 4S

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readers. Suffice it to recall its basic idea. Applied to epistemic concepts, this idea is that in each application knowledge (information) amounts to the elimination of some of a number of objective "options" which we can think of as realistic scenarios concerning the part of reality we are speaking of. The more of those options someone (say b) can exclude, the more he or she can be said to know. These options or scenarios are what is called in philosophical discussion "possible worlds". This label is highly misleading, for it seems to presuppose that the set of options is given once and for all as it were globally. If so, each of the options will have to abe all-comprehensive, that is, to take in all possibilities past, present, and future. Then the options will look rather like those Leibnizian alternative world histories that are usually thought of when a philosopher speaks of "possible worlds'. This is not all what is intended here, however. All that is required to get my version of possible-worlds semantics off the ground is that in each application of the concept of knowledge the situation can be conceptually articulated as it were locally into excluded and admitted options. The admitted scenarios are assumed to be all the options which are compatible with what everything b knows. Then b knows that X if and only it is the case that X in each of the admitted scenarios. They will be called b's knowledge worlds, more fully epistemic b-altematives to the world we are considering. These scenarios need not be anything so grand as to merit the pretentious term "possible worlds". They can be simply the different things that might happen or obtain in some relatively small part of the world, e.g., in an experimental situation. 4 In such particular situations, it is usually clear what all the possibly relevant scenarios are. In contrast, there are excellent reasons for thinking that the set of aUlogically possible worlds (needed if the set of all alternatives is assumed to be given to us globally) is an illegitimate totality.5 With these provisos in mind, it is not hard to see how the logical problems Frege discusses pertain to the objects of knowledge. One's first uneducated impulse is to think that the objects of knowledge are the usual "furniture of the world", i.e., physical objects, persons, artifacts, etc. However, it is precisely this prejudice that Frege's problem is calculated to shatter. Essentially, Frege starts from the idea that language works completely referentially, i.e., that all our expressions do is to stand for or represent certain entities. These entities are usually the normal entities we prima facie like to think as being the objects of knowledge. If this referential picture were the right model of the functioning of our language, then the rule of inference known as the Substitutivity ofIdentity, in short SI, would be valid, i.e., would always lead from true premises to a true con-

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clusion. For what this inference rule says is that expressions referring to the same object are interchangeable, i.e., formally: (a = b) S(a)

hence: S(b) And clearly this rule would be valid if all that "a" and "b" did were to stand for their respective references. Yet this rule of inference fails in contexts involving such epistemic concepts as knowledge, belief, etc. Here is a simple example which nevertheless is not any more simple-minded than Frege's own, since it is only a variation of one of them: (1) (First premise)

morning star = evening star

(2) (Second premise)

Ramses knew that (morning star = morning star)

(3) (Putative conclusion) Ramses knew that (morning star = evening star) Thinking of Ramses as some sufficiently early Egyptian, we can here assume (1)-(2) to be true but (3) false. Hence SI fails. We shall consider two different ways of coping with this problem situation. (A) Frege's solution.

(i) Frege would obviously like to have the expressions of our language merely stand for their usual references. The failure of SI is interpreted by him to show that this is impossible. He introduces a special class of entities, called "senses", to do the extra work. (ii) Frege characterizes the "sense" of an expression e by saying that more is involved in it than merely the reference of e. The sense of e includes also the way this reference is given. We may perhaps think of such a sense as that objective element in our conception of the entity in question which enables us to refer to it (e.g., to think about that particular entity). It is the postulation of these extra intensional entities (senses) that has prompted many philosophers to criticize Frege and to reject his solution to the problem. (iii) The way senses perform the job they were introduced to perform is as follows: Frege distinguishes two different kinds of contexts. He has been fol-

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lowed here by virtually all philosophers in substance, but not terminologically. Frege calls the two kinds of contexts direct and indirect. A more common terminology is "extensional" and "intensional". Another pair of terms is (referentially) transparent and (referentially) opaque. Whatever the term, contexts governed by such verbs as "knows", "believes", etc. are paradigmatic instances of the latter kind of context. (Cf. (2) and (3) above.) Thus the general problem can be said to be to explain the failure of SI in intensional (opaque) contexts. According to Frege, in extensional (direct) contexts an expression e expresses its sense and refers to its reference. The sense is to "tool" by means of which the reference is captured. The picture is this: (4) expression

~

sense

~

reference

In extensional contexts, S is valid. (Impertinent query: what are senses needed for, anyway, in such contexts?) In intensional contexts (according to Frege) a curious switch takes place. The expression now refers to what is usually its sense. The picture is this:

~

(5) expression

(~)

sense

(~reference).

Thus, according to Frege, all our expressions are "systematically ambiguous": they literally mean (refer to) different things in direct (transparent) and indirect (opaque) contexts. (iv) Applied to our example, in (2) and (3) (but not in (I)!) the two expressions "morning star" and "evening star" do not refer to certain heavenly bodies, according to Frege. This is because they occur in an intensional context. In (2) - (3) these terms referto (what usually are) their sense. The reason (1) - (2) fail to entail (3) is then that while (1) guarantees the identity of the usual references of the expressions "morning star" and "evening star", the step from (2) to (3) now requires more: it requires the identity of the senses of the two expressions. (v) Notice that Frege's solution requires that senses be what he calls objects, that is, particular entities. For otherwise they could not function as the sometime references of our expressions, i.e., their references in intensional contexts. (vi) Frege does not discuss how the premises (1) - (2) could (should) be strengthened to vindicate the validity of the inference. Implicit in his discussion is an answer, however. In order to restore the inference, we need instead of (1) the identity of the senses of "morning star" and "evening star".

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But notice carefully that Frege never, never, never, reinterprets the identity (1) to mean this. He cannot do so, because in (1) the identity occurs in an extensional context. Hence Frege cannot be said to re-interpret our usual notion of identity in any way. It is not even clear that Frege can express the identity of senses by means of any explicit sentence. There is no sentence in his own formal language, as he develops it in Begriffschrift6 and Grundgesetze7 which would do this. Admittedly, he says in "Uber Sinn und Bedeutung" that we can refer to the senses of our expressions by prefacing them with "the sense of "; but he never uses this possibility systematically himself. There probably was a deeper reason for this silence. As van Heijenoort has shown, Frege did not believe that semantical relationships such as the identity of senses could in principle be expressed in language. Hence his treatment of SI in opaque contexts is doomed to remain incomplete at the very best. (vii) Since we are according to Frege dealing with senses (intensional objects) and not ordinary references in contexts governed by such verbs as "knows", "believes", "remembers", etc., these intensional objects must be considered as the proper objects of knowledge, belief, memory, etc. Even in transparent contexts, we have to reach fIrst the sense of an expression (or more generally of an act) and only then by its means the reference of the expression or act, assuming that senses can be considered as independently existing entities. Hence the senses are as it were the primary objects of our acts of knowledge, belief, memory, etc. (B) Possible-worlds solution. S (i) The basic idea of possible-worlds semantics is that the notions (e.g. knowledge, belief, perception, etc.) which create an in tensional (opaque) context are precisely those that force us to consider several options or "possible worlds", i.e., not just the actual one but a number of alternatives to it. In discussing what someone knows, these alternatives are all the worlds compatible with what he (she) knows. Thus in (2)-(3) they are all the "scenarios" compatible with what Ramses knew. The novelty is not that we have to consider new entities (intensional entities) besides references, but that we have to consider what our expressions refer to in several different "possible worlds" (i.e., in the different scenarios we have to heed). (ii) The failure of the inference from (1)-(2) to (3) is now explained by pointing out that on this scheme (1) means just that the two terms "morning star" and "evening star" pick out the same object (the same heavenly body, viz. the planet

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Venus) in the actual world. But since we are in (2)-(3)(see B(i) above) considering other possible worlds as well, we cannot interchange the two expressions, for in the other possible worlds they may pick out different entities (particulars, logicians' "individuals"). (iii) Indeed, this is precisely, what happens in my examples. The worlds considered there are Ramses' "knowledge worlds", i.e., all worlds compatible with everything he knew. Whatever Ramses knows is true in all of them, and vice versa. Since it assumed that Ramses did not that the morning star and the evening star are identical, in some of his knowledge worlds they are not. (iv) Notice how this treatment is a virtually inevitable consequence of the basic idea of analyzing knowledge in terms of excluded and admitted alternatives (options, or scenarios, misleadingly called "possible worlds"). (v) Note further that no entities of a new type are postulated in the possibleworlds solution to the problem of the failure of SI. No failure of referentiality or reference to strange new entities is needed. All we need is (cf.(iv)) a multiplicity of scenarios we have to consider. By way of a slogan, instead of a failure of referentiality we are dealing with multiple referentiality. (iv) In particular, the objects of knowledge,belief, etc. are on the possible worlds view our old friends, such a physical objects persons, artifacts, etc. No outlandish new entities have to be postulated to serve as objects of such "propositional attitudes".

(C) Comparisons. Certain further comparisons between Frege's account and the possible worlds account and certain further developments are relevant here. (i) On Frege's account, all expressions are systematically ambiguous; on the possible-worlds account, there is no such ambiguity. What changes from application to application is the set of possible worlds in which the reference of the expression is considered, i.e., the set of worlds alternative to the given one. But this set is determined in an orderly way by the person, occasion, and the modality (propositional attitude) we are dealing with. This is a ruIegoverned determination which we understand as soon as we understand the modality (intensional concept) in question. For instance, to know what John believes is to know which "possible worlds" are compatible with what he believes and which ones are not. (ii) Possible-worlds account suggests an answer to a question which seems to me admirably suited to clarify the situation further but which Frege does not raise. This is the question as to what further premise or assumption can serve to restore the validity of SI. Now we can see what the answer to this question

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is. This extra premise must obviously say that the two terms in question must pick out the same individual in each relevant worlds. Now what these relevant worlds are depends on the context in a way that requires an extensive discussion.9 Hence no general form of the "missing link" or the missing extra premise will be attempted here. However, in most cases the import of the extra premise is clear. For instance, in (1 )-(3) the relevant worlds are all of the know ledge worlds of Ramses. Hence the extra premise will say that the identity (1) holds, not just in the actual world, but in all of the Ramses' knowledge worlds. But requiring this amounts to Ramses' knowing the identity. Hence the missing premise is the purported conclusion (3) itself, which makes this particular application of the corrected SI trivial. In other examples it is not equally trivial. In other examples it is not equally trivial. For instance, from (6) Herzl knew that Loris was a great poet and (7) Loris=Hofmannstahl it follows that (8) Herzl knew that Hofmannstahl was a great poet only in conjunction with the strengthened form of premise (7),viz. (9) Herzl knew that (Loris=Hofmannstahl) (iii) This is obviously the right extra premise. In contrast, Frege's account is defective here. It requires for the substitutivity in our example (1)-(3) that "morning star" and "evening star" have the same sense, i.e., are synonyms. This is a sufficient but not a necessary condition for the substitutivity of identity. For instance, two names which are known by John to refer to the same individual are obviously intersubstitutible in contexts John's knowledge is concerned, even when the two names don't have the same sense. The same holds mutatis mutandis for other person and other propositional attitudes. This is not a merely cosmetic defect in Frege's theory, either. It vitiates in effect his avowed purpose of explaining why identities like (1) can be informative. Such an identity is of course informative for Ramses if and only if it is not already known to him. However, according to Frege, it should be informative as soon as its two

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sides don't have an identical sense. Hence there is obviously something wrong with his account. Our comparison thus supports strongly the possible-words theory. This theory yields the right prescription for the extra premise needed to vindicate SI (in a modified form) whenever such an explicit premise is available. (iv) The affmity between the two accounts (Frege's account and the possible-worlds account) may nevertheless be claimed to be greater than first appears. It may be suggested that a possible-worlds semanticist can reconstruct Frege's theory within his own, more comprehensive theory. In order to see this, recall Frege's explanation to the effect that the sense of an expression e includes the way in which the reference of this expression e is given. Now possible worlds semantics offers us an explication of this dark saying. For a logician, a "way of being given" possesses an obvious meaning. This "way" can be conceptualized as thefunction in the abstract mathematical sense in which any dependence and even co-variation can be expressed in the form of a function. The argument value (independent variable) of this function is the possible world w we are considering. The function value (dependent variable) is the reference of e in w. The function itself may be tentatively identified with the sense of e. It is sometimes called the meaning function associated with

e. 10

The idea on which this terminology is based is intuitive in its own right. To understand an expression, say, i.e., to grasp its meaning, can naturally be thought of as ability to pick up the reference of e in a variety of different circumstances. This is precisely the idea codified in the concept of meaning function. This idea also shows that there is a deep affinity between my version of the possible worlds account of meaning and the functionalist approach to semantics and the philosophy of mind. Notice how it is the basic idea of our "possible-worlds" analysis ofthe situations as involving several options or scenarios that opens the possibility of reconstructing Fregean sense as meaning functions. These options ("possible worlds") provided an argument range for meaning functions. But how faithful is this reconstruction? The following are some of the most salient comparisons: (a) If meaning functions behaved like Frege's "senses", it would be the identity of the meaning function associated with "morning star" and "evening star" that restores (used as an additional premise) SI in (1)-(3) above. However, it was seen that it is Ramses' knowledge of the identity (1) that is needed to vindicate this particular application of SI. Hence we have here a difference between Frege's approach and mine.

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(b) The difference is nevertheless somewhat smaller than may first appear. Ramses' knowledge of the identity (1) means that its two sides pick out the same entity (reference) in all of Ramses 'knowledge worlds. But this means that the meaning functions associated with "morning star" and "evening star" agree on these "possible worlds". In other words, it is the identity of meaning functions (my reconstruction ofFrege's "senses") as restricted to the relevant worlds that vindicates SI (when used as an additional premise). In our example, these worlds are Ramses' knowledge worlds. What they are in other cases requires a further inquiry. The ideas on which this inquiry will have to be based are implicit in what I have already said. (c) Hence the main difference between my approach and Frege's seems to be that I am examining the relevant problems locally whereas Frege is considering them globally .11 If Fregean senses are construed as meaning functions, they have to be thought of as being defined for all possible worlds as its arguments in one fell swoop. In contrast, in my approach, meaning functions have 10 be defined only for the options ("worlds") involved in each particular application of my approach taken one by one. This difference is not neutral here, however. Frege's treatment makes use of the set of all possible worlds. The reason it relies on this set is that Frege uses in effect the notion of the identity of senses. Interpreted as meaning functions, two senses are identical (in the usual mathematical sense) if and only if their function values agree/or all the relevant argument values. The set of such argument values thus has to be defined in order for this notion of identity 10 make sense. Now the notion of the setof all (logically) possible worlds is a highly dubious one. I have elsewhere discussed the very serious difficulties that beset this notion. 12 I expect them to turn out to be insoluble. Hence the "local" character of my theory (my version of possible worlds semantics) is a definite advantage. It enables usto dispense with the dubious totality of all possible world. It is richly ironic that possible-worlds semanticists have frequently been suspected of operating with illicit global entities. In reality it is Frege, not possible-worlds theorists of my ilk, who in effect rely on such suspect totalities as the set of all possible worlds. If anything, their being suspect is an argument for my approach, not against it. (d) The most important difference between Frege's "senses" and my meaning functions is also the most relevant one to our problem concerning the objects of knowledge (and of other propositional attitudes, such as belief, memory, etc.). Frege's "senses" can be thought of as the objects of such attitudes because they are particular entities in our actual worlds, albeit abstract ones. In contrast,

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meaning functions, unlike Fregean "senses", are literally neither here not there, that is to say, neither inhabitants of the actual world nor of anyone of its alternatives. They are functions which admit worlds as their arguments, and hence cannot be members of anyone world. In spite of considerable similarities between senses and meaning functions, the latter cannot be construed as objects of knowledge, belief, or any other propositional attitudes. To do so means committing an illicit reification of the several values of meaning functions into one entity which is then somehow placed inside the actual world. (e) One reason why Frege was led to the temptation of carrying out such a reification was that he was obviously considering (in so far as his thinking can be represented within my framework at all), not meaning functions as abstract set-theoretical entities (sets of pairs of correlated argument values and function values), but their opcrationalisations in the form of some "algorithm" or effective rule or "recipe" which can in principle be used to extract the function value from an argument value. This is in itself commendable. Meaning functions as abstract mathematical entities cannot be "real" meanings which anyone can actually grasp and contemplate. Indeed, possible worlds semantics must be developed further so as to be able to introduce such "real" meanings. However, this commendable quest of what in our days would be called psycholinguistic realism apparently led Frege to the temptation of reifying meaning functions into single entities. (v) In fact, the whole problem of the objects of knowledge and other propositional attitudes is brought to a focus much more sharply by another problem which Frege, unlike such latter-day logical saints as Quine, never considered. It is the failure of another logical inference rule called existential generalization (in short, EG) in epistemic and other intensional contexts. The rule authorizes us to move from a statement S(b) in terms of a singular term "b" to the corresponding existentially generalized statement (3 x) Sex), Le., to the statement that says that there is (that's what "( 3 x)" expresses) an individual (say x) of whom all those things are true that were said to be true of bin "S(b)".

Once again, if all that our expressions did would be to stand for their references, EG could obviously be valid. If something is true of any individual, is true of some individual; or so it seems. Yet it fails in epistemic contexts. Here is an example: (10) (premise)

George IV knew that (w =w)

(11) (putative conclusion) (3x) George IV knew that (w = x)

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where "w" is a shorthand for "the author of Waverley." The inference from (10) to (11) fails because (11) obviously has the force of (12) George IV knew who w is. This knowledge is clearly not implied by (10). What can be said of this new puzzle? Following up its implications will give us a fresh perspective on Frege's problems. The following remarks are in order here: (a) Frege could have used the failure of EG in opaque context as a concurrent general reason forintroducing intensional entities, in the same way he uses the failure of SI. For he could legitimately have concluded that ordinary objects, considered solely qua inhabitants of the actual world, are not all that is involved in opaque contexts, because if they were, EG would be valid. (b) Yet the specific solution Frege proposes is powerless in trying to deal with the failure EG. His general strategy was to argue that in opaque contexts we are dealing with our ideas of the usual references of our expressions, not with these references themselves. But if so, there is no hope for him to break down the step from (10) to (11). For if what we are dealing with in them are the good King's ideas, then surely the conclusion (11) ought to follow from (10). For then (11) would presumably say that there is a sense of an individual which George IV knew to be identical with the sense of "the author of Waverley". Hence Frege's strategy does not work; he cannot explain the failure of EG in the way he thought he could explain the failure of SI. (c) In contrast, the problem is solved at once by the possible-worlds theory. For from this vantage point the obvious reason why the inference from (10) to (11) fails (even assuming that the good King knew that w existed) is that the term "w" picks out different individuals from the different possible worlds we are considering. Then there is no one individual that could serve the role of x in (11), even if in each world the individual referred to by "w" there fills the bill. Hence the failure of EG is from the possible-worlds vantage point as fully predictable as that of SI. This is precisely what happen in our example. The reason why we cannot go from (10) to (11) is that the term "w" does not pick out the same individual in all the possible worlds compatible with what Gcorge IV knew, i.e., that George IV did not know who w is. But this is precisely the conclusion (11) to be inferred. Hence to infer (11) from (10) is literally to argue in circle. (d) This observation is worth spelling out more fully. Once again, possible worlds semantics shows what additional premise is that will serve to restore the

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inference. Suppose, for instance, that we are dealing with the purported inference from (13) George knows that Sew) to

(14) (3x) George knows that Sex) where Sew) does not contain any terms which would create opaque contexts. Here (14) obviously says that George knows who (say x) is such that Sex). According to the idea just employed, (13) is enough to guarantee the truth of (14) if and only if there is some (one and the same) individual who is picked out by "w" in all the relevant possible worlds, i.e. with whom w is identical in all of them. Intuitively speaking, we must have as the extra condition (15) (3x) in all the relevant possible worlds (w

=x).

This is not a well-formed expression in our notation. It can be converted into one, however, by noting what the relevant possible-worlds are. They are all the worlds compatible with what George knows. Hence, a proposition is true in all of them if and only if George knows it. Hence (15) is tantamount to (16) (3x) George knows that (w =x). This is, then, the requisite extra premise. It is very natural intuitively, too, for it says that George knows who w is.13 Clearly this is precisely the missing premise. For knowing that so-and-so did something does not help George to know who did it unless he knows who so-and-so is. Now we can see how neatly this intuitive idea is reflected by the possible-worlds treatment. In other examples, other collateral premises will be needed. In so far as they can be formulated explicitly, they can be found by means of a similar line of thought. The only difference between the different cases is that different classes of possible worlds are being considered in different contexts. Hence what we need for the purpose of locating all the different requisite extra premises is an analysis of how the class of relevant possible worlds is determined as members of which a given individual is considered in a given sentence. Such analysis can be carried out, but we shall not try to do so here. (e) Frege' s ideas cannot be defended here even to the limited extent to which they could be partially vindicated in terms of the possible-worlds analysis in

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the case of SI. (Cf. C (iv) above.) For no manipulation of our counterpart of Frege's idea of sense, viz. of the concept of meaning function, can be of help here. What is needed is something new over and above the idea of a meaning function, viz, the idea of a constant meaning function, i.e., a meaning function which picks out the same individual from all of the relevant possible worlds. And clearly this concept cannot be defined just by means of the set of meaning functions or their restrictions to some suitable limited range of arguments. It is thus not far-fetched to surmise that Frege might have been less happy with his theory as he in fact was if he had tested it by means of examples based on the failure ofEG and not only those based on the failure of SI. Be this as it may, it is clear that the failure of EG offers strong evidence in favor of the possible-worlds treatment as compared with Frege's theory. (f) The fact that the extra premise needed to restore EG is different from that needed to vindicate SI may be used to lay to rest the myth that the failure of referentiality in epistemic and other intensional contexts is somehow due to a mysterious property of these contexts called their referential opacity. If this were the explanation, i.e., if this term were taken seriously, one and the same extra assumption would presumably restore their referential transparency. This is not the case. We need different auxiliary premises to restore SI and to restore EG. (g) The possible-worlds treatment of the two problems offers an explanation of the difference. The treatment needed for SI presupposed only that we can compare the references of two different terms in each possible world for identity. In contrast, the treatment needed for the purposes of understanding the failure of EG presupposed that we can compare the references of one and the same term in different possible worlds for their identity. To do so presupposes that we have criteria of cross-world identity, i.e., that we can as it were draw "world lines" connecting the embodiments of one and the same individual in different possible worlds. I shall not discuss here the fascinating problems connected with cross-identification, beyond pointing out that it is the mistaken global viewpoint that has led most philosophers either to pernicious mystifications concerning the problem or else to refusal to take it seriously. In most local applications of my framework, it is clear not only how the world lines run but also how they are drawn. (h) Now it may seem that another line of defense is being built for Frege. For it now seems that we indeed have to reckon with objects of knowledge, belief, and other epistemic modalities different from a naive realist's objects of knowledge and belief, viz. different from ordinary physical objects, persons, artifacts, etc. For in some obvious sense it is the world lines that we quantify

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over in contexts involving propositional attitudes. This is seen especially clearly when we write out the explicit truth conditions for sentences containing whconstructions with "knows", "remembers", "perceives", etc. as the main verb. These truth conditions turn on world lines in the crucial case of quantified sentences. One does not have to accept Quine's dictum that "to be is to be value of a bound variable" to acknowledge that world lines are somehow the "real" objects of knowledge and other propositional attitudes. (i) Does this mean that the naive view of the objects of knowledge and other epistemic attitudes is mistaken and some modified Frege-type view correct? Indeed, don't world lines answer precisely to Frege's description of Sinne as involving both a reference and the way in which it is given? And are we not in reality dealing with these world lines and not with individual members of this or that particular world? The answer is that the contrast on which this last question is predicated is mistaken. This contrast is sometimes called an opposition of worldbound individuals vs. world lines as individuals. It is not the case that world lines do not fill the bill as objects of knowledge because they are "neither here not there", i.e., not members of anyone world. What we should do here is not to set up a contrast between worldbound individuals and world lines, but to recognize that world lines are an indispensable means of speaking and thinking of the usual perfectly ordinary-looking entities, the ordinary denizens of the actual world. What we must realize is that in order to consider them as poten tial members of other possible worlds (scenarios), as we have to do in epistemic contexts, we must have world lines at our disposal. But to use these world lines is not to reify them into independent entities. To employ them is nothing more than to consider our regular individuals qua characters in more than one scenario. What is overlooked in the fallacious contrast of worldbound individuals vs. world lines as individuals is that, without world lines, it does not even make sense to compare the inhabitants of different worlds for identify. Hence the very idea of "worldbound individuals" which are supposed to be prior to world lines and not "really" identical to any inhabitants of another world is intrinsically incoherent. It amounts to denying the possibility of trans world comparisons and in the same breath making such comparisons. Hence the fact that world lines are inevitably involved in all "quantifying in" does not mean that the objects of knowledge are in any philosophically relevant sense entities other than our ordinary physical objects, persons, artifacts, etc. Rather the appropriate conclusion is that in speaking and thinking about such ordinary entities much more is often involved than philosophers and logicians have suspected. One thing that is involved are precisely those criteria of cross world identity which are codified in our world lines. Quine has coined

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the slogan "no entity without identity". This slogan turns out to be eminently appropriate. It helps us to appreciate the involvement of world lines in our normal concept of an individual. For it is precisely world lines that define cross world identities. For this reason they are inextricably involved in our discourse about our old friends the ordinary individuals, as soon as several "worlds" (scenarios) are involved. Thus Frege was in one respect right, viz. in thinking that in in tensional contexts something more is involved over and above the entities we naively think of as objects of knowledge and belief, considered merely as members of one universe of discourse. This extra element which is involved here is the set of ways in which the several references are given to us, just as Frege suggested. These "ways of being given" are now codified in my "world lines". Where Frege went wrong was in reifying these "ways of being given" into entities existing in their own right in the actual world. The same mistake vitiates many recent discussions of Frege 's problems. For instance, consider the question that is addressed frequently to possible-worlds theorists: What is it that you are really quantifying over? What are your real individuals, worldbound entities or world lines? This question is based on the same reification of world lines into independent entities as we saw Frege committing. Hence it is out of order, and irrelevant as a basis for objections to the possible-worlds theory. NOTES 1 Frege, G.: 1892, 'Uber Sinn und Bedeutung', Zeitschriftfur Philosophie und philosophische Kritik 100, 25-50. In my paper, I shall not try to spell out in full detail how it is that the problems and solutions I am attributing to Frege are manifested in the letter of the Fregean texts. Rather, I am trying to show the tremendous relevance Frege's problems (and different solutions offered to them) possess for epistemology and not just for the philosophy of language. A belief in this relevance has been implicit in my work on epistcmic concepts for a long time. Its crystallization is due to Merrill B. Hintikka, who had independently (and almost certainly earlier) arrived at the same belief and also anticipated a larger number of specific points made in this paper than I probably am myself aware of. 2 By propositional attitudes, I mean (following Russell) whatever is meant by a personal verb which admits of a that-construction. 3 The most interesting possibility here is to interpret the reasons which a number of eminent philosophers (Moore, Russell, Ayer, etc.) have given for the in-

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troduction of sense-data as being basically analogous to Frege's argument from the intensionality of epistemic contexts to the need of special intensional entities, the senses. According to this interpretation, sense-datum philosophers argued from the intensionality of perceptual contexts to the need to postulate a special class of direct objects of perception, the sense-data. I have developed this line of interpretation elsewhere; see especially 'On the Logic of Perception', Models/or Modalities, D. Reidel, Dordrecht, 1969. It can be extended to include all Russell's objects of acquaintance; cf. my papers: 1975, 'Objects of Knowledge and Belief: Acquaintances or Public Figures', The Intentions o/Intentionality, D. Reide1, Dordrecht, and: 1974, 'Knowledge by Acquaintance-Individuation by Acquaintance,' Knowledge and the Known, D. Reidel, Dordrecht. I shall not expound this highly interesting line of thought here nor discuss the question as to what creates a special temptation to postulate unusual objects of direct perception. 4 In other words, the intended way of thinking about the applications of possible-worlds semantics is precisely the same as the way in which we think of the applications of probability calculus. In fact, possible-worlds semantics can almost be thought of as a qualitative counterpart to Kolmogorov's measuretheoretical treatment of probability. (It is qualitative in the sense that the different options ("possible worlds") or sets thereof are not assigned numerical measures.) Indeed, our possible words were nothing but the points of one's probability space (sample space). If we tried to apply the usual probability theory to the universe at large la Leibniz (or perhaps rather la Laplace), we would run into difficulties which are analogous with those that possible- worlds semantics has been blamed for. Yet no one takes those difficulties seriously as an objection to the general viability of probability calculus, certainly notat their face value. The critics of possible-worlds semantics are thus in effect committed to rejecting all our familiar probabilistic conceptualizations lock, stock, and barrel. 5 I have argued this point in: 1980, 'Standard vs. Nonstandard Models,' in E. Agazzi (ed.), Modern Logic, D. Reidel, Dordrecht, and: 1982, 'Is Alethic Modal Logic Possible?',Acta Philosophica Fennica, 35,89-105, reprinted in this volume. 6 Frege, G.: 1879, Begriffsschrift, L. Nebert, Halle. 7 Frege, G.: 1893, Grundgesetze der Arithmetik. Band I, Hermann Pohle, Jena. 8 I am not in this paper trying to distinguish my variant of possible-worlds approach from those favored by others, such as Montague, David Lewis, Dana Scott, Saul Kripke, Alvin Plantinga, and others, except by way of emphasizing the "local" character of its intended applications, which certainly goes against the views of several other philosophers. It is only fair to emphasize my indeb-

a

a

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tedness to the ideas of Richard Montague, however. For them, see R. Thomason (ed.): 1974, Formal Philosophy: Selected Papers of Richard Montague, Yale V.P., New Haven. 9 A brief discussion is offered in my monograph The Semantics of Questions. and the Questions of Semantics (Acta Philosophica Fennica. 28, No. 4), Societas Philosophica Fennica, Helsinki, 1976. 10 In more general terms, meanings (meaning entities) are construed as functions from possible worlds to extension (references) of the appropriate logical type. This idea was first developed systemically by Richard Montague; see note 8 above. 11 This global character of Frege's semantical and epistemological theorizing is one of its most striking features. Cf. here van Heijenoort, J.: 1967, 'Logic as Language and Logic as Calculus', Synthese 17, 324-330. 12 See note 5 above. 13 In general, we can in this way obtain a logical analysis of sentences of the form a knows + wh-construction (indirect question). This account can be generalized to other wh-constructions and used as a foundation of a theory of direct questions. For the latter, see op. cit., note 9 above.

IMPOSSIBLE POSSIBLE WORLDS VINDICATED It has often been claimed that the by now familiar possible-worlds analysis of propositional attitudes like knowledge and belief which I have advocated since 1962 is unrealistic/ if not downright mistaken, because it apparently commits us to the assumption of logical omniscience, that is, to the assumption that everyone knows all the logical consequences of what he knows, and analogously for all the other propositional attitudes. Since the assumption of such logical omniscience is obviously mistaken, this commitment seems to constitute a grave objection to the whole possible-worlds treatment of propositional attitudes. The main purpose of the present paper is to show that no commitment whatsoever to logical omniscience is incurred by the possible-worlds analysis of knowledge or of other propositional attitudes. First we nevertheless have to see precisely how the alleged commitment is supposed to come about. The possible-worlds analysis of knowledge can be formulated as follows: (I) A sentence of the form 'a knows that p' is true in a world W iff p is true in all the epistemic a-alternatives to W, i.e., in all the epistemically possible worlds which are compatible with everthing a knows in W. The failure of logical omniscience can be formulated as follows. (2) There are a, p, and q such that a knows that p, p logically implies q (i.e., (p::> q) is logically true), but a does not know that q. Here the notion of logical truth (validity), is to be analyzed in the usual model-theoretical fashion: (3) A sentence is logically true iff it is true in every logically possible world. The criticism mentioned in the beginning of this paper can be taken to be based on the imcompatibility of (l )--(3). However, they are not incompatible yet in the form just given to them. A contradiction between (I )-(3) is in the offing only in conjunction with the following further assumlJtion. (4) Every epistemically possible world is logically possible. (That is, every epistemic alternative to a given world W is logically possible.)

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A contradiction between (1)-(4) now comes about as follows. Assume that there are (say, in the actual world) a, p, and q as in (2). Then in virtue of (I) a's not knowing that q means that there is an epistemically possible world, more specifically, an epistemic a-alternative to the actual world, say W', in which q is false. Likewise, a's knowing that p means that in p is true in each such alternative world. In particular, p is therefore true in W'. According to (4), these epistemic alternatives are also logically possible worlds. In particular, ut is a logically possible world. Now according to (3) the assumption that (p ::J q) is logically true means that q is true in each logically possible world in which p is true. Since W' is a case in point, q must be true in q. But q was already found to be false in W', whence the contradiction. To this contradiction between (1)-(4) philosophers have in effect reacted in different ways. For instance, the positivistic doctrine of the noninformative (tautological) character of logical truths can be understood so as to imply the denial of (2). Since a already knows that p and since the logical implication from p to q cannot (in view of the tautologicity of logical truth) contribute any objectively new information to what he knows, he in reality knows whatever there is objectively speaking to be known about q. This line of thought has meanwhile been discredited rather thoroughly.2 However, that still leaves several different prima facie options open. The criticisms I have referred to amount to blaming the contradiction on the possible worlds analysis of knowledge (I). What has not been pointed out in the literature, however, is that the source of trouble is obviously the last assumption (4) which is usually made tacitly, maybe even unwittingly. It is what prejudges the case in favor of logical omniscence and hence leads into a con flict with the denial (2) of such omniscience. The reason for my saying this ought to be clear. According to the intended interpretation of the epistemic a-alternatives to W they are all the contingencies which are left open by whatever a knows in W. Some of these contingencies can of course be merely apparent ones which a has to be prepared for solely because of the limitations of his powers of logical and conceptual insight. To req uire, as (4) does, that these include only situations ('worlds') which are objectively (logically) possible therefore prejudges the case in favor of logical omniscience. It presupposes that a can eliminate all the merely apparent possibilities. This is blatantly circular, however. Just because people (like our friend a) may fail to follow the logical consequences of what they know ad infinitum, they may have to keep a logical eye on options which only look possible but which contain hidden contradictions.

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Hence the real culprit here is (4), not (2) or (I). The way to solve the problem of logical omniscience is hence to give up the assumption (4). This means admitting 'impossible possible worlds', that is, worlds which look possible and hence must be admissible as epistemic alternatives but which none the less are not logically possible. Admitting them solves our problem for good. For then we can have (1)(3) all true together. The option - q left open by a's knowledge can be realized in some epistemic alternative U while (p :J q) is happily true in every logically possible world, as long as the epistemic alternative U is not among these logically possible worlds. The difficulty now is to give a reasonable account of these strange worlds that are epistemically but not logically possible. How can we accomplish that neat trick? It is not difficult (I have argued on several earlier occasions) to give an interesting syntactical account of what the descriptions of 'impossible possible worlds' (logically impossible but epistemically possible worlds) might look Iike. 3 However, at first sight it might seem not only very hard but completely impossible to make honest model-theoretic (semantical) sense of 'impossible possible worlds'. This task is apparently made all the more difficult by the restricted range of options that are at all natural here. Attempts have in fact been made to construct a model theory of impossible worlds by adopting some sort nonstandard interpretation of logical constants. 4 However, this course is very dubious. The very problem was created by people's failure to perceive the logical consequences of what they know far enough. Of course these logical consequences must be based on the classical (standard) interpr-::tation of connectives and quantifiers. Thus an attempted nonstandard interpretation is either bound to be beside the point or else to destroy the problem instead of solving it. But if we cannot change the interpretation of logical constants, what else can we do here? Precious little, it might seem. My 'surface models' were intended to supply a model theory for the breakdown of 'logical omniscience' (i.e., for a concept of knowledge satisfying (2)). 5 However, in the form in which the theory of surface models was first formulated, they do not look like real honest-to-god models at all. Fortunately, the twist Veikko Rantala has recently given to the theory of surface models (following a hint dropped in my original paper on surface models) provides a new strikingly realistic type on nonclassical models for

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first-order sentences. In his theory, the 'impossible possible worlds' are not in the least impossible. They are merely changing worlds. Or, more accurately speaking, they are invidiously changing worlds: they are models whose domain may change as we investigate it. The basic idea is, as Rantala points out, precisely the same as that underlying the use of urns (boxes) with a changing population of balls occasionally considered in probability theory. The point is not just that the composition of the box may change, but that it changes between one's successive draw of balls from the urn. Rantala accordingly uses the apt term "urn model" for these new models for firstorder sentences. They satisfy both our main desiderata. The interpretation of propositional connectives is precisely the usual one, and in a sense also quantifiers behave in their wonted way. Nevertheless, even some logically false sentences can be true in urn models. A brief introduction to the theory of urn models is given in Veikko Rantala's paper, 'Urn Models: A New Kind of Nonstandard Model for FirstOrder Logic.'6 In its general form, the concept of an urn model is nevertheless too broad for my purposes here. In order to see this, and to see how the idea of urn model can be specified so as to be relevant to our present needs, let us recall the basic idea of epistemically but not logically possible worlds: they were worlds so subtly inconsistent that the inconsistency could not be expected to be known (perceived) by an everyday logician, however competent. This idea has an obvious realization in the realm of urn models. Ordinary models ('logically possible worlds') can be thought of as a subset of the class of all urn models. They are simply the invariant urn models ('invariant worlds'). In order to be 'epistemically possible', an urn model must vary so imperceptibly as to be indistinguishable from an invariant model at a certain fixed level of logical acumen. This prompts the more general question as to what one can in principle observe about a world - whether changing or invariant - one is living in. It is here that the ideas of constituent and of surface model come to their own. In so far as the different individuals of an urn model are distinguishable from each other only by their properties and by their relations to the other members of the domain of the urn model (as I shall assume in this paper), the different possible complexes of experience one can have by observing at most d individuals together are represented by the different constituents of

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depth d. This is the intuitive epistemological counterpart to the deductive role of constituents as the logically strongest propositions of depth d. What constituents are like is sketched in Rantala's paper and described in some detail in my earlier publications. 7 Very roughly speaking, a constituent C~d) of depth d is a finite set of finite trees (in the precise mathematical sense of the word), each with a unique lowest element (node), and each of length d. (It is to be observed, and kept in mind, that when constituents are spoken of as trees, much of the customary imagery which is associated with them has to be reversed, with consequent awkwardness of the earlier terminology. For instance, what I have earlier called the depth of a constituent and what was just referred to as its length would now be called more naturally its height.) Each node (element) of each tree comes with a specification as to how an individual connected with it is to be related to individuals corresponding to the nodes lower down in the same branch (and how an individual corresponding to it is related to itself). The successive nodes of each branch describe, in that order, a sequence of d individuals that one can draw from a model M in which C~d) is true, and conversely each such sequence will have to be described by some branch or other. At each node no, the top segments (above no) of all the branches passing through no describe all the different continuations of the sequence of individuals one has had to draw from the model to climb up to no. (This is the common lower segment of all these branches.) The model I am speaking of here can be either an urn model or an ordinary (invariant) model. My ill-named surface models (generalized so as to omit the repetition requirement and the truncation requirements) are simply model-theoretical counterparts to constituents. They constitute the finest partition of different kinds of urn models one can observationally distinguish from one another without considering sequences of individuals longer than d. Now how can we test whether a constituent as I ha'/e described it represents draws from an invariant model or a changing one? Metaphorically speaking: How can one tell whether one is living in an 'invariant' world or a 'changing' one? In either case, all that one can observe are the different ramified sequences of different kinds of 'balls' (individuals) one can 'draw' from the 'urn' (world). If so, surely the hallmark of an invariant world can be that the supply of different kinds of individuals one can obtain in any one draw must be the same. Saying this presupposes of course that the

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draws are draws with replacement. Otherwise a small exception will have to be made for the individuals already drawn. They are no longer available, although some of them were available at earlier draws. Conversely, if the supply of individuals that confronts us at the different draws is the same, as far as we can tell on the kind of observable evidence we have available, then surely we are dealing with an urn (a world) which is either invariant or else varies so imperceptibly as to be indistinguishable from an invariant one. Let us restrict our attention to evidence that can be derived from the observation of sequence of individuals of length d at most. This means restricting our attention to evidence codified by constituents of depth d, i.e., to those bodies of evidence which are the corresponding surface models. In the tree that such a constituent is, the different kinds of individuals available to us after a sequence of draws of individuals a I , a2 , . _. , ak (which takes us to a given node no, corresponding to the individual ak) are represented by the nodes covering no (i.e., immediately above no). Likewise, the different choices available to us when we chose ak are represented by the nodes covering the node n I immediately below no. The requirement that the two sets of individuals must be identical now implies that the part of the tree above no (skipping no itself) must be the same as the part above n 1. (The identity refers also to the relations of corresponding nodes to nodes below nd These two parts cannot be quite the same, however, for their heights are different. Hence what can be required here is that the part above no is the same (in the sense explained) as the part above n I after the last (highest) layer of nodes in it has been omitted. However, this is precisely the truncation requirement imposed on my surface models. 9 If we practice draws with replacement, there must also be immediately above no a node n~ related to every node in the same way as any given node n, below no somewhere in the same branch. (For the replacement implies that each of the individuals drawn earlier must again be available when we have reached ak.) This, however, is precisely the repetition requirement I have imposed on surface models. lo By examining the joint consequences of the repetition requirement and of the truncation requirement we can see that they pretty much exhaust the consequences of the idea that the supply of individuals must be the same at each draw, as far as evidence codifiable by constituents of depth d is concerned.

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But the truncation requirement and the repetition requirement characterize prccisely those constituents which are not trivially inconsistent. Hence we obtain a characterization of those urn models which are invariant or vary so subtly as to be indistinguishable from invariant ones on the levcl of evidcnce codifiable by constituents of depth d: they are the urn modcls which satisfy some constituent of depth d which is not trivially inconsistent. Such urn models will be called d-invariant. Urn models which are d-invariant but not invariant simpliciter will play the role of the epistemically possible but not logically possible worlds whose desirability was motivated in the beginning of my paper. It is a truly remarkable fact that many urn models are d-invariant without being really invariant. That is to say, they satisfy the requirement that draws from the 'urn' always seem to be made from the same supply of individuals as far as we can tell on the basis of evidcncc codifiable by constituents of depth d, and yet fail to be true in any invariant urn model. Hence therc in fact are plenty of urn models available for the rolc to which I have cast epistemically but not logically possibly worlds. My definition of such worlds seems to have the awkward consequence of making my epistemically but not logically possible worlds rclative to the parameter d. However, this relativity is neither unexpected nor difficult to overcome. The worlds in question were calculated to be the ones which a certain person a envisages as bcing compatible with cverything he knows. Their totality depends naturally on his acumen - and on the level of analysis he is practicing. The more insight he gains, the more merely apparently possible 'worlds he can eliminate. This is accurately reflected by the fact that a dinvariant world need not be a (d + I)-invariant world, even though the converse relation does hold. More generally speaking, we can see that to identify cpistemically possible worlds with d-invariant ones amounts to measuring peoplc's logical insight in a way which is as uniform as it is intuitive. We have seen that an urn model is not d-invariant if its variability is betrayed by a review of all the sequences of draws of d successive individuals from the domain of the model. Translated into the language of epistemically possible worlds this says that a world is not epistemicaIIy possible at the d: th level of analysis if its impossibility can be scen by considering successive draws on no more than d individuals from the domain of the world in question. It is obvious that even though this is not the only possible way of gauging people's logical acumen,

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it is an eminently natural one. One aspect of its naturalness is its modeltheoretic import. Unlike many other indices of the difficulty of a logical problem (such as the length of proofs), mine does not depend on any particular axiomatization of first-order logic. Other reasons for the general theoretical interest of just this measure are indicated in earlier papers and books of mine. The parameter d is not so difficult to get rid of, either, for many relevant purposes. We started out by considering a failure on the part of a to be aware of the logical consequences of some particular proposition p he was assumed to know. Now p comes to us with a definite level of analysis already associated with it. For it has itself a fixed depth d, i.e., a fixed number of layers of quantifiers at its deepest. In other w,?rds, in p we are considering at most d successive draws of individuals from the model which is supposed to make p true or false. Hence the question as to whether a person a who knows that p has to know also a certain logical consequence q of p is naturally discussed by reference to d-invariant urn models, that is, by reference to sequences of at most d draws of individuals from the domain. This many draws he will have to consider in spelling out to himself what p means, whereas there is no logically binding reason why he should consider sequences of draws of any greater length. Sometimes it is natural to consider the question of logical omniscience as it were also from the receiving end, that is to say, from the vantage point of the consequence q and not only the premise p. In other words, sometimes we may want to require that a understands not only p but also q in answering the question whether he knows that q. Then the relevant worlds are the urn models invariant at the depth of (p J q), i.e., at the depth max [depth(p), depth(q)]. On this suggestion, the model-theoretically motivated solution of the problem of logical omniscience coincides precisely with the syntactically motivated solution I have argued for earlier. For according to the latter, a logical implication from p to q supports an inference from

a knows that p to

a knows that q only if (p J q) is what I have called a surface tautology. What this means is that all the constituents in the normal form of p but not in the normal form of q at the depth of (p J q) are trivially inconsistent at this depth. But this

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readily seen to be tantamount to the requirement that (p :J q) be true in all the urn models invariant at its own depth. Hence the semantical solution of the problem of logical omniscience obtained here coincides with the syntactical (proof-theoretical) solution examined in my earlier work. We might summarize the main arguments of this paper as follows. (l) The only reasonable way of solving the problem oflogical omniscience is to countenance worlds that are epistemically possible but not logically possible. (2) Such worlds may be identified with those urn models which vary so subtly as to be indistinguishable from invariant ones at a certain level of analysis. (3) These worlds are described by inconsistent but not trivially inconsistent constituents. (4) Hence my earlier syntactical solution to the problem of logical unmiscience receives an honest semantical (model-theoretical) backing, for the upshot of (l )-(3) is that only surface tautologies must be known by everybody, which is just what the syntactical solution says. In (4), 'everbody' of course means 'everbody who understands the propositions in question'. Urn models and d-invariant urn models offer interesting possibilities for model-theoretical (semantical) reconstructions of a large number of other ideas, including those of proposition and meaning. However, in this paper I shall stick to the the problem of logical omniscience.

Academy of Finland and Stanford University NOTES 1 For the analysis, see Knowledge and Belief (Cornell U.P., Ithaca, N.Y., 1962); Models for Modalities (D. Rcidel, Dordrecht, 1969); The IlItelltiolls oflmentionality and Other New Models for Modalities (D. Reidel, Dordrecht, 1975). 2 Cr. my book, Logic. Language-Games, and Information (Clarendon Press, Oxford, 1973). 3 See e.g., 'Surface Information and Depth Information', in laakko lIintikka and Patrick Suppes (eds.), Information and Inference (D. Reidel, Dordrecht, 1970), pp. 263-297; 'Knowledge, Belief, and Logical Consequence', Ajatus 32 (1970) 32-47; and Logic, Language-Games. and Information (note 2 above), especially chapters 7-8 ann 10). 4 For instance, MJ. Cresswell works with a modified truth-definition for negation in his papers 'Classical In tensional Logics', Theoria 36 (1970) 347-372, and 'Intensional

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Logics and Logical Truth', Journal of Philosophical Logic 1 (1972) 2-15. See 'Surface Semantics: Definition and Its Motivation', in Hughes Leblanc (ed.), Truth. Syntax. and Modality (North-Holland, Amsterdam, 1973), pp. 128-147. 6 See above pp.45S-474. 7 See especially the last chapter of my book, Lo~ic. Language·Games. and Information (note 2 above). CL also 'Surface Information and Depth Information' (note 3 above). 8 See 'Surface Semantics' (note 5 above), pp. 134-136. 9 'Surface Semantics' (note 5 above), pp. 135-136. 10 Ibid., p. 136. 5

Jaakko Hintikka and Merrill B. Hintikka TOWARDS A GENERAL THEORY OF INDIVIDUATION AND IDENTIFICATION

1. TIIE IMPORTANCE OF POSSIBLE WORLDS The most important recent development that falls within the scope of this meeting, "Language and Ontology", is the somewhat amorphous body of ideas, conceptualizations, and results which is best known as possible- worlds semantics. 1 Its eminence is well founded. We consider it as self-evident as anything in philosophy that one cannot do justice to actual human experience without a conceptual system that includes possibilia. It does not suffice to speak of different objects, different properties, different relations, etc.; at some point we also have to speak of different things that can happen or could have happened. To put the same point in more vivid terms, our life is intrinsically and inevitably acted against a backdrop of unrealized possibilities. Jaakko Hintikka has articulated this idea by connecting the use of unrealized possibilia with the concept of intentionality in which several philosophers, notably Husserl, have seen the gist of human thinking, and outlined a theory of intentionality based on this relationship? The need of considering unactualized possibilia means that our logic must be such that in it we can handle different and incompatible entities of the same logical type as facts: possible states of affairs and possible courses of events. And the model theory of these counterfactual entities is (in its basic aspects) precisely what is known as possible-worlds semantics. This theory therefore ought to be an absolutely vital part of every philosopher's repertoire. Its power is shown in a dramatic way by the way it can be used to solve the basic problems concerning nonextensional contexts which Frege thrust to the center of attention of logicians, philosophers of language, and ontologists? These problems have paradigmatic manifestations in the failure of the plausible-looking logical principles of the substitutivity of identity and of existential generalization in intensional contexts. The suspicions of possible-worlds semantics which are still frequently voiced in the literature are not only unfounded; they amount to a monumental refusal to follow some of the most promising insights of contemporary philosophy. 73

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2. SOME MAIN PROBLEMS OF POSSIBLE-WORLDS THEORY This does not mean, however, that a philosopher cannot entertain well-founded reservations vis-a-vis possible-worlds semantics. Indeed, possible-worlds semantics is certainly not the last word on the subjects with which it deals. On the contrary, it quickly leads in almost every direction to further problems which are deep, important, and far from easy to solve. It would be a serious mistake, however, to take these problems to constitute an objection to the basic ideas of possible-worlds semantics. On the contrary, we consider it a tremendous advantage of possible-worlds semantics that it leads one to raise these profound and profoundly significant problems and to formulate them with a clarity which typically promises further insights into them and in some cases even definitive solutions. We see one of the major merits of possible-worlds semantics in the fact that it has prompted these problems. Possible-worlds semantics has said the last word on a number of limited issues. This is not its claim to importance, which rather lies in the fact that possible-worlds semantics has said the first serious word on a large number of deep problems. This paper can be seen as a case study, illustrating the general diagnosis just proposed. The one particular problem we shall mainly discuss is that of crossidentification. In spite of its apparent narrowness, it soon leads to some of the most central issues in contemporary philosophy, including philosophy of language, metaphysics, and philosophy of science. It also overlaps with two other general problems which arise naturally within possible-worlds semantics. They are the problem of basic semantical relationships, mentioned as problem (iv) below, and the interrelations of individuation and identification, mentioned as problem (v) below. In order to put our enterprise into a perspective, it may nevertheless be in order to illustrate the general diagnosis we have offered by means of examples of parallel problems. (i) Even though the basic ideas of possible-worlds semantics appear unproblematic, they lead to serious problems as soon as one tries to absolutize them in the sense of considering complete possible worlds and complete sets of possibilia. 4 This second attempt turns out to be especially dubious for sharply defined concurrent logical reasons. The idea of a fixed set of possible worlds, so dear to Leibniz, who even conceived of God as choosing between the members of such a "logical space" of all possible worlds, is hence extremely dubious, well-nigh incoherent. Other problems arise if we try to think of different alternatives which have to be considered together in possible-worlds semantics as entire (complete) worlds. Rather, most of the intended applications are to what might be called scenarios rather than to entire world histories. Hence the cus-

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tomary label "possible-worlds semantics", originally inspired by Leibniz, has proved seriously misleading. Perhaps we should rather speak of possibiliasemantics or the semantics of alternative scenarios, or even to steal back a term and to speak of "situation semantics".5 One possible cure lies in limiting the class of possible worlds to those which are accessible to our conceptualizations and knowledge-seeking activities. Such a "transcendental" limitation on the class of possible worlds would parallel in an interesting way Kant's program in his Transzendentalphilosophie, but this modem counterpart to the Kantian program has scarcely been formulated, let alone carried out. (ii) One of the stock objections to a possible-worlds analysis of such intensional (and intentional) notions as knowledge, belief, memory, and indeed all the other propositional attitudes is that it seems to give rise inevitably to the problem of "logical omniscience": each person is asserted to know all the logical consequences of what he or she knows, to believe all the consequences of what he or she believes, etc., and even to know that his or her neighbors know all the consequences of what they know. A possible cure has been suggested by Jaakko Hintikka, first along ~roof­ theoreticallines6 and later--using Rantala's seminal concept of urn model -also along semantical (model-theoretical) lines. 8 This solution, as well the problem to which it is a solution, turns out to have an intimate connection to several central classical problems and doctrines in the history of philosophy, mostly in the philosophy of logic, mathematics, and psychology. They include, prominently, Kant's views on mathematics, space, time, and the analytic-synthetic distinction,9 Aristotle's logic and his theory of action, 10 and Peirce's "first real discovery" .11 (iii) On the basis of possible-worlds semantics, one can build a genuine semantical theory of questions and answers.12 However, particularly in its applications to natural languages, this theory turns out to be handicapped by certain hidden limitations. The most important limitation turns out to be the assumption of compositionality which is often ascribed to Frege and which says that the meaning of a complex expression is a function of the meanings of its constituent parts. 13 In spite of being a cornerstone of much of twentieth-century logical and linguistic theory, this assumption is arguably inadequate to handle the semantics of natural languages. (An argument has in fact been produced by Jaakko Hintikka. 1') This motivates a critical look at the foundations of most of twentieth-century thinking on the logical analysis of language.

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(iv) Perhaps the most general new (new in this context) problem is the question of the basic representative relations between language and the world. Logicians are wont to assume one such set of basic referential relations as being given at anyone time, and study what happens to the references of complex expressions on the basis of these fundamental relations of reference. A case in point is the logic and ontology ofWittgenstein's Tractatus, where the basis of language is a given fixed set of name-object relations. IS The other two leading ideas of Trac tatus, the so-called picture theory of language and the theory of truth-functions, can be viewed as efforts to spell out how the meaning of atomic propositions (picture theory) and complex propositions (truth-function theory) is determined on the basis of those name-object relations. 16 In a relativized form we find the same situation in Tarski-type theories of truth, which all operate in terms of unanal yzed "valuations" or" assignments" .17 They are not related to each other in any significant way or analyzed so as to enable us to see what they consist in. Basically, all that happens in logical semantics is an examination of how the references (including truth-values) of complex expressions are determined on the basis of such primitive valuations. In possible-worlds semantics, we have to consider the references of our expressions in more than one "world". As a consequence, if we merely followed the received research program of logicians and logical semanticists, we would have to take much more for granted than we do in extensional languages. It would not suffice to specify the references of all our expressions in the actual world, i.e., to assume one valuation function which assigns a reference to each basic symbol. Instead, we would have to assume, for each primitive expression of our language, a (partial) function ("meaning function") which specifies its reference (if any) in the different relevant scenarios ("worlds"). Forinstance, what was a name, with a single individual as its reference, now has as its meaning (reference) a function ("individuating function") which for each given world defines the embodiment of the particular individual in question in that given world. 1S (A way of visualizing such a function is in th the form of an imaginary "world line" which connects those several embodiments of the same individual with each other.) The totality of such world lines defines what counts as a method of identification for individuals. If we do this, it will indeed be possible to extend a Tarski-type approach to possible-worlds semantics. Indeed, Montague semantics is but this observation writ large. 19 However. it becomes more and more unsatisfactory to leave this whole complex network of basic meaning functions. world lines, etc. totally unanalyzed.

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Worse still, as some critics of possible-worlds semantics have not been slow to point out, the way in which we have to draw the world lines is more strongIy dependent of the context of use and other ~ragmatic factors than most of the other aspects of natural-language semantics. This is in reality no ground for criticism, however, only an indication of the necessity to supplement presentday formulations of possible-world semantics by a theory of how world lines are to be drawn -- and how the other types of meaning functions are actually chosen in our own conceptual system. The context-dependence of these choices shows that other factors are at work here than were considered in traditionallogical semantics.21 Once again, the new problems into which possible-worlds semantics leads us are highly interesting. On the one hand, the specific differences between different ways of drawing world lines (identifying individuals) are often highly interesting. The differences are sometimes of a conceptual nature, as in Jaakko Hintikka's distinction between identification by acquaintance and identification by description?2 Sometimes they are connected with problems in the philosophy, and even the substantive theory, of various disciplines. For instance, the differences between different conceptions of the self can often be interpreted as being differences between different methods of identification?3 On the other hand, the study of identification opens the door for understanding ideas and theories which have not been connected with the theories in logical semantics. Later in this work, we shall try to indicate one important connection of this kind. In spite of this potential value of an inquiry into the principles of human identification procedures, logicians tend to brush them under the rug. For instance, Kripke has recently claimed that the concept of a permanent (enduring) material object must be taken for granted and not analyzed in some more basic terms?4 We shall later in this paper show that this claim is not well founded. Maybe the criteria of identification must be taken for granted if one is only interested in doing traditional logic and logical semantics. However, this does not mean that the problem of identification does not present a most important challenge to philosophers. This is one of the challenges to which we are trying to rise in this paper. (v) This challenge is connected with another item of unfinished business. We have been speaking of the problems of identification. They comprise both the problem of cross-identification (identification of the inhabitants of different "worlds") and the problem of re-identification (identification of entities at different times of the same temporal course of events). It is not hard to believe,

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even apart from Jaakko Hintikka's specific arguments,25 that the two problems are interrelated. In both problems, a sweeping assumption is being made, an assumption which possible-worlds semantics helps us to uncover and to question. In both cases, it is assumed that the structures whose members are being compared with each other for identity--in the one case, possible worlds, in the other, different temporal cross-sections of one world history--have as it were already been articulated into individuals, their properties and interrelations, etc. Such a categorial structuring is what is meant by the individuation of the ingredients of the "world" in question. The problem here is not just that this presupposition of the enterprise of identification has not been spelled out. There is no reason to think that identification can be understood in isolation from individuation, and some prima facie reasons to think that they are not independent. Hence even those happy few philosophers who have as a matter of fact discussed the problems of identification have missed a piece of their puzzle. A modest attempt to correct this state of affairs will be made later in this paper. 3. 1HE PROBLEM OF CROSS-IDENTIFICATION The problem which we shall use as one guideline in this paper is precisely the problem of cross-identification. Perhaps the simplest (and at the same time highly important) context in which it comes up is the possible-worlds explanation why existential generalization (EG) fails in intensional contests?6 Formulated in abstract terms, EG seems unproblematically valid. If something, say A[b] is true fo a suitably specified individual, say of b, then surely we can infer that the same thing is true of some individual or other, i.e., infer (3x)A[x]. Looked upon in the light of an example, however, EG appears trivially invalid. From (1) Victoria knows that her favorite book is written by Lewis Carroll (where "Lewis Carroll" plays the role of the "b" of the abstract formulation) we obviously cannot infer

(2) (3.x) Victoria knows that her favorite book is written by x. Indeed, (2) obviously says the same as (3) Victoria knows who her favorite book is written by,

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which makes it completely clear that (2)(=3) does not follow from (1).17 The possible-worlds explanation ofthe failure ofEG is that the term "b" may pick out different individuals in different worlds we are considering in intensional contexts. If so, there is no single individual whose existence can be asserted in the way this is done in the alleged conclusion (:3x)A[x]. This is precisely what happens in (1)-(2). For there the worlds involved are Victoria's knowledge worlds (worlds compatible with everything she knows). But if so, the nom de plume "Lewis Carroll" picks out different individuals in some of Victoria's knowledge worlds unless she knows who Lewis Carroll is. If she does, the truth of (2) does follow from that of (1). If she does not, as is eminently possible, the conclusion does not follow .. The one aspect of this elegant and powerful explanation which interests us here is that in it an appeal was made to the notion of identity and non-identity of individuals in different worlds. In brief, one of the basic moves of possibleworlds semantics--the explanation of the failure of EG--thus presupposes the possibility of cross-identification. If possible worlds semantics is on the right track, we do in our conceptual system somehow manage to cross-identify. One way of seeing this is to note the equivalence of (2) and (3). By the same token, the simpler sentence (4) (3x) Victoria knows that Lewis Carroll is x

which says model-theoretically precisely that "Lewis Carroll" picks out one and the same individual x in all of Victoria's knowledge-worlds, is synonymous with (5) Victoria knows who Lewis Carroll is. It is thus seen that propositions of the b knows + a subordinate wh-question have objectively defined truth-conditions (objectively defined meaning) precisely to the same extent that we can cross-identify.18 Even though the fonner objectivity is prima facie not beyond question--as Quine has aptly brought out29 we are in any case dealing with down-to-earth questions of meaning here?O Closer examination will convincingly show, we believe, that people do follow objective principles of cross-identification, even though their choices between different methods of identification are more heavily dependent on pragmatic factors than the rest of their semantics. Assuming, then, at least for the sake of argument, that we competent speakers of English can cross-identify, how do we manage to do so? This is

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one of the places where the too grandiose connotations of the term "possible world" seem to have misled some philosophers.31 They have thought ofpossible worlds as entire universes, each self-sufficient, without any communication or overlap. Then it is hard to see how one can identify individuals in so discrepant frames of reference. We don't believe it is entirely accidental that Leibniz, the most influential adherent of the undiluted possible-worlds idea, ended up considering any two individuals occurring in two different worlds as different.32 4. CROSS-IDENTIFICATION BY SPATIOTEMPORAL CONTINUITY But if the possibilia between which we are cross-identifying are alternative states of affairs or courses of events in a small part of the world, as we suggested that they typically are, it is a different story. For one reason or other, the "possible worlds" we are considering usually have a relatively large part in common, or else can be extended so as to share such a common part. For instance, in considering a small part of the universe, we usually keep the rest of the world fixed. In making alternatives to different parts comparable with each other, we have to extend them; and in so doing we normally rely on assumptions as a result of which the extensions share a sizable common part. In an extreme but not atypical case, the differentpossible worlds are different possible continuations of a shared past history.3 Such a common ground can be used for the purposes of cross-identification. Suppose that we are given a (manifestation of a) physical object il in a world Wl and another physical object i2 in another world W2. How can we try to find out (in principle) whether or not it and i2 are the same individual? What one can do is to follow each of them in space and time in its respective world toward the common ground by means of spatiotemporal continuity. If they coincide there, they are identical; if not, not If we cannot trace them to the common ground, this method fails. In such a case, we are likely to consider the two individuals different, or else resort to other, secondary identification methods?4 Being able to follow an individual in space and time is essentially what the task of reidentification is addressed to. Hence the account just outlined (due to Jaakko Hintikka) amounts to a partial reduction of cross-identification to reidentification. For the main burden in cross-identification falls in Jaakko Hintikka's scheme on being able to follow (in principle) an individual in space and time toward the common ground. Here the advantages of not considering each possible world in splendid isolation from others are beginning to tell. This account has to be supplemented by a discussion of the cross-identification of abstract objects, which we shall not try to provide here. However, that

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problem of cross-identifying abstract entities clearly is not the direction in which the major problems lie. It is not the abstract objects like numbers whose cross-identification is likely to cause difficulties in the first place. This admittedly partial account of cross-identification can serve as a basis of highly interesting arguments concernin§ the role of the origin of an individual in cross-identification, which John Locke 5 and later Saul Kripke36 have made so much of; concerning the role of causation in cross-identification; concerning the cross-identification of events (they cannot be moved around in spacetime, and hence can be cross-identified only when they are on the common ground of the worlds we are considering on a certain occasion); and concerning the consequences of this special position of events in cross-identification (the cross-identification of events is relative to a propositional attitude; the problem of contingent future events reappears as a difficulty of cross-identifying them; etc.). However, we cannot discuss these conclusions before we have first secured a better foundation for the underlying theory. Hence we shall for the time being focus on the even more central problem of precisely how cross-identification can take place. The account just outlined was suggested by Jaakko Hintikka. Recently it has been justifiably criticized from two different directions. On the one hand, Saul Kripke37 and W. V. Quine38 have pointed out how difficult it is to make precise sense of the idea of spatiotemporal continuity on which the first part of Jaakko Hintikka's account was based. The second part has been criticized by Esa Saarinen,39 who has argued that the identity of even such individuals as make their appearance on the common ground a number of possible worlds is not always well defined for all those worlds. His point is undoubtedly well taken. For instance, in epistemic contexts these individuals are all those in which the knower in question positively knows something under some description or other. If world lines passing through them were unproblematic, we would know of all of them what or who they are. This is clearly not the case in real life, however. Hence Saarinen's point is an apt one. Moreover, the idea of a "common ground" shared by a number of possible worlds has to be handled with care. Primarily, we are not dealing with a common part of space-time, but a shared store of facts. For instance, in the case of knowledge, the "common ground" is the totality of known facts. ("Common ground is a totality of facts, not objects", we could say, parodying Proposition 1.1 ofWittgenstein's Tractatus.) It is only by courtesy offurther assumptions that we can hope to reify a totality of common facts into a shared spatio-temporal part. And when we cannot do so, the use of continuity in cross-identification seems to be a lost cause.

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All this shows that a deeper account of cross-identification is badly needed. It is our self-imposed task in this paper to present the basic idea of a detailed account of re-identification and thereby also of cross-identification, of physical objects. 5. A DIFFERENTIAL-EQUATION MODEL OF THE RE-IDENTIFlCATION OF MASS POINTS Jaakko Hintikka's account has nevertheless persuaded some critics in one major respect, perhaps even to a slightly higher degree than he originally intended. Both W. V. Quine and Saul Kripke appear to be saying now that we would be able to cross-identity (at least up to a point) if we only could re-identify.40 (Characteristically, these two philosophers draw opposite conclusions from this predicament. Quine now considers re-identification as a highly suspect enterprise, while Kripke urges us to take the re-identification of physical objects for granted.) Hence it is not entirely misleading to illustrate the general problem of cross-identification by a simplified version of the re-identification problem. This is a Flatlander's41 re-identification problem, the problem of reidentifying two-dimensional objects in a changing two-dimensional world. To simplify (or perhaps rather to complicate) the problem further, let us imagine first that our Flatlander's world is a world of (two-dimensional) hydrodynamics. At each geometrical point there is at each time a point mass. These are moving around in some way or other. They can of course have properties and relations. Since we are here restricting our attention to re-identification by spatiotemporal continuity, these properties and relations will not play any role in what follows, however. Now it is obvious that simply by comparing the states of our Flatland at different moments of time there is absolutely no hope of re-identifying between these time-slices by anything like continuity. Even a Leibnizian God couldn't decide who's who and what's what in the different successive states of our Flatland just by looking at these states one by one completely frozen and unrelated to each other. Something else has to be given for re-identification by continuity or anything like that to make sense. What is that additional information? It is here that our main suggestion comes in. By way of a thought-experiment, we shall assume that the imaginary Leibnizian God sees something over and above the different frozen momentary states of the world. Let's assume that He (or She) also sees how each state is changing at the time, in the sense of seeing the velocity vector of each mass point at the time. Less metaphorically expressed, we are assuming that for each

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point mass with co-ordinates x, y, we are given the components of its velocity vector in the form of certain functionsf,g: (6) dx dt

r!Y.dt

=f(x,y,t) = g(x,y,t)

Does (6) help our Leibnizian God to re-identify (identify mass points between different time slices of the Flatland)? Yes, provided that God can solve the pair of ordinary differential equations (6). For its solutions are precisely the world lines of Flatlander's mass points. These solutions are a family of pairs of functions x(t),y(t), each pair giving the co-ordinates of one point mass at different times. A graphic representation of the situation might look like this: Fig. 1

t

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Only some velocity vectors and only one solution have been depicted here. It is clear that the "real" re-identification problem in three-dimensional space instead of Flatland can be handled in the same way. The only difference is that the situation is more difficult to envisage and to depict graphically. The equations (6) now of course become (7)

dx

dt

~ dt dz dt

=f(x,y,z,t) =g(x,y,z,t) =h(x,y,z,t)

What we have here is a fIrst step in building up a differential-equation model of reidentification and cross-identifIcation. There is of course an element of abstraction and simplifIcation in any such model. Precisely how much, will be commented on later. The best evidence for the realism of our model lies in the light it throws on the actual problems ofre-identification and cross-identification. The fIrst stage we have so far reached already enables us to draw some interesting conclusions. 6. CONCLUSIONS FROM THE MODEL For one thing, our simple observations in a sense vindicate the possibility of using something like continuity successfully for the purpose of re-identification. At the same time, we can now see that the situation is much more complicated than simple references to continuity can possibly do justice to. Later, we shall uncover further complications. They show jointly that earlier suggestions to the effect that re-identifIcation of physical objects takes place by means of continuity in space and time are seriously oversimplified and in that sense deserve the criticisms that have been levelled at them. For another thing, it is known from the existence theorems for ordinary differential equations that there exist solutions for (7) as soon asf, g and h satisfy certain technical conditions. 42 This reflects the ease with which we in real life carry out (in principle) re-identifications. The solutions, even when they exist, nevertheless need not be analytic functions or functions which in some other sense admit of an explicit definition.43 This point is relevant to Kripke's recent criticisms of the role of continuity in cross-identification.44 It has been indicated that there is much to be said for such criticism. Kripke seems to assume, however, that continuity theorists

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ought to be able to define explicitly the relations which are represented by world lines. This requirement is far too strict, however. We have seen that world lines can be defined implicitly in a perfectly satisfactory sense via the differential equations to which they are solutions. We cannot assume that the solutions themselves are in general explicitly definable in any interesting sense. At the same time. if the solutions are regular enough, they don't have to be defined everywhere in order for them to be extendible by means of the usual mathematical sense of extending (sufficiently regular) functions. 45 It follows thatf,g. and h don't have to be defined everywhere for the world lines to be definable more widely, perhaps even everywhere (apart from singularities). 7. OBJECTS AS BEING DEFINED BY SINGULARITIES It is in any case clear that the use of sets of ordinary differential equations like (6) or (7) can only be the first step in building a satisfactory model of re-identification. The ordinary individuals of our three-dimensional world are typically three-dimensional objects, and even Flatlander's objects are two-dimensional. In neither case are they like the mass points we have so far dealt with. One possible mathematical formulation of this observation is to say that over and above the "state variables" x,Y,z,t we also have certain additional "important variables" Uj which are functions of the state variables: (8)

Uj

= Uj(x,y,z,t)

These can encode such information as which object occupies the point (x, y, z) at the time t plus possibly other relevant information about the objects. The task of re-identifying ob!ects is to study the variables (8) on the basis of the differential equations (8).4 In practice this means to study the singularities of the solutions of the ordinary differential equations (7). The basic idea is simple and intuitive enough. For the sake of illustration, it is clear what a normal "physical objcct" is for a FIatIander. It is a connected, smooth set of solutions to (6) (world lines) bounded by a region of singularities whose cross-section with each time slice (t =constant) is a closed curve C. The points on the curve are all singularities. The following picture may illustrate the situation:

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Fig. 2

Only a couple of world lines have been depicted here to illustrate the idea that inside the closed curve the world lines run smoothly, e.g., change into each other continuously. The region inside such a closed curve C of singularilies is precisely what an object is for a Flatlander. The counterpart to this for (7), i.e., for re-identification in three-dimensional space, is clear, even though the picture is harder to draw. 8. SOME PROPERTIES OF THE MODEL Here we have reached a point where three important observations can be made. (i) First, our differential equation model has led us to an analysis, however rough and tentative, of the concept of a spatiotemporally persistent physical object. Saul Kripke notwithstanding, in our model we do not have to take the notion of an enduring physical object for granted; we can offer a structural analysis, however sketchy, of it.

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(ii) Second, this analysis shows how to overcome the artificial separation between identification and individuation which was registered and lamented above. As Figure 2 graphically shows, the way in which the Flatlanders conceptually cut up their flat land (i.e., divide it into those regions which correspond to our three-dimensional objects) is determined by singularities in the very same solutions differential equations as define lines of re-identification of mass points (and afortiori define the re-identification of objects). In this sense, individuation (in our model, the articulation of time-slices into separate objects) is inseparable from identification (in our model so far, re-identification). This result is perhaps not surprising in one respect. It is not entirely surprising that the way differences between different objects are as it were first created is connected with our recognition of these same objects later. The bite of our observations lies, not in the mere existence of a link between individuation and identification, but in enabling one to begin to see what that link is.

(iii) The third main observation we can make is perhaps the most interesting one. It is seen by asking: what is the conceptual and mathematical nature of the link between individuation and identification which we have found? How are persistent physical objects constituted? The answer which is implicit in what has been said is that a decisive role is played by singularities in the solutions of certain sets of ordinary differential equations. Moreover, these singularities have to be stable in some intuitive sense. (The putative boundaries of physical objects which are constituted by these singularities must not break and spill their contents.) Now the study of such stable singularities happens to be an interesting and sophisticated mathematical subject. One branch of such mathematical theorizing has recently received intensive attention under the somewhat sensationalistic title "catastrophe theory" .47 Indeed, our general formulation above (in terms of the variables (9)) of the task of individuation is very nearly identical with Sussmann's interim characterization of the aims of catastrophe theory in his useful expository paper. 48 Ifwe were trying to be as flamboyant as Rene Thorn, we would undoubtedly call our model of individuation and identification the catastrophe theory of reference. The substantial point to be made here is that our model turns out to be interesting also as a mathematical object. We have managed to relate the philosophical problems of individuation and identification to highly nontrivial mathematical theories. In order to avoid misunderstandings it may be in order for us to disassociate ourselves in so many words from the philosophical pronouncements of the father of catastrophe theory, Rene Thom. 49 Many of his apercus strike us as impressionistic. However, we do believe he is on the right general track in

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believing that there is a very real connection between what is meant by an object and the mathematical concepts of stability and singularity which are central to catastrophe theory. We cannot pursue the details of this connection here, however. Even in its present shape, the connection we have uncovered may at least serve to make the task of re-identification respectable in the eyes of those philosophers who, like Quine, seem to doubt the possibility of making interesting objective sense of the process of re-identification actually presupposed in people's conceptual practice.50 (iv) In particular, there is an idea which is important in catastrophe theory and which is obviously crucial for our concept of an objecti explicated along the lines we are following here. It is the idea of stability.5 Not only do we have to have singularities in the solutions of the differential equations (6). For each constant t, the singularities must define a closed curve for each object to be "constituted", and these curves must change continuously with time. Stability phenomena of this kind are especially important for the concept of a physical object, it seems to us. (v) It is nevertheless clear that "classical" catastrophe theory alone will not suffice here, as useful conceptually as it is likely to be. In the theory, various relatively strong regularity assumptions are in effect imposed on our functions f,g ,h. It is fairly clear that not all functions we have to consider in real life satisfy these conditions. What we are hence offered by catastrophe theory is an ideal case ofindividuation and identification of objects which is not likely to be found in practice. In general, the course of individuation--including its success or failure-depends heavily on the functions/. g. and h. These are of course given empirically, not a priori. Hence the abstract mathematical theory of individuation cannot tell everything about the extent to which our individuation processes-processes that constitute our macroscopic physical ontology--are at the mercy of brute facts. There cannot be a transcendental deduction of the existence of ultimate simples like the "objects" of the Tractatus. 9. THE PRIMACY OF SPACE AND TIME Another general suggestion of our model is that the conceptual priorities of most philosophers' ontology are topsy-turvy. Ever since Aristotle (or perhaps rather Democritus), philosophers have typically tried to find the basic, mutually independent building-blocks, the true individuals, which form the basic units of the world. Aristotle postulated substances which were according to him

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characterized by "particularity and 'thisness"'; Leibniz postulated monads; and the young Wittgenstein postulated the "objects" of the Tractatus. Nor have mathematicians and logicians been immune to such atomism. Many of them have seen in set theory, with its discrete elements of sets, the true foundation of mathematics. Almost all logicians have used as their paradigm predicate calculus whose inte~retation involves a "universe of discourse" consisting of discrete individuals. 2 If our analysis of the concept of a physical object is on the right track, philosophers' given discrete individuals are not such basic stuff as our world is made of, conceptually speaking, but are constituted out of re-identified mass points as bunches of solutions to sets of differential equations. For this constitution, something essentially like a spatiotemporal framework is needed, even though mathematicians are apt to generalize our old-fashioned Euclidean space into sundry abstract spaces and manifolds. Hence there is a sense in which space and time are more basic conceptually to our ontology than the notion of an individual object. By the same token, geometry is a more fundamental branch of mathematics philosophically than set theory.53 One further implication of this tentative conclusion of ours is that good old Immanuel Kant receives a somewhat surprising vindication. He believed that we can conceive of individuals only in space and time. All intuitions (Anschauungen), which he defined as representations (Vorstellungen) of particulars,54 must appear to us in space and time, Kant says. Jaakko Hintikka has argued that Kant's basic line of argument for this tenet of his is fallacious,55 for he assumes that the process by means of which we come to know particulars is sense-perception (sense-perception, the whole of sense-perception, and nothing but sense-perception) whose forms Kant identifies with space and time. Now we can see that Kant arguably has a second line of defense for the primacy he assigns to space and time, even if this fallacious assumption is removed. He could have argued for the primacy of space and time by analyzing the concept of a persisting physical object. If we are on the right track in our analysis, such an analysis must rely on the framework provided to us by space and time, which are therefore more basic ideas than that of an individual physical object. The conceptual priority of space and time has other important implications. Among other things, it shows that the term "possible world" is in one respect strikingly inappropriate .56 If we are to be able to speak of some of the actually existing individuals as members of other possible states of affairs, and if the cross-identification between them and the actual worlds happens by and large as our model prescribes, all those alternative "worlds" must share at least part of space-time with the actual world. In so far as "worlds" -- whatever is meant by this term in other respects--are assumed to involve a spatiotemporal system

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and to be identified by means of this system, these different states of affairs we have just considered cannot be labelled different worlds, for they have a spacetime in common. Perhaps it would be better for philosophers to speak of different possible courses of events in one and the same world than to use the metaphysically loaded term "possible world". This terminological change does not make any difference to what we have said in this paper (or elsewhere) about the ill-named "possible-worlds semantics", but it may perhaps remove some of the wrong connotations which philosophers have associated with the term. In particular, it helps to make more intuitive why cross-identification need not be the mysterious, almost paradoxical enterprise which it has looked like to several critics of possible-worlds semantics.

10. THE PRIMACY OF MATTER The spatiotemporal framework is nevertheless only a tool in the actual identification and individuation of physical objects. What determines the outcome of the process is the triple functions/. g, h. What these functions specify in our model is essentially the totality of motions of mass points. They are the rock bottom of identification and individuation. In this way, it is seen that in actual applications the semantical articulation of the world is not based on abstract logical considerations, but on material reality and its laws of motion. Identification and individuation are rooted firmly in the material realities. NOTES 1 This approach exists in many different variants. Here we have in the first place in mind the version formulated by Richard Montague; see R. Thomason (ed.): 1974, Formal Philosophy: Selected Papers of Richard Montague, Yale University Press, New Haven; D. R. Dowty, R. E. Wall, and Stanley Peters (eds.): 1981, Introduction to Montague Semantics, D. Reidel, Dordrecht. For other approaches, see, e.g., D. Lewis: 1972, 'General Semantics' in Donald Davidson and Gilbert Harman (eds.), Semantics of Natural Language, D. Reidel, Dordrecht, 169-218; Jaakko Hintikka: 1969, Modelsfor Modalities D. Reidel, Dordrecht; and Jaakko Hintikka: 1975, The Intentions ofIntentionality, D. Reidel, Dordrecht. 2 See Jaakko Hintikka: 1975, 'The Intentions ofIntentionality', in op. cit., and Jaakko Hintikka: 1980, 'Degrees and Dimensions of Intentionality', in Rudolf HaIler and Wolfgang Grassl (eds.),Language, Logic, andPhilosophy: Proceed-

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ings of the Fourth International Wittgenstein Symposium, HOlder-PichlerTempsky, Vienna 69-82, reprinted in this volume. 3 Cf. here Jaakko Hintikka: 1980, 'On Sense, Reference, and the Objects of Knowledge', Epistemologia, 3, 143-64, reprinted in this volume. 4 These problems have been discussed in Jaakko Hintikka: 1982, 'Is Alethic Modal Logic Possible?', Acta Philosophica Fennica 35, 89-105, reprinted in this volume; and in Jaakko Hintikka: 1980, 'Standard vs. Nonstandard Logic', in E. Agazzi (ed.), Modern Logic: A Survey, D. Reidel, Dordrecht 283-296. 5 Cf. here Jaakko Hintikka: 1983, 'Situations, Possible Worlds, and Attitudes', Synthese 54, pp. 153-62, reprinted in this volume. 6 See Jaakko Hintikka:1975, 'Knowledge, Belief, and Logical Consequence', in Hintikka, op. cit., Ch. 9, and Jaakko Hintikka: 1973, Logic, LanguageGames, and Information, Clarendon Press, Oxford, especially Ch. 7 and 11. 7 Rantala, V.: 1975, 'Urn Models' ,Journal of Philosophical Logic, 4, 455-74; reprinted in E. Saarinen (ed.): 1979, Game-Theoretical Semantics, D. Reidel, Dordrecht,347-66. 8 Hintikka, Jaakko: 1975, 'Impossible Possible Worlds Vindicated ' ,Journal of Philosophical Logic, 4, 475-84; reprinted in this volume. 9 See Jaakko Hintikka: 1973, Logic, Language-Games, and Information, Clarendon Press, Oxford, Ch. 7-9; Jaakko Hintikka: 1974, Knowledge and the Known, D. Reidel, Dordrecht, Ch. 6-10. 10 See Jaakko Hintikka: 1978, 'Aristotle's Incontinent Logician', Ajatus, 37, 48-65. 11 See Jaakko Hintikka: 1980, 'C.S. Peirce's "First Real Discovery" and its Contemporary Relevance', The Monist, 63,304-15. 12 See Jaakko Hintikka: 1976, The Semantics of Questions and the Questions o{ Semantics, North-Holland, Amsterdam. 1 On the importance of this principle, cf. e.g. B. Hall Partee: 1977, 'Possible Worlds Semantics and Linguistic Theory', The Monist, 60, 302-26 and 306-08; B. Hall Partee: 1975, 'Montague Grammar and Transformational Grammar', Linguistic Inquiry, 6, 203-300. 14 See Jaakko Hintikka: 1981, 'Theories of Truth and Learnable Languages', in S. Kanger and S. Ohman (eds.), Philosophy and Grammar, D. Reidel, Dordrecht,37-57. 15 Wittgenstein, L.: 1961, Tractatus Logico-Philosophicus, Routledge and Kegan Paul, London. 16 Cf. here our book: 1986, Investigating Wittgenstein, Basil Blackwell, Oxford. 17 Cf. A. Tarski: 1956, 'The Concept of Truth in Formalized Languages', Woodger (ed.), Logic, Semantics, Metamathematics Clarendon Press, Oxford

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and the Gennan version, A. Tarski: 1936, 'Der Wahrheitsbegriff in den formalisierten Sprachen', Studia Philosophica, 1,261-405. Tarski's procedure in defining truth for quantified sentences even involves quantifying over evaluation functions, which hence cannot be said to be analyzed by means of truthdefinitions. 18 This analysis of meanings is the crucial idea of possible-worlds semantics. 19 The role of Tarski-type truth-defmitions as the main inspiration of Montague has not been fully spelled out in the literature. 20 See e.g. W. V. Quine: 1976, 'Worlds Away' ,Journal ofPhilosophy, 73, 85963. 21 Cf. Jaakko Hintikka: 1986, 'Quine on Who's Who', in P. Schilpp and L. Hahn (eds.), The Philosophy of w. V. Quine, The Library of Living Philosophers, Vo!. XVIII, Open Court, LaSalle, Ill., 209-26. 22 See especially Jaakko Hintikka: 1972, 'Knowledge by Acquaintance--Individuation by Acquaintance', in D. Pears (ed.),BertrandRussell: A Collection of Critical Essays Doubleday, Garden City, 52-79, reprinted in Hintikka: 1974, oy. cit., 212-33. 2 This promising idea has never been pursued in the literature. For the materials to be dealt with, cf. A. Kaplan: 1977,In Pursuit of Wisdom, Los An~eles, secs. 46 and 47. 4 Kripke, S.: 1979, 'Identity Through Time', paper delivered at the SeventySixth Annual Meeting of APAEastem Division New York 1979. 25 See especially Jaakko Hintikka: 1975, 'Quine on Quantifying In', in Hintikka, op. cit. 26 Cf. here Hintikka: 1980, op. cit. 27 Note that this problem is completely independent of the possible nonexistence of Lewis Carroll. 28 In this way, we can obtain a general logical analysis of the natural-language semantics of the constructions of the fonn knows + subordinate wh-question. 29 See Quine. 1976. 30 Philosophers have confused here two different questions, on the one hand the question as to whether there are objective criteria of meaning for sentences involving such construction as knows + interrogative clause, and on the other hand such questions as to whether those criteria are constant from one application to another or whether they are contextually detennined or whether the criteria are precise or not. Partial contextual dependence and imprecision are undoubtedly facts of life here, but it would be a major fallacy to take them to show that the criteria themselves are not objective or that they cannot remain constant throughout a "local" application. For instance, if Jaakko Hintikka is right that the contrast in natural languages between the construction knows +

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interrogative clause and knows + a direct object is largely a distinction between two essentially different ways of drawing world lines of cross-identification, then to deny the reality of the distinction between the two ways of cross-identifying is to deny that the contrast between the two constructions in languages like English has any objective meaning. Only Quine seems to have the courage of his convictions and to be willing to draw such conclusions, which of course would relegate large parts of natural-language semantics to the waste-paper basket as pragmatics. 31 lan Hacking has aptly pointed out the kinship between Leibniz and such modern possible-world theorists (in effect) as Rudolf Carnap. See, e.g., I. Hacking: 1971, 'The Leibniz-Carnap Program for Inductive Logic' ,Journal of Philosophy, 68, 597-610. What remains to be added is merely that this emphasis on "large worlds" is not intrinsic to the contemporary twentieth-century possible-worlds approach, only to some particular forms of it (such as Carnap's). 32 See B. Mates: 1968, 'Leibniz on Possible Worlds', in B. van Rootselaar and J. F. Staal (eds.), Logic, Methodology, and Philosophy of Science Ill, NorthHolland, Amsterdam, 507-29; reprinted in H. G. Frankfurt (ed.): 1972,Leibniz: A Collection of Critical Essays, Doubleday, Garden City, 335-64. 33 The representativeness of this case is seen, for example, from the fact that branching time trees are the most common type of a model structure used in the semantics of tense logics. This case is nevertheless subject to important limitations which greatly reduce its usefulness as a general paradigm. 34 Cf., e.g: 1975, 'Quine on Quantifying In', in Hintikka, op. cit. 3S Locke, J.,An Essay Concerning Human Understanding, Book 11, p. 440 of the A. C. Fraser edition. 36 See, e.g., S. Kripke: 1972, 'Naming and Necessity', in Davidson and Harman (eds.), op. cit., 253-355, especially p. 314. 37 See Kripke, 1979. 38 See Quine, 1976. 39 Saarinen, E.: 1979, 'Continuity and Similarity in Cross-Identification', in Esa Saarinen et al. (eds.), Essays in Honour of Jaakko Hintikka D. Reidel, Dordrecht 189-215. 40 See Quine, 1976, and Kripke, 1979, respectively. 41 Abbott, E.A.: 1952, Flatland: A Romance ofMany Dimensions, Dover, New York. 42 See, e.g., E. L. Ince: 1956, Ordinary Differential Equations, Dover, New York 71-72. 43 Trivially, if the functionsf.g.h do not have higher order derivatives, then the solutions x(t), y(t), and z(t) don't, either. Hence the solutions can be analytic

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only if the functions/. g, and h are. Yet the solutions exist on much weaker conditions. 44 Kripke, 1979. 45 For the basic ideas see e.g. E.T. Whittaker and G. N. Watson: 1927 ,A Course Modern Analysis, Cambridge University Press, Cambridge, 96-98. o Cf. here H. J. Sussmann's useful survey paper: 1975, 'Catastrophe Theory', Srthese, 31, 229-70, especially 230-32. 4 See e.g., Yung-Chen Lu: 1976, Singularity Theory and an Introduction to Catastrophe Theory, Springer Verlag, New York/Heidelberg, or P. T. Saunders: 1980, An Introduction to Catastrophe Theory, Cambridge University Press, Cambridge. 48 Sussmann, 1975. 49 Cf. e.g., R. Thorn: 1975, Structural Stability and Morphogenesis, Reading, (but cf. HJ. Sussmann and R. Zahler: 1978, 'Catastrophe Theory as Applied to the Social and Biological Sciences: A Critique' ,Synthese, 37,117-26). Thorn comes closest to our present subject in his papers 'Topologie et Linguistique', in: 1970, Essays on Topology, Dedicated to G. de Rham, Springer Verlag, New York/Hedelberg 226-48; and 'Langue et Catastrophes: Elements pour une Semantique Topologique', in M.M. Peixoto (ed.): 1973, Dynamical Systems, New York/London 619-54. 50 Cf. Quine, 1976. 51 Cf. e.g. Sussmann, 1975. 52 For the role of this paradigm in recent language theory and for logicians' gradual disenchantment with it, see Jaakko Hintikka: 1981, "Semantics: A Revolt Against Frege", in Guttorm Floistad and G.H. von Wright (eds.), Contemporary Philosophy: A New Survey, I, Nijhoff, The Hague, 57-82. 53 This is of course a radical and controversial perspective on the foundations of mathematics, which in the last hundred years has been dominated by formal logic and set theory. We cannot explore the implications of our new perspective here. 54 Cf. Jaakko Hintikka: 1969, 'On Kant's Notion of Intuition (Anschauung)', in T. Penelhum and J.J. MacIntosh (eds.), The First Critique: Reflections on Kant's 'Critique of Pure Reason', Wadsworth, Belmont 38-53. 55 See Jaakko Hintikka: 1973, 'Quantifiers, Language-Games, and Transcendental Arguments' ,in Jaakko Hintikka, Logic, Language-Games, and Information, Clarendon Press, Oxford; Jaakko Hintikka: 1974, 'Kant on the Mathematical Method', in Jaakko Hintikka, Knowledge and the Known, op. cit.; Jaakko Hintikka: 1982, 'Semantical Games and Transcendental Arguments' in E.M. Barth andJ.L. Martens (eds.) Argumentation: Approaches to Theory Formation, Benjamins, Amsterdam, 77-91.

g[

ON INDIVIDUATION AND IDENTIFICATION

liS

56 For the semantical history of the term "world", see C.S. Lewis: 1967, Studies

in Words, Cambridge University Press, Cambridge, chapter 2.

ON THE PROPER TREATMENT OF QUANTIFIERS IN MONTAGUE SEMANTICS The grammatical and semantical theories of the late Richard Montague present us with a most interesting treatment, perhaps the most interesting existing treatment, of certain aspects of the syntax and semantics of natural languages. 1 These theories are not satisfactory in their present form, however, not even if we restrict our attention to those linguistic phenomena that Montague himself primarily wanted to cover, together with certain closely related phenomena. The most central of these seems to be the variety of ways in which quantification is represented in natural languages. This concern is highlighted by the title of Montague's last published paper, 'The Proper Treatment of Quantification in Ordinary English'. In my own paper, I shall concentrate on the nature of naturallanguage quantifiers for the same reasons as Montague. In view of the importance of the problem of treating natural-language quantifiers, it is in order to point out and to discuss a number of shortcomings of Montague semantics in this department. It is of course the very precision and force of Montague's treatment that lends a special interest to these shortcomings. Just because Montague was so successful in carrying out certain general strategic ideas in the formal theory of language, the shortcomings of his treatment point to general morals in the theory and methodology oflinguistics and of the logical analysis of natural language . Of the general ideas underlying Montague's theories, the following three may perhaps be singled out here: (i) The analysis of meaning entities as functions from possible worlds (more generally, points of reference) to extensions. 2 (ii) The idea that semantical objects are correlated with each meaningful expression by rules which correspond one-to-one with the formation rules (syntactic rules) by means of which the expression is built Up.3 The meaning of a well-formed expression is in other words derived stage by stage in step with the operations through which it is put together syntactically. (The rules of semantics work their way from inside out.) (iii) The idea that such quantifier phrases as 'every man' and 'a girl' 97

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behave semantically like other singular terms.4 Of course, this is in some rough sense obviously rather close to the syntax of English. Montague's highly interesting idea was to devise a semantics in which the same holds, that is, in which the sentences 'John is happy' and 'every man is happy' are on a par. 5 Of these principles, (i) is the main principle underlying possible-worlds semantics. It can be considered an outgrowth and generalization of Camap's ideas of the semantics of modal logic. 6 (ii) is a form of a principle often attributed to Frege. (iii) is perhaps the principle most original with Montague, but even it had been partly anticipated by Bertrand Russell in the l-'rincip/es of Mathematics. 7 The general idea (i) will here come into the play only partially, through the treatment of individuals in the different possible worlds. This aspect of Montague's theories can in fact be described very simply: Montague assumed a constant domain of individuals as the range of those functions which are the senses of singular terms. 8 Although my several objections to Montague semantics and Montague syntax in its present form are not unrelated, they can be collected into two different groups, one dealing mainly with difficulties arising in connection with the idea (i) and the other with problems related to the strategy (iii). The latter leads us to cast some doubts also on the assumption (ii). In what follows, I shall mainly keep in mind Montague's formulations in his paper, 'The Proper Treatment of Quantifiers in Ordinary English', in short PTQ. I shall assume that my readers are familiar with the main features of Montague's theories. One limitation of Montague's treatment is the absence of any analysis of subordinate questions in epistemic contexts - that is to say, of constructions like 'knowing who', 'remembering where', 'seeing what', etc. This is a philosophical limitation because of Montague's avowed interest in clarifying the nature of such philosophical entities as the objects of propositional attitudes. 9 The limitation seems to me important also linguistically and logically. Elsewhere, I have shown that for a large class of casespossibly all of them - English wh-phrases (indirect questions) are nothing more and nothing less than quantifier phrases. 1o Hence any proper treatment of quantification in ordinary English presumably ought to cover them. Now there is a natural way of accommodating a large class of sub-

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ordinate questions in a possible-worlds semantics. It is the treatment I suggested more than ten years ago. 11 It is illustrated by the paraphrase of (I)

John knows who the prime minister of Norway is

in terms of the that-construction as

(2)

(3x) John knows that (the prime minister of Norway=x).

(The values of variables here are of course assumed to be persons.) The naturalness of this paraphrase need not be advertised. What else can we mean by knowing who a is than knowing of some particular individual that he is a? I have shown earlier how this translation can be carried out more systematically. 12 It is not un problematic, however, until the precise assumptions concerning the individuals over which 'x' ranges are spelled out and defended. That will be my main aim in the next few paragraphs. Of course we have by any token to distinguish here between de dicto and de re readings of (I). 13 The former is (2), and the latter will be representable as something like

(3)

(3x) (x=the prime minister of Norway & (3y) John knows that (x= y)).

Here it is said that John knows of the individual who in fact is the prime minister of Norway who that individual is, without presupposing that John can identify him as the prime minister. Clearly, (3) does not entail (2). It goes without saying that we also have to analyse knowledge here in terms of a special kind of alternativeness relation which for any world Wand any person b picks out the set of all worlds compatible with everything b knows in W as epistemic b-alternatives to W. Yet such translations do not work in the framework of Montague semantics. I suspect that Montague may have perceived some of the difficulties himself and may have been deterred by them from trying to treat the highly important problem of subordinate questions in his semantics. Symptoms of trouble· are easily found. They are nicely illustrated by the fact that in the very natural extension of Montague semantics we are here envisaging, the following sentences are valid:

(4)

(x) ((3y) (x = y)::J (3y) (y = x & (3z) John knows that (y = z)))

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(x) ((3y) John knows that (x= y)) ::>(3y) (y=x & (3z) Bill knows that (y=z))

Quantifiers must here be given a suitable semantics. What it is will soon be explained informally. Given this reading, what (4) says is that John knows of each actually existing individual who that individual is (in the de re sense). What (5) says is that Bill knows of each individual whose identity is known to John who that individual is, again in the de re sense. Both (4) and (5) are in most cases blatantly false, and therefore should not be considered valid. To be more careful, this conclusion is unproblematic as long as we do not have to care about the possible nonexistence of individuals in epistemically possible worlds. I shall soon argue that such nonexistence does not alter the picture, however. It is easy to see what the source of the trouble is. Montague assumes that there is a fixed set of individuals (possible denotations of name phrases) which serves as the range of the functions that constitute meanings of name phrases (cf. assumption (i)).14 Barring only the possible non-existence of some of these individuals in some worlds (which Montague does not allow anyway in PTQ15), any member of any world is therefore tied by a Kaplanesque TWA or 'trans world heir line' to some individual in any other world. In this sense, any individual is well defined in all these worlds. This is what forces us to say that (4) and (5) are valid in the kind of extension of Montague semantics we are envisaging here. Hence we must allow more freedom in our treatment of trans world heir lines. For one thing, we must not assume that they can be continued ad libidum, for that turns out to be ad absurdum. Now in Montague's own formulations of intensionallogic, we do not have to worry about possible nonexistence, for one and the same individuals are avaiiable to us as possible denotations of name phrases in each possible world. Hence the criticism just presented applies to Montague's own semantics. However, it is more interesting to ask whether Montague semantics can be modified in a natural way so as to accommodate the facts of the situation. What if we allow for the possible nonexistence of individuals in some worlds? 16 It turns out that my objection is still applicable. The point can be put

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as follows. In order for John to know who Homer was it is not necessary that his knowledge excludes all worlds in which Homer fails to exist. It is for this reason that I said that in quantifying into a knowledge-context like '(3x) John knows that F(x)' we need not presuppose that a world line exists connecting an existing individual from each of John's epistemically possible worlds. What is required is merely that we can tell of the individual in question whether or not it exists in each given world. This is precisely the case with John's knowledge of Homer when he knows who Homer was. His knowledge must merely exclude worlds of which one cannot tell whether Homer existed there or not. They are precisely the worlds in which the candidates for Homer's identity are not narrowed down to at most one person. (Thus we see that the question concerning the continuation of world lines in the sense just indicated is really quite different from the question concerning the possible failure of individuals to exist.) It thus turns out that what I have said of(4} and (5) remains valid also in the teeth of the possible nonexistence of individuals because we have to presuppose a semantics in which an existential sentence involving quantifying into an epistemic context, for instance, (6)

(3x) John knows that F(x}

can be true even when no world line picks out an existing individual x from each of John's epistemically possible worlds satisfying F(x}, as long as the question whether or not that individual exists there makes sense in each such world. 1 7 (What is being ruled out is merely a situation in which it is in principle impossible to tell whether or not the individual in question exists in one of these worlds.) In still other words, when we are trying to extend a world line of an individual i to a new world W, we have to distinguish between two different kinds of failure: (a) We can tell what the case would have to be in W for i to exist there, but we can in principle ascertain that it does not. (Uniqueness holds, but not existence.) (b) It makes no sense to ask whether i exists in Wor not. (The candidates for the role of i are not narrowed down to one at most, or are not well defined at all.) The fundamental reason for this second kind offailure is (I have argued) that the 'trans world heir lines' can only be drawn on the basis of comparisons between the different worlds in question. These

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comparisons utilize certain regularities (for instance, spatiotemporal continuity) obtaining in each of them. If these regularities fail in a world W, there just is no way of trying to find 'counterparts' for a given individual in W. In order for (6) to be true, there will have to be at least one world line connecting all of John's knowledge-worlds which does not exhibit any failures of the second type (b). It may exhibit failures of type (a). The naturalness of this requirement was already argued for, and will also be illustrated below. The details of this type of semantics is spelled out a little more fully in my earlier papers. If we merely allow failures of the first kind (a), the awkward sentences (4H5) will still be valid in our semantics. Hence we must recognize the possibility that world lines break down in the more sweeping fashion (b) and not only in the relatively innocuous way (a). This marks an important further step away from Montague's oversimplified assumption of a constant domain of individuals, independent of the different possible worlds we are considering. Now the semantics just presented is not chosen at random. It seems to me to be precisely the one which is needed to enable us to interpret (2H5) in the intended way as translations of certain wh-sentences of English. 18 Hence it represents the best hope there is to straighten out Montague semantics so as to be able to handle wh-phrases. The situation may be illustrated further by considering sentences of the form (7)

John knows that Homer did not exist.

Here we are saying that in each of John's epistemically possible worlds Homer fails to be around. That implies that in each of them it makes sense to ask whether Homer existed there or not, in other words, it implies that we can in principle specify what it would mean for Homer to exist there. Hence we have to distinguish here especially sharply between the uniqueness of an individual in each alternative (in the sense that it makes sense to ask whether this individual exists there or not) and its existence in each of them. Homer's epistemically possible nonexistence does not make his identity unknown to John. On the contrary, in order for John to know that Homer does not exist, he may have to know who Homer (that very individual) is.

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What all this adds up to is that there is no way in which an unmodified Montague semantics can cope with wh-phrases (subordinate questions). Barring a radical reformulation, the only means of accommodating failures of world lines to be continued ad libidum in Montague semantics is to allow for the individual in question to fail to exist in some possible worlds. What we have seen means, however, that this kind of failure is not at all what is needed here. In order to handle the very question of the epistemic possibility of nonexistence of particular individuals, we have to allow for a more radical kind of failure of a world line. In some cases, such a world line cannot be continued to a new world in the sense that there is no way of telling whether the individual in question exists there or not. And in the current Montague semantics there just is no way of allowing for this. This does not invalidate the general principle (i), but it puts it into a new perspective. Meaning entities are still functions from possible worlds (contexts of usage) to extensions, but this set of extensions is not a constant one nor even a variable subset of some fixed given superset. We just have to allow much less well-behaved world lines than Montague was prepared to eountenance. This problem comes up in the course of his discussion in PTQ. There he is led to maintain (on p. 240) that the only viable reading of sentences like (11)

John is seeking a unicorn and Mary is seeking it, too

is one which entails that there in fact are unicorns. It is true that on the only natural reading of (11) the quantifier implicit in it is the one on which 'a unicorn' has wider scope than 'is seeking'. However, examples like (11) illustrate vividly the fact that such a reading should not commit us to the existence of unicorns. For obviously two people can look for the same individual even when it does not exist. 19 Such examples as (11) therefore serve to point to the same difficulty with Montague semantics as I have been calling your attention to. This particular problem involved in (11) can of course be corrected merely by allowing well-defined individuals not to exist in some possible worlds, which involves only a relatively modest change. However, the natural reading of slightly more complicated sentences brings in all the difficulties we have discussed. The following is perhaps a case in point:

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John does not know whether any unicorns exist, but he is nevertheless seeking a unicorn because Mary is seeking it, too. Here John must be able to recognize one particular unicorn (for otherwise it would not be true that he is seeking it) in spite of countenancing its possible nonexistence. Plenty of other specific problems are easily forthcoming which illustrate the same general fact, viz., the impossibility of extending Montague semantics so as to cover wh-constructions without revising substantially the assumptions concerning the treatment of individuals in this semantics. By and large, the requisite changes amount to allowing for the possibility of sufficiently ill-behaved world lines. Ifwe make the precise assumptions Montague makes in PTQ, sentences of the following form are all valid: (8)

John knows that (3x) (x=a)

:J

(3x) John knows that (x=a)

where a is a proper name. However, on the proposal we are considering (8) says that John knows who is referred to by a proper name as soon as he knows that it is not empty. This is of course often false. Thus world lines cannot run together with the lines connecting the individuals referred to by a given name. Similar points can be made about common nouns. They just cannot pick out the same individuals in all the worlds we want to consider, contrary to what Montague assumes. Otherwise, we could not analyse sentences like (9) It seems to John that this bush is a bear along the lines here envisaged into the language of possible-worlds semantics. (No other half-way reasonable analysis has been proposed.) Other problems arise when the same treatment is extended to perceptual concepts. 20 (This will have to be done if all wh-constructions are to be discussed, for perceptual verbs sport such constructions rather prominently.) For instance, all the sentences of the following form will be contradictory in the proposed extension of Montague semantics:

(10)

(3x) (3y) (x = y & it appears visually to John that x is to the right of y).

Yet on one reasonable interpretation of (10) it describes a perfectly

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possible and in fact not especially recondite situation, viz., one in which John sees one object as two. What the trouble here is, is that world lines may sometimes split (when we move from a world to its alternatives). Yet in the present-day formulations of Montague semantics this simply cannot happen. For it is the same set of individuals - or possibly a subset of it - that crops up in each possible world as its domain. Hence no splitting or merging is ever possible. Yet there is no general reason to rule out such a behavior of world lines completely.21 A striking way for the world lines to 'misbehave' is for them to split into two entirely different sets of world lines, connecting the same set of worlds but proceeding in different ways. I have shown earlier that two different warps of world lines are needed in order to spell out the semantics of the direct-object contradiction with such verbs as 'sees', 'perceives', 'remembers', and 'knows'. 22 It follows that the treatment of individuals (world lines) in Montague semantics will have to be loosened in this respect, too. I am not saying that Montague semantics cannot be modified so as to correct these defects. This has after all been done already in somewhat different versions of possible-worlds semantics. 23 The interesting point is not even that this involves a fairly radical reformulation of the semantics underlying .Montague's intensional logic. It seems to me that an interesting general point here is that there is a great deal of tension in this very matter of the treatment of individuals in one's possible-worlds semantics between on the one hand pragmatic and linguistic realism and on the other hand mathematical elegance. Only this elegance looks to me a little too much like the spurious elegance which according to Georg Cantor should be a concern of tailors and shoemakers rather than of logicians. Those shortcomings of Montague-type semantics that we have noted are also interesting in that they point to the direction into which any satisfactory possible-worlds semantics will have to be developed. There is another class of problems with quantifiers in Montague semantics. They are more of the nature of problems that so far have been left untreated in Montague semantics than difficulties about what it already contains. It is nevertheless highly interesting to see what perhaps can be done about them along the lines Montague indicated.

ESSAY 7

106

By and large, Montague grammar and Montague semantics show how many quantificational ambiguities come about as a result of the possibility of building up the ambiguous expressions in more than one way. This applies both to purely quantificational ambiguities like

(12)

a woman loves every man

(if it is an ambiguity) and ambiguities involving the interplay of quantifiers and intensional notions, for instance, (13)

John is seeking a dog.

However, the account we obtain from Montague grammar and Montague semantics is unsatisfactory as it stands, even in its overall features. What it explains is why certain expressions can be ambiguous, not which expressions in fact are ambiguous. Taken at its face value, it predicts far too many ambiguities. 24 In other words, it does not give any account of the grammatical principles by means of which natural language often resolves ambiguities involving quantifiers. These principles are among the most important aspects of natural-language quantification, and should therefore be covered by any proper treatment of quantifiers in ordinary English. One class of disambiguating principles deal with the logical order (scope) of different semantical elements in an expression. How indispensable such ordering principles may be is shown by the fact that disregarding them can even lead one's syntax astray. For instance, as soon as a Montague-type grammar allows for the formation of conditionals, it will also allow (unless modified) the step from

(14)

if he contributes, he will be happy

(15)

if every man contributes, he will be happy

to

which is not grammatical (except in a context which provides an antecedent for 'he'). This step simply uses Rule S 14 of PTQ with n=O. The underlying reason for the difficulty is clearly the fact that in English 'if' has the right of way with respect to 'every', so that the 'every man' in (15) cannot pronominalize 'he'.25 Additional principles are thus needed in Montague grammars to

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regulate the order in which the different syntactical and semantical rules may be applied. They are of interest because they would represent an entirely new type of ingredient in Montague's theories. It is not clear, however, that some of them could not simply be built into the syntactical rules. For instance, by any token the first principles needed here include something like George Lakoff's global constraints on the derivation of quantified expressions. 26 They say in effect that a quantifier in a higher sentence has a wider scope than a quantifier in a subordinate one and that the left-right order serves as a tiebreaker for quantifiers in the same clause. These can presumably be built into Montague-type formation rules, at least partly. However, they do not hold without exceptions. Hence the whole situation needs more scrutiny before we can be happy with any of the existing treatments. Moreover, certain special quantifiers in English involve systematic violations of Lakoff's constraints. Their meaning can in other words be described only in terms of certain special ordering principle (scope conventions). The most important of these quantifiers in English is 'any'. I have recently developed what looks like a promising analysis of its semantical behavior in English. Can it be accounted for in a suitable extension of Montague semantics? Let us take some examples. Let us consider the following sentence: (16)

John dnes not believe that Mary likes any boy.

This has (besides the colloquial sense of 'believing not') only one nondeviant meaning in English, viz. the one which can be represented as follows (17)

,..., John believes that (3x) (x is a boy & Mary likes x)

Now how could (16) be built up in a suitable extension of Montague grammar? In order to obtain the right reading, some expressions of the sort indicated in (IS) (next page) must be constructed in the course of the process of building up (16). The details do not matter greatly here. The point is that somewhere along the line in constructing the that-clause we must deal with the expression 'any boy'. Now the semantical object correlated with it must be

ESSAY 7

IOX

lik~/eo like himo

(18) Mary

T any boy

I~~

~/

Mary likes any boy

the same as that correlated by Montague with 'a boy'. Otherwise we just cannot get in the existential quantifier which (17) shows we need. This is a disaster, however, for other examples show that the semantical object that must be correlated with 'any boy' is the same as is correlated with 'every boy'. In fact, this is the case in (19)

Mary likes any boy

occuring alone. 2 7 Hence the way in which a semantical object is correlated with 'any x' must depend on the context in which this expression occurs. This is apparently a serious violation of the Fregean principle (ii). Now the plausible-looking ways out of this difficulty are not very satisfactory. (Of course it is primarily a difficulty only for someone who believes in (iiHiii).) The way out closest at hand is probably to try to generate (16) in a way which involves the insertion of 'any boy' for a variable only at some later stage of the formational history of(16), perhaps so as to obtain it from 'any boy' and (20)

John does not believe that Mary likes himo.

However, the resulting reading of(16) is not tenable. And even ifit were, it would not catch the intended one, viz. (17). For (16) says that it is compatible with what John believes that Mary should fail to like any boy, whereas the reading obtainable through (20) says that of each boy it holds that John fails to believe that Mary likes him. The latter is, e.g., compatible with John's mistakenly believing in the existence of other boys liked by Mary and hence compatible with the falsity of (17).

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Another way out is not much better. It is to say that 'any' is ambiguous, that there are essentially different uses of 'any'. Although this seems to be the current consensus among linguists,28 it is not a very satisfactory view intuitively, and constitutes an instant black mark against the kind of approach I am criticizing as soon as an alternative theory is developed which makes 'any' unequivocal. Such a theory seems to be in the offing, as a matter of fact. 29 What is worse, this attempted way out does not offer us any real diagnosis of the semantical behavior of 'any' in ordinary English. I shall not attempt such a diagnosis here, although I believe that one can be given. Suffice it to say that it is the peculiar way in which the negation enters into (16) that makes the difference in this particular case. 30 What we have seen is nevertheless enough to illustrate the main features of the situation. What we need is a way of telling how the interpretation of 'any x' depends on the context- e.g., a way of going back to 'any man' in (16) when we come to the negation. There are perhaps ways of trying to do so while preserving some elements of Montague semantics. All of them nevertheless involve violations of the Fregean principle (ii) in spirit, if not in the letter. They all mean that we cannot build the semantical objects connected with a complex expression step by step in a natural fashion. At some point we have to go back to the earlier stages of the derivation and revise them in the light of later stages. Instructions to do so may perhaps be coded in different ways in the notational aspects formation rules. However, this will only mean that they do not realize faithfully the spirit of the Fregean idea (ii). Here we are in fact dealing with a general methodological point. Chomsky has repeatedly emphasized that there is in principle no difference between a 'generative' and an 'analytical' point of view in transformational grammar. 31 The very same rules which enable us to assemble a sentence automatically yield a way of as it were disassembling it. However, this remark is not applicable without qualifications. In semantics, one may want to abide by a principle which is not symmetrical with respect of building and of analysing sentences. The prime example is just the Fregean principle (ii).32 If our semantical rules operate from the outside in, we can afford to let this principle be violated, for we can always look from the outside into the depths of a sentence to make the semantical role of an inside constituent depend on its context. This is not always feasible

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if the Fregean principle (ii) is strictly adhered to. Thus, in semantics the direction of our rules may make a great deal of difference, and I believe that the same holds for the syntax of 'any', too. It is for this reason that examples like (16) above are so interesting. They suggest that instead of trying to stick to the Fregean principle (ii) we should perhaps start thinking in terms of rules of semantical interpretation which operate from the outside in, unlike the semantical rules of Montague semantics. Of course the situation is not a cut-and-dried one. There are tricks of coding information into suitable grammatical devices which can surreptitiously transmit it from one part of one's expression into another so as to create an illusion that the Fregean principle (ii) is adhered to when in reality it is not. Independently of any particular problem, however interesting it may be in itself, it seems to me that the general question of whether one can stick to the Fregean principle (ii) in a natural Montague-type semantics probably has to be answered in the negative. I cannot discuss here problems connected with the third major idea of Montague's mentioned earlier, viz. (iii), at length. I can nevertheless register my belief that the most natural way of carrying out the principle (iii) leads us away from the principle (ii).33 In other words, meaning entities are not to be constructed step by step from simpler ones in tandem with syntactical operations. Rather, they should be thought of, in some cases at least, as rules of semantical analysis. In brief, the proper treatment of quantifiers in ordinary English will differ from Montague's in this important respect, too. Academy of Finland NOTES 1 See the following papers by Montague: 'Pragmatics', in Contemporary Philosophy: A Survey (ed. by Raymond Klibansky), La Nuova Italia Editrice, Florence, 1968, pp. 102-122; 'On the Nature of Certain Philosophical Entities', The Monist 53 (1969),159-194; 'English as a Formal Language', in Linguaggi nella societa e nella tecnica (ed. by Bruno Visentini et al.), Milan, 1970, pp. 189-223; 'Universal Grammar', Theoria 36 (1970), 373-398; 'Pragmatics and Intensional Logic', in Semantics of Natural Language (ed. by Donald Davidson and Gilbert Harman), D. Reidel, Dordrecht, 1972, pp. 142-168; The Proper Treatment of Quantification in Ordinary English', in Approaches to Natural Language (ed. by laakko Hintikka, lulius M. E. Moravcsik, and Patrick Suppes), D. Reidel, Dordrecht and Boston, 1973, pp. 221-242.

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Cf. also Richard Montague's shorter papers and notes on related topics, including 'Comments on Moravcsik's Paper' in Approaches to Natural Language, pp. 289-294; (together with Donald Kalish) 'That', Philosophical Studies 10 (1959), 54-61; 'Logical Necessity, Physical Necessity, Ethics, and Quantifiers', Inquiry 4 (1960), 259-269. The development of Montague's views on the foundations of logic and linguistics was not without sharp turns, however. At one point he rejected altogether intensionallogic as a viable tool of logical, philosophical, and grammatical analysis. This rejection was not recorded in print, however. (Cf. nevertheless his paper, 'Syntactical Treatments of Modality', Acta Philosophica Fennica 16 (1963), 153-167.) 2 Cf., e.g., 'Pragmatics and Intentional Logic' on the specification of intensions. 3 Cf., e.g., 'English as a Formal Language', pp. 202-203. 4 Cf., e.g., PTQ, pp. 233-234 and passim. 5 As seen from PTQ, p. 233, rule T2, Montague in effect proposed to use as the semantical object correlated with 'every man' the class of all predicates all men have, and as the semantical object correlated with 'John' the class of all the predicates John has. The desired parallellism then becomes obvious. However, the naturalness or unnaturalness of this procedure (especially in connection with the semantical objects correlated with such phrases as 'the wife of every man' or 'the brother of some woman') has not been discussed satisfactorily in the literature. 6 See my paper, 'Carnap's Semantics in Retrospect', Synthese 25 (1972-73), 372-397. 7 See Chapter 5, entitled 'Denoting', in The Principles of Mathematics, Alien and Unwin, London, 1903, pp. 53-65. Peter Geach finds further anticipations in the medieval literature; see Logic Matters, Blackwell, Oxford, 1972, pp. 6, 8. 8 Cf., e.g., 'English as a Formal Language', p. 193, and PTQ, p. 231. 9 Cf. 'On the Nature of Certain Philosophical Entities'. 10 In a forthcoming study of natural-language quantification. Cf. also next few references. 11 Knowledge and Belief, Cornell University Press, Ithaca, N.Y. 1962, Ch. 6; 'The Modes of Modality', reprinted in my Models for Modalities, D. Reidel, Dordrecht, 1969, Ch. 5. 12 See the papers collected in Modelsfor Modalities. 13 This important distinction has not yet received the systematic modern treatment it amply deserves. See nevertheless my Models for M odalities, pp. 120-121. 14 See PTQ, p. 230. 15 See PTQ, p. 231, clause (7). 16 This was in fact allowed in Montague's earlier formulations. Cf., e.g., 'Pragmatics and Intensional Logic', p. 146. 17 This shows up in the treatment outlined in my paper 'Existential Presuppositions and Uniqueness Presuppositions' (Models for Modalities, Ch. 7) in the form of the independence of '(3x)(x=a)' and '(3x)b knows that (x=a)'. 18 Other reasons were given (however sketchily) for this kind of treatment in my paper 'The Semantics of Modal Notions and the Indeterminacy of Ontology', in Semantics of Natural Language (ed. by Donald Davidson and Gilbert Harman), D. Reidel, Dordrecht and Boston, 1972, pp. 398-414. 19 This is the starting-point of Peter Geach's problem of 'intentional identity', cf. Logic Matters, Blackwell Oxford, 1972, Ch. 4.4. 20 Cf. my 'On the Logic of Perception' in Models for Modalities (note 11). 21 Cf. my 'Existential Presuppositions and Uniqueness Presuppositions' (note 17). 22 See 'On the Logic of Perception' (note 20). 23 Cf. 'Existential Presuppositions and Uniqueness Presuppositions' (note 17).

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24 In 'English as a Formal Language', p. 217, Montague mentions that "English has ... certain ... devices for reducing ambiguity." He lists several, including the peculiar behavior of 'any'. Unfortunately.neither Montague's diagnosis of the reasons for the peculiar behavior of 'any' (it is alleged to have the maximal scope) nor the cure he prescribes (changing the syntactical rules for other quantifiers) are correct, it seems to me. 25 Notice that this problem is not solved by the procedure Montague advocates in 'English as a Formal Language', p. 217 (see the preceding footnote). 26 See George Lakoff, 'On Generative Semantics', in Semantics: An Interdisciplinary Reader (ed. by Danny D. Steinberg and Leon A. Jakobovits), Cambridge University Press, Cambridge, 1971, pp. 232-296, especially pp. 240-246. Notice that their effects on the scopes of quantifiers can always be gathered from the surface structure, however. 27 If you do not find this plausible, feel free to change the original example (16) into 'John does not believe that Mary can seduce any boy', which clearly contains an existential quantifier, not a universal one, in the description of what John fails to believe. 28 Cf. Edward S. Klima, 'Negation in English', in The Structure of Language (ed. by Jerry A. Fodor and Jerrold J. Katz), Prentice-Hall, Englewood Cliffs, N.J., 1964, pp. 246-323_ especially pp. 276-280. 29 I am in the process of trying to develop one, based on what I call the game-theoretical semantics for natural-language quantifiers. 'Quantifiers vs. Quantification Theory', Linguistic Inquiry (forthcoming). 30 Klima's theory (note 28) correctly predicts that 'any' has existential force in (16). It fails for other reasons, however, and hence does not offer an acceptable way out here. Montague was right, it seemed to me, in holding that 'any' has only the force of a universal quantifier, Klima notwithstanding. 31 See, e.g., Noam Chomsky, 'Deep Structure, Surface Structure, and Semantic Interpretation', in Semantics (note 26), pp. 183-216, especially pp. 187-188. 32 Of course, ] am assuming here that transformations do not always preserve meaning. The alleged meaning preservation of transformations seems to me a lost cause, however, by any reasonable standards. 33 See note 29.

ef.

THE CARTESIAN COGITO, EPISTEMIC LOGIC AND NEUROSCIENCE: SOME SURPRISING INTERRELATIONS One cannot discuss contemporary philosophy of mind without the ghost of Descartes skulking around in the shadows. And one cannot understand Descartes without understanding his famous cogito insight, put forward for the first time publicly 350 years ago. 1 Twenty-five years ago I showed what the nerve of the Cartesian insight is? Descartes is not inferring sum from cogito, but demonstrating to himself his own existence by performing an act of thinking. The expression co gito does not mark a premise from which sum is inferred, but a thought-act which reveals (as long as it goes on) to Descartes the entity that he is? Descartes's little skit is analogous to someone's, say Mark Twain's, proving his existence to a skeptic by confronting the doubter and confirming his existence to him by saying: "I exist." Of course any other thought-act (in Descartes's case) or language act (in Mark Twain's case) would have done the trick equally well. This opens the door to Descartes's dramatic gambit of attempting to doubt, nay, to deny, everything. When he then tries to deny to himself his own existence, by so doing he on the contrary proves that he exists. In Mark Twain's case an analogous purpose is served by the language act of declaring the rumors of his demise to be exaggerated. This performatory interpretation of the co gito has been subjected to various criticisms, but on a closer examination they turn out to be based largely on misunderstandings of my explanatory strategy.4 However, the peI:formatory interpretation does not alone provide a satisfactory answer to the next question which is likely to occur both to Descartes and to his readers. What is the entity whose existence is demonstrated (in the sense "exhibited", not in the sense "proved") in the cogito? Descartes tried to argue from cogito ergo sum to sum res cogitans. But what kind of res is it that he is talking about? Philosophers like Lichtenberg have complained that Descartes is not justified in concluding the existence of a thinking substance from his insight. Instead of the word cogito, whose first-person suffix smuggles in the idea of a person, Lichtenberg intimates, all that Descartes could legitimately have said is es denkt, "thinking is going on".5 But more has to be said here if we are to accord to Descartes's insight any force whatsoever. For we cannot use the co gito performance to conclude the existence of any being whatsoever without knowing what the conceptual status of the entity is whose existence is at stake. In the opening scene of an amusing novel by Italo Calvin06 Charlemagne demands a reason why one of his knights has his visor down. An answer comes from the inside of the armor: "Sire, I don't exist." Is this a counter-example to the performatory in113

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terpretation of the co gito? 7 Of course not, for there is a sense of existence in which Calvino's knight is wrong himself and in which he existed after all. In the fictional world ofCalvino's witty story, the knight does exist in one sense quite well, to the extent of being able to serve as the hero of the entire novel. But Calvino is making a salutary philosophical point by illustrating the fact that there are modes of being in which even the capacity of performing a speechact is not a conclusive proof of existence. What makes Calvino's knight different from all other knights is that he does not enjoy bodily existence. In view of the tremendous variety of modes of existence, it might seem difficult to say anything interesting as to what kind entity it is that Descartes perhaps proved to exist in the cogito. This impression is unjustified, however, provided that we attend to sufficiently general distinctions between logically different kinds of entities. In order to see what can be concluded here, we are well advised to note a peculiarity of the Cartesian cogito. It is sensitive to how the agent is referred to. If instead of cogito, ergo sum Descartes had said co gito, ergo Cartesius est, he would have fallen flat on his face. In fact, I once saw a French cartoon where the joke was precisely the absurdity of this conclusion. Why? The performatory interpretation yields a clue. If I run into a gentleman in the street who utters the words, "Mark Twain exists," that does not prove Mark Twain's existence to me unless I recognize the speaker as Mark Twain himself. In the analogous case of a speech act, it admittedly helps to switch to the first-person pronoun "I". If a gentleman says to me "I exist", I may very well be convinced of his existence. But if I don't know that he is Mark Twain, his speech act does not help to convince me of Mark Twain's existence. Likewise, Descartes's thought act is not without its presuppositions. In order to use a thought-act as a ground of the existence of certain entity, or a certain kind of entity, Descartes must know that the thinker in question is that entity or that kind of entity. Now what kind of entity can be proved to exist by the Cartesian method? Here it is helpful to borrow an idea (and a slogan) from Quine: "No entity without identity." What identity conditions is the kind of entity subject to that is concluded to exist by Descartes? Here a clear-cut answer can be based on my distinction between two kinds of methods of cross-identification. 8 This distinction is one of the most fruitful ideas in the philosophical analysis of the last few decades. It is also one of the most neglected ones. It is the theme of the present paper. The contrasting modes of identification can be called perspectival and public, even though these terms are somewhat misleading. For instance, there is nothing private or subjective about the perspectival mode of identification, even though it is relative to a person. It merely uses, as it were, a coordinate

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system which is defined by reference to a particular perceiver or knower but which in itself depends only on objective general principles and on the possible situations (scenarios, logicians' ill-named "possible worlds") between which world lines of identification are drawn. Perhaps "subject-centered" and "object-centered" might be better terms than "perspectival" and "public". The distinction is clearest in visual perception. There one can use as one's identificatory framework some person's, say John's, visual space. Persons and bodies occupying the same slot in this visual space (in the different situations compatible with what John sees) can be considered identical, even if John does not see who they are. This results in a perspectival or subject-centered identification principle. That it is not the only possible one here, nor the only one we actually use, is obvious. For the very fact that John does not see who these chaps are means that in the different situations compatible with his visual information they are (in an obvious sense) different persons. What is involved in nevertheless insisting that that man over there is one and the same person is perspectival identification. What is involved in seeing who he is identification based on public (object-centered) criteria. From visual perception this distinction can be extended to the level of other cognitive concepts, including memory and knowledge. In the case of memory, my personal reminiscences can serve to span a four-dimensional framework of cognitive relations to people, places and events into which I can fit some people and some entities of other kinds but not others. It can be used as an identificatory framework in the same way as John's visual space, albeit it is somewhat less sharp in structure. Furthermore, John's first-hand cognitive relations to his environment (in general, including both perception and memory) likewise create a framework that can be used for identification. 10 I have shown that the two methods (kinds of methods) correspond roughly to the truth-conditions of two different kinds oflinguistic expressions. 11 A person, say b, is a publicly identified entity for John on the basis of his momentary visual information if it is true that (1) John sees who b is. For other propositional attitudes we have analogous constructions, e.g., (2) John remembers who b is. (3) John knows who b is.

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For the perspectival mode of cross-identification, the analogous identificatory statements are (4) John sees b. (5) John remembers b. (6) John knows b. The distinction will be explained more fully in the course of this paper. But already at this stage of analysis, important conclusions can be drawn. One casualty of my distinction is Kripke's notion of rigid designator. 12 It is immediately seen to be relative to the mode of identification. For a rigid designator is supposed to pick out the same individual from each situation ("world") in which it exists. But the mere possibility of distinguishing between different modes of identification shows that what counts as the same individual is not determined absolutely but only by the method (criterion) of cross-identification that is being employed. The same goes for that unacknowledged anticipation of Kripke's notion of rigid designator, Bertrand Russell's notion of logically proper name. 13 Thus the notion of rigid designator is useless as a tool of philosophical analysis if it is not accompanied by a diagnosis of the particular kind of crossidentification on which each of its uses relies. From what has been said it likewise follows that there cannot be a single class of expressions in natural language which can be recognized as rigid designators by their linguistic status alone. The expressions of natural language that come closest to rigid designators in the case' of the public mode of crOSS-identification are proper names, even though it is clear that even they are not always rigid. They are in fact "bent", e.g., in epistemic contexts. I may fail to know to whom a proper name N.N. refers. Then I have to operate with different epistemic alternatives in which "N.N." is "bent" in the sense of picking out different individuals in some ofthe different scenarios compatible with everything I know. In brief, it makes sense to ask: Who is N.N.? The vernacular expressions that most faithfully play the role of logically proper names in the case of perspectival identification (most clearly, visual cross-identification) are the ostensive particles this and that. It is no accident that they were included (together with the tricky first-person singular I) by Russell among the few "logically proper names" in English. In general, the main difference between Russell and Kripke is that Bertie restricts his attention to

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the perspectival mode of identification, Saul to the public one, both blissfully oblivious of having made a choice between two alternatives. This distinction between the two different identification methods (and, afortiori, between individuals differently identifiable) explains the curious feature of the Cartesian cogito noted above. In order for me to be convinced of Mark Twain's existence by his speech-act I have to be an eye-witness (a perhaps rather an ear-witness) to the act. I have to be present and see and hear what goes on. Mutatis mutandis, the same goes for Descartes's self-observed thought-act. The certainty which this act generates (it it does) can only pertain to the existence of a perspectivally identified entity, not to the existence of a "public figure". Small wonder, therefore, in view of the ways in which the two modes of identification are expressed in everyday language, that the persuasiveness of the original co gito cannot be extended to prove the existence of public objects. "I think, therefore Cartesius exists" is a logician's joke even in Descartes'sown mouth. The self whose existence is supposed to be certified must be one of Descartes's objects of acquaintance, an object of immediate awareness, capable of being pointed to (attended to) in thought, a mental "this" or "that". What this result implies for the exegesis and the evaluation of Descartes's line of thought requires a separate examination. Obviously there is good news and there is bad news here. On the critical side, every true Wittgensteinian will feel called upon to challenge the idea of private ostension which was just found at the bottom of the Cartesian argument. l4 On the positive side, if Descartes really was justified in his fundamental claim, then he must have reached an immediate awareness of his self. lS This would presumably put to him a privileged position to tell us what that self is like. This would simply be analogous to the fact that if I was actually convinced of Mark Twain's existence on the basis of his say-so, then I cannot have failed to have an eyewitness's knowledge of his appearance and/or his voice. In any case, the role of perspectival identification in the Cartesian argument (or performance) calls our attention to the double life of the first-person singular pronoun I. It can rely on either one of the two principal identification methods. Sometimes it serves to refer to a perspectival individual, sometimes to a public one. It is fairly clear, however, that the former element is the dominant one. If a statesman wants to speak of himself as a public figure, then he will be tempted to resort to using his name instead of the first-person pronoun, as Charles de Gaulle did. For another example, if I am giving an oath and saying, "I, Jaakko Hintikka, hereby solemnly swear," the duplication of noun phrases is not a tautology but serves to equate a perspectival individual (the person who is uttering the words) with a public person (the bearer of the name).

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This predominance of perspectival identification is even clearer in the case ofthe second person singular pronoun you. Normally, uttering a sentence containing it will result in a meaningful proposition only if the hearer is present and capable of being pointed to. Perhaps the best way of illustrating the dynamics of the cogito is to think of Cartesius pointing his finger mentally at Rene and saying, "You are thinking, therefore you exist." As I indicated, the distinction between the two modes of identification is the theme of this paper. It is easy to work out an explicit logic for the distinction. Since the values of quantified variables have to be, as we all learned on uncle Quine's knee, well-defined individuals with well-understood criteria of identity, the two methods of cross-identification will correspond to two different pairs of quantifiers. 16 If the public ones are (:3x), 0Iy) and the perspectival ones (Ex), (Ax), the formal counterparts to (1)-(3) are (7) (:3x) John sees that (b =x) (8) (3x) John remembers that (b = x) (9)* (3x) John knows that (b = x). The last one of these will be abbreviated (9) (3x) KJohn (b = x). More generally, we obtain in this way an analysis of constructions of the form knows + a wh-clause (subordinate wh-question). For instance, (10) John knows who stole the diamonds has the counterpart (11) (3x) KJohn (x stole the diamonds). In contrast, (4)-(6) are rough translations ofthe following: (12) «Ex) John sees that (b = x). (13) (Ex) John remembers that (b = x). (14) (Ex) John knows that (b = x).

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(14)* (Ex) KJohn (b = x). The correspondence between (4)-(6) and (12)-(14) is not the only possible one, however. E.g., in the "translation" (12) "seeing bIt is taken to require recognizing In the weaker sense in which "seeing bIt simply means laying one's eyes on b, (4) should be expressed by

bY

(15) (Ex) «x =b) & (Ey) John sees that (x = y».

In the corresponding sense, (5)-(6) should be translated as (16) (Ex) (x = b & (Ey) John remembers that (x = y» (17) (Ex) (x= b & (Ey) KJohn (x = y».

For instance, in (17) b is one ofJohn's acquaintances even though he need not know b as b. In fact, here we have found a solid basis for a logic of such locutions as seeing as and knowing as. Alas, it would take us too far to develop such a logic here.Both pairs of quantifiers behave among themselves in the same way. For instance, the conditions of existential generalization are parallel in the two cases. For instance, from (18) KJohn S[b]

(where S[b] does not contain any intensional operators) we cannot infer either (19) (3x) KJohn S[x] or (20) (Ex) KJohn S[x]. These inferences are vindicated, however, by an additional premise which for (19) is (9)* and for (20) is (14)*. This treatment of the interplay of quantifiers and epistemic operators is easily generalized.

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It is not difficult to form an idea what the contrast between the two modes of identification amounts to when applied to visual cognition. To identify b in the perspectival sense means finding a slot for b among my visual objects, in other words, locating b visually. This means in effect being able to answer a "where" question. In contrast, identifying b in the sense of public cross-identification means being able to put b on the map of abstract impersonal knowledge. It means being able to interpret what one sees, it is tempting to say. It means being able to answer a "who" or "what" question. The explanations can easily be extended to other propositional attitudes. For instance, for knowledge the relevant frames of reference are not, in the case of public identification, visual spaces or personally remembered sequences of events, but those presupposed in books like Who's Who or The Social Register or in the files of FBI. There is obviously a sense in which public identification amounts to an interpretation of what one sees, to assigning a meaning to our sensations. There is even an analogy here between perceiving a word as a geometrical configuration and perceiving it as a meaningful word. But such ways of expressing the import of public identification methods are highly dangerous. Perspectival identification offers us, at least locally and temporally, a fully worked-out conceptual framework for speaking about our environment which is self-contained and does not need any further interpretation. For instance, there is no closer connection between semantics and the public system of identification than there is between semantics and the perspectival system. It is important to realize, however, that such explanations as rely on the ways of expressing the two contrasting modes of expression in natural languages are inevitably only partial and that they can be misleading. There is an important linguistic reason for this difficulty. We have seen that in a suitable logical symbolism there obtains a far-reaching symmetry between the expressions for the two different kinds of identification. In contrast, no equally close symmetry is found in languages like English. There we encounter only one set of wh-words which operate as the relevant quantifiers. These crypto-quantifiers rely predominantly on public identification. Perspectival identification has to be expressed by all-purpose constructions like the direct-object construction. These makeshift constructions do not bring out explicitly the underlying symmetry between the two kinds of identification methods. They cannot do the whole job, either, but must be supported by other means. Often the selfsame wh-constructions must be recalled to active duty in a new role, viz. to express perspectival rather than public identification. This is perhaps clearest in the case of wh-questions. Suppose I walk into a departmental meeting. Depending on the situation, I may be prompted to ask

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two different kinds of who-questions. Suppose that I know who the members of the department are: I know their names, I have read their CV's, their entries in Who's Who, etc. However, I have not met them and I don't know what they look like. In such circumstances, I may ask: (21) Who is the chairman? Here "the chairman" refers to the visually identified person who is sitting at the head of the table wielding the gavel. The answer might then be the name of the relevant person, say "Warren Goldfarb" (if the department in question is the Harvard philosophy department). But I can also buttonhole a member present and ask, "Please, who around here is Warren Goldfarb?". What is going on? In the first case, I have a perspectivally given entity (the chairman) for whom I am looking a niche among the departmental members publicly known to me. This is a case of attempted public identification: I am trying to find out who (which public individual) the (visually identified) chairman is. In the second case, we are dealing with perspectival identification. I am trying to locate Warren Goldfarb among my visual objects. Notice that I might equally well have asked: "Please where around here is Warren Goldfarb?" or even "Can you see Warren Goldfarb and point him out to me?" Thus who-questions can express both kinds of identification, even though its use in perspectival identification may be a little forced. Furthermore, it is admittedly natural to use where-constructions in referring to perspectival identification, especially in a visual context. But it can also be used, perhaps equally naturally, in locating persons, objects and events in an impersonal public space. This may be illustrated by the contrast between the following examples: (22) Where does Queen Elizabeth live? (23) Where is the telephone? Hence characterizing the contrast between public and perspectival identification by speaking of what-questions and where-questions can be misleading. Another important conceptual point can be read off from the formal representations (7)-(20). There is only one knowledge-operator in all these expressions. In other words, only one kind of construction (viz. knowing that) is the last analysis involved here. The distinction I have drawn is between two different kinds of identification, not between two different kinds of knowledge.

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And the same goes of course for other cognitive concepts than knowledge, such as seeing, perception in general, and memory. This is important to realize because the same or at least closely related distinction is sometimes expressed (misleadingly) by speaking of types of knowledge. The best known instance is undoubtedly Bertrand Russell's distinction between knowledge by acquaintance and knowledge by description. 1S Later in this paper, we shall find other examples. Thus there obtains an asymmetry between the two modes of identification in natural languages. In the language of epistemic logic, however, there obtains a far-reaching symmetry between the two modes. This is witnessed by examples like (7)-(9) and (12)-(14). In this sense, the two modes of identification are on a par syntactically. This observation cuts deeper than might first seem to be the case. One of its manifestations will illustrate its consequences. Epistemic logic yields as one of its more striking applications a criterion of (conclusive) answerhood for whquestions. 19 If someone asks, (24) Who lives here? the epistemic state that the speaker is trying to bring about is one in which he or she can truly say (25) I know who lives here. This has the logical form (26) (3x) KI (x lives here) What an actual reply, say "b", brings about at best is a situation in which the questioner can say, truly, (27) KI Cb lives here). Hence the reply "b" is a conclusive answer only when (27) implies (26). But from epistemic logic we know that that is not always the case, in fact, the implication holds iff the following extra premise is available to the questioner: (28) (3x) KI Cb = x). What (28) says is of course

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(29) I know who b is. This requirement is of course eminently natural. A reply "b" does not help the questioner to find out who lives here if he or she does not know who b is. What is the counterpart to the conclusiveness condition (28) for perspectival identification? Let us consider the question (30) Who around here is N.N.? The reply might, e.g., consist in saying "the man farthest on the right" or "that man" (pointing). Let the term (noun phrase) offered by the addressee of the question as a reply be "cf'. Then the formally analogous conclusiveness condition will be (31) (Ex) KI (d = x) Now what does that mean? Taking "K!" to express visual knowledge, as it is natural to do in the example at hand, (31) will clearly say that the questioner sees d. Of course this is on the common sense level trivially a necessary condition for the reply "d" to serve its purpose. Of course an ostensive answer will not do unless the questioner does not see the object the answerer is pointing to. What is far from trivial is that this condition on conclusive ostensive answers is not a merely pragmatic requirement but a corollary to the formal (syntactical) symmetry between the two modes of identification. Even the fine print of the formal analogy matters here. As was pointed out above, the natural-language expression (32) I see d is in fact ambiguous, in fact it can have the force of either (33) (Ex) I see that (d = x) (which is what (31) says if the information presupposed there is visual) or (34) (Ex) (d = x & (Ey) I see that (x = y» which is probably the closest translation to the natural-language phrase (32) that we can find. The difference is that for the truth of (34) it suffices that I merely lay my eyes on d; I do not have to recognize that visual object as d.

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But this is obviously insufficient for the reply "cl' to serve its purpose in the kind of example that was envisaged. In an ostensive context, I have to recognize d as the object the answerer is pointing out for me. Hence the precise syntactical analogue (33) is needed in the conclusiveness condition for perspectival (ostensive) questions, not just any approximate translation of (32). This illustrates both the explanatory force of the analysis offered here and, more specifically, the extent of the formal (syntactical) analogy between the two modes of identification. I shall return to this analogy later. In other ways, too, the distinction between the two modes of identification is a strikingly robust explanatory principle. The distinction between perspectival and public identification is thus interesting in its own right It is turning out, however, that it is also connected in a dramatic way with actual cognitive science. There we encounter, completely independently of what philosophers and epistemic logicians have done, a distinction between two cognitive systems which are in operation in spontaneous human cognition. Here I shall mostly follow the presentation of the distinction given in Dr. Lucia Vaina's forthcoming book, From Perception to Co gnition?O Vaina calls the two cognitive systems the where-system and the what-system and otherwise explains them in ways that often are strikingly reminiscent of the way the perspectival vs. public distinction was drawn above. Concrete examples are found below. Vaina notes that the two systems are in operation on the level of higher cognitive functions, although they can be seen most clearly on the level of visual cognition. In general, Vaina adopts the framework which was introduced by David Marr and which Marr elaborated in concrete term in the case of shape perception.21 In this framework, three main stages of visual information processing: (i) processing single features of the stimulus; (ii) integrating stimuli, which leads to (iii) perceptual categorization of shapes, textures, etc.; (iv) associating meaning to shapes, textures, etc., so as to obtain objects of the kind that is relevant, e.g., to recognition tasks. The near-identity of the distinction Vaina discusses and my distinction between the two modes of identification will be argued for below. It represents an interesting example in which logico-semantical analysis can reach results which have considerable relevance to down-to-earth cognitive science. What is truly dramatic here is that this down-to-earth character of the distinction could not be more fundamental. The distinction between the two cognitive systems is in fact not completely new. What is recent is the discovery that the distinction between the two system is grounded on brain anatomy. As Vaina puts it,22

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The elegant work that comes out of Mishkin's laboratory (1979), (1983), (1981) provides impressive evidence that the different visual areas are hierarchically organized into two cortical visual pathways, one processing the information about "what" the stimulus is and the other about "where" it is. The first pathway consists of a multisynaptic occipitotemporal projection system which connects the striate, prestriate and inferior temporal lobe. Its main function is visual identification of objects. This pathway is further connected to limbic structures in the temporallobe and ventral parts of the frontal lobe, and as such it may effect cognitive associations and motor acts. The second pathway connects the striate, prestriate and inferior parietal areas, and it is specialized for the visual location of objects. Subsequent connections of this pathway to the dorsal limbic and dorsal frontal cortex suggest the mechanisms employed in construction of spatial maps and visual guidance of motor acts. This distinction between two types of visual perception is not new, however, their cortical localisation, as proposed by Mishkin's group, is novel. There is something symbolically appropriate here, I cannot help feeling. I am apparently at the brink of becoming the first philosopher since Descartes who has related his philosophical views to up-to-date anatomical discoveries. Moreover, the views in question were introduced above by considering a Cartesian problem. The identity of Vaina's distinction with the one drawn above can be argued for in different ways. It is strongly suggested already by the characterization of the two systems as the "what" system and the "where" system. Better arguments are nevertheless obtained by considering the cumulative evidence concerning the disturbances of the two systems. If the distinction between the two cognitive systems is correct, it is to be expected that there are two kinds of behavioral disturbances, viz. spatial disturbances and visual recognition disturbances. As Vaina notes, this distinction is established "most elegantly ... in Newcombe and Russell's work (1978). They showed that a clear distinction can be made between spatial and visual recognition deficits, although they frequently ... occur in combination.',23 A vivid idea of the contrast is reached by considering particular manifestations of the failure of the one or the other system to operate satisfactorily. Several of the suggestion that can elicited from actual observations have considerable philosophical interest in their own right. An especially instructive case is color perception, which is often thought of by philosophers as a purely perceptual phenomenon involving only pure unedited sense-impressions. This turns out not to be the case, however, in the sense that a patient's full concep-

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tual repertoire for colors may be disturbed even though no defect can be found in the patient's color sensations. (For instance, the patient is not color blind.) In one case, "damage to the occipito temporal cortex produced agnosia for colour consisting in an inability to name colours or point to them in absence of disturbances of colour perception. ,,24 Thus color perception apparent! y belongs to the "what" (public) system. A philosopher is here reminded by Wittgenstein's sometime thought-experiment in which color concepts rely on a color chart with which objects must be compared for the purpose of establishing their color.25 Disturbances of the "what" system can be compared, conceptually, with damages to the color chart as distinguished from disturbances of the patient's color sensations. Even though the empirical realities turn out to be incompatible with some details of Wittgenstein's doctrine (for instance, color-blindness cannot be explained by reference to what a color-blind person can or cannot do), we are not far removed here from Wittgenstein's ideas of colors as presupposing a rich conceptual structure, a "color space" or "color geometry". On the level of associative functions, this is characteristic of the "what" system in general. Defects in that system appear typically in the form of mistakes and failures to place perceptual information properly within an impersonal conceptual framework. As Teuber puts it (quoted by Vaina), "a normal percept ... has somehow been stripped of its meaning. ,,26 For instance, in "visual object agnosia the patient can see the object presented to him visually, he can produce drawings and match it accurately, but he cannot name it or demonstrate its use. ,,27 In view of Quine's cute reference to what is clearly a public identification task as "matching a face with a name",28 it is amusing to note the phenomenon called prosopagnosia. It "describes the inability [of a patient] to recognize familiar faces although often the patient perceives faces normally (e.g., discrimination and matching are normal). ,,29 However, the anatomical location of prosopagnosia has not been conclusively established, even though functionally it obviously amounts to an inability to relation perspectival information to a public framework. The disturbances of the "where" system are equally striking, and equally obviousl y related to the counterpart of this system among the two modes of identification. The most fundamental feature of the perspectival mode of identification is, well, its perspectival character. It presupposes a vantage point that depends on the perceiver or rememberer or knower. This vantage point is defined in the case of visual perception by the individual's own body, its location and orien tation. Hence it is significant that many of the disorders of what Vaina calls the "where" system pertain to "spatial disorders relative to the

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individual's own body.,,30 They include "errors in recognizing, naming or pointing out on command various parts of his own body, disorders of the body image" etc. (loc. cit.).More generally, the assimilation of the "where" system to the perspectival identification system leads us to expect that disturbances of this system should manifest themselves in visual disorientation in the absence of visual object agnosia (which relates to the other system). This expectation is quickly fulfilled, according to Vaina: 31 The elegant and thoughtful work of Holmes (1918,1919) remains perhaps even today the most detailed and eloquent example of deficits in the visual exploration of space and their complex consequences for many spatial tasks. He reported six patients who suffered penetrating missile wounds to both posterior parietal areas and subsequently exhibited disturbances in orientation and space localization by sight, and were unable to estimate absolute and relative distances,lengths, sizes and thicknesses. These patients could not differentiate which object was nearest and which farthest, which was most to the left or most to the right. They were unable to determine or compare size of objects. This resulted in patients running into objects when walking. All these patients exhibited the symptom of misreaching as well. These examples show beyond reasonable doubt the close relationship between my perspectival vs. public distinction and Vaina's "where" vs. "what" distinction. Hence the vivid clinical examples at the same time serve to illustrate my distinction which otherwise might smack of an artificial invention of an abstract logician. We can go further than this, however. Conceptual analysis does not have to imitate Minerva's Owl, however, and to begin its flight only after the workday of cognitive scientists has come to an end. The insight of the near-identity of the two distinctions enables a philosophical analyst to apply some of his or her critical tools for the purpose of clarifying the issues on the side of empirical research and perhaps even for the purpose of suggesting some new departures. Here I shall try to sketch only a few. An especially subtle question is the relation of the so-called "where" system to space and geometry. We have seen that certain spatial phenomena, especially the recognition of certain kinds of movement, belong to the public ("what") system. More generally, the impersonal public framework can in principle contain a geometrical (e.g., geographic) system. If so, then we would have to be doubly careful in speaking of space and the psychological processing of space and spatial relations, for we would have to distinguish physical space from per-

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ceptual space, and the two would belong to different systems. The label

"where" system would then also turn out to be misleading. It appears that in this direction more work is needed both by way of conceptual analysis and by way of empirical work. An especially central question is whether physical space is conceptually independent of perceptual space, i.e., whether physical space belongs in some sense to the "what" system or whether it belongs partly to the "where" system. (Of course, the real relations of the two may turn out to be more complicated than either alternative.) Again, we are moving in the vicinity of old philosophical problems. For instance, Kant would have answered my question by maintaining the total primacy of visual space. That the situation is quite complex is suggested by empirical results" Teuber (1973) advanced the hypothesis that different spatial abilities were mediated by different parts of the brain. Thus, spatial orientation to external objects is mediated by the parietal region [where the "where" system is located], particularly the right; spatial discrimination involving the subject's own body is mediated by the left frontal region.,,32 There are several fascinating types of evidence available here. Benton reports the fascinating case of De Renzi (1962), who was unable to make localizations on a city map but could correctly name its streets, public buildings and gates. However, he could not specify the spatial relationship among those elements that he could verbally identify. Thus one must carefully differentiate between verbal knowledge of space and spatial knowledge of space. Perhaps "spatial knowledge of space" presupposes an ability to imagine oneself mentally in the relevant location, and hence would belong to the perspectival system. Another difference to note is that between memory for routes, or topographical arrangement (e.g. one's house) and the ability to do mental spatialoperations required in ambulation (Butters and Barton, 1970 and Butters et aI., 1970). One could perhaps speculate that the handling of the ambulatory space is done in multiple coordinate systems. One system is object centered, which is desirable (Marr and Nishihara, 1977, Marr, 1981, Vaina, 1983 and Vaina, 1985) for shape and object recognition regardless of position in space; this may also be used for recognition in space. Another must be viewer-centred, needed for relatin~ to the space around as a function of himself (Vaina and Perett (1985»? These speculations are especially interesting in that the contrast between the two coordinate systems begins to resemble closely my contrast between perspectical (viewer-centered) and public (object-centered) frameworks of

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identification. (In fact I explained my distinction precisely by speaking of two different frameworks not unlike coordinate systems.) If so, Vaina's distinction is no longer a subdivision of the "where" system, but a contrast between the "where" and the "what" systems. Here awareness of the conceptual situation may help to clarify the empirical issues. Likewise, a suggestion is yielded by the logico-linguistic analysis of the two correlated distinctions. It was found above that the two kinds of identification are expressed differently in natural languages. If the two go together with functionally and anatomically distinguishable cognitive systems, disturbances of these two systems can be expected to show up in the form of linguistic disturbances. I am not aware of any actual data, but it the results reached here will in any case show cognitive scientists where to look for such evidence. Admittedly, the situation is made more complicated by the fact that in natural languages the two contrast systems are not matched by two equally clearly contrasting sets of expressions, as was pointed out above. The linguistic disturbances can therefore be expected to take the form of the use of expressions for one mode of identification in the role of the other rather than, e.g., the form of patient's losing part of his vocabulary. There are still other connections between conceptual analyses and empirical work, and other suggestions that are prompted by noticing the connections. Earlier, it was pointed out that the distinction between perspectival and public modes of cross-identification applies also to memory. (Cf. here (2), (5), (8), (B), and (16), above.) It may therefore be expected that the same contrast should have caught the attention by empirical investigators of human memory. This expectation is resoundingly fulfilled, this time not by neurophysiological discoveries but by theories in traditional psychology. Endel Tulving has sought to distin~uish from each other what he calls episodic menwry and semantic menwry. 4 It does not require great ingenuity to see that this contrast is basically the same as that between perspectival and public identification. Indeed, Tulving compares it himself to Russell's distinction between knowledge by acquaintance and knowledge by description.35 He also relates his ideas about memory to a contrast between "where" and "when" questions on the one hand and "what" questions on the other,36 thus almost conforming to Vaina's very terminology. The conceptual insights we have reached in the present paper seem to be highly relevant to Tulving's ideas, and can in fact be used to criticize them and to put them into perspective. For instance, it is fairly obvious that what Tulving is getting at is not really semantic memory in the sense of memory for meanings, even though Tulving seems to run the two together occasionally.37 Rather, so-called semantic memories are memories which have, as it were, been inter-

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preted by relating them to a public framework, so that the subject knows what the memories are about and in that limited sense can assign a "meaning" to them. Of course, what we have here is merely a special application of the remarks made above concerning the nature of public identification in general. Also, it was seen that the distinction between the two types of cross-identification does not mean a distinction between two different kinds of knowledge or two different kinds of seeing. In the case of these two cognitive concepts there is little temptation to postulate a distinction, except perhaps for a believer in the contrast between knowledge by acquaintance and knowledge by description. The analysis presented here shows that there is no more reason to assume a distinction between two different kinds of memory. Tulving's contrast is not really a distinction between episodic and semantic memory but between subject-centered and object-centered frameworks in which the objects of memory can be identified. These remarks have consequences even for the experiments and other empirical data which Tulving presents for his views?8 I cannot pursue the details here, however. Suffice it to emphasize how they illustrate the relevance of conceptual analyses for actual empirical research in different branches of cognitive science. Conversely, experiment-generated work can help to show the realism of suitable conceptual analyses. My distinction between the two modes of crossidentification is a case in point, as we have seen. Now the possibility of this distinction is grounded on the possibility of drawing the world lines of crossidentification in more than one way. This in turn creates a distinction between perceptions, items of knowledge, and memories which dependend on some particular method of cross-identification and those that do not. In practice this typically means a distinction between recognizing a particular object and recognizing (e.g., in terms of its functional characteristics) what kind of object it is. There seems in fact to be good reasons to believe in the psychological reality of this distinction. But what are the philosophical upshots of all this discussion? What is its consequences for the contemporary philosophy of mind? To some extent, each of you will have to draw your own conclusions. There are nevertheless a couple of general suggestions here to which I want to draw your attention. First, the correlation between the two modes of identification, which belongs firmly to semantics, and the two cortical pathways provides a live example of those rare birds whose very existence is frequently doubted by philosophers, "psychophysical laws". The relevance of such an impeccably confirmed psychological correlation for philosophers' animadversions about questions like the mind-body problem ought to be obvious.

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Furthermore, and most importantly, my observations are relevant to the frequently voiced view that a satisfactory psycholinguistic or, more generally, cognitive-psychological theory: should in the last analysis be syntactical, because it should be computational?9 A purely syntactical theory in the intended sense would exclude all semantical (and thereby in effect all informational) concepts, all references to what the different features of the computational processes that go on in the human mind and in the human organism represent What has been found here offers little aid and comfort for such a view. At least the present stage of our knowledge, the best way of specifying what the function of certain cortical pathways is, is to speak of their functions. In the case of the two cognitive systems discussed above, these functions even seem to be partially expressible in logical terms, by speaking of certain methods of cross-identification. These methods or modes are of course as semantical as anything can be. Hence a purely syntactical theory just is not what is needed here. This observation is lent a sharper edge by the far-reaching syntactic similarity of the ways in which the two modes of identification are naturally expressed. This striking parallelism was pointed out earlier. It throws harsh critical light on recent methodologists' frequent emphasis on syntactical and computational explanations in cognitive science. For instance, assume for the sake of argument that the formal symmetry between two modes of identification obtains in some suitable "language of the mind" or "mentalese". Then a mere formal translation (mapping) of the expression of some language or language fragment into this "mentalese" cannot be a fully satisfactory explanation for the phenomena which depend on the distinction between the two cognitive systems, for the mapping can be done (because of the symmetry) in two different ways. The two sides of the symmetry can only be distinguished from each other semantically, not syntactically. Thus, even though the distinction between the two cognitive systems is made in the framework of an algorithmic approach to cognition in the sense of Marr and Nishihara,40 its counterparts in the logical analysis of cognitive concepts belongs firmly to what logicians and philosophers could not help recognizing as semantical (model-theoretical) conceptualizations. Thus the present paper can serve as yet another reminder of the fact that semantical (informational) concepts and conceptualizations can play an important role in what is called a computational theory in cognitive science. Hence the suspicions that some philosophers and psycholinguists seem to harbor about semantical (informational) concepts appear to be groundless. It would in fact be richly ironic if an effort were at the present time to banish the concept of knowledge and the tools of epistemic logic from cognitive

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science in the interests of a purely computational approach. For recently the very theorists of computation and computational approaches to thinking and intelligent functioning, viz., computer scientists, especially researchers in AI, have discovered in a large scale the relevance of the notion of knowledge and have even rediscovered philosophical logicians' old epistemic logic.41 However, another observation can be made here by reference to what has been found in this paper. It serves to clarify the role of epistemic and other semantics-based concepts in cognitive science. The informational character of such crucial concepts as knowledge does not mean intentionality in any sense of this dangerous expression which would presuppose consciousness. In fact, the case study here outlined shows that the duality of the two different identification tasks is a fact of live even for automata, at least on the level of visual perception. In order to see this, you can imagine a robot which has an optical device by means of which it can scan its environment and recognize objects by means certain systematic characteristics, e.g., numbers painted on them. Such a robot can be programmed to perform two different kinds of functions. It may be programmed to be capable of receiving a characterization of an object, in my illustration, a number, and to scan its environment in search of an object meeting that characterization (having that number painted on it). Or else it can be programmed to try to identify objects by means of its optical device, e.g., to find the number painted on a given object. The former task means essentially answering a "can you see" or "where" question, i.e., a perspectival identification task. The latter problem means answering a "what" or "who" question, i.e., accomplishing a public identification. This distinction is not imaginary, either. Artificial intelligence researchers have drawn it independently of the considerations offered in this paper or reported there. 42 This fact illustrates vividly the independence of the distinction between the two modes of cross-identification of intentionality in the conventional sense of the term. In conclusion, even though I am presenting in this paper only a case study, it does have -- it seem to me -- a potential impact on philosophical discussions of mind and of the way it ought to be studied. This impact is partly due to what I can only perceive as the alienation of philosophers from actual working problems in psychology and in cognitive science. In the works of most contemporary philosophers of mind, I miss any real Fingerspitzenge/uhl for what goes on in the studies that seem to be most indicative of what actually goes on in a human organism when it (she, he?) carries on what is called thinking and also indicative how those processes are related to their expressions in language and logic.

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NOTES 1 Rene Descartes: 1637,Discours de la methode, lan Maire, Leiden. This paper was originally presented as my contribution to the 1987 meeting of lIP on Descartes and the Contemporary Philosophy of Mind. 2 Jaakko Hintikka: 1962, 'Cogito ergo sum: Inference or Performance?', Philosophical Review 72,3-32. 3 This immediately explains the curious temporality of Descartes's insight. ..... I had only to cease to think for an instant of time, and I should then (even although all the other things I had imagined still remained true) have no ground for believing that I can have existed in that instant. (Discours, Part IV). 4 For instance, the well-known criticism by Fred Feldman: 1973 (see his paper 'On the Performatory Interpretation of the cogito', Philosophical Review 83, 345-363) is predicated on the mistaken idea that I am trying to explain the nature of Descartes's thesis simply by acknowledging its character as an existentially self-verifying sentence, almost as if I were trying to present a syllogism with existentially self-verifying as a middle term. This is a radical distortion of what I did in the original paper. A great deal of further argument is needed to show why and when an existentially inconsistent sentence is absurd to utter. S See L. Chr. Lichtenberg and Fr. Kries (eds.): 1800-1803, Georg Christoph Lichtenbergs Vermischte Schriften, 1·5, Gottingen, especially 2, p. 96. 6 Italo Calvino: 1977, The Nonexisting Knight & The Cloven Viscount, lIarcourt Brace Jovanovich, New York, especially pp. 3-7. 7 If it is possible for someone to say, "I don't exist", without thereby falsifying what he is saying, how can Descartes's thought that he doesn't exist be selfrefuting? Yet everything depends here on the precise sense of "exist". 8 See Jaakko Hintikka, 1969: Models for Modalities, D. Reidel, Dordrecht, chapter 'On the Logic of Perception'; The Intentions of Intentionality, D. Reidel, Dordrecht, 1975, chapters 34; 'Knowledge by Acquaintance -- Individuation by Acquaintance', in D. Pears, editor, Bertrand Russell: Critical Essays, Doubleday, Garden City, NJ., 1972, pp. 52-79. 9 You can think of the totality of your fIrst-hand memories as constituting a long drama (or, perhaps more realistically, a long-running soap opera). There is a fixed slate of characters (roles) in such a play, and they can be discussed as well-defIned individuals even if you don't know who the actors are in their "real life outside the theater", i.e, who they are identifIed by public criteria. For instance, my next-door neighbors can play defInite roles in such a soap opera without my knowing what their names or professions or their social security numbers are, i.e., without my knowing what usually counts as indications of

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knowing who they are. Notwithstanding all this ignorance, I can of course be said to know them. 10 In 'Knowledge by Acquaintance - Identification by Acquaintance' (note 8 above) I argued that perspectivally identified entities were roughly speaking those we are acquainted with in Bertrand Russell's sense. For Russell, see his (1981) 'Knowledge by Acquaintance and Knowledge by Description', in Mysticism and Logic, Longmans, London, 1918, pp. 209-232. 11 See the papers mentioned in note 8 above. 12 See Saul Kripke: 1980, Naming and Necessity, Harvard University Press. Kripke characterizes his "rigid designators" by saying that each of them necessarily refers to the same individual in every possible world in which this individual exists. But this does not tell us anything whatsoever before we know what counts (in our conceptual system) as being the same individual in different worlds. 13 See Bertrand Russell, Mysticism and Logic, op. cit., p. 224. 14 Even though it is a fundamental mistake to think that Wittgenstein in any sense denied the reality of knowability of private experiences, he certainly would not have countenanced private criteria of identification. Cf. here Merrill B. Hintikka and Jaakko Hintikka: 1986, Investigating Wittgenstein, Basil Blackwell, Oxford, ch. 10, especially sec. 4. 15 No wonder Descartes moved (in(the second meditation) immediately from his cogito insight to the thesis sum res cogitans. 16 See here also the works mentioned in note 8 above plus Jaakko Hintikka: 1976, The Semantics of Questions and the Questions of Semantics (Acta Philosophica Fennica, 28, no. 4), The Philosophical Society of Finland, Helsinki. 17 In the past, philosophers occasionally quarrelled about whether the subject must have recognized b in order for it to be true to say that she or he has seen b. Cf., e.g., C.D. Broad, G.J. Warnock and EN.A. Vesey in Robert J. Swartz (ed.): 1965,Perceiving, Sensing, and Knowing, University ofCalifomia Press, Berkeley and Los Angeles, pp. 29-83. The controversies were futile, however. All we have is a distinction between two different senses of the English directobject construction "a sees b". 18 See note 10 above. 19 See here The Semantics of Questions and the Questions of Semantics (note 16 above). 20 Forthcoming in Synthese Library, Kluwer, Dordrecht. My references are to a draft version of the book. See also John H.R. Maunsell, 'Physiological Evidence for Two Visual Subsystems', in Lucia Vaina (ed.): 1987, Matters of Intelligence, D. Reidel, Dordrecht, pp. 59-87.

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21 David Marr's work is summarised in his book (1982) Vision, Freeman San Francisco. See also David Marr and H.K. Nishihara: 1978, 'Representation and Recognition of the Spatial Organization of Three-Dimensional Shapes', Proceedings of the Royal Society London B, vol. 200 (1978), pp. 269-294. 220p. Clt., . p. 9 . 23 Op. cit., p. 11. 24 Op. cit., p. 15. 25 Cf. Ludwig Wittgenstein: 1953, Philosophical Investigations, Basil Blackwell, Oxford, I, secs. 48-49; 1958. The Blue and Brown Books, Basil Blackwell, Oxford, e.g., pp. 3, 13-14,86-87, etc.; 1977. Remarks on Colour, Basil Blackwell, Oxford, especially I, sec. 59; Merrill B. Hintikka and Jaakko HintikkaInvestigating Wittgenstein, op. cit., especially ch. 11, secs. 10-14. 26 0p. cit., p. 14. 27 Op. cit., p. 14. 28 See W.V. Quine: 1976, 'Worlds Away', Journal of Philosophy, vol. 73, pp. 859-863; and cf. Jaakko Hintikka, 'Quine on Who's Who', in Lewis E. Hahn and P.A. Schilpp (eds.), The Philosophy of W. V. Quine (Library of Living Philosophers, vol. 18), Open Court, LaSalle, Illinois, pp. 209-226. 29" . . p. 16 . vama, op. Clt., 30 Op. cit., p. 17. 31 Op. cit., pp. 19-20. 32 Op. cit., p. 18. 33 Op. cit., p. 18. 34 Endel Tulving: 1983, Elements of Episodic Memory, Clarendon Press, Oxford, with further references to the literature. The connection between Tulving's distinction and mine was first pointed out to me by Barry Loewer ~~ersonal communication). Op. cit., pp. 17,41,58. 36 0p. cit., pp. 25, 35. 37 Cf., e.g., op. cit. p. 49: ..... semantic memory develops before episodic memory. Kinsbourne and Wood (1975), for instance have pointed out that people learn 'word meanings and such semantic information before there is any evidence of episodic remembering' ...... Tulving is not unaware of the pitfalls of the term "semantic", however; cf. op. cit., pp. 28-29. 38 In chapter 5, e.g., on pp. 79-83 of op. cit. Tulving describes experiments in which the episodic vs. semantical distinction was tested by testing inter alia subjects' memory for the meaning of words. This is not at all a representative situation. It would have been better to test the contrast by means of, e.g., comparisons between memories of events involving known and unknown people. In fact, Tulving does rely on the mirror image of such a situation, which is ex-

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emplified by the Warrington-Weiskrantz effect. (Op. cit., pp. 30-31,94-95, 115-116.) 39 Cf., e.g., Stephen Stich: 1983, From Folk Psyclwlogy to Cognitive Science, The MIT Press. 40 Cf. David Marc and H.K. Nishihara, 1978: 'Visual Information Processing: Artificial Intelligence and the Sensorium of Sight', Technology Review 8, pp. 2-22, and the works mentioned in note 21 above. 41 Cf., e.g., Joseph Y. Halpem (ed.): 1986, Reasoning About Knowledge, Mor§:an Kaufmann Publishers, Los Altos, CA. 2 The distinction is a well-entrenched part of the folklore of AI. For an early formulation, see R. Paul, G. Falk and J.A. Feldman: 1969, 'The Computer Representation of Simply Described Scenes' ,Reports of the StanfordArtificial Intelligence Project AIM-107, Computer Science Department, Stanford University.

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or a whIle, it seemed that my dialogue with Van Quine-a dialogue partly real, partly fictional-had been carried as far as it could profitably be continued. I The salient points of this dialogue are worth surrnning up. Quine's old objections to modal logic were not all dispelled by the development of a genuine semantics (model theory) for modal logics, contrary to what the first fullfledged possible-world semanticists had hoped-and believed. The interpretational problems Quine had so vigorously made us aware of merely seemed to settle down on a new location: on the problem of cross-identification. 2 Against the superficial contrary claims of Kripke, Montague, and others, I argued that we cannot take cross-identifications for granted. It does not suffice simply to postulate a domain of individuals which would be prior to the possible worlds they inhabit and each of which then would (or would not) make its appearance in any given world. 3 There is every reason to think that Quine would approve of the purported conclusions of my arguments. Indeed, if I am not mistaken, Quine's arguments against modal logic preserve their sting even after their precise address is changed so that they now are directed against the possibility or at least the reasonableness of cross-identification. This shift of focus admittedly means that some of Quine's old problems can be solved. In particular, Quine's problems concerning identity are independent of the cross-identification problem, and hence beyond the reach of Quine's modified criticisms. 4 But other criticisms of his, especially those directed against the possibility of mixing quantifiers and modal operators, will apply with vengeance--or so it seems. We have to recognize, moreover, that the 'world lines' of cross-identification (notional lines each connecting the embodiments or roles of one and the same individual in different possible worlds) are not determined by God, Nature, or Logic, but are in principle drawn by ourselves. They are not drawn arbitrarily, it is true, but by means of various objective considerations, such as continuity in space and time, continuity of memory, and location in someone's 137

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visual space. Moreover, they are objectively retraceable once they have been drawn, independently of an individual language user's thoughts and doings. Nevertheless, these lines of cross-identification could in principle be drawn differently. 5 Furthermore, the presuppositions on which the tracing of world lines rests can fail, and will fail if we consider sufficiently distant and sufficiently irregular worlds. (The reason is that these presuppositions amount to postulating various general regularities, such as the continuity of physical objects in space and time and the going together of bodily continuity and continuity of memory.) Moreover, such irregular and dissimilar worlds have to be considered in the semantics of so-called logical or alethic modalities (logical necessity and logical possibility). Hence we cannot have a set of world lines spanning all the worlds we need in alethic modal logic. 6 Since these world lines define the individuals we quantify over when we use modal logic (more accurately, when we 'quantify into' modal contexts), we do not have well-defined individuals at our disposal in any realistically interpreted quantified modal logic. In virtue of the inseparable conceptual tie between quantifiers and individuals, which Quine has aptly emphasized, a quantified modal logic is impossible if we want to be able to interpret it in the obvious, intended way in a large scale (and not just 'locally', to wit, with respect to some previously restricted narrow class of possible worlds).? Thus Quine turns out to be basically right in his criticism of quantified modal logic. A realistically interpreted quantified alethic modal logic is impossible. However, the reasons for this failure of quantifiers to mix with logical necessity and logical possibility are deeper than Quine realized. There is nothing intrinsically impossible or even awkward about cross-identification. I have argued that a great deal can be done for cross-identification by means of resources Quine himself countenances, especially by means of the continuity of objects in space and time. Whatever difficulties there may be are due to the presuppositions of these methods, which will fail in many logically possible worlds. Recently, Quine has signalled his qualified agreement with this view of the problem of cross-identification as operating essentially like re-identification. 8 It can be argued that these presuppositions are normally satisfied for several other concepts which behave in many respects like logical modalities. Most of the so-called propositional attitudes are cases in point. Hence a quantified epistemic logic is interpretationally feasible, and so are quantified logics of belief (quantified doxastic logic), memory, perception, etc. (It is instructive to see that Quine has always been more tolerant towards propositional attitudes than towards logical modalities.)9 But this relative success of quantified logics of propositional attitudes has no a priori guarantee, either. Success is found when people's propositional attitudes are sufficiently strong and sufficiently sweep-

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ing. For the problem is whether we can limit our attention to worlds that are sufficiently similar to each other and sufficiently orderly. Now in (say) doxastic logic the relevant possible worlds are all the worlds compatible with what someone believes. Hence these worlds are of the desired sort if and only if that person has sufficiently strong beliefs (so as to exclude enough possible worlds) and sufficiently specific beliefs (so that the remaining worlds are orderly enough). Of course there cannot be any a priori guarantee of this. Quantified logics of propositional attitudes are thus possible only in virtue of people's rationality, I am tempted to say. Of course there is nothing wrong, or even strange, in saying this; it merely amounts to saying that the applicability of logic to people's propositional attitudes presupposes that they are rational. There exists no informed discussion in the literature of the question as to whether the worlds considered in using those modalities we employ in meaning theory are similar enough and regular enough to allow for an interplay with quantifiers. We may call these analytic modalities. (Once again, we are in the vicinity of Quine's ideas in that he has emphasized the parity of analyticity and modality.) There nevertheless is little hope, it seems to me, to save them from the same fate as logical modalities. Thus my exchanges with Quine have established a much larger area of agreement than either of us probably expected. Even though a large number of smaller problems remain, it is not clear that a discussion of Quine's views is the right way of attacking them. The same goes for the big problem of our actual cross-identification methods. Esa Saarinen has cogently pointed out how some of my earlier statements on this subject rest on partial oversimplifications. But Quine's views do not seem to offer either insights or inspiration for further work in this direction. 10 However, two interesting new avenues of further discussion have recently opened up. On the one hand, a new skeleton has been found in the cupboard of semanticists of modal logic, one which Quine obviously will relish. 11 On the other hand. Quine has sought to complement his criticism of alethic modal logic by giving reasons for being suspicious of the logic of propositional attitudes as well. 12 Dispelling these suspicions offers a natural occasion to clarify certain important issues concerning the foundation and the uses of epistemic logic, and of the logic of propositional attitudes more generally. I shall in this paper consider only the second of these two new subjects. Epistemic logic is a particularly instructive proving ground for the issues Quine raises concerning the logic of propositional attitudes, because we have a rich supply of different grammatical constructions in terms of verbs for knowledge and a rich supply of pretheoretical linguistic and logical ideas, sometimes misleadingly labelled 'intuitions', concerning them. 13 Most of these so-called 'intuitions' can be related to what we do in epistemic logic. This is a merit which Quine acknowledges in connection with my analysis of quantified epi-

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stemic logic. 14 For instance, constructions in which one quantifies into an epistemic context are typically captured in English by interrogative constructions with verbs like 'knows' .15 A case in point is (I) Albert knows who wrote Coningsby can be thought of as being (admittedly by way of first approximation only) equivalent with (2) (Ex) K Albert (x wrote Coningsby). The variable x has to be thought of here as ranging over persons. This is determined by the fact that the interrogative word in (I) is 'who'. For different whowords, we have to assign different ranges to our variables. In particular, the interesting 'uniqueness conditions' which express the conditions on which we can quantify in (in the sense the conditions on which existential generalization is valid in a given context) often have idiomatic English counterparts. For instance, (2) can be inferred from (3) KAlbert (Beaconsfield wrote Coningsby), that is, (3)* Albert knows that Beaconsfield wrote Coningsby only in conjunction with the further premise (4) (Ex) KAlbert (Beacons field = x). But what (4) says is clear: (5) Albert knows who Beaconsfield is. Moreover, it is equally clear already pre-theoretically that (5) expresses the condition on which (I) is implied by (4). The corresponding uniqueness conditions for more complex cases can be expressed in a similar manner (whenever they can be expressed in the first place). I am nevertheless afraid that Quine is praising my epistemic logic for a wrong reason. He writes on my criterion for the admissibility of quantifying in: "Unlike the criterion for a rigid designator, this brings matters gratifyingly close to home. It is very ordinary language indeed to speak of knowing who or what something is." 16 Here Quine seems to me to turn the right heuristic priorities upside down. He seems to suggest in effect that we should employ our pre-theoretical insights concerning epistemic expressions in natural languages to elucidate what goes on in the formal language (or languages) of epistemic logic. For instance, there is a hint of a suggestion in Quine that by considering an English sentence like (I) we can see more clearly what (2) means. And even if this semantical priority of natural language and ordinary discourse were not what Quine has in mind here, it is very much the working assumption of Boer and Lycan, whose work Quine refers to with approvaL I? Even if he is not committing the mistake I am about to criticize, he is condoning it. It is admittedly true that connections between logician's canonical notations and our familiar vernacular--connections which perhaps in some cases amount

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to relations of synonymy-play an extremely important role in developing the theory of formal languages, and especially their semantics. But such connections are best viewed as happy outcomes of applications of one's basic logical and semantical theory, which must first be developed. Such pleasant connections as were illustrated above are hoped-for end products of formal semantics, not its starting-points. Quine's hint exemplifies what seems to me one of the most pervasive and pernicious mistakes in contemporary philosophy of logic and philosophical logic: neglect of the fact that formal languages not only can be but ought to be, metaphorically speaking, a philosophical logician's 'mother tongue' or 'first language', first of course not genetically but systematically. Somewhat less metaphorically expressed, the first and foremost virtue of formal languages is the ease with which their semantics can be presented. For instance, Tarski-type truth-definitions for suitable formal languages constitute the clearest example of a semantical theory of the kind Davidson is looking for. 18 But the greater semantical clarity of suitable formal languages as compared with natural ones implies that formal languages can in principle be understood and mastered independently of the messy ways in which the same things are expressed in natural languages and independently of the even messier ways in which natural languages are translated into logician's standardized discourse. Were it not for this semantical clarity of formal languages, a favorite strategy of many theorists of language would not make much sense. This is the strategy of elucidating the phenomena of natural languages by trying to translate their sentences into a formal logician's 'canonical notation'. For, if the latter were not semantically superior to our informal jargons, what would be gained by such translations? Hence the mistake I have been criticizing is more than a little strange for Quine of all people to commit. For he has, by and large, relied on translational strategies. 19 What is more, I have surmised that Quine has been led in much of his work in ordinary extensional languages by an exceptionally clear semantical vision, even though he apparently does not think that we can theorize on a large scale about the semantics of our familiar home language. 20 Hence it seems to me that Quine is not giving the languages of epistemic logic the same semantical credit he is giving the ordinary extensional languages, especially to the language of quantification theory. An instructive case study of how much easier and how much more informative it is to build the bridges between natural languages and the languages of an epistemic logician from the vantage point of the latter (and especially from the vantage point of the semantics of epistemic logic) is offered by the neat solution that I have given to what may be labelled the dual ostension paradox.21 This apparent paradox deals with the use of who-questions in ordinary discourse. For instance, somebody might walk into a meeting room and ask, pointing,

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(6) Who is the man over there? The questioner obviously wants to be brought to a position where he or she can say, truly, (7) I know who the man over there is. An appropriate response to the question might be to say, for instance, "Sir Norman Brook". This would normally bring the questioner to a point where he or she can truly say (8) I know that the man over there is Sir Norman Brook. But another person might walk into the same room, for instance with a message in hand, look around, and ask (9) Who around here is Sir Norman Brook? The questioner now presumably wants to be in a situation where he or she can truly say (10) I know who around here is Sir Norman Brook. Now an appropriate answer might consist in pointing to someone and saying, "that man over there." Thereupon the questioner can normally say, truly, (8). The logic underlying this perplexing double use of interrogatives has exercised philosophers and linguists. 22 How can who-questions be used in such dissimilar ways? How can the same information (the information codified by (8)) (serve as an answer to entirely different questions? What is the logic of (6)-(10), anyway? Cook Wilson used similar examples to claim that formal logicians could not cope with the allegedly different uses of 'is'. 23 Linguists and logicians alike have nevertheless failed to find a satisfactory account of the paradox. For instance, the brand-new and in many ways impressive theory of the logic and semantics of questions by Lauri Karttunen does not yield an explanation of the dual ostension paradox.24 Even the ingenuity and patience of Steven Boer and William Lycan has not produced anything like a real theory for this paradox. 25 Furthermore, a formalization along the same lines as in (2) and (4) above does not automatically solve the problem, either. Yet the problem is solved in one fell swoop as soon as we realize that we have here an instance of the use of two different cross-identification methods in one and the same situation. I had earlier shown the need of considering both methods quite independently of all questions about questions or their uses. 26 In (6) and (7), we are relying on the usual "descriptive" cross-identification methods. Hence (7) can be paraphrased in epistemic logician's jargon by using the same quantifiers as were employed earlier: (11) (Ex) K( (the man over there = x) But since a quantifier relies on a notion of individual and since the notion of individual is (when employed in epistemic contexts) relative to a method of cross-identification, we have to ascribe a different quantifier to (9) and (10), and to paraphrase (10) as, say,

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(12) (3x) K. (Sir Norman Brook = x) where "(3x)" is a quantifier relying on what might be called perceptual methods of cross-identification. They are a special case of what I dubbed (borrowing a semi-technical term from Russell's early work) cross-identification methods . 27 bY acquaintance. These cross-identification methods are in every serious practical sense unobtainable simply by contemplating and analyzing the ordinary-language expressions in question. Yet they are naturally and easily thought of (especially in the case of perception) at once as soon as we conceptualize that situation in terms of possible states of affairs and cross-identification between them, in effect, conceptualize it in semantical terms. For what are the relevant possible states of affairs here? They are all the states of affairs compatible with what the person in question perceives, for instance, sees. What they share most conspicuously is a matching distribution of a number of objects (those the person in question sees) in the perceiver's visual space. In brief, the perceptual alternatives to a given state of affairs share a common perceptual space, for instance a visual space. What could be more natural than to use this perceptual space as our framework of cross-identification, that is, to identify with each other objects occupying corresponding places in them?28 (We even have informal ways of speaking of such cross-identification, albeit somewhat misleadingly. For instance, we can describe perceptual cross-identification by saying that it amounts to considering objects in the perceiver's environment merely as his perceptual objects.) It turns out that this is precisely the cross-identification method that is needed for '(3x)' if the sentence (12) is to behave in the right way. Notice, for one thing, that this distinction between the two cross-identification methods and hence the distinction between '(Ex)' and '(3x)' cannot be made through any usual kind of restriction imposed on the range of the variable 'x'. For, in so far as we are considering the actual world only, we need precisely the same range of values for 'x' in either quantifier, viz., persons (or persons present on the occasion in question). The perceptual cross-identification method is not any easier to recognize directly from the linguistic evidence when this evidence is extended to include some of the most striking and most satisfying consequences of my semantical observations. In order to see what they are, we need first a general observation. From examples like (6)-(8) we can see that the uniqueness conditions I mentioned earlier will do a second duty as conditions for full (conclusive) answers.29 For (7) is what the questioner wanted to be brought about, while (8) is what the response "Sir Norman Brook" brought about. This response is therefore an answer if and only if (8) implies (7). But the inferential step from (8) to (7) is one of existential generalization.

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As was already mentioned, this inference is justified only in the presence of the further premise, which in this case is (13) (Ex) K. (Sir Norman Brook = x), i.e., "I know who Sir Norman Brook is." Thus an epistemic logic yields as an extra bonus a criterion of answerhood (in the sense of a criterion of the conclusiveness of replies). What is even more remarkable is that the same theory works for both kinds of questions and answers. Now how can we verify this claim? We are led by my theory to expect that the condition for "that man over there" to be a (conclusive) answer to (9) is (14) (3x) K. (that man over there = x). What does (14) say? It says that that man over there, that is, the man pointed at, is one of the questioner's acquaintance-objects. Normally, this amounts to saying that the questioner sees that man over there. 30 Needless to say, this is obviously the correct-and by hindsight trivial---<:riterion for an ostensive reply to be a satisfactory answer. (Trying to answer (9) by pointing to a man will succeed only if the questioner sees who is being pointed al.) What is far from trivial is that this condition of answerhood to ostensive questions is correctly predicted by my semantical theory. We can also see what the colloquial renderings of many sentences with a perceptual quantifier are. For instance, (15) (3x) I see that (Sir Norman Brook = x) means that Sir Norman Brook is identical with one of my visual objects; which obviously means that I see him. In this way we obtain more generally an analysis of grammatical direct-object constructions with epistemic verbs, i.e., such verbs as 'sees', 'perceives', 'remembers', 'knows', etc . . . . 31 This analysis is in terms of the that-construction with the same verb plus quantifiers relying on acquaintance. This result is full of both philosophical and linguistic consequences. Among the philosophical consequences there is the possibility of understanding much of Russell's philosophy in 1905-1914 on the basis of the insight that he considered only quantifiers by acquaintance as being irreducible. 32 This is, I have shown, the gist of his attempted 'reduction to acquaintance'. Small wonder also that he for a while maintained that there are only three logically proper names (i.e., singular terms which always satisfy the uniqueness condition), viz., 'this', 'that', and T. These, indeed, are among the few words which cannot fail to refer to a unique perceptual object in so far as their use is being understood. Yet all this wealth of intralinguistic observations cannot seriously have been expected to make it evident to anyone what is really going on in the dual ostension paradox semantically, that is what real logic of the paradox is. The data could not be much simpler, and they have always been easily accessible to anyone. Yet they had not led any earlier analysts to the idea of quantifiers

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relying on acquaintance. The only natural way to them is semantical, and that is the way Quine seems to overlook. All the nice connections between the logical notation and various natural-language and indeed ordinary-language expressions that we just uncovered are applications of my semantical theory, not steps leading to it. Indeed, there is more evidence of Quine's oversight. In the very act of praising my uniqueness conditions he misunderstands their role. Quine writes, after having explained what the analogues of the uniqueness conditions (13) and (14) are for belief (they look like (13)-(14) except that 'believing that' plays the role of "knowing that"; they are the conditions on which singular terms obey the usual laws of quantificational logic): Hintikka's criterion for this superior type of term was that Tom (i.e., the person in question) knows who or what the person or thing is; whom or what the term designates. The difference is accountable to the fact that Hintikka's was a logic of both belief and knowledge. 33

This means that Quine thinks that I am using only one kind of uniqueness condition, viz., (13). Yet the first look at the semantical situation shows that the relation between the respective uniqueness conditions for two different propositional attitudes is one of analogy, not of identity. Uniqueness conditions formulated in terms of knowledge do not carry over to other notions. The point is very simple: a uniqueness condition like (4) says that the singular term in question (,Beaconsfield') picks out one and the same individual in all the relevant possible worlds. For knowledge, these relevant worlds are all the worlds compatible with what someone ('Albert') knows. Uniqueness of reference in all these worlds is precisely what (4) expresses. But when we are considering, say, what Albert remembers, the relevant possible worlds are those compatible with everything Albert remembers. The condition for the name 'Beaconsfield' to point out one and the same individual in all of them is not (4) but (16) (Ex) Albert remembers that (Beaconsfield = x) This need not be implied by (4). Likewise, in speaking of what Albert believes the uniqueness condition is . (17) (Ex) Albert believes that (Beaconsfield = x); and analogously for other propositional attitudes. These conditions do not exhibit any regular relationship of implication one way or the other to (4). The fact that (17) does not allow for an English paraphrase analogous to (5) (even though, e.g., (16) obviously does) admits a separate but natural explanation. 34 The need of varying the uniqueness conditions from one propositional attitude to another is so obvious semantically that Quine's oversight on this point can only mean that he is not giving the semantical viewpoint a run for its money. A sharper insight into the semantical situation would have saved Quine

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from another mistake. In criticizing my use of uniqueness conditions for quantifying in Quine writes: 35 Each belief world will include countless bodies that are not separately recognizable objects of the believer's beliefs at all, for the believer does believe still that there are countless such bodies. Questions of identity of these, fTOm world to world, remain ... devoid of sense .... Yet how are they to be dismissed, if one is to quantify into belief contexts? Perhaps the values of such variables should be limited to objects that the believer has pretty detailed views about. How detailed? Here Quine is simply confused, it seems to me. Of course there is no difficulty in quantifying over individuals in some alternative doxastic world. Consider, for instance, the world which an operator for epistemic possibility invited us to consider. This operator will have the force of "in some world WI compatible with everything Jack believes, it is the case that-." We can quantify over the denizens of WI simply by using a quantifier inside that operator. Why should there be any difficulty? Perhaps because we might want to consider the inhabitants of WI also qua neighbors of ours in our local world, i.e., in the actual world WO" But this in itself legitimate problem has nothing to do with criteria of uniqueness or crossreference. It is due to limitations of the notation of conventional modal logic which never allows us to return in an outside-in evaluation process to worlds considered earlier. 36 It can be cured by enriching the conceptual basis of modal logics, for instance by adjoining to their logical vocabulary Esa Saarinen's 'backwards-looking' operators. 37 It is relevant to note here that we may be able to trace an individual from WI back to Wo even if it does not satisfy the appropriate uniqueness condition like (16)-( 17) above. These conditions require that an individual can be cross-identified between all the alternative worlds. Here we are concerned only with tracing the individual back and forth between WI and WO. In general, Quine is wrong in alleging that attempted cross-world identifications do not make any sense for those inhabitants of an alternative world which do not satisfy the uniqueness conditions. On the contrary, such crossworld comparisons must make sense in order for us to be able to say that they don't satisfy the relevant uniqueness condition. What the falsity of such a condition means is merely that one's search for a counterpart to the given member of a possible world does not always succeed. Once again, both the diagnosis and the cure are crystal clear once we adopt the semantical (possible-worlds) vantage point. From this vantage point, Quine's parting question in my latest quote from him is seen to be merely rhetorical. Quine's most serious charge against my treatment of quantified epistemic logic by means of uniqueness conditions is the claim that these conditions are what he calls "indexical." After having acknowledged that "it is very ordinary language indeed to speak of knowing who or what something is" (as one has to do in the uniqueness conditions) he continues: 38

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However, ordinarity notwithstanding, I make no sense of the idiom apart from context. It is essentially indexical. You may ask who someone is, hearing his name and seeking his face; you may ask the same, seeing his face and seeking his name; you may ask the same, hearing his name and seeing his face but wondering about his claim to distinction. 'Who is he?' makes sense only in the light of the situation. Failing such light, the right answer is another question: 'What do you want to know about him?' Correspondingly the notion of knowing who someone is, or what something is, makes sense only in the light of the situation.

Quine is of course right about the variability of the truth-conditions of 'knowing who somebody is' statements (and likewise for 'knowing what something is' statements). Indeed, he acknowledges that I had pointed out that very variability fourteen years earlier. 39 But does this semantical unstability spoil the job uniqueness conditions are doing in epistemic logic and in the logic of questions? Only if their role is misunderstood, it seems to me. The weakness of Quine's argument is betrayed, at least by way of example, by his first illustration of the vagaries of 'knowing who someone is' statements. This first illustration ("hearing his name and seeking his face [or] . . . seeing his face and seeking his name") is nothing but the paradox of dual ostension analyzed above. Far from contributing evidence against my theory, this application is one of its most striking successes. One excuse for spilling as much ink as I did above on the dual ostension paradox is just that Quine in effect tries to use it as his prize specimen counter-example against quantified epistemic logic. In more general terms, we can see the faflaciousness of Quine's conclusion by examining the role of uniqueness conditions (i.e., if the critical 'who someone is' and 'what something is' statements like (4)-(5), or (11)-(12» in my epistemic logic. Once again, attention to the semantical situation serves us well. What happens is that the truth-values of sentences of the form 40 (18)

(Ex) K(b = x)

and by the same token those of sentences of the form (19)

(3x) K(b = x)

(where 'b' is an individual constant) become largely independent of the truthvalues of other types of simplest sentences, including the usual atomic ones. Indeed, sentences of the form (18)-( 19) can be considered a new class of atomic sentences. This reflects the fact that world lines are not determined in any simple way by the attributes of the individuals they connect. For this reason, the variability of the truth-conditions of 'who someone is' statements is predictable on the basis of my theory, and hence scarcely an objection to it.41 Moreover, my theory offers us several insights into the actual variation of the truth-conditions of sentences like (18)-(19). The contrast between crossidentification by acquaintance and by description mentioned above is a case in point. This contrast is related to a large number of subtle philosophical and Iin-

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guistic issues. My references to Bertrand Russell above will serve to indicate what some of the relevant philosophical issues are. Others are connected with Kant's notion of 'thing in itself,42 and with Husserl's theory of perception43 to mention only a few. These interesting relationships should have whetted a philosopher's logical appetite instead of turning him away from uniqueness conditions as being semantically unstable. Other examples of how the issues that come up on connection with the variability of the truth-values of uniqueness conditions can be of great theoretical interest will be given below. Meanwhile, the nature of QUine's mistake is worth emphasizing. My theory, like any comparable semantical theory, gives an account of how the truth-values of complex sentences depend on those of simpler sentences, ultimately atomic ones. 44 In any particular application, the way in which the truth-values of atomic sentences are determined is taken for granted. Since the simplest uniqueness conditions (18)-( 19) behave like atomic sentences, their truth-values also have to be taken as being given. But the truth-conditions of (18)-( 19) are essentially the same as criteria for drawing world lines. Hence, semantically speaking, world lines have to be assumed to be drawn before any application can get off the ground. Drawing those world lines is never itself a part of the application. The theory is essentially about the interplay of the truth-conditions of atomic and non-atomic sentences. For instance, it shows that (and how) the truth-values of all 'knows+ -a-wh-word' sentences depend on the truth-values of sentences of the form (18)-(19), that is, of the truth-values of the simplest 'knowing who someone is' and 'knowing what something is' sentences. Quine's criticism is not even calculated to affect this central part of my theory. Quine deals entirely with what one can say of sentences of the form (18)-(19), i.e., of the new atomic-like sentences. Hence it is simply beside the point as a criticism of my semantics of epistemic logic. An analogy may be instructive here. When Quine tries to criticize epistemic logic by pointing out the context-dependence of (17)-( 18), it is just as if someone were to attempt to criticize the usual truth-table analysis of propositional connectives by claiming that some of the sentences they serve to combine are context-dependent, fuzzy, or otherwise semantically suspect. Although those shortcomings of certain atomic sentences might be highly interesting in their own right and might in fact lead to further developments in an amplified propositional logic, they scarcely constitute a viable argument for criticizing current propositionallogic and its semantics. Quine's criticism of my use of uniqueness conditions is equally unconvincing, for it leaves epistemic logic proper untouched. All that this logic claims is that, no matter how the world lines are initially drawn, the structure of the rest of the semantics remains the same. This claim is both non-trivial a priori and highly plausible a posteriori in the light of evidence, as exemplified among other things by the unexpected paral-

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lelism between (11) and (12) and by the even more surprising logical parallelism between their natural-language counterparts. (This parallelism shows that uniqueness conditions operate mutatis mutandis in the same way no matter whether world lines are drawn by acquaintance or by description.) This claim is not affected by Quine's criticisms. An application of my epistemic logic does not presuppose that world lines are drawn once and for all by context-independent means, as Quine in effect assumes. All that is required is that throughout anyone particular application the world lines do not change--or if they change, that different warps of world lines be indicated by different quantifiers. Hence Quine's criticism is totally without any force. However, his observation concerning the vagaries of our actual criteria of knowing who is characteristically acute, and poses the further problem as to how to account for this criterial unstability. Even apart from the explanations already given, there are in fact several features of my semantics which serve to make the contextdependence of uniqueness-conditions both natural and interesting. One major source of semantical context-dependence in the general area of the logic of questions is easily pinpointed. It is the role of uniqueness conditions in question-answer relations and their precise import. There is a prima facie methodological reason why logicians and linguists had not reached the simple but deep analysis of the question-answer relation that was outlined above. Logicians and linguists have tried to find a criterion of answerhood that would depend only on the logical and/or grammatical properties of the given question, which are independent of the linguistic and pragmatic context of the utterance in question. (I suspect that when Quine demands of my epistemic logic semantical context-independence, he is operating in the same spirit as these earlier theorists of language.) My solution to the problem of the nature of answers does not depend on such context-independent properties alone. As shown by examples like (4) and (11) above, my conditions of answerhood depend also on what the questioner knows in the sense of knowing that. This knowledge of course varies from one occasion to another. If we are dealing with questions and answers, we must realize that one of the very functions of responses to a question ('answers' in a wide sense of the word) is to supply such collateral information as is needed to make true that uniqueness condition which serves on that particular occasion as the criterion of answerhood. This heavy reliance on the informational background of the different speakers makes my analysis of both direct questions and subordinate questions with 'knows' as the operative verb contextual in a sense which I have spelled out. It is probably an important part of what Quine in effect had in mind. Yet it does not justify his criticism in the least. It is true that this epistemic context-dependence goes against the aims of many linguists and logicians, apparently including Quine. However, it does not make my semantics of epistemic concepts or the corresponding logic any less objective or any less sharp. It may be considered partly

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as an acknowledgement of the fact that the relationship between a question and its answers is intrinsically a discourse phenomenon. 45 The epistemic backgrounds of a question and of an answer to it are typically different (otherwise the question would most likely be pointless) and cannot therefore be 'factored out' as similar differences are normally dealt with in sentence semantics. In brief, this kind of context-dependence is merely a symptom of our being engaged in text semantics and not merely in sentence semantics. And this is definitely a merit of my analysis and not a shortcoming. In general, in spite of repeated claims to the contrary, logical analysts of language have restricted their attention far too narrowly to sentence phenomena (e.g., sentence semantics) at the expense of text phenomena (e.g., text semantics). This epistemic context-dependence of what counts as a conclusive answer to a given who-question is nevertheless different from the variability of the truth-criteria of those very uniqueness conditions themselves which define the conclusiveness of a putative answer. It is the latter, not the former, that Quine seems to have in mind in his specific criticisms. It was already pointed out above that the truth-values of uniqueness conditions are largely independent of the truth-values of other types of simplest sentences. What this means is that the world lines spanning those states of affairs or courses of events we are in effect considering can be drawn in different ways without upsetting the rest of our semantical situation. Indeed, casting the question in the form of a problem of drawing lines of cross-world (crosssituation) identifications is an excellent way of conceptualizing and even partly operationalizing different criteria of knowing who and making understandable people's choices between them. In some cases, it is possible to give systematical characterizations of the difference between different ways of drawing such world lines. The acquaintance-description contrast is a case in point. In many cases, it is nevertheless impossible to offer more than a pragmatic account of what happens in ordinary discourse. Moreover, the account has to be geared to a specific application. It is remarkable, however, that even in such cases my framework allows for explanations which are simply impossible in competing frameworks. This can of course be shown only by examples. To take a trivial one, Evelyn Waugh quotes somewhere in his diaries the old sexist saying: "Be nice to young girls. You never know who they will be." What is the semantical force of 'knowing who' here? It is obviously a nonstandard one, apparently offering aid and comfort to Quine. It is indeed a safe bet that no philosophical theories of personal identity will predict the truth-conditions of this old saw. Yet when it is thought of in terms of world lines, the force of Waugh's dictum is embarrassingly obvious. When different future courses of events are compared with each other, our male chauvinist snob is treating as identical women married to the same gent. We don't understand Waugh without realizing that that's how he is drawing his world lines of nubile women. His reasons for

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doing so are blatant enough, but don't properly belong to the province of logical semantics. This example is of course philosophically trivial in its own right. What is not trivial is that essentially the same kind of analysis can be given of many uses of 'identity' and 'knowing who' in psychology and psychiatry.46 It would take us too far to examine examples of such use in detail here. It is sufficiently obvious, however, that current logical and linguistic semantics or philosophical theories of personal identity are incapable of explaining the meaning of the locutions in question. Criteria of personal identity which rely on bodily continuity or on the continuity of memory cannot account for the meaning of a psychiatrists's words when he or she is describing how a patient came to realize who he was. In contrast, an analysis which construes the patient's insight as his coming to be able to recognize himself as the same person under several different possible courses of events which may involve changes in the patient's psyche clearly has a great deal of promise here. Such an analysis is codifiable in terms of possible-worlds semantics, which once again prove to be not only a versatile tool of philosophical theorizing but also the natural framework for spelling out the meaning of our locutions. Fuller details will have to wait for another occasion. The indications just given suffice to illustrate my point, however. Far from being an argument against my semantics for epistemic logic, the variability of the truth-conditions of uniqueness conditions thus opens the door to a large number of highly interesting applications and hence on the contrary constitutes a strong argument for it, Quine notwithstanding. Moreover, it is precisely the semantical apparatus of possible worlds (possible states of affairs or possible courses of events) and cross-identification between them that makes these applications possible. In dismissing uniqueness conditions, those verbal counterparts of world lines, because of their context-dependence and because of their consequent variability of meaning, Quine is in effect trying to exclude from the purview of philosophical logicians some of their most promising areas of application. JAAKKO HINTlKKA DEPARTMENT OF PHILOSOPHY FLORIDA STATE UNIVERSITY JULY

1979

NOTES I. This has of course been a part of a larger dialogue between Quine and modal logicians in general. A survey of some of its earlier stages is presented in Dagfinn F16l1esdal, "Interpretation of Quantifiers", in van Rootselaar and Staal, editors, Logic.

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Methodology, and Philosophy of Science III Amsterdam: North-Holland, 1968), pp. 271-281. I strongly feel that many modal logicians have not appreciated the force of Quine's criticisms. I have myself tried to do justice to them in my paper "Quine on Quantifying In" in laakko Hintikka, The Intentions of Intentionality and Other New Models for Modalities (Dordrecht and Boston: D. Reidel, 1975), pp. 102-136, which was originally intended as my contribution to the present volume. Some of the salient points of that paper will be summarized here. 2. Cf. W. V. Quine, review of Milton K. Munitz, Identity and Individuation, Journal of Philosophy 69 (1972): 488-497. 3. See the different essays collected in my The Intentions of Intentionality (note 1 above). Dana Scott has voiced related doubts in his unpublished paper, "Is There Life on Possible Worlds?". Many of the flaws in the views of Montague, Kripke, et al. still remain unacknowledged and partly unrecognized, however. 4. See "Quine on Quantifying In" (note I above), especially pp. 118-124. 5. Much of the interest of this observation lies in the further thesis of mine that these world lines are as a matter of fact drawn in at least two entirely different ways in our own conceptual practice. For this stronger claim, see below-and see also my books The Intention of Intentionality (note I above) and Models for Modalities (Dordrecht: D. Reidel, 1969), especially chapter 8, "On the Logic of Perception". 6. See "Qui ne on Quantifying In" (note 1 above), especially pp. 128-131. 7. The role of such tacit limitations has remained largely undiscussed in the literature, in spite of their tremendous importance. It is only in virtue of such 'transcendental' limitations of our attention that our analytical modalities can be hoped to be viable at all. (See below.) Moreover, such tacit presuppositions have in effect played an important role in the thoughts of several major philosophers, including Kant, who restricted the realm of possibility to what is "empirically possible", Husserl, whose notion of "motivated possibility" serves to limit our "horizon" of possible further determinations of objects, and Wittgenstein, who emphasized the role of agreement in judgements as a precondition of communication within a speech community. In connection with Kant, this point was first emphasized to me by Moshe Kroy. 8. See W. V. Quine, "Worlds Away", Journal of Philosophy 73, 22 (December 16, 1976) 859-863, especially first paragraph. This paper of Quine's is partly a reaction to my "Quine on Quantifying In", and my present paper can be thought of as a rejoinder to Quine's paper. An excellent independent reply to Quine is to be found in Robert Kraut, "Worlds Regained", Philosophical Studies 35 (1979). 9. See, e.g., W. V. Quine, "Quantifiers and Propositional Attitudes", reprinted in The Ways of Paradox (New York: Random House, 1966), pp. 183-194. 10. See Esa Saarinen in Merrill B. Hintikka et aI., Essays in Honor of Jaakko Hintikka (Dordrecht and Boston: D. Reidel, 1979). 1\. See my paper, "Standard vs. Nonstandard Logic" in Modern Logic, edited by E. Agazzi (Dordrecht and Boston: D. Reidel, 1981), pp. 283-296. 12. See "Worlds Away" (note 8 above). 13. I have offered some comments on the role of so-called intuitions in philosophical argumentation in "Intuitions and Philosophical Method", Revue internationale de Philosophie 35 (1981): 74-90. 14. See "Worlds Away" (note 8 above), p. 863 15. See my Knowledge and Belief (Ithaca, N.Y.: Cornell University Press, 1962). Important further observations concerning the treatment of natural-language locutions with "knows" are presented in my monograph The Semantics of Questions and the Questions of Semantics, Acta Philosophica Fennica, vol. 28, no. 4, (Amsterdam: NorthHolland, 1976).

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16. "Worlds Away" (note 8 above), p. 863 17. Steven E. Boer and William G. Lycan, "Knowing Who", Philosophical Studies 38, 5 (November 1975): 299-244. 18. See, e.g., Donald Davidson, "Truth and Meaning", Synthese 17 (1967): 304333. 19. That is, by and large, Quine's strategy in the second half of Word and Object (Cambridge, Mass.: MIT Press, 1960). 20. Much of Quine's philosophy of language is colored by his adherence to the assumption I have called the idea of language as the universal medium. Cf. here my papers, "Semantics: A Revolt Against Frege", in G. Floistad, editor, Contemporary Philosophy: A New Survey, Volume I (The Hague: Martinus Nijhoff, 1981), pp. 5782, and "Is Truth Ineffable?" (forthcoming). 21. The gist of my solution is given in my monograph The Semantics of Questions and the Questions of Semantics (note 15 above), section 3.6. 22. The problem was first posed to me by Barbara Hall Partee. 23. John Cook Wilson, Statement and Inference (Oxford: Clarendon Press, 1926), pp. 117-119. (I owe this reference to Harry Lewis.) 24. Lauri Karttunen, "Syntax and Semantics of Questions", in Henry Hiz, editor, Questions (Dordrecht and Boston: D. Reidel, 1978). 25. See op. cit. (note 17 above). 26. See Models for Modalities (note 5 above), especially chapter 8, and The Intentions of Intentionality (note I above), especially chapters 3-4. 27. See my paper "Knowledge by Acquaintance-Individuation by Acquaintance", in David Pears, editor, Bertrand Russell: Modern Studies in Philosophy (Garden City, N.J.: Doubleday, 1972), pp. 52-79, reprinted in laakko Hintikka, Knowledge and the Known (Dordrecht and Boston: D. Reidel, 1974), 212-233. 28. Think of the information supplied by someone's momentary visual perceptions as being summed up in a photograph. If this photograph does not enable one to tell who a certain person in the picture is, then it allows for more than one alternative state of affairs such that in some of the different states of affairs that figure is a different person. (Different person, that is to say, by our usual descriptive criteria.) But it is perfectly obvious that there is at that location in the picture one and only one person, a person about whom we can make various judgments. In doing so, we are treating him or her as a well-identified individual, and this well-definedness can only refer to what I have called perceptual criteria of cross-identification. In the different states of affairs which the picture admits of we treat those individuals as one and the same who correspond to the same character in the photograph. 29. See The Semantics of Questions and the Questions of Semantics (note 15 above), sections 2.6, 3.1-3.3. 30. This would be strictly true if (14) had read "(3x) I see that (that man over there = x)". In so far as we are in (14) dealing with knowledge on the basis of my visual perception above, asl indicated that we are doing, the difference does not matter. 31. Cf. The Intentions of Intentionality (note I above), chapter 3; "Knowledge by Acquaintance-Individuation by Acquaintance" (note 27 above). 32. See "Knowledge by Acquaintance-Individuation by Acquaintance" (note 27 above). 33. "Worlds Away" (note 8 above). 34. The explanation is outlined in The Semantics of Questions and the Questions of Semantics (note 15 above), section 4.6. 35. "Worlds Away" (note 8 above), p. 863. 36. This limitation of conventional modal logic was first pointed out by David

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Kaplan and his associates of UCLA. See David Kaplan. "Ted and Alice and Bob and Carol", in Jaakko Hintikka et al., Approaches to Natural Language (Dordrecht and Boston: D. Reidel, 1973), pp. 490-518. The intuitive idea of an outside-in evaluation procedure is vindicated by my game-theoretical semantics; see Esa Sarrinen, editor, Game-Theoretical Semantics Dordrecht and Boston: D. Reidel, 1978). 37. See his papers in Saarinen, editor, Game-Theoretical Semantics (note 36 above). 38. "Worlds Away" (note 8 above), p. 863. 39. Knowledge and Belief (note 15 above), p. 149n. 40. For different subscripts of "K" (more accurately, for different knowers), (18)(19) are to be taken to be logically independent of each other. 41. What is directly predicted is of course only the possibility of such variability. The versatility of ordinary discourse readily turns this possibility into actuality, however. 42. See Knowledge and the Known (note 27 above), chapter" 'Dinge an sich' Revisited" . 43. See The Intentions of Intentionality (note 5 above), title essay. 44. This is precisely what a semantical theory cl la Davidson is supposed to achieve; cf. note 18 above. In this respect, Davidson's program is not affected by the criticisms I level against some of its other features in my paper, "Theories of Truth and Learnable Languages", in Jaakko Hintikka and Jack Kulas, The Game of Language (Dordrecht and Boston: D. Reidel, 1983), pp. 259-292. 45. Cf. "Semantics: A Revolt Against Frege" (note 20 above), last section. 46. Instructive examples of distinctions and other considerations which easily can be subjected to a possible-worlds analysis are offered by Abraham Kaplan's unpublished discussion of selthood, which partly reproduces sections 46 and 47 of his book In Pursuit of Wisdom (Los Angeles: Glencoe Press, 1977).

Merrill B. Hintikka and laakko Hintikka

HOW CAN LANGUAGE BE SEXIST? Prima facie, our title question may seem pointless. Barring bigots, virtually everybody will agree that language is frequently used in a sexist way. Why, then, the question? We are formulating the title of the paper in this way because it serves to call attention to a general predicament of feminist philosophy as a serious theoretical enterprise. The sexist uses of language which first come to most people's minds are likely to instantiate relatively uninteresting aspects of language. Examples are offered by sexism expressed through purely emotive meaning and by those sexist uses of language which directly reflect sexist customs and institutions, for instance the different ways of addressing a person in Japanese. There is no problem as to how such sexism is possible in language; nor is there any interesting intellectual problem as a how such sexist usages can be diagnosed and cured. Once we have our emotions in line and our institutions and customs freed from sexism, no residual problem remains. Or so it seems. This discussion illustrates certain criticisms which are often levelled in general at feminist philosophy. While the social problems addressed by feminist philosophy are usually acknowledged to be real and important, it is frequently denied that their diagnosis and solution requires or leads us to any new philosophical, methodological, or other theoretical insights. Hence feminist philosophy comes to seem a misnomer. The problems with which it deals do not appear to have a sufficiently important theoretical component to be labelled philosophical; hence the analyses and solutions it offers are thought not worthy of the designation 'philosophy'. This is a view we are trying to combat by means of a case study. We suggest that a number of sexist uses of language illustrate interesting general theoretical problems. The diagnosis of such sexist uses hence involves serious problems of theoretical semantics. Even though there is in some cases no question as to how sexist language is possible, in others the very mechanism through which it comes about presents an interesting problem. In this paper, we are less anxious to solve this general theoretical problem we see raising its head here - it is too large for one paper anyway - than to recognize it, and less concerned with the details of instances of sexist language and sexist 155

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language use than with their connection with the general problem we are posing. Through pointing out this connection, we are trying to give a concrete example of the theoretical interest of problems naturally arising from feminist concerns. The theoretical problem we are posing is the following: In virtually every important current logical or philosophical approach to semantics, a set of representative relations between language and the world it deals with is taken for granted. For instance, in Tarski-type truth defInitions, the valuation of nonlogical constants is taken for granted. 1 In Montague semantics, the meaning functions associated with primitive words are likewise taken for granted. 2 And in approaches which rely on translation to some privileged "language of thought", the semantics of the target language is likewise left largely unanalyzed. 3 What we wish to suggest is, fust, that the principles according to which these basic representative relations between language and reality are determined need much more attention than they are now given and that awareness of these principles is vital even for the understanding of and for the applications of contemporary formal semantics. We are tempted to speak of a subsystem of language (a subset of the totality of rules governing language) which is in some sense more fundamental than the subsystem studied in present-day formal semantics. For reasons which emerge somewhat more fully in what follows, we call the latter the structural system and the former the referential system. 4 This formulation is somewhat oversimplified, however, in that there is more interplay between the two systems than our schematic first statement leads one to expect. Furthermore, it is not clear that all the phenomena we have in mind are connected closely enough with each other on either side of the fence to justify us in speaking of a real (sub )system. Hence the preliminary formulation of our theme and the term "referential system" must be taken with a grain of salt, and must be considered as being tentative and exploratory in nature. In any case, we shall illustrate the general thesis by means of discussions of a few narrower problems. We shall also indicate how a couple of specifIc manifestations of sexism of language exemplify our general theoretical problem. Some aspects of the referential system are sometimes classified as belonging to pragmatics rather than to semantics. Such labels are harmless as long as they do not mislead us into expecting that such "pragmatic" phenomena are somehow intrinsically related to the many other items also relegated to "the pragmatic wastebasket", to use Yehoshua Bar-Hillel's expression.

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For instance, we do not see any interesting connection between what we call the referential system and discourse-theoretical (e.g., conversational) phenomena. As long as the referential system works and does not vary contextually, it remains relatively inconspicuous. (By ''working'', we mean here sufficing as the sole or main input into the structural system.) This inconspicuousness is one of the reasons why so little attention has been paid to it. For the same reason, the occasions when some aspect of the referential system varies, or proves insufficient for the purpose of understanding the semantics of some natural-language expression, are likely to offer the best quick illustrations of our theses. We shall ftrst try to give an example where the referential system does not by itself supply enough information to enable tht; structural system to operate in the way it is in these days usually expected to operate. This example is offered by a word whose force has perhaps been discussed more than that of any other single word: the word "good". Of course we cannot here exhaustively discuss the problems connected with it. We shall Simply suggest that the way it operates is to rely on some evaluation principle but to leave it for the context to settle which one this evaluation principle is. On some occasions, the speaker may, e.g., rely on some set of values he or she shares with the audience or at least assumes to be familiar to the audience, whether or not its members actively subscribe to them. But on other occasions, the speaker - who could then be, for instance, a moral reformer - might use the same words to announce a new valuation principle. Preexisting valuations are typically determined by someone's interests. 5 But when Socrates claims to be a virtuous man, an agathos, while refusing to participate in public life and neglecting his family's welfare, he is not only not relying on an existing valuation principle for one's actions. He is also not relying on any known interest to express his point. He was proclaiming a new morality by making judgments which presuppose it (Le., presuppose the valuation prinCiples which constitute the proclaimed new morality).6 The reason why we have classifted this context-dependence of "good" as belonging to the referential subsystem of language should be obvious. What is at issue is which cases the predicate "good" can be correctly applied to, Le., which extension (reference) it has. Since such extensions of our primitive terms are what is assumed to be given prior to the usual (structural) analysis of the semantics of natural language, which is the currently favored type of semantical analysis of any notion, a single evaluation principle would be needed in order for this word to be capable of being handled in the usual

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approach. However, it is part and parcel of how the referential system operates that in the case of this word no unique scale or principle is forthcoming. This implies that one's actual use of "good" (in the several constructions into which it can enter) may rely on tacit evaluations or interests. These can be present without our noticing their presence. A small but subtle instance is offered by the difference in meaning between the English expression a good man and its literal counterparts in other languages, e.g., German, Swedish and Finnish. The difference is strikingly illustrated by comparing a passage from G. E. Moore's autobiography (in the Library of Living Philosophers volume devoted to him)7 with Yrjo Hirn's essay (originally written in Swedish) on 'Voltaire's heart'.8 Moore tells of one of his schoolteachers that he was not only a good man but also a benevolent man. Moore's words indicate clearly that he takes benevolence not to be a component of goodness, which has to do with such things as being conscientious and high-principled. In contrast, Hirn describes at some length Voltaire's noble efforts on behalf of oppressed and persecuted individuals, and goes on to argue that these good works were not only reflections of Voltaire's high humanitarian principles and of his efficiency in putting them into practice. They show, Hirn argues, that Voltaire was a genuinely humane, caring person, in brief, en god miinniska (a good man). What is going on here is of course that the ambiguity of the English word man between a human being and a male of the species has led to the use of a good man where the tacitly presupposed interests are not those we presumably have in all our fellow human beings but those which we are likely to have in fellow citizens, business partners and colleagues, who are clearly presumed to be males. The former include primarily at least a minimum of concern with the basic welfare of other human beings. A good man would by this token be a humane man, a good representative of mankind, i.e., a kindly or kind man. (Interestingly, these two uses of kind are in fact etymologically related.)9 Indeed, this is precisely what happens in several of those languages which do not exhibit the same ambiguity as English. For instance, for a German em guter Mensch is, well, not unlike a Mensch in the colloquial Yiddish sense. In contrast, the interests of the other kind are what have lent the English words a good man their customary force. They signal the virtues a fellow citizen or colleague is expected to exhibit. What of the woman who is citizen and colleague? Can she be a good man? That closely analogous phenomenon has pervaded the psychological concept of a healthy adult: in so far as a human being is a healthy woman, she fails to be a healthy adult, and in so far

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as she is a healthy adlllt, she fails to be a healthy woman. IO Such unwitting sexism cuts much deeper, it seems to us, than e.g., any emotively sexist uses of language. This diagnosis is supported by the observation that the same ambiguity and the same sexist presupposition is found with vengeance in the ancient Greek.ll There the relevant interests were predominantly interests in another citizen-soldier, i.e., the military interests, however defensive, that all citizens of a polis presumably had. A much more general part of the referential system are the principles which determine the individuation of the particular entities we talk about in our language. Jaakko Hintikka has argued elsewhere that the best way of conceptualizing these principles is in terms of what is usually (and misleadingly) called pOSSible-worlds semantics, i.e., by consideling what the "embodiments" or "roles" of our individuals were in a range of possible situations or possible courses of events. 12 Whatever one can say of this approach in the last analysis, it serves to clarify several aspects of the central conceptual problems in this area. For instance, it leads to the insight that a major role in identifications across the boundaries of possible worlds is played by re-identification, i.e., by the principles which enable us to speak of the same entities as (often) existing at different stages of one and the same course of events. It is characteristic of the state of the art that many of the very best philosophers flatly refuse to consider the details of these principles. W. V. Quine doesn't think that any reasonable, theoretically respectable principles can be discovered,l3 while Saul Kripke claims that we have to postulate temporally persistent individuals as a primitive, unanalyzable presupposition. 14 Notwithstanding such views, we believe that a further analysis of the re-identification and cross-identification principles has a tremendous philosophical and possibly also psychological and automation-theoretical interest. As the basic theoretical situation remains almost completely uncharted, we cannot survey it here. Instead we will discuss some of the related issues. One pertinent observation here is the following: On the possible-worlds model, the referential system has to include two partly independent components. IS On the one hand, the references of our primitive non-logical constants such as singular terms, predicates, function symbols, etc. in each possibJe world have to be specified. On the other hand, the imaginary "world lines" (which connect the roles of the same particulars in different worlds) have to be drawn. Each of these is a part of the objective foundation of ordinary (structural) semantics. The relative independence of these two tasks,

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the interpretation of nonlogical constants world by world and the drawing of the world lines (which span several worlds), implies that the corresponding two ingredients of the referential system can to some extent be varied independently. This does in fact happen, and such a variation of a part of the referential system is one of the phenomena in our language that can awaken philosophers' and linguists' interest in (or at least attention to) the referential system. In order to see what such a variation might amount to, we must note a few facts here. In many typical cases, we are dealing with the possible worlds compatible with someone's knowledge, belief, or other propositional attitude. For example, let us consider what Jane knows. This is specified by the set of all possible worlds compatible with what she knows, called Jane's epistemic alternatives or her "knowledge worlds". Whatever is true in all these epistemic alternatives is Known by Jane, and vice versa. Hence a singular term, say "b", picks out the same individual in all of Jane's epistemic alternatives (goes together with a world line) if and only if it is true that (1)

(3x)Jane knows that (b = x).

More colloquially, (1) obviously says the same as (2)

Jane knows who b is.

Now the ways in which world lines are drawn can vary without changing the evaluation principles which affect one world at a time. Hence the truth conditions of (1) and (2) can be varied accordingly without affecting the rest of the referential system. More generally, it is (among other things) in the variation of the force of phrases of the form knows + an indirect question that the variation of world lines can be "seen". Possible-worlds semantics shows what the cash value of such variation is. It is a question of what the person in question would consider as the same individual in different actual and possible situations, what he or she would "count as" the same individual. Not surprisingly, sexism can rear its head occasionally here, too. The diaries of that inveterate male chauvinist, Evelyn Waugh, offer an example. He quotes there the old saw worthy of Polonius: "Be kind to young ladies. You never know who they will be." The possibleworlds framework instantly reveals the mechanism ofWaugh's sexism: Waugh is in effect treating women married to the same gent as being interchangeable, formally speaking, as nodes of one and the same "world line" connecting individuals in future courses of events.

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Such variation has been taken by Quine to indicate that something is wrong with the possible-worlds semantics of sentences like (1) and (2). All the variation is in the referential system, however. The structural system, which is the subject matter Quine was in effect commenting on,16 is of course completely unaffected by this variation. One of the central problems in this area is how the world lines are drawn, i.e., how we as a matter of fact handle cross-identification in our conceptual system. We are in the process of developing a theory of actual cross-identification}7 Unfortunately the subject is too large to be expounded here, and we must hence confme ourselves to a promissory note as far as the general problems of identification and individuation are concerned. Instead, let us consider a couple of the many interesting narrower issues involved in the general problem of cross-identification. David Lewis has in effect claimed that cross-identification takes place according to similarity: those individuals in different possible worlds are as it were declared identical ("counterparts" in Lewis' terminology) which are most closely similar to each other .18 "Similarity" is not intended to be a primitive notion in this approach. Rather, the relevant comparison may involve several different and differently weighted similarity considerations. This is not the only a priori possibility, however. Instead of comparing individuals one by one, we may try to compare the structures of the two possible worlds in question at large and try to match them. Individuals corresponding to each other in the closest match we can achieve would be Lewisian counterparts. Such possible cross-world· comparisons obviously depend much more on the relational and functional characteristics of the denizens of the different scenarios ("possible worlds") we are envisaging than on the essential properties of the entities involved in the compariosn. For instance, these non-essentialist modes of cross-identification may depend on the continuity properties of the entities in question, which are of course relational rather than essential properties. What is striking here is that certain psychological studies suggest that there may be sex-linked differences (whether innate or culturally conditioned does not matter for our purposes) in the very matter of such assimilation comparisons. For instance, some studies seem to show that boys tend to bracket together objects (or pictures of objects) whose intrinsic characteristics are similar, whereas girls weight more heavily the functional and relational characteristics of the entities to be compared. 19 For instance, boys frequently bracketed together such entities as a truck, a car, and an ambulance, while girls bracketed such entities as a doctor, a hospital bed, and an ambulance.

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More generally, women are generally more sensitive to, and likely to assign more importance to, relational characteristics (e.g., interdependencies) than males, and less likely to think in terms of independent discrete units. Conversely, males generally prefer what is separable and manipulatable. 20 If we put a premium on the former features, we are likely to end up with one kind of cross-identification and one kind of ontology; if we follow the gUidance of the latter considerations, we end up with a different one. Moreover, it is not hard to see what the difference between the two will be. All identification which turns on essential properties, weighted similarities, or suchlike, presupposes a predetermined set of discrete individuals, the bearers of those essential properties as Similarity relations, and focuses our attention on them. In contrast, an emphasis on relational characteristics of our individuals encourages comparisons of different worlds in terms of their total structure, which leads to entirely different identification methods, which are much more holistic and relational. The suggestion - and we do not intend it to be more than a suggestion - we make here is now clear: it is not just possible, but quite likely, that there are sex-linked differences in our processes of cross-identification. The differences are such as not to be manifested either very frequently or very blatantly. But in the more refined areas of speculative thought, such differences might very well have their consequences. Indeed, cross-identification methods are in an obvious sense constitutive of our ontology. Hence, what we are suggesting is that language could perhaps be, if not sexist, then at least sexually biased and sensitive to sex differences in the very respects that are most closely related to the structure of our ontology. Lest this suggestion strike the reader as unrealistic, let us note some of its consequences and ramifications. Quite independently of the perspective from which we are here viewing the problems of ontology and cross-identification, it is arguable that Western philosophical thought has been overemphasizing such ontological models as postulate a given fixed supply of discrete individuals, individuated by their instrinsic or essential (non-relational) properties. These models are unfavorably disposed towards cross-identification by means of functional or other relational considerations. Is it to go too far to suspect a bias here? It seems to us that a bias is unmistakable in recent philosophical semantics and ontology. There we fmd almost everyone postulating a given domain of discrete individuals whose identity from one model (world) to another is unproblematic. An especially blatant example of this trend is Kripke's notion of a rigid designator,21 which becomes virtually useless as soon as cross-identification is recognized as a problem. (No wonder Kripke

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has been led to argue that the re-identification of temporally persisting physical objects must be taken for granted.) Another conspicuous part of the same syndrome is philosophers' surprising slowness in appreciating Jaakko Hintikka's discovery of the duality of cross-identification methods (the descriptive and the perspectival one),22 which breaks the hegemony of neat prefabricated individuals in philosophical ontology. It is hard not to see in this strong tendency a preference of independent but manipulative units similar to the sex-linked preference several psychologists have noted. Similar points can be made about earlier history of philosophical ontology. Separability and "thisness" were the characteristic marks of Aristotelian substances,23 which are historically the most important proposed ontological units of the world. Conversely, we may very well ask whether Leibniz' ontology of monads, whose identity lies in their reflecting the whole universe, has really been given its due. 24 Even though firm documentation is extremely hard in these matters, at the very least we obtain here a challenging perspective on the history of philosophical ontology. At the same time, our questions illustrate the systematic interest within language theory of the referential system we have tentatively postulated. For it is problems of individuation and identification which constitute perhaps the most important ingredient of any serious study of the referential system at large, and hence of philosophical ontology. NOTES 1 Cf. Alfred Tarski, The concept of truth in formalized languages', in Alfred Tarski, Logic, Semantics, Metamathematics, Clarendon Press, Oxford, 1956, pp. 152-278. 2 Cf. Richmond H. Thomason (ed.), Formal Philosophy: Selected Papers of Richard Montague, Yale V.P., New Haven, 1974; D. R. Dowty, R. E. WaD, and S. Peters,lntroduction to Montague Semantics, D. Reidel, Dordrecht, 1981. 3 Cf., e.g., leery A. Fodor, The Language of Thought, Thomas Y. CroweD, New York, 1975. 4 Further observations concerning this distinction are made in laakko Hintikka and Merrill B. Hintikka, 'Towards a general theory of individuation and identification', partly forthcoming in the proceedings of the Sixth International Wittgenstein Symposium, Holder-Pichler-Tempsky, Vienna, 1982. S This point is weD argued in the seminal last chapter 'The word "good" , of Paul Ziff, Semantic Analysis, CorneD, V.P., Ithaca, N.Y., 1960. 6 Cf. here A. Adkins, Merit and Responsibility, Clarendon Press, Oxford, 1960. 7 P. A. Schilpp (ed.), The Philosophy of G. E. Moore (The Library of Living Philosophers), Tudor, New York, 1952, pp. 3-39, especiaDy p. 9. 8 Yrjo Him, 'Voltaires hjarta', in Yrjo Him, De iagerkronta skopiaggen, Soderstrom & Co., Helsinki, 1951.

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9 For an interesting discussion, see chapter 2 of C. S. Lewis, Studies in Words, second ed., Cam bridge U.P., Cam bridge, 1967. 10 Cf.lnge K. Broverman, Donald M. Broverman, et al., 'Sex-role stereotypes and clinical judgments of mental health', Journal of Consulting and Clinical Psychology 34, No. 1 (1970),1-7. 11 Cf. Adkins, op. cit. (Note 6 above), especially chapter 3. 12 See his books Models for Modalities, D. Reidel, Dordrecht, 1969, and The Intentions of Intentionality, D. Reidel, Dordrecht, 1975. 13 Cf. W. V. Quine, 'Worlds away', Journal of Philosophy 73 (1976), 859-863. 14 Cr. Saul Kripke, 'Identity through time', paper delivered at the Seventy-Sixth Annual Meeting of APA Eastern Division, New York, December 27-30, 1979. 15 This point has been implicit in laakko Hintikka's work ever since the last chapter of Knowledge and Belief, Comell U.P., Ithaca, N.Y., 1962. 16 Op. cit. (note 12 above). 17 'Towards a general theory ofindividuation and identification' (note 4 above). 18 David Lewis, 'Counterpart theory and quantified modal logic', Journal of Philosophy 65 (1968),113-126. 19 Cf., e.g., 1. Kagan, H. A. Moss, and I. E. Sigel, 'The psychological significance of styles of conceptualization', in 1. C. Wright and 1. Kagan (eds.), Basic Cognitive Processes in Children (Society for Research in Child Development Monograph 28, no. 2), 1963. 10 Cf. e.g., Eleanor E. Maccoby, 'Sex differences in intellectual functioning', in Eleanor E. Maccoby (ed.), The Development of Sex Differences, Stanford U.P., Stanford, 1966, pp. 25-55. 11 Saul Kripke, Naming and Necessity, Harvard U.P., Cambridge, Mass., 1980. 11 Cr. 'On the logic of perception' in Models for Modalities (Note 12 above); 'Knowledge by acquaintance - individuation by acquaintance' in laakko Hintikka, Knowledge and the Known, D. Reidel, Dordrecht, 1974. 13 Cr. Aristotle, Categories, ch. 5. 14 Cf. laakko Hintikka, 'Leibniz on plenitude, relations, and the "Reign of Law"', in Simo Knuuttila (ed.), Reforging the Great Chain of Being, D. Reidel, Dordrecht, 1981, pp. 259-286.

ON DENOTING WHAT?* Russell put forward his 1905 theory of denoting on the basis of evidence which he said is "derived from the difficulties which seem unavoidable if we regard denoting phrases as standing for the genuine constituents of the propositions in whose verbal expressions they OCCUr."1 What are these difficulties? In developing his theory of sense and reference, Frege had discussed the failure of the substitutivity of identity (SI) in intensional context and the related problem o( why identity-statements can be informative. Russell discussed both these problems, but at the same time he broadened the range of paradigmatic semantical problems to also include the problem of empty terms, which can, among other things, manifest itself in the form of a failure of existential generalization (EG) in intensional contexts. Russell thought that his theory of definite descriptions solved both these groups of problems, the old Fregean (SI) problems and the new (EG) ones. Indeed, his theory does go a long way towards providing a neat technique by means of which we can deal with particular manifestations of these particular difficulties. It does not provide us with a deeper insight into aetiology of the problems, and hence by-passes rather than solves some of the real problems concerning denoting terms. Let us have a closer look at Russell's discussion. Russell's contextual elimination enables him to avoid the problems which are due to empty reference. For instance, from "the present King of France is the present King of France" we cannot prove by EG that there is someone who is the present King of France, albeit merely because the premise is construed by Russell to assert the existence of a unique self-identical present King of France and hence to be false. But what about other problems? The main step in Russell's solution to the problems caused by the failure of SI was his distinction between what he called primary and secondary occurrences of definite descriptions/ and the observation that according to his theory of such descriptions SI holds for primary but not for secondary occurrences. 165

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Russell's distinction is illustrated by the two readings of (I)

George IV did not know whether Scott was the author of Waverley.

If the occurrence of "the author of Waverley," in short primary one in (I), it has the force (2)

(3x)[A(x) & (y)(A(y)

=> y = x)

«7 )A(x», is a x

& -George IV knew that

(Scott = x)]. In other words, when a definite description has a primary occurrence apud Russell in a sentence s, the existential quantifier which figures in the Russellian paraphrase of s has the maximal scope. We are then speaking of someone's propositional attitude (e.g. knowledge) toward some particular individual, irrespective of how that individual is referred to. More likely, however, the intended reading of (1) assigns to the description what Russell calls a secondary occurrence: (3)

-George IV knew that (3x )[A(x) & (y )(A(y) => y (Scott = x)].

= x)

&

In general, on the secondary reading of a definite description sentence s, the operative existential quantifier is supposed to have the smaller of two possible scopes. Unfortunately, apparently unbeknownst to RusselI, frequently the existential quantifier employed in the paraphrase of s prescribed by Russell has more than two possible scopes. For instance, Russell does not note that sentences like (I) have on his own theory a third legitimate reading, viz. (4)

-(3x)[A(x) & (y)(A(y)

=> y = x)

& George IV knew that

(Scott = x)]. What is much more important, RusselI never quite reached the full awareness of the crucial fact that there is a type of failure of EG which is not due to failures of existence and which consequently is not dealt with explicitly in his theory. To see what is, consider the trivial-looking sentence (5)

George IV knew that the author of Waverley is the author of Waverley.

On its most trivial reading, it becomes, simplified,

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ON DENOTING WHAT?

(6)

George IV knew that (3x)(A(x) & (y)(A(y):J Y = x».

What (6) says is simply that the good King knew that one and only one person wrote Waverley. In contrast, on its most nontrivial reading, (5) has the force of (7)

(3x)(A(x) & (y)(A(y):J y = x) & (A(x) & (y)(A(y):J Y = x»).

George IV knew that

What (7) says is that George IV knew of the unique person who in fact wrote Waverley, that he (or she) did so. Since knowledge implies truth, (7) is logically equivalent with (8)

(3x) George & x = z),

IV knew that (3z)(A(z) & (y)(A(y):J y

= z)

which in turn is equivalent with (9)

(3x)

George IV knew that (the author of Waverley = x)

where the definite description has a secondary (minimal scope) occurrence. A couple of interesting observations are prompted by this line of thought. First, (9) is obviously (with the definite description interpreted as having a secondary occurrence) what is meant by saying that George IV knew who the author of Waverley is. This observation is generalizable, and seems to yield a viable account of what seems to have been the major gap in Russell's theory, viz. its inability to yield an explicit analysis of constructions of the form: knows + wh-clause. In general, (10)

a

knows who (say x) is such that A(x)

will become (11)

(3x) a

knows that A(x)

However, this natural idea leads quickly into dire trouble, unless further changes are made in Russell's theories. For one thing, now EG breaks down in a way which cannot be traced to the nonexistence of denoted individuals (failure of denotation) and which cannot be treated by means of Russell's theory of definite descriptions. For there obviously are, for each person a, lots of people whose proper names and whose existence is known to a but of whom a does not know who they are. Assume that Charles Dodgson was a case in point

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for Queen Victoria. Then we have to say, assuming that (11) is the right analysis of (10), (12)

- (3x) Victoria knew that (Charles Dodgson = x)

But (12) is trivially false, on principles which Russell seems to have espoused. For clearly it is true that (13)

Victoria knew that (Charles Dodgson = Charles Dodgson)

and from (13) we obtain by EG (14)

(3x) Victoria knew that (Charles Dodgson = x),

which is the negation of (12). Hence we have a blatant contradiction resulting from eminently natural ideas. This paradox does not involve (at least not prima facie) definite descriptions at all. Hence it cannot be solved by means of RusseII's theory. Moreover, we can assume that Queen Victoria knew Charles Dodgson's existence. Hence we are not dealing with a problem caused by a failure of proper names like "Charles Dodgson" to refer. This problem, which might at first seem to be merely a minor difficulty facing formal logicians who are trying to adjust their formalization to the realities of natural language, can in fact be given an ontological turn. The possibility of generalizing existentially with respect to a singular term, say" b", in a given context, say" F(b)", is the same as the question whether b is an admissible value of a bound variable. In so far as there is some truth to Quine's adage "to be is to be a value of a bound variable," this question becomes ipso facto a question as to whether b is a bona fide existent. In so far as we are dealing with epistemic contexts, our question therefore becomes one concerning the ontology of the objects of knowledge, perception, and belief. Much more is then at stake here than one of logician's self-inflicted problems of formalization. Thus we have a puzzle quite as interesting as those Russell considered explicitly. I believe that it is a better paradigm problem than Russell's explicit puzzles and that it should be classified as being an instance of such a failure of EG as is not due to a failure of existence. Hence we have the following classification of some of the main

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ON DENOTING WHAT?

puzzles in this field: Manifestation

Utilized by

(a) failure of SI Frege. Russell (b) failure of EO (i) because of an existential failure Russell (ii) because of a failure of uniqueness Hintikka

I have listed the last puzzle as being due to a failure of uniqueness because this is its obvious and elegant diagnosis in possible-worlds semantics. For instance, in (12}-(14) the problem is not that Charles Dodgson does not exist in the actual world or in any of the world compatible with Queen Victoria's total knowledge, but rather that in some of these knowledge worlds the proper name "Charles Dodgson" picks out a different individual from the one it picks out in some others. (This is a direct corollary to the Queen's not knowing who Charles Dodgson is, together with the definition of the set of relevant worlds as being all those that are compatible with what she knew.) Accordingly, even though Charles Dodgson exists in each one of the relevant worlds considered separately, there is no one unique individual of whom we can say that he was known to Victoria to be Charles Dodgson. Hence (14) does not follow from (13). This solution of the problem, though I believe it to be the correct one, prejudges the interpretation of Russell's thought, however. In order to avoid anachronisms, we have to go back to the problem situation and to see what avenues are left open to Russell - and to other philosophers. But was the problem situation I have described really Russell's? I strongly believe that this problem situation does not come about by means of 20-20 hindsight. Even though Russell never considers it explicitly, it is very much present in the background of what he is doing, and it affects strongly our evaluation of his arguments and views. Several symptoms of the main problem are unmistakably present in Russell's writings, as we shall find. Hence the failure of most philosophers in the Frege-Carnap-Church tradition to consider the uniqueness problem (the breakdown of EG because of a failure of the uniqueness of reference) is a serious gap in the recent discussions.

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Far too many post-Russellian logicians and philosophers have been barking up the wrong paradigm. Even though Russell never explicitly acknowledges this problem situation, it is thus my surmise that he not only was trapped in it but that he in effect felt the pressures that being in it entails. For instance, by putting his different pronouncements together we can see (or, rather, we shall soon see) that Russell countenances almost in so many words the equivalence of knowing who did something and there being an individual of whom it is known that he (she) did it. Moreover, and more importantly, I believe that recognizing the problem situation Russell was in helps us to understand some of the most striking features of his thought in 1905-1914, notably the connection he thought there obtained between his theory of definite descriptions and alleged reducibility to acquaintance. Independently of Russell, the main ways out of the paradox other than the one offered by possible-worlds semantics are clearly the following: (i) (ii) (iii)

One can try to deny the rendering of (10) as (11). One can try to interpret apparent proper names like "Charles Dodgson" as hidden definite descriptions. One can try to re-interpret the range of bound individual variables in (11).

Did Russell perhaps try one of these ways out? Let's see. (i) Many subsequent philosophers have in effect taken the first line. This, however, is a lost cause if I ever saw one. For one thing, if the equivalence of (10) and (11) is given up, we lose an eminently natural way of analyzing constructions of the form knows + wh-clause in natural languages. The philosophers and logicians taking this way out have in fact completely failed to provide a satisfactory analysis of such constructions. Moreover, this way out does not even work. For the line of thought connected with (12)-(14) does not really depend on the possibility of translating (10) as (11), even though this translation makes it especially easy to motivate the argument. For the formal expression has to be given some viable interpretation or other. If our bindable individual variables range over genuine honest-to-Iogic individuals, this interpretation can scarcely fail to assign to (14) a force which apart

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from minor niceties has the force of Victoria's knowing who Charles Dodgson is. For what more could there conceivably be to knowing who C. D. is than knowing of some genuine, flesh-and-blood individual that he is C. D.? The only way of avoiding the identification of (10) and (11) is to assume some kind of substitutional interpretation of quantifiers. But such an interpretation is, if not quite a fool's paradise, then only a formal logician's paradise. It may be all right as a formal logician's game but no satisfactory explanation of this alleged interpretation has ever been given. It is greatly to Russell's credit that there is in his writings no single trace of his trying to take this spurious way out. In his philosophical thought in the period 1905-1914 Russell obviously had little sympathy with the way (i) out of the problem. Instead, an equivalence of (10) and (11) is very nearly implied by what Russell says. At one point, he describes the knowledge we have merely by description as follows: It would seem that, when we make a statement about something only known by description, we often intend to make our statement, not in the form of involving the description, but about the actual thing described. That is to say, when we say anything about Bismarck, we should like, if we could, to make the judgment ... of which he himself is a constituent. In this we are necessarily defeated, since the actual Bismarck is unknown to us. But we know that there is an object B called Bismarck, and that B was an astute diplomatist. We can thus describe the proposition we should like to affirm, namely, 'B was an astute diplomatist' where B is the object which was Bismarck. 3

We are not taking a liberty with Russell's words or ideas if we take him to be saying here that the logical form of his sample sentence illustrating knowledge by description is (3b)(b = Bismarck & we judge that b was an astute diplomatist) where "b" takes actual objects as its values. (We are certainly dealing with an objectual interpretation of quantifiers here.) Clearly (15) is an analogue to (11), and its equivalence with (10) is assured by Russell's statement that we know Bismarck, albeit only by description. Hence Russell definitely was not trying to take the way (i) out - or, perhaps a little more cautiously put, Russell could not have opted for the alternative (i) if he had consciously faced our trilemma. Admittedly, on another occasion4 Russell characterizes knowledge by mere description by saying that it is what "we know in cases where we (15)

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know propositions about 'the so-and-so' without knowing who or what the so-and-so is." This supports rather than contradicts my point, however, for it turns out that Russell is in such passages merely thinking of different criteria of knowing who or what. (ii) .But what about the next way out, viz. (ii)? Russell admittedly wanted to construe many natural-language names as hidden definite descriptions, for instance indicating his willingness to replace "Bismarck" by "the first Chancellor of the German Empire." He is therefore sometimes thought of as favoring what I have called way (ii) out. This is basically a misconception. The second attempted way out sweeps the problem under the rug instead of solving it. By construing natural-language proper names as tacit definite descriptions, one can hope to eliminate all the particular counter-examples taken from ordinary discourse. But what is the intended interpretation of the logical language? The defenders of this way out must presuppose some domain of individuals whose members can have "proper" names, i.e., proper names which do not reduce to definite descriptions. Moreover, in all interesting applications, not all these individuals have identities which are known to everybody. Hence we are back at the same problem from which we started. On the interpretation which Russell was presupposing, there are in fact plenty of entities which serve as legitimate values of bound variables and which in principle can be given proper names. They will create precisely the same problem all over again. Construing the usual proper names as hidden definite descriptions is thus a treatment of symptoms rather than of the underlying illness. (iii) Indeed, from such statements as have been quoted, we can see what Russell's unspoken attempted solution to our problem is. He is in effect redefining the range of his bound individual variables so as to be restricted to individuals we are acquainted with. For their names, and for such names only, EG holds. Hence they are the only acceptable values of bound variables, and therefore we are in effect quantifying over the set of those individuals we are acquainted with. The names of all other individuals are construed as hidden definite descriptions. Thus we can now see how the problem we have attributed to Russell's background helps to explain one of the most surprising and most distinctive features of Russell's thought in 1905-1914. This

ON DENOTING WHAT?

173

feature is a logical corollary to the idea that our bound variables range over known individuals only. What happens in Russell's theory of definite descriptions is that a definite description is eliminated in context in favor of quantifiers. To paraphrase Russell, all propositions in which definite descriptions occur are reduced to propositions in which no such descriptions occur, only quantifiers ("the notion 'is always true' occurs in it only," Russell might have said) and quantified variables. Now the force of these reduced propositions depends on the range of bound individual variables in them. Russell's restriction of the range of bound individual variables to known individuals thus has an important consequence for what his theory of definite descriptions amounts to in applications. It is often said that the gist of Russell's theory of definite descriptions is to eliminate all apparent references to non-existent individuals ("the present King of France") in favor of quantification over actually existing entities, thus maintaining commendable ontological economy. This is only a part of the story, however. Russell's reduction goes further: his quantifiers range over objects of acquaintance only. The former feature of Russell's theory is needed to handle those failures of EG which turn on the use of empty definite descriptions. The fact that Russell goes further than this shows that he was in effect worried about the other failures of EG as well, even though he never acknowledged the fact, to others or to himself. The most ingenious feature of Russell's 1905 theory of denotation, and its most influential feature, was to show how denoting phrases denote - or, rather, don't denote - in that their apparent job is done by quantifiers. The most remarkable aspect of Russell's theory is nevertheless what these phrases denote, or, rather, what their deputies, the quantifiers, range over. The particular form of Russell's further restriction on the ranges of quantified variables is obviously motivated by Russell's epistemological concerns. However, the fact that Russell felt the need of such a restriction in the first place can only be explained by reference to the problem situation we outlined above. Otherwise, Russell's use of his restriction is bound to appear completely circular. Toward the end of "On Denoting" Russell puts forward the prima facie astonishing claim that his theory of definite descriptions entails what he elsewhere calls reducibility to acquaintance. "One interesting result of the above theory of denoting is this: ... in every proposition that we can apprehend ... , all the con-

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stituents are really entities, with which we have immediate acquaintance."s Why should such reducibility to acquaintance be entailed by Russell's theory of definite descriptions? At first sight, there seems to be no reason to assume the entailment. The theory of definite descriptions merely shows how to paraphrase sentences containing such descriptions in terms of quantifiers. Russell's contextual analysis of definite descriptions does not in itself in any way predjudice the question as to what these quantifiers range over. The only reason why Russell can think that his theory of denoting (including his treatment of definite descriptions) implies his theory of knowledge by acquaintance is apparently by assuming that the values of the variables in the analysans of each sentence containing definite descriptions range over objects of acquaintance. But such an assumption seems to be patently circular. It assumes precisely what was to be proved. This prima facie circularity is the more puzzling as the alleged link between definite descriptions and reducibility to acquaintance seems to have been - at least historically speaking - Russell's main reason for maintaining the latter. This apparent petitio principii also shows strikingly that a further explanation is needed for the actual import of Russell's theory of definite descriptions and other denoting phrases. They are analyzed by Russell in terms of quantifiers. When a the-phrase (definite description) denotes, it denotes an actual individual. 6 However, the most remarkable facet of Russell on denoting is what such successfully denoting phrases are supposed to denote: they denote objects of acquaintance. It is this crucial feature of Russell's theory that I am trying to account for by reference to the further problem complex, involving failures of EG due to lack of uniqueness, apparent need of restricting the ranges of bound individual variables, and so on. The fact that Russell in fact assumed in his theory of definite descriptions a limitation of the ranges of bound individual variables to objects of acquaintance is strikingly illustrated by his own example of (in effect) a primary occurrence of "the author of Waverley" in 0), i.e. (in effect) his example of (2). The only difference is that instead of "George IV did not know that" Russell has "George IV wished to know whether." Russell writes: "The latter [i.e. the secondary occurrence reading] might be expressed by 'George IV wished to know, concerning the man who in fact wrote Waverley, whether he was

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175

Scott.· This would be true, for example, if George IV had seen Scott at a distance, and had asked 'Is that ScottT. "7 As a closer analysis of questions shows, the very form of Russell's sample query, put to the mouth of the good King, shows that it is an ostensive question, i.e., one which involves quantification over acquaintance-individuals. It seems to me remarkable and revealing that it did not occur to Russell to use an example which dealt with an individual of whom he knew who he or she was. Instead, Russell used an example which dealt with an individual perceptually known to him. Why? Are not the usual flesh-and-blood individuals whose identity is known to us what we are normally dealing with in speaking of the actual individuals, and not mere objects of perception? Why require acquaintance? Indeed, it might seem that merely perceptual objects are among the least suitable ones for Russell's purposes, for we often do not know of them who or what they really are. Hence the kind of uniqueness we need is typically not present in them. In saying that we need to evoke this problem complex in order to account for Russell's thought I am of course not saying that Russell himself faced it squarely, nor saying that he ever solved it in a half-way satisfactory manner. He was not on a completely wrong track, however. The right solution is obtained by means of my possible-worlds analysis of the different epistemic and perceptual locutions, it seems to me. I cannot give a full account of it here, but have to refer the reader to earlier expositions. Indeed, one of the best reasons for attributing the "quantifying in" problem to Russell is that he very nearly gives the right solution to it, i.e. a solution which is right both in terms of any possible-world theory and in view of intuitive examples. For consider once again what Queen Victoria knew and didn't know. In the context of such a consideration, when is Charles Dodgson a bona fide individual whose name can be substituted for bindable variables which are being quantified from the outside? On my analysis, this is possible if and only if Charles Dodgson is one and the same individual in all the relevant possible worlds, i.e., if and only if it is true that (15)

(3x) in all the relevant worlds it is true that (Charles Dodgson = x).

But what are the relevant worlds? In view of the assumption we made as to what we are talking about, they are all the worlds compatible

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with what Queen Victoria knew. But then a sentence is true in all of them if and only if it was known to be true by the Queen. Hence (15) is tantamount to (14). (14)

(3x) Victoria knew that (Charles Dodgson = x)

As already suggested, (14) is essentially equivalent to (16)

Victoria knew who Charles Dodgson is.

And the truth of (14) seems to be an instance of the precise conditions Russell sets up for quantifying in. For he seems to say that the objects of acquaintance, which are the admissible values of bound variables, are precisely the individuals of whom we know who or what they are. (Cf. the quote above from Mysticism and Logic.) Furthermore, this condition seems to be the right one intuitively. For surely it follows from b's knowing that A(d) that b knows who (say x) is such that A(x) if and only if b knows who d is. Otherwise knowing that A(d) does not yet answer the who-question. Hence Russell's treatment of "quantifying in" seems to be essentially right, even if it is not based on a satisfactory analysis of the problem situation. An amusing historical coincidence is worth recording here. My treatment of quantifiers in intensional contexts has been called a "restricted range interpretation." This label betrays an abject failure to understand what the logical situation is. The values of quantified variables have to be restricted (whether one likes it or not) to individuals well defined for the set worlds we are in effect considering. If the actual world is one of them, then the range of our variables is indeed a subset of the actually existing individuals. But the set of worlds varies with the propositional attitude and the person holding this attitude. The set does not have to contain the actual world. If so, it may happen that the range of our variables is a superset of the set of actual individuals. (The attitude in question may be belief, and our believer may have a correct belief concerning the identities of all actual individuals. But he may mistakenly believe that there exist further individuals whose identity he fancies he knows.) Hence my interpretation can be called with equal justice an extended-range interpretation as a restricted-range interpretation. In contrast, Russell seems to have been inclined towards a truly restricted-range interpretation. He was tempted to restrict the values

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of his bound variables to objects of acquaintance. He never reached a full clarity in this matter. Nor did he realize that the whole business of cross-identification comes into play only in intensional contexts, a fact that may have helped to make the tact restriction look even more innocent in his mind. This account of the conditions of validity of EG depends crucially on the possibility of telling in principle which individual in a given world is identical with which individual (if any) in another one. Such "counterparts" or "embodiments of the same individual" can be thought of as being connected with an imaginary line, the "world line" of the individual in question. How are these world lines to be drawn? An important part of the conceptual landscape in which Russell's work moved is that we can - and indeed do, in perfectly ordinary discourse - draw two different warps of world lines. One of them identifies those denizens of several worlds which coincide when they are traced by spatio-temporal continuity to the common part of these worlds. The other set of world lines are drawn by identifying the individuals that as it were occupy the same location in someone's "co-ordinate system" defined by her or his first-hand cognitive relations to different individuals. In the simplest case this co-ordinate system is one's perceptual space. Adapting a pair of terms of Russell's for our purposes, we shall call these systems of world lines drawn by acquaintance (or the ostensive world lines) and descriptive world lines, respectively. Suppose we are considering John's knowledge. I have shown that in such a context b is a well-defined individual in the sense of following a descriptive world line if and only if (16)

John knows who b is.

In contrast, b is a unique individual in the sense defined by ostensive world lines if and only if (17)

John knows b.

By the argument presented earlier, (16) and (17) have the same form, but with a different kind of initial existential quantifier. In the rest of this paper, we shall render (16) by (18)

(Ex) John knows that (b = x)

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and (17) by (19)

(3x) John knows that (b

= x).

As I have argued in an earlier paper,s Russell systematically confuses the two kinds of quantifiers. He realizes - albeit only tacitlythat he has to restrict his attention to well-defined individuals. What he needed for his conclusions, especially for reducibility to acquaintance, was a restriction to individuals well-defined as far as individualization (non-identification) by acquaintance is concerned. Yet many of his locutions presuppose the other kind of world lines. For instance, we only have to recall Russell's statement that we have knowledge merely by description in cases where we know propositions about "the so-and-so" without knowing who or what the so-and-so is. In the light of my findings, this seems to assume unambiguously individuation by description. (Witness Russell's interrogative construction with "knows"!) Yet Russell's own examples of merely descriptive knowledge concern Bismarck and Julius Caesar. Surely Russell knew, and expected his readers to know, who these gentlemen were. His whole point is that we don't know them, i.e., we are not acquainted with them. From this perspective, we can locate Russell's principal success and his principle failures. He realized, however dimly, that in quantifying into intensional contexts the viable values of the bound variables cannot include all and sundry actually existing individuals. Only such individuals as are being referred to in a certain sense determinately or uniquely can qualify. What Russell did not realize is that this restriction cannot be defined by reference to the actual world only, but is essentially a matter of comparing the different worlds compatible with the propositional attitude in question. Even more importantly, he failed to realize that individuals in these alternative worlds can be compared with each other for identity in two different ways, by acquaintance and by description. Of course, the latter contrast is present in Russell, but he tries to 'project it back to the actual world, to construe it as a relation between different denizens of the real world of ours. (Alternatively, he wants to get rid of the objects of mere description altogether.) An abundance of examples can be found to illustrate these points. Several of them are indicated in my paper 'Knowledge by Acquaintance - Individuation by Acquaintance.'9

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Going back to the paradigm problems which Russell claimed to provide evidence for his 1905 theory, we can now see that Russell was also bothered by a further problem, viz. the problem of the failure of EG for reasons other than nonexistence or, more generally, by the problem of unique reference. Yet he never took explicit cognizance of this problem. A somewhat anachronistic way of putting the main point of this paper is to surmise that Russell would have ended up with a theory remarkably like mine if he had but focused on this problem instead of the ones he had primarily before his mind's eye. Unfortunately, this is not the whole story. Russell would not have accepted the interpretation I have outlined as a fair representation of either the spirit or the letter of his views. The reason for this descrepancy is merely another mistake of Russell's, however. The view I have attributed to him is not what he actually held, but what he was committed to holding. The real historical reason why Russell thought that his elimination of definite descriptions in favor of quantifiers proved (or helped to prove) reducibility to acquaintance was not that he thought that these quantifiers range over objects of acquaintance. Rather, he thought that the elimination of all denoting phrases apparently referring to other kinds of objects in favor of any sorts of quantifiers whatsoever is sufficient to do the trick. This presupposes that quantifiers carry no ontological commitment; only denoting phrases do. It is fairly obvious that this is what Russell thought. Variables, especially bound variables, were for him merely a notational device. He did not realize that in the kinds of first-order languages he was using the main interpretational (ontological) burden is carried by quantifiers and their variables. In brief, he failed to realize the truth of Quine's adage "to be is to be a value of a bound variable." (We can now see, incidentally, how pertinent Quine's adage is in an appropriate historical context.) Or, to put the same point in different terms, the observation just made is excellent evidence for Warren Goldfarb's claim that Russell was not yet operating with a fully developed modern concept of a quantifier. 10 Another way of making the same point is to recall Russell's adage that "every proposition which we can understand must be composed wholly of constituents with which we are acquainted." Russell's theory of definite descriptions enables him to eliminate apparent constituents which would not satisfy this requirement in favor of

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quantifiers and bound variables. In order to carry out the elimination, these must be assumed to range over descriptively identified individuals. (Otherwise, the real Bismarck will not be one of the admissible values of the variable by means of which we say that there is an individual of a certain kind). But then these quantifiers cannot properly be elements of the resulting proposition. For they surely would enter into the proposition through their value-ranges, and these value-ranges do not consist of individuals which we are acquainted with. Russell's mistake seems to have been twofold. (1) On the one hand, in 1905 he did not any longer think of quantifiers and bound variables as being genuine constituents of propositions. His analysis of quantifier phrases (other than definite descriptions) may have encouraged this mistake. He even called bound variables "apparent variables." (2) On the other hand, he tended to think of the values of bound variables as individuals individuated by acquaintance (as we have seen). Either mistake would explain Russell's procedure; together they make it almost inescapable. The view I have been tentatively ascribing to Russell earlier in the paper is what he would have been committed to if he had not made his first mistake. Since he never made up his mode between the two mistakes, it is impossible to impute a clear view to the actual historical Russel!. However, it is pertinent to the understanding and evaluation of his early thought to follow certain lines of thought further which Russell clearly was tempted to take but did not pursue very far. Now we can also see why Russell was so insensitive to all possible distinctions between different kinds of quantifiers. A notational device is a notational device; it does not need the specification of a domain for its interpretation, and hence it is not sensitive to changes in this domain. We can also see the reason why Russell might be suspected of holding a substitutional interpretation of quantifiers after all. He did not hold such an interpretation in contradistinction to the objectual one, but he did not yet have a fully developed objectual interpretation, either. This observation falls happily under my initial theme, however, instead of being a change in my overall interpretation of Russell. I believe that if Russell had taken a closer look at the failure of EG in epistemic and other intensional contexts, he would have been forced

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to realize also the role of quantifiers as a cornerstone of the referential apparatus of the kinds of languages he was dealing with. These observations nevertheless show that the title of this paper is not entirely accurate. Perhaps it should have been called 'On What Denotes What?' NOTES

* The

writing of this paper was made possible by the John Simon Guggenheim Memorial Fellowship I held in 1979-80. 1 Bertrand Russell, 'On denoting,' originally published in Mind in 1905, referred to here as included in R. C. Marsh, editor, Bertrand Russell: Logic and Knowledge, Essays 1901-1950, The Macmillan Company, London, 1956, pp. 39-56. (See p. 45.) 2 Op. cit. pp. 52-53. l Bertrand Russell, 'Knowledge by acquaintance and knowledge by description,' in Mysticism and Logic, Longmans, Green and Co., London, 1918, pp. 209-232, cf. p. 218. 4 Mysticism and Logic (note 3 above). (See the beginning of the paper.) 5 Op. cit., pp. 55-56. 6 'On denoting,' loco cit., p. 51. 7 'On denoting,' loco cit., p. 52. 8 'Knowledge by acquaintance - Individuation by acquaintance,' in David Pears, editor, Bertrand Russell: A Collection of Critical Essays, Doubleday, Garden City, N.Y., 1972, pp. 52-79. (See pp. 67-68. 9 Note 8 above. 10 Warren Goldfarb, 'Logic in the twenties: The nature of the quantifier,' Journal 0/ Symbolic Logic 44 (1979), 351-368.

DEGREES AND DIMENSIONS OF INTENTIONALITY In the title essay of my book, The Intentions ofIntentionality, 1 I proposed a touchstone for the intentionality of a concept in Brentano's and Husserl's sense of the term. According to this suggestion, a concept is intentional if and only if we have to consider several possible situations or courses of events in their relation to each other in spelling out the semantics of the concept. I dubbed this claim the thesis of intentionality as intensionality. By way of an intuitive explanation, the thesis says that the hallmark of intentional, that is, conscious and conceptualizable mental life is that it is transacted against the backdrop of a range of unrealized possibilities. This thesis is by no means new. It is closely anticipated among others by John Dewey. According to him, "many definitions of mind and thinking have been given. I know", Dewey continues, "of but one that goes to the heart of the matter: response to the doubtful as such"? Dewey's "mind and thinking" is obviously related intimately with the intentiona1. Moreover, "the doubtful" manifests itself for Dewey in the form of a range of open possibilities. For instance, in the field of the volitional, mental life strives "to actualize one of its possibilities rather than another" (op. cit., p. 226). Hence Dewey's definition of the mental comes close to the thesis of intensionality as intentionality. (This remarkable anticipation was pointed out to me by Merrill B. Hintikka.) A more recent example is offered by William Kneale who in his paper "Intensionality and Intensionality,,3 argues "that entertainment of propositions is essential to thinking in that wide sense in which thinking includes all mental life except bare sentience". Not unlike myself, Kneale also argues against the "development ... to be found in the writings of Husserl and many of his followers" which consists in "using the adjective 'intentional' of mental events with the sense of 'directed on an object'''. The main assumption which distinguishes my basic idea from Kneale's is the familiar possible-words interpretation of propositions as classes of possible worlds (or as the representative functions of such classes). Recently constructed logical and semantical theories, especially the socalled possible-worlds semantics, offer us much better opportunities for defending and developing further the thesis of intentionality as intentionality than were available to the earlier proponents of similar ideas. This paper is calculated to use some of the tools of possible-worlds semantics to deepen my thesis and at the same time to put it in a somewhat wider perspective. One application of these tools is the following. What perhaps is the strongest argument for my thesis of intentionality as intentionality turns on the analysis of the concept of meaning, or perhaps rather on the analysis of various mean183

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ing concepts. When Brentano and Husserl speak: of directedness in connection with mental acts, they do not mean directedness in the literal geometrical sense. Instead of directedness, they might equally well have spoken of meaning. What they are saying is that it is a characteristic of conscious mental life that it can point beyond itself in the sense of meaning (referring to) something outside itself. Phenomenology, it is not unfair to say, is but a general study of meanings and meaningfulness. Hence the question as to where the gist of intentionality lies is tantamount to the question as to how the concept of meaning is to be understood and explicated. Recently, this question has mostly been studied in connection with the special case of linguistic meaning. However, this is not a bad paradigm case, for Husserl asserted in so many words that all meanings in his sense can in principle be expressed as linguistic meanings.4 To this question, possible-worlds semantics gives a sweeping and at the same time profound answer. Meanings are functions from possible worlds to extensions. Even if this answer is only the fIrst approximation to the true account (see Partee5 for important doubts which are in effect partly answered in Hintikka 1975~, it suffIces to show the logical type of meaning concepts. What is important here is that meaning concepts involve essentially and deeply a multiplicity of possible worlds. Possible worlds are the arguments of the functions that are meanings. If there were not a multiplicity of such arguments, we could not speak: of meaning functions. Thus possible-worlds semantics offers strong evidence for my thesis, which may in fact be initially viewed as a corollary to this interesting theory, which has already proved its mettle even in the linguistic analysis of meanings? Any further evidence for the meaning analysis that possible worlds semantics offers is thus ipso facto evidence for my thesis. However, possible-worlds semantics is in none of its current versions the last word on the subject, but requires further development. Indeed, I shall try to indicate later in this essay how pushing the anal ysis of meaning concepts further lends fresh support to my approach to intentionality (cf. the penultimate paragraph of this paper, below). In this respect, and in several others, effective defense of my thesis presupposes sharpening it and considering it in a wider framework. Some of these improvements are prompted by certain apparent counter-instances to the thesis of intensionality as intensionality. One does not have to look far for primafacie objections, either. The apparent counterexample closest at hand is perhaps constituted by physical (causal or natural) modalities. Their semantical import can scarcely be spelled out without speaking of several alternative courses of events. Yet causal necessities do not seem to be intentional in the least. They are not characteristic of conceptualizable mental acts, nor

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products of such acts. No one, it may appear, would be likely to claim that they are intentional. This appearance is deceptive, however. An interesting way of putting the prima facie objection we are considering into a wider perspective is to point out that there are in fact actual historical instances of such "intentionalistic" view as were just envisaged. Some of the sharpest and most interesting arguments and theories in the history of philosophy are calculated to prove precisely the intentionality of physical modalities in the sense here intended. For instance, what is David Hume's celebrated criticism of causality (causal necessity) supposed to establish? Not that there does not in fact obtain regularities in nature which legitimately make us expect that a certain event follows a certain other event in specifiable circumstances. Hume does not try to dissuade us from believing that fire will bum and food nourish in the future, too. What he is trying to establish is that there is nothing in the realities of the situation beyond the actual succession of events. There is, he alleges, no single "impression" of which the "idea" of a causal nexus (causal necessitation) could be derived. It is entirely a contribution of the human mind, operating according to certain psychological laws, a "customary connection or transition of the imagination", to use Hume's own words. In brief, causal modalities are according to our good David creations ofthe human mind, which pretty nearly means that they are intentional in Husserl's sense. They point beyond what is given to us in perception, and they allow for the concei vable nonexistence of the effect even when the cause is present. Both phenomena--that of pointing to our intending something beyond the given mental contents themselves and the possible nonexistence of the intended object or fact--are characteristic of intentional phenomena. Thus my rough and ready criterion of intentionality may be right or wrong as applied to causal modalities, but it cannot be thrown out of court without at the same time challenging Hume's arguments against causality. This intentionality of the concept of causation according to Hume is easily obscured because of the relatively passive role the human mind plays in the genesis of the concept, according to him. Hume ascribed it, not to reason, but to custom. This does not invalidate my point which of course applies afortiori to theories of causality in which, as in Kant's theory, causal relations are put into the object by ourselves through certain categorizing activities of our minds. Another apparent counter-example to the thesis of intensionality as intentionality is constituted by logical (analytical) modalities. They have been held to be objective and nonpsychological. Yet they are among the best known examples of concepts which require an assortment of possible worlds to spell out their semantics. The notions of analytical necessity and analyticity are close-

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ly related to linguistic meanings, which surely are objective factors, independent of our beliefs and other psychological states. Isn't the thesis of intentionality as intensionality overturned by the familiar concepts of analytical (conceptual) necessity and possibility? Again, somewhat older thinkers have done part of my job for me. Much of W. V. Quine's famous criticism of analyticity (analytical modalities) and of meaning amounts to arguing that analyticity and related concepts belong in the familiar Brentano dichotomy to the intentional side. Indeed, Quine has repeatedly recorded his adherence to Brentano's thesis of an irreducible distinction between intentional and physical concepts. His criticism of meanings is deliberately construed as a part of a larger campaign against intentional notions in general. One especially clear symptom of the intentionality of meanings according to Quine is their dependence on beliefs. Apparently we cannot establish, on the basis of the kind of evidence Quine countenances, a person's semantics (meanings) without knowing his beliefs, and we cannot establish his beliefs without knowing what meanings he associates with the expressions of his language. In spite of the promissory notes recently issued by Donald Davidson,8 Quine remains unconvinced that the two can be separated in any indirect way, either, and even more unconvinced that meanings can somehow be purged of their intentional character. For my purposes, it can thus be said that Quine is doing to analytical modalities essentially the same as Hume did to physical modalities: he is trying to intentionalize them. Quine, in brief, is the David Hume of semantics. A third primajacie counter-example fares similarly. Critics who doubt the realism of possible-worlds semantics frequently overlook completely that one of the disciplines most basic for all investigations of nature and society, viz. probability theory, is habitually couched in terms which are tantamount to possible worlds semantics. Probability, for a mathematician, is nothing but a normed measure on a sample space. And the elements of this space, the sample space points, are the best examples of the systematic use of possible worlds before their introduction to the semantics of modal logic. In this spirit, Kolmogorov's axiomatic treatment of probability theory can be thought of as a probability theorist's counterpart to the model theory of modal logic founded by Kanger and others in the late fifties. Admittedly sample space points can in actual applications look much more modest than Leibnizian possible worlds. They can be, to borrow an apt phrase from L.J. Savage, "small worlds", for instance alternative courses which an experiment can take. But, then, I have for a long time insisted that the grandiose Leibnizian connotations of the term "possible-world" are badly misleading anyway. Indeed, a theoretical statistician's "small worlds" appear to me the best antidote to those excesses of possible-

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worlds semantics which have provoked Dana Scott to query, at least half seriously, "Is there life on possible worlds?" In view of this large-scale use of possible worlds in probability theory, probabilities concepts should be intentional according to my thesis of intentionality as intensionality. One's first impression is to find this conclusion counter-intuitive to the point of being ridiculous. And yet an influential school of mathematicians and statisticians maintains just what this conclusion says. I am referring to theorists of subjective probability, of whom Bruno de Finetti and L.J. Savage are perhaps the best known ones. For them, subjective probability is the only probability. If they are right, another possible worlds concept is in reality psychological or intentional. My thesis thus cannot be faulted by reference to probability concepts without fIrst refuting de Finetti and L.J. Savage. If you like analogies, you can thus put my observations in the form of the following "proportion": ~

causal modalities

=

~

analytical modalities

=

de Finetti probability

This parallelism does not constitute more that a persuasive argument for my thesis of intentionality as intensionality. However, it suffices to show how rich in interesting philosophical suggestions the thesis is. These suggestions are not exhausted by the parallelism, either. In all the three cases summed up in the equation, a prima facie counterexample to my thesis leads to some of the most interesting theories concerning the concepts which at first seemed to serve as counterinstances to the thesis. These theories do not so much refute the putative counterexamples as show that the status of these concepts vis-a-vis the dimension intentional-nonintentional presents an interesting problem. This makes it advisable to try to put the whole concept of intentionality into deeper perspective, as I shall try to do in the rest of this essay. By analyzing the very concept of intentionality further we can hope to throw some light on the relation of concepts like causality, meaning, and probability to psychological concepts. The strategy I shall follow in so doing is a familiar problem solving technique in conceptual analysis. Often an apparently dichotomous concept can be understood better and can be made to show a richer structure by turning it into a matter of degree. A striking recent example is Veikko Rantala's theory of definability.9 He does not begin by asking when a theory specifIes uniquely a concept occurring in it, i.e., asking when the concept is definable in this theory. Instead, he asks how much freedom the theory leaves to the concept. This in-

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determinacy or uncertainty is a matter of degree, and definability is obtained as the special case in which the uncertainty vanishes. By so turning definability into a matter of more or less Rantala has been able to develop its theory into an elegant analogue to the usual model theory. One advantage we can often gain by turning a qualitative concept into a comparative one in philosophical analysis is to be able to test one's rational reconstruction against intuitive judgements of degree and not only against black-and-white judgements. For instance, we can try to see whether our results concerning greater or lesser degrees of intentionality of different concepts, such as knowledge, belief, logical modalities, physical modalities, etc., square with our collateral insights into their comparative status vis-a-vis the mental. One of the virtues of the thesis of intentionality as intentionality is that it immediately shows how intentionality can be--and ought to be--a matter of degree. The thesis says that a concept is intentional insofar as in its semantics we have to go beyond the actual world and to consider also a number of alternatives to it. It is part and parcel of the spirit of this thesis that the farther away from the actual world we have to venture in order to spell out the semantics of a concept, the more intentional the concept is. This suggestion is in keeping with the general idea of the intentional as being closely related to the mental. For it is only by means of thinking that we can transcend the bounds of the actual, and the farther one can reach into the outer space of unrealized possibilities, the greater the ontological powers of one's mind are. It is the hallmark of conscious, directed human thought that it does not merely reproduce or mirror reality. It can actively anticipate, direct, reject, disapprove of, be surprised by, like, and dislike what actually happens and indeed compare in a plethora of other ways tacitly or explicitly what is with what might be. In terms of Husserl 's metaphor, the further away the objects are to which an act can be directed, the more intentional the act is. The concept of thinking presupposed here receives an eloquent expression in Juhani's words in Aleksis Kivi's Seven Brothers: B ut listen, a man can think what he wants, think himself master of the whole world or a creeping dung-bettle. Look, he can think God, devils, angels, all mankind, and the beasts of the sea, air, and land dead; think the world, Hell and Heaven vanished like a bunch of tow in a fire .... So can the thought of a man fly down here, and who can cast nets in its path? What I am suggesting is that the degree of intentionality of a concept can be measured by the extent of the flight it requires one's thought to undertake, that is, by the distance of the alternative worlds it introduces from the actual world.

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This distance we can interpret as the dissimilarity of the worlds in question, the actual world and its alternatives. But if this is the way of measuring degrees of intentionality, it is seen at once that there is not one but several different kinds or perhaps rather dimensions of intentionality. For it is obvious that a possible world can differ from the actual world in many different ways. These will correspond to as many dimensions of intentionality. We can also ask which of them are more important than others, and why. Moreover, we can try to see whether our initial problem cases which did not admit of a simple qualitative classification into the intentional or into the nonintentional class can be explained in comparative terms. Here is a list of some of the ways in which an alternative world can resemble, and by contrast differ, from the actual one: (a) Facticity. In the case of some propositional attitudes and other notions, there is a presupposition of success in reaching the truth. One can only know what is the case; what is necessary is actual; and so on. In terms of possibleworlds semantics, this means that each world is always a member of the set of alternatives to it which the concept we are dealing with in effect invites us to consider, and hence is maximally similar to one of them.

(b) Conservation of the existence of individuals from one world to another. A world can be similar to one of its alternatives in that the same (or partly the same) individuals exist in them. Conservation of individuals means that this is always the case. This principle can fail in two different ways. (i) Existence may not carry over from a given world to all its alternatives. (ii) Individuals may exist in alternative worlds even when they do not exist in the actual one. Thus we have here two closely related kinds of intentionality. (c) Conservation of the identity of individuals. This principle may likewise fail in two ways. World lines of individuals may (i) merge or (ii) split when we move from a world to its alternative. (d) Extendibility of world lines. I have argued elsewhere that world lines cannot be taken for granted, i.e., that they cannot always be extended to a new world. When extendibility fails, we cannot in principle tell of a denizen of one world whether or not it exists in another. Such failures have two forms: (i) A world line cannot be extended from a given world to its alternatives. (ii) A world line cannot be traced from and alternative back to the world it is an alternative to.

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(e) Logical standardness (invariance) o/worlds. Perhaps the most radical way in which a putative alternative world can differ from the actual one is to be somehow logically non-standard. Usually such nonstandard character of a world is manifested as the failure of some logical law in it.

(t) Methods 0/ drawing world lines. There might seem to be an exception to my use of similarity between worlds as the main criterion of the intentionality of the concept that introduces alternative worlds. This apparent exception is based on the correct observation that the principles for drawing world lines might be different for different intensional concepts. Sometimes they are more objective, sometimes they depend more heavily on some person's acts. It does not matter very much whether this last criterion of intentionality can be put under the same heading as the others. There is in any case close kinship between the different cases, for world lines are often drawn by means of various considerations of similarity. And degrees of similarity is precisely what determines degrees of intentionality on the idea which we are here pursuing. Thus what the methods of drawing world lines give us, is not so much an independent index of intentionality but a different symptom of the same kinds of intentionalityas the other criteria, especially the failure of (d), indicated in the first place. Criterion (t) might be described by saying that in it we are not dealing with the distance from the actual world to its alternatives but rather with the relative strength or weakness of the ties which bind these alternatives to the actual world. These "ties" are of course interpreted as the world lines which connect the manifestations of an individual in different worlds with each other. Criterion (t) explains why perception and direct personal memory are less intentional than, say, belief. For (as I have shown earlier) in their case world lines are drawn between the actual world and its alternatives (not between different alternatives) by means of causal chains. Such links are much less of the nature of free constructs of the human mind than other kinds of world lines. It is also important to realize that by and large world lines (counterpart relations, to use David Lewis's term) are determined solely by reference to the worlds they connect. As a first approximation, they are therefore independent, e.g., of the particular person whose propositional attitudes we may be considering. But this does not mean that the world lines are in principle independent of the tacit conventions of the whole language community or of the modes of operation of the human mind in general. It is dependencies of the latter kind hat we are here primarily interested in. They may lead to a preponderance of one warp of world lines rather than the others for this or that particular inten-

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tional notion. Thus the differences in the methods of drawing world lines are sometimes manifest as differences between diffcrent intentional notions. Several further explanations are in order here. By world lines, I mean of course notional lines that connect the embodiments or manifestations of the same individual in different possible worlds. A world line can fail to be extendible to a new world or two entirely different reasons. In some cases, the individual can be seen to fail to exist in the world in question. This is what is at issue in (b) above. In other cases, it does not even make sense to ask whether our individual exists in the newly found world. This is what (d) deals with. It represents a much more radical departure from a uniformity among possible worlds than the mere failure of existence. Yet very few philosophcrs have as much as tried to make the distinction. One reason for this is that several contemporary logicians and philosophers have dismissed the whole problem of cross-identification as trivial, and simply postulated in their semantical theory a set of individuals which mayor may not crop up in each possible world. This bland assumption is a most unsatisfactory procedure, however, and such critics as Quine are in my judgement entirely right in calling this bluff of Kripke, Montague, and their ilk. Hence the breakdown of world lines in the deeper sense with which (d) is concerned is a live option, and has to be discussed here. In speaking of alternatives to a given world in (a)-(f) I mean something more specific than just any other world we have to consider in spelling out the semantics of the given one. I am presupposing the usual possible worlds analysis of propositional attitudes and other modal concepts in terms of a two place relation, the relation of alternativeness, on the class of relevant possible worlds. This relation depends on the bearer of the propositional attitude in question. Alternatives to a given world are then simply the worlds that have this relation to it. As I have indicated earlier, to speak of a propositional attitude is in the eyes of a logician nothing more and nothing less than to speak of the associated alternativeness relation. To speak of what someone knows is to speak of the class of worlds compatible with everything he knows, for what he knows is shown precisely by asking which alternatives concerning the world his knowledge excludes and which alternatives it admits of. Other propositional attitudes can be analyzed similarly. It might seem that I am overlooking the most straightforward and most fundamental symptoms which can show that we are considering several possible worlds at the same time. These are the respective failures of (g) the substitutivity of identity and of (h) existential generalization. This suggestion has some specious plausibility.

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Indeed, I have pointed out repeatedly myself how neatly the "multiplicity of possible worlds" idea explains the breakdown of these two modes of inference. Thus (g) breaks down because two terms which actually pick out the same individual need not do so in alternative worlds, and hence need not be intersubstitutable in discussing these alternatives. Furthermore, (h) fails because the term with respect to which we are generalizing existentially does not pick out the same individual in the several alternatives we are tacitly considering. Since the possibility of these disturbing phenomena is obvious, my explanation for the breakdown of (g) and (h) essentially depends only on the fact that several possible worlds are being considered. However, the converse dependence does not obtain. All that the breakdown of (g) and (h) presupposes is a referential multiplicity, which can come about in ways other than a multiplicity of the worlds in which reference takes place. And when our terms have multiple reference for reasons other than that several possible worlds are involved, the invalidity of (g) and/or (h) does not indicate intentionality at all. A concrete counterexample to the use of the failure of (g)-(h) as criteria of intentionality is offered by quotation. In the context of quotation, both (g) and (h) fail. Yet there is so little intentionality to quotation that even Quine is ready to countenance it in his semantics. In spite of a not inconsiderable plausibility, the failure of (g) and (h) hence cannot serve as a reliable symptom of intentionality. Howard Morick has in effect defended the failure of (g) as a necessary and sufficient condition of intentionality. (See "Extensionalizing the Nonpsychological", Philosophy and Phenomenological Research, vol. 36, 197576, pp. 551-553, and "Opacity and Mentality", ibid., vol. 42, 1981-82, pp. 128-129.) His initial formulation is fallacious, however, as was pointed out by James A. Thomas, "Morick on Extensionality for de re Sentences," ibid. vol. 38 (1977-78), p. 544, and by Herbert Heidelberger and G. Lynn Stephens, "Transparency and Modality," ibid. p. 549. Morick's attempted correction is without any plausibility whatsoever, for he assumes that meanings cannot be defined without reference to what thinkers mean, i.e., cannot be defined in terms of Fregean thoughts without reference to actual mental acts. A general perspective on (a)-(f), especially on (a), is obtained by noting that my general idea of measuring the "distance" between a world and its alternatives can be used in two different ways. We can ask what the maximal difference is between the actual world and its several alternatives, or we can ask what the corresponding minimal difference is. The facticity condition (a) amounts to requiring that the minimal distance be zero; i.e., that any given world is among its own alternatives. The failure of

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this condition is clearly an interesting symptom of intentionality. Among other phenomena, it accounts for why knowledge is a less intentional notion than belief. For knowledge, unlike belief, satisfies the facticity condition. The term "facticity" may be in fact somewhat misleading. For we may require that the minimal distance between a world and its alternatives be zero only for some worlds, which need not include the actual (the given) world. This happens, I have argued, with deontic modalities. (The intuitive idea is that whatever is obligatory in a given world is true in each of its deontic alternatives, for these alternatives can be thought of as deontically perfect worlds. And what is obligatory in a deontically perfect world must be done there.) If this restraint on the models of deontic sentences is accepted, we have partial explanation why deontic concepts are usually taken to be non intentional or at least intentional to a very low degree. The failure of (a) is closely connected with the ideas of phenomenologists. One of their crucial considerations was the possible nonexistence of the object to which an act is directed. The object need only "inexist" in the act, Bretano intimates. This may seem to pertain to (b) rather than to (a). However, it is amply clear in Husserl that he is countenancing objects of such acts as the judgemental or otherwise propositional in nature. For such acts, the mere inexistence (failure of actual existence) of the object of an act amounts to a failure of facticity. Hence the criterion of intentionality based on the failure of (a) is an important one in understanding the views of phenomenological philosophers. How strongly facticity or its absence colors a concept is perhaps best seen (or felt) from the striking, sometimes even shocking, effects of ascribing even limited facticity to a concept which normally does not display it. Such an ascription is made dramatic use of by Paavo Haavikko in his libretto to Aulis Sallinen's opera The Horseman. In the opening scene the Merchant says: I do not wish for anything. I do not fear. Why should I dare to wish for anything when my wish is once fulfilled? And why should I dare to fear anything when fear at once comes true? Corresponding measures of intentionality based on the maximal distance from a world to its alternatives allowed by a concept seem to me much less important. By this measure, logical (analytical) modalities would be much more intentional than physical (causal) ones, for logically possible worlds can differ from the actual world much more radically than those that have to be physical-

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ly possible. For instance, all the actually valid natural laws would presumably have to hold in the latter worlds but not in all of the former ones. This suggestion is in agreement with the intuitive idea that logical modalities are more intentional than the physical ones, being to a large extent creations of the human mind. I do not fully trust this intuition, however. A philosopher in the Humean tradition would likewise have to disagree with the same intuition, for such a philosopher must consider "relations of ideas" as beyond the control of one's mind while causal concepts are only customary links in one's mind generated by habit rather than forced on as by objective relations of our ideas to each other. This skepticism is reinforced by observing that the maximal distance between a world and its alternatives allowed by knowledge is larger than that allowed by belief. (Since knowledge entails belief, all one's "belief worlds" are among one's "knowledge worlds".) Hence according to the unreconstructed form of the criterion under scrutiny, belief would be less intentional than knowledge. In fact, the opposite is clearly the case. Moreover, similar observations can be made concerning the relation of logical modalities to propositional attitudes. Some logically possible worlds are likely to be wilder than worlds which actually believed to be possible or which are epistemically possible (compatible with everything someone knows), i.e., farther away from the actual world. Yet logical modalities are clearly less intentional than propositional attitudes. Hence the maximal distance measure yields wrong comparisons between the degrees of intentionality of different concepts. A sensitive index of intentionality is the failure (c), i.e., the failure of identities between individuals to carry over from one world to another. This index requires a few preparatory comments, however, for a failure to preserve identities has been held to be impossible. When such failure happens on the way from a given world to its alternatives, we have a counterexample to the wellknown law (SI) \
::J

(F[x]

::J

F(y]))

which is sometimes called the bound variable form of the substitutivity of identity. An essentially equivalent form is \
::J

necessarily (x =y».

The failure of (SI) is to be distinguished from the failure of the substitutivity of identity for arbitrary singular terms. The latter fails simply because a singular term can refer to different individuals in different worlds. This possibility

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is obvious as soon as possible worlds framework is accepted. It is far less clear whether identities between genuine individuals can fail to carry over from one world to another. What such a failure would mean is that world lines can branch. Such branching has often been held to be obviously impossible, especially when it is supposed to happen in stepping from a world to its alternatives. Yet no conclusive argument has been presented for the impossibility of branching. One of Saul Kripke's putative arguments for (SI) consists in first pointing out that the validity of (SI) amounts to ruling out branching. Then the answers that a branching situation involves a violation of the transitivity of identity: one individual in (say) the actual world would be identical with two members of an alternative world. These two would not be identical even though by transitivity they ought to be. Hence he takes (SI) to be inviolable. This line of thought is patently circular, however. Transitivity of identity can mean two different things, either transitivity in one and the same world or transitivity across world lines. The plausibility which seems to belong to transitivity of identity pertains to the former case, not the latter. Indeed, to assume transitivity for the trans world case is precisely to rule out branching. Hence the argument assumes what it is designed to prove. Other logicians and philosophers have claimed that we cannot make sense of identity and quantification in intensional contexts unless (SI) is valid. This is demonstrably false, however. As soon as world lines have been defined, we can formulate precise truth conditions for sentences containing whatever intensional notions we are dealing with, with quantifiers and identity present, completely independently of the behavior of world lines. Surely nothing more can reasonably be asked for the purpose of making sense of a class of sentences than to give explicit recursive truth conditions for them. It is doubly ironic that any philosopher who has defended conventional systems of modal logic should object to a rejection of (SI) by saying that without (SI) we cannot make sense of modal and intensionallogics. For what (SI) does is to rule out branching in the special case in which we move from a world to its alternatives. In order to rule out merging (i.e., branching in the opposite direction) we must have as a valid sentence (IS)

0/x)0/y) (possibly (x =y) ::> x =y).

Now (IS) is not valid in several conventional systems of quantified modal logic, induding those originally proposed by Ruth Barcan Marcus. If we can make sense of these systems, we must therefore allow branching when we travel homewards. But there is nothing to choose between the two directions interpretationally. The only reason why they are not distinguished in conventional

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systems of modal and intensionallogic is the accidental fact that they did not happen to contain what Saarinen has called backwards-looking operators. Hence anyone who has ever defended conventional systems of modal logic interpretationally has in effect defended splitting world lines and thereby (by the parity of cases) branching, i.e., the rejection of (SI). In the field of that small-scale model of cross-identification, reidentification in time, branching makes perfectly good sense, even though it may be a relatively rare phenomenon. A computer may be disassembled and put together in the form of two separate computers. Later, the process may be reversed; and so on. Hence there can scarcely be anything unimaginable about world lines which split and merge. The role that re-identification plays in cross-identification in fact gives useful clues as to how we might envisage the branching of world lines to take place. There may nevertheless be good structural reasons why branching will be an exception and not the rule. If world lines are not given to us globally but pieced together from infinitesimal elements like the solution of a differential equation, then branching will correspond to a singularity, and hence presumably be a relatively rare phenomenon. I have no doubt that the arguments that have been given against the branching of world lines are circular in a very deep sense. They are in the last analysis based on the idea that the only way of understanding the semantics of quantified discourse is to postulate some fixed domain of individuals. This illicit assumption is perhaps seen most clearly in Kripke's claim that alternative possible worlds are constructed by ourselves from ready-made individuals. Speaking of possible worlds is empty talk as long as it does not have some consequences in possible experience, abstracting of course from all merely contingent limitations of experience. The rest is metaphysics in the pejorative sense of the word. Hence possible worlds are best thought of as being determined by the associated possible totalities of experience. Then it becomes clear that there cannot by any absolute rejection of branching. It is easy to describe possible experiences in which a given actual individual has more than one counterpart. What the prohibition against branching amounts to is therefore a deliberate or unwitting policy decision to concentrate on only some types of possible experience without any satisfactory justification for doing so. That the failure of (c) is indeed a sensitive indication of intentionality, is shown by its behavior vis-a-vis different concepts. It can be maintained that logical necessity, physical necessity, and analytical necessity satisfy (c) ("what is, necessarily is what it is, and not another thing"). Conversely, it can be argued that several other concepts which are obviously more intentional than

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these varieties of necessity violate (c). Cases in point are knowledge ("not everything that is, is known to be what it is, nor known not to be another thing"), belief, perception, etc. One of the best arguments for my dimensionalized approach to intentionality is its ability to do justice and to put into a critical perspective the "logical" criteria of intentionality proposed most prominently by Roderick Chisholm. 10 It has been complained that these criteria seem to have little to do with each other. My analysis explains this impression: different Chisholmian criteria turn out to deal with different dimensions intentionality. At the same time, my analysis shows the hidden common factor in the Chisholm criteria. For they all turn out to be closely related to the several dimensions of intentionality which were mentioned earlier in this paper and which are all based on the same basic idea. Of the possible criteria which Chisholm does not think are correct I have already commented on two, viz. on the failure of (g) and (h), and pointed out why they are not satisfactory criteria, in spite of their plausibility. Chisholm calls the failure of the substitutivity of identity "referential opacity", and distinguishes it from substitutivity of clauses on the basis of a shared truth-value. The failure of the latter he calls "nonextensionality", and rules it out as a criterion of intentionality because the concept of necessity also involves violations of nonextensionality. We have already seen that this argument of Chisholm's is not unchallengeable. It is nevertheless clear that we do not have here an important criterion of intentionality. The perspective offered by the dimensions (a)-(f) at the same time enables us to sharpen Chisholm's criteria and to correct their defects. Consider first those criteria of Chisholm's which are in terms of the ordering of quantifiers and intensional operators. They are illustrated by the breakdown of the following implications. (1) a believes that every individual F's :::> of each individual a believes that it F's. (2) Conversely. A formalization of (1) might be

(3) Ba ('Vx) F(x)

:::> ('v'x)(3y)(x=y &

BaF(y»

(4) A formalization of (2) is naturally obtained as the converse (3).

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Chisholm's explanations of the reasons for the failure of (1)-(2) are not entirely clear. Their upshot is nevertheless fairly unmistakably an appeal to the failure of (b) as a criterion of intentionality. For instance, Chisholm writes, in explaining why (1)-(2) fail: ...one may believe falsely, of some nonuniversal set of things (some set comprising less than everything there is), that is comprised everything there is; and...one may believe falsely, of a universal set of things, that it does not comprise everything there is. In my terms, these two mistakes amount to two mirror-image situations in which (i) there are individuals which do not exist in one's belief worlds and in which (ii) there are individuals which exist in some of one's belief worlds but which do not exist actually. These are precisely failures (b)(i) and (b)(ii), respectively, explained above. What Chisholm does not realize, however, is that (1) and (2) can fail in a fundamentally different and deeper way. In order to see this, imagine a situation in which the relevant values of my bound variables are politicians in California. Imagine first that I believe that they are all of them lawyers by training. Assume further that I have no beliefs whatsoever as to which politicians there are in the great state of California, beyond the ones I know of. In particular, there is not anyone set of politicos which I believe to exhaust the class. Does it follow that I believe of each California politician that she or he is a lawyer? Obviously not, in spite of the fact that by Chisholm's lights it ought to follow. The reason for the failure of the inference is that there may be lots of politicians of whom I do not have any idea who they are. I do not disbelieve their existence (or lawyerhood); I just do not entertain any beliefs about them. The very question whether I believe something about one of them (including existence) does not arise. In my possible world terms, this means that there are members of the actual world who are not connected by any world line to individuals in my belief-alternatives. This does not mean that they do not exist in my belief-alternatives. It means that the question of their existing or not existing there does not arise. What this amounts to in my scheme (a)-(t) is (d)(i), that is, the failure of world lines to be extendible from the actual world to its alternatives. Similar examples show that the failure of the converse implication (4) need not be due to the reasons Chisholm restricts his attention to, that is, not due to the failure of some doxastically possible individuals to exist actually. Rather, the inference breaks down because of the failure of some world lines of individuals to be extendible from alternative worlds back to the actual one. In

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other words, the inference breaks down because of a failure of the type (d) (ii) in my scheme. In other words, Chisholm's operator switch criteria of intentionality are a mixture of my criteria (b) (i)-(ii) and (d) (i)-(ii). I strongly suspect that Chisholm's criteria obtain whatever plausibility they have from (d)(i)-(ii) rather than from (b)(i)-(ii). The breakdown of world lines between certain worlds establishes are much deeper gulf between them than a mere failure of some welldefined individuals to exit in one but not the other. Chisholm 's mistake illustrates contemporary philosophers' overemphasis on questions of existence and nonexistence. In reality, questions of well-definedness (i.e., questions of the extendibility of world lines) are more important and much more revealing. The difference between the two sets of questions should be obvious. For an individual i to be well-defined for a world W it must make sense to ask whether i exists in W. If the answer is yes, i exists in W. If the question is impossible to answer, i is not well defined in W. This latter fact can be expressed somewhat loosely by saying that the world line of i cannot be extended to W. The same overemphasis recurs in the discussions which Chisholm's operator-switch criteria originally prompted. Virtually all the attention in the first round of papers was focused on questions of existence. Chisholm's current favorite criterion is formulated by him in a way which I cannot help finding inappropriate. According to this criterion, a propositional operator p is intentional iff p(S) is contingent (neither logically true nor logically false) for each value of "S". If this is what Chisholm means, there are no intentional concepts whatsoever by his criterion. For put p = John believes that, S = (S 1 & - SI). For the concept of belief to be intentional in Chisholm 's sense, it must be possible for John to believe in the explicit contradiction (SI; & - SI). This seems to me to be obviously and trivially impossible. For, as Chisholm will undoubtedly agree to, the issue is not what John might say he believes, but what he really can or cannot believe with full understanding of what is involved. If John believed that (SI & - SI), what would the world have to be like according to his belief? How would he describe that world? And what would count as evidence of his belief's being true? Chisholm's formulation of his criterion is obviously beyond redemption. I strongly suspect that what Chisholm intends is something different. It is tempting to reply to the criticism just presented as follows: Even if John cannot be expected to believe in an explicit contradiction (SI & - SI), there are lots of logically equivalent sentences which are logically false but in which John can perfectly well believe. Any logical contradiction whose contradictoriness is subtly hidden will serve as an example.

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I agree with the premise of this rejoinder. It fails to save Chisholm's criterion, however. For what is argued for in the rejoinder is no longer the contingencyof P(S) for all values of "S" but the failure of logical equivalence to guarantee substitutivity (with the preservation of meaning and truth). For as soon as that substitutivity is given up, I can perfectly well maintain the logical falsity of (5) John believes that (SI & - SI) while admitting the contingency of (6) John believes that S2 where S2 is some subtly contradictory sentence. What is really being claimed in Chisholm's criterion is hence that a concept is intentional iff the analogue to "logical omniscience" cannot be assumed to obtain within its scope. In other words, concept is intentional iff logical equivalence fails to guarantee substitutivity in a context governed by it. In any case, quite apart from Chisholm, this is obviously a highly interesting potential criterion of intentionality in its own right. This incidentally shows that we cannot hope to save Chisholm's formulation by taking the relevant values of "S" to be propositions rather than sentences. For by the same token as I just presented, logical equivalence cannot naturally be taken to guarantee identity of propositions. This corrected variant of Chisholm 's main current criterion of intentionality can be analyzed further. In some of my earlier papers and books I have shown what the natural distinction is between those logical equivalences which allow for a substitution in epistemic contexts and those that do not. l1 The argument carries over to other propositional attitudes. The distinction is made natural by its intuitive interpretation. "Trivial" equivalences preserving substitutivity are those which can be established without considering individuals which have not already been introduced at either side of the equivalence. Substitutivity fails when the equivalence cannot be seen to obtain without introducing auxiliary individuals into the argument. It turns out to be possible to relate this syntactical (proof-theoretical) criterion to semantical (model-theoretical) conceptualizations. Veikko Rantala has shown how to extend the usual notion of model (possible world) so as to allow a world to change in a certain way as we explore itP If the investigation is thought of as a succession of selections of individuals to be considered in their relation to each other, the set of individuals in the world available to be

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selected is allowed to change between such "draws". In view of the analogy of these generalized models and probability theorists' models Rantala calls his new models urn models. Classical models are of course a subclass of urn models, viz. invariant urn models. Noninvariant urn models are clearly nonstandard in the sense of my criterion (e). It turns out that some urn models change so subtly that they cannot be told apart from invariant ones at some fixed level of analysis. 13 Moreover, it turns out that the worlds that are thus indistinguishable from classical (standard) models are precisely the ones that have to be considered in connection with such centrally intentional concepts as knowledge and belief. For it can be shown that an equiValence is trivial in my sense and hence allows for substitutivity in intentional contexts iff it is true in all these "almost invariant worlds" at the level of analysis which is naturally associated with the equivalence. In sum, a concept is intentional according to this line of thought iff it involves almost invariant (or other noninvariant) worlds, over and above standard ones. This is of course nothing but a special case of my criterion (e) of intentionality. Furthermore, I have argued that this sharpened form of (e) is also the true gist in Chisholm's main criterion of intentionality. It seems to me in fact that (e) defines what is by far the most important dimension of intentionality. The criterion which (e) yields accordingly leads to results which are closer to our pretheoretical ideas about the intentionality and nonintentionality that those that any other criterion (a)-(d) or (t). This can be seen from the following list of answers which different criteria yield as to whether a concept is intentional in the dimension that goes together with that criterion. (The entry 1/2 means that the criterion applies only to some possible worlds or to some transitions from one possible world to another.)

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CRITERION a Knowledge Belief Memory Perception Obligation Causal Modalities Analytic Modalities Probability (a) objective (b) subjective

b

+ + + + + 1/2 + + + + +

+ +

e

f

c

d

+ + + + +

+ + 1/2 + + + + + 1/2 + + + + ? ?

+ ? ?

? ?

+

From the vantage point we have reached, we can now see our initial problems in a sharper relief. The main reason why causal modalities, analytical modalities, and probability are felt to be nonintentional is in my view connected with dimension (e). These notions do not involve logically nonstandard models. For instance, what is implied logically by a causally necessary proposition is itself causally necessary. Thus the true--and largely valid--reason why these notions look nonintentional is that they are intentional only to a low degree or, putting the point more accurately, are intentional only in unimportant dimensions of intentionality. Notice that logical and analytical modalities are nonintentional also by my criterion (c). There is something more to be said here, however. Those philosophers, logicians, and mathematicians who have maintained the subjective (for us, intentional) character of probability or of analytical modalities have sometimes done more than just to argue for this way of looking at the concept in question. They have occasionally associated their general theoretical viewpoint with definite claims of the structural properties of the concept in question. Some of these claims are highly interesting for our purposes here. The clearest instance is LJ. Savage, who argued that probability (which for him meant subjective probability) must not be invariant with respect to logical equivalence. 14 This will imply some changes in the usual Kolmogorov axioms for probability. But which changes? L.J. Savage's suggestion has provoked some amount of attention among theoretical statisticians. They have not come up with a satisfactory way of implementing Savage's proposal. From what has been said earlier it can be seen that my syntactical (inferential) criteria of substitutivity, backed up by Rantala's urn models, will do the job.

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From our present vantage point, what is especially interesting is that this change makes the concept of probability intentional according to the one criterion, viz. criterion (e), which was found above to be the most important one. It is thus eminently satisfactory to find that the same mathematicians and statisticians who have sought to make probability an intentional notion substantially have also tried to turn it into an intentional one according to my criteria. Somewhat similar things can be said of analytical modalities (meaning concepts) as LJ. Savage said of probability. If meanings are to be something that human beings can actually grasp and otherwise handle, they must not be invariant with respect to logical equivalence. For logical equivalence is not an effective (computable) notion. Hence, true identity in meaning cannot go together with logical equivalence even apart from all questions of independence of primitive concepts), for then we could not always know whether two sentences or two utterances mean the same thing. Indeed, the best candidate for a humanly graspable concept of meaning is one on which identity in meaning (and hence substitutivity) is restricted precisely in the way I indicated above in connection with "almost invariant worlds". (This is the change in the usual possible-worlds analysis of meaning which was foreshadowed above in connection with my comments on possible-worlds semantics as a form of meaning analysis.) But even if this particular explication of meaning is not accepted, any concept of meaning on which meanings can actually be grasped by the human mind leads inevitably to a violation of (e) and hence to intentionality by the corresponding criterion. Far from being counter-examples to my approach to intentionality, the notions mentioned in the beginning, especially probability and analytical modalities, in fact provide interesting evidence for the dimensionalized version of the approach. IS NOTES I JaakkoHintikka: 1975,TheIntentionsofIntentionalityandOtherNewModels [or Modalities, D. Reidel, Dordrecht, 192-222. 2 John Dewey: 1960, The Questfor Certainty, Dover, New York, p. 224. 3 William Kneale: 1968, 'Intentionality and Intensionality', Proceedings of the Aristotelian Society, Supplementary Volume 42, 73-90. 4 Edmund Husserl, Ideas: General Introduction to Pure Phenomenology, sec. 124.

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Hall Partee: 1980, 'Semantics--Mathematics or Psychology?', in Bauerly, Egli and von Stechow (eds.), SemanticsfromDifferent Points of View, Springer-Verlag, Berlin, 1-14. 6 Jaakko Hintikka: 1975, 'Impossible Possible Worlds Vindicated', Journal of Philosophical Logic 4, 475-84. 7 Cf. Barbara hall Partee: 1977, 'Possible Worlds Semantics and Linguistic Theory', The Monist 60,303-26. 8 See, e.g., the work collected in his Inquiries into Truth and Interpretation, Clarendon Press, Oxford, 1984. 9 Veikko Rantala: 1977, Aspects ofDefinability (Acta Philosophica Fennica 28, no. 4), Societas Philosophica Fennica, Helsinki. 10 Roderick M. Chisholm: 1967, 'Intentionality', in Paul Edwards (ed.), The Encyclopedia of Philosophy, Macmillan, New York. 11 See, e.g.,Jaakko Hintikka: 1974, Logic, Language-Games. and Information Clarendon Press, Oxford; 1974, 'Knowledge, Belief, and Logical Consequence', in J.M.E. Moravcsik (ed.), Logic and Philosophy for Linguistic, Mouton, The Hague, 165-176. 12 Veikko Rantala: 1975, 'Urn Models: A New Kind of Nonstandard Model for First-Order Logic', Journal of Philosophical Logic 4, 455-74. 13 See Jaakko Hintikka, 'Impossible Possible Worlds Vindicated' (note 6 above). 14 See L.J. Savage: 1967, 'Difficulties in the Theory of Personal Probability', Philosophy of Science 34,305-10. IS Some material in the early parts of this essay has previously appeared in my papers, 'Intentionality and Physical Modalities', in: Ilkka Niiniluoto et. al.( eds.): 1977, Studia Excellentia: Essays in Honour of Oiva Ketonen (Reports from the Department of Philosophy, University of Helsinki, no. 3), Helsinki, 15, and 'Degrees and Dimensions ofIntentionality' , in: Umberto Eco (ed.): 1978, Semiotica testuale: mondi possibili e narrativita (= Versus, Vols. 19-20), Milano.

5Barbara

My work on this paper was made possible by a Fellowship from the John Guggenheim Memorial Foundation for 1979-80 and by support from the Florida State University.

SITUATIONS. POSSIBLE WORLDS, AND ATTITUDES 1.

POSSIBLE WORLDS AS POSSIBLE SITUATIONS

I once read about a cannibal tribe in which nobody could become a chieftain without disposing of one of the earlier ones and eating him. It seems to me sometimes that philosophers must be descendants of that tribe. When a philosopher develops a new theory, it almost invariably seems more important to him to use it to try to clobber an earlier one rather than to try to see if the two are perhaps complementary - and to see what there is, perhaps, to be learned from the earlier theory. This is very much the relation of situation semantics to possibleworlds semantics.) The latter was always intended, by myself at least, to be thought of as being applied in the same way as the probability calculus (with which it is indeed intrinsically connected), that is, applied in such a way that the alternatives considered in possibleworlds semantics need not be states of cosmology or world history; they could be considered as "small worlds", as alternative courses that an experiment might take. This, of course, is how probability calculus has always been applied in practice and is intended to be applied. I have suggested that instead of "worlds" in "possible-worlds semantics" we might be well advised to speak of "scenarios". If I had been really smart, I would have called the whole subject "possible-situations semantics". At least some of the recent misunderstandings would then have been avoided. For instance, in what I have called perceptual cross-identification the alternatives considered must be of the nature of situations. For there must be in each of them a particular perceiver, and they must all share that perceiver's perceptual space. At this point, however, possible-worlds semanticists have been negligent. Even though some of us have recognized the need of applying the theory to situations rather than worlds (in the vulgar sense of the word), we have not taken the next step and studied the interrelations of smaller and larger situations. For instance, what I 205

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have called descriptive cross-identification normally takes place between chunks of the world larger than a given perceptual situation. Hence, contrasting it to the perceptual cross-identification, as I have also done, virtually presupposes some way of comparing with each other smaller and larger "situations". Yet, mea culpa, I have done little to develop an actual theory for such comparisons. In this respect, the "situation semantics" of Barwise and Perry is a most welcome addition to the conceptualizations employed by possibleworlds semantics. For one of its most important novelties is a variety of ways of comparing different situations with each other and otherwise relating them to one another. Something like it ought to have been developed in any case by possible-worlds semanticists. An especially interesting subject in this direction is how small egocentric situations are assembled together so as to approximate a larger overall objective "world picture." Much more detailed attention should nevertheless be paid to the structure formed by different situations than has been done so far. There should be at least three different kinds of relations obtaining between them: spatial relations, temporal relations and relations between finer and coarser types. One suggestion I venture here is that these three systems of interrelations can probably be studied profitably in isolation from each other for some important purposes, without bringing in all the dimensions of the structure in one fell swoop. For instance, I have shown elsewhere 2 how the semantics of English temporal discourse, including tenses, can be formulated in terms of treatment where the worlds (situations) are temporal crosssections of a branching course of events (branching, that is, when one moves toward the future). This treatment applies much more widely than to the simple sample sentences considered by Perry and Barwise. On a technical level, the compatibility of situation semantics and possible-worlds semantics is strikingly suggested by Alice ter Meulen's variant treatment of situation semantics. 3 (I don't know if it has been officially blessed ex cathedra as a version of situation semantics; but that's how she has presented it.) In her treatment, the formalized counterpart to a situation turns out to be to all practical purposes my concept of a model set, which of course has been my trusted old helpmate in dealing with possible-worlds semantics. What is new is the study of the interrelations of richer and poorer model

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sets. And this is what possible-worlds semanticists ought to have studied on their own anyway a long time ago. 2.

ELIMINATING LOGICAL OMNISCIENCE

The fact that situation semantics complements rather than contradicts rightly understood possible-worlds semantics is vividly seen from some of the uses to which Barwise and Perry put it. One problem is worth discussing at some length as a sample illustration of what I have said. Barwise and Perry make a big play of how situation semantics helps us to get rid 'of the ridiculous assumption of logical omniscience which possible-worlds semanticists are prey to. Now theit: treatment does contain a novelty, and probably quite a useful one. I will not re-explain here how they deal with the failure of inferences of the form: (1)

a sees b to X;

therefore (2)

a sees b to Y;

where X'ing logically implies Y'ing. The main point is that their solution of the paradox of logical omniscience is in terms of the relation between richer and poorer types of situations. As I said, it is impeccable as far as it goes. Not surprisingly, it is needed most badly in situations involving that most situational of all propositional attitudes, perception. But is it fair to flaunt this as a triumph of situation semantics over possible-worlds semantics? Scarcely, for two reasons. First, just because the new solution traffics in relations of coarser and finer types, it belongs to those questions (as was indicated above) which were not raised (rather than answered wrongly) by possibleworlds semantics. Secondly, and more importantly, some possible-worlds semanticists have solved their problem of logical omniscience, even though Barwise and Perry don't care to mention it. This problem is quite different from theirs, and it haunts the Barwise-Perry theory quite as much as it used to haunt old-fashioned unreconstructed pre-Rantala possible-worlds semantics. The failures of logical omniscience Barwise and Perry have chosen to consider are essentially due to the insertion of new descriptive (non-logical) terms in the conclusion,

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over and above what is mentioned in the premises of an inference we are sometimes nescient about. The failures Rantala and I have considered are due to the logical complexity of the inference, more specifically, to the need of considering auxiliary individuals in order to see the validity of the inference. This is an entirely different ballgame (or at least a different language game). To see what I mean, consider a couple of examples: (3)

Robert saw someone give each boy his own book.

(4)

Robert saw each boy be given some book by someone.

Does (3) logically entail (4)? In the Barwise-Perry theory, it does. However, it seems to me at least arguable that it should not do so. lf this example is not convincing enough, here is another one. Suppose that I am engaged in playing domino games of the variety to which Hao Wang related the decision problem of the entire predicate calculus. That is, I am trying to fill the Euclidean plane with square dominoes of a finite number of different sorts, with the proviso that at least one domino of each sort has to be used. (Of course, adjacent sides of any two dominoes have to match.) On certain occasions, I can truly say of such a game, on the basis of my visual inspection of the situation: (5)

I see this domino task to be impossible to complete.

For instance, I can see that two adjacent sides of a given domino cannot be matched by any dominoes without creating a "hole" which cannot be filled by dominoes of any of the available sorts. (This is something I can literally see.) In other cases, I cannot truly say (5). Yet on the Barwise-Perry theory (5) should be true of any noncompletable domino problem as soon as I see what the available sorts of dominoes are, for the incompletability follows logically from that visual information. Of course this (possible worlds) version of the problem of logical omniscience can be solved. Indeed, it has been solved by Rantala and Hintikka. 5 There is hence nothing here for the situation semanticists any more than for the possible-worlds semanticists to worry about. The approach can be of situation semanticists complemented by evoking the Rantala-Hintikka treatment of the problem so as to restore sweetness and light. My only thesis here is to point out the

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symmetry of the situation. In the same way as old-fashioned possibleworlds semanticists need situation semantics to solve the first puzzle of logical omniscience, situation semanticists need urn models (and all that) to solve the second puzzle of logical omniscience. Who's in a position to eat whom here? Or, to put the same point in somewhat less charitable terms, as far as logical omniscience is concerned, situation semantics has won the race which possible-worlds semantics has (wrongly) refused to enter. It has lost the other race, a race which both situation semantics and possible-world semantics must eventually enter. 3. RE-IDENTIFICATION

Another problem in which situation semanticists and possible-worlds semanticists are in the same boat is the important problem of reidentification. Indeed, the situation-semantical way of viewing the question has the disadvantage of tending to hide the problem. For instance, when one speaks in situation semantics of the overlapping of two situations, one presupposes that the shared part is selfsame in the two situations. Yet the re-identification problem is very real indeed. Its urgency should be brought home to everyone at this particular moment by the strongly negative conclusions which both Quine and Kripke claim to have reached concerning it. 6 Quine claims that there is no way of explaining how re-identification takes place, and that we hence should despair of the whole process. Kripke claims that there is no way of explaining re-identification, and that we should therefore postulate it without further ado, at least for physical objects. It seems to me that these instructions are counsels of irresponsible despllir and irresponsible optimism, respectively; and it also seems to me that in neglecting the problem situation semantics overlooks a philosophical problem of the first magnitude. Of course, possible-worlds semanticists have likewise largely neglected the problem, too, but at least the problem is seen more clearly, for instance in the tense-logical applications of possible-worlds semantics. 4.

THE DIMENSIONS OF SITUATIONS

If there is one respect where situation semantics and possible-worlds

semantics, though comparable in letter, differ in spirit, it is the

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following: as was indicated above, situation semantics in effect postulates a many-dimensional structure of different situations, characterizable in terms of spatial and temporal relations, relations of overlapping and inclusion, etc. Now all this is compatible with possible-worlds semantics, at least in my version. However, there is one dimension of variation of situations which for possible-worlds semantics is absolutely crucial. Possible situation - pardon, possibleworlds - semantics is based on the assumption that when intensional notions enter the discussion, each situation must be considered against the background of other situations which are just like it except for being merely possible. In other words, possible-worlds semantics insists that, over and above the variation of situations with respect to their spatial and temporal relations and the relations of greater coarseness or refinement, there must be another dimension of variation, as it were, in the dimension of mere possibility. What is essential in the ill-named possible-worlds semantics is precisely what is revealed by glimpsing into that particular dimension. I hasten to add that such a dimension as possibility is easily and naturally introduced through what looks like mere spatiotemporal structure. For instance, a branching time structure creates for each situation s a set of alternatives in the sense of possible-worlds semantics, viz., the set of all the situations s which in the other branches of time have the same temporal (and, if needed, spatial) co-ordinates as s. (This, in fact, is an important avenue through which modal concepts enter the semantics of our ordinary discourse.) If situation semanticists are willing to think of their multi-dimensional structure of different situations in such a way as to allow for these alternatives, or otherwise allow for the dimension of possibility, they can handle the same problems as possible-worlds semanticists. However, it also then becomes entirely problematic whether there is any substantial difference between situation semantics and possibleworlds semantics, apart from such detailed technical problems as whether a time-structure which branches only towards the future suffices for a realistic semantics. (It does not, I shall argue elsewhere.) 5.

OTHER COMPARISONS

It is not clear to me what the attitude of Barwise and Perry is to this question. They list four problems which by their own admission they do not deal with in their paper. Characteristically, these are all

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problems which the introduction of the possibility dimension solves immediately and obviously. (I have recently reminded my readers of how readily possible-worlds semantics disposes of such Fregean problems as opacity and the cognitive content of attitudes. 7 Of this whole group of problems, suffice it to say here only the usual sapienti sat.) 1 don't doubt that situation semanticists can try to deal with some of these problems by adding a sufficient number of epicycles, without bringing thesis theory to coincide with a suitably extended version of possible-worlds semantics. This will not change the overall comparative situation. For if a fair comparison between possibleworlds semantics and situation semantics is what's being done, the Barwise-Perry list of four problems could, and should, be extended to a list of fourteen, nay, forty problems which possible-worlds semantics has successfully solved but which situation semantics in its present form has not. If you need samples, here are a few: Over and above opacity conceived of as the failure of substitutivity, there is the manifestation of opacity as a failure of existential generalization even when existence as such does not fail. Over and above the task of explaining the failure of either inference, there is the problem of producing the extra premises which serve to restore the validity of the inference in question. Over and above the study of the uses of subordinate questions governed by epistemic verbs, there is the task of developing a semantics for direct questions, including the task of finding criteria for (conclusive) answers to questions. Over and above the task of explicating the direct object construction with events as objects, there is the still-to-be-accounted-for use of the direct object construction with particulars as direct objects. What is particularly close to the interests of philosophers is the use of such direct objects to be understood as objects of acquaintance as postulated by Russell. If you want to try your hand at something a little bit more complicated, 1 suggest that you study multiple and nested questions and try to develop a theory for them. Or, which turns out to be an especially subtle task, try to develop a theory for questions containing (outside) quantifiers. One of the more general tasks here is to give a semantics for wh-constructions 'with epistemic verbs. One of the more limited tasks is to explain why the wh-construction is not found with all the relevant verbs - and why the direct object construction (with a particular object) is not found with some of the same verbs. When comparisons are made between possible-worlds semantics

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(of the kind I have practiced) and its competitors, as are in effect made in the paper we are discussing, it is only fair that the almost total failure of all the competing approaches to deal instructively with any of these questions be registered. Apart from such comparisons, there are several features of situation semantics that seem to me less than completely happy. Only one is registered here: it is the reliance of Barwise and Perry on the function c introduced on p. 671. The reason why the use of this function seems to me dubious is the following. One of the main purposes of semantics is to offer a model, or at least a framework for a model, which would show how the speakers of language can refer to whatever they refer to and mean whatever they may mean. For instance, possible-worlds semantics can be thought of as a crude outline of a kind. The speaker or hearer of language grasps a certain funtion: a function from possible worlds to references. By examining the given world she or he can find out what the argument of this function is, which enables her or him to reach, via the meaning function, the intended reference. Now Barwise and Perry start in their explanations of meanings from the facts of reference-in-situation: " ... a component representing the connections c between certain words and things in the world implicit in any meaningful use of those words." They go on to define meanings and interpretations in terms of this function c. Now I should have thought that the real criteria of a realistic theory of meaning and reference is to show how c is determined by meanings. For surely to understand an expression is to grasp its meaning, which determines c. The authors' procedure makes it very hard for me to appreciate the resulting theory. 6.

BIG WORLDS VS. SMALL WORLDS

What has been said needs a qualification, which pertains especially to section 1 above. I was speaking there exclusively for myself to a larger extent than I spelled out. lan Hacking 8 has tried to trace a tradition in the use of both probabilistic concepts and possible-worlds concepts within which possible worlds are interpreted as big worlds, possible universes, and not as "small worlds" in the sense of say, L. J. Savage. 9 Hence my appeal to the parallelism between probability theory and possible-worlds semantics perhaps does not suffice to

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vindicate my claim that possible-worlds semantics is to be thought of as a theory of situations (small worlds) and not only of "big" worlds (entire universes). Perhaps not; perhaps I have to disentangle myself more firmly from Lebniz and Carnap than I have so far indicated. However, Hacking's fascinating perspective and the research that supports it does not make any difference to my main point. It is that there is absolutely nothing in the basic ideas - or, for that matter, in the technical development - of possible-worlds semantics that would preclude or discourage an application of this theory to situations rather than to entire universes. Here the analogy with probability calculus and its measure-theoretical "semantics" is especially instructive; no one is likely to think that probability calculus or even Carnap's inductive logic can be applied only to situations in which the sample set of points represents entire world histories. It may be that Carnap had one designated application in mind, which was to such grand worlds. If so, I don't agree with him, and don't want to be bracketed together with Carnap. Hence the existence of a Leibniz-Carnap "big worlds" tradition does not make any difference to what I said earlier in this note. The Florida State University

NOTES I This note was written as a comment on Jon Barwise and John Perry, 'Situations and Attitudes,' Journal of Philosophy 78 (1981), 668-91, presented at the APA Symposium on the Logic of Perception and Belief, December 30, 1981. 2 'Semantical Games and Temporal Discourse,' Linguistics and Philosophy 5 (1982), 3-22. ) Alice ter Meulen, 'Partial Models for Speaker Reference' (forthcoming). 4 Cf. here Hao Wang, 'Remarks on Machines, Sets, and the Decision Problem,' in J. N. Crossley and M. A. E. Dummett (eds.), Formal Systems and Recursive Functions, North-Holland, Amsterdam, 1%5, pp. 304-20; Robert Berger, The Undecidability of the Domino Problem (Memoirs of the American Mathematical Society, No. 66), Providence, R.I., 1%6. I See their papers (the last two in the volume) in Esa Saarinen (ed.), Game- Theoretical Semantics, D. Reidel, Dordrecht, 1979. 6 Cf. Saul Kripke, 'Identity Through Time,' paper delivered at the Seventy-Sixth Annual Meeting of APA, Eastern Division, New York, December 27-30, 1979; and W. V. Quine, 'Worlds Away,' Journal of Philosophy 73 (1976), 859--63.

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Jaakko Hintikka, 'On Sense, Reference, and the Objects of Knowledge: Epistemologia 3 (1980), 143-64. 8 See lan Hacking, The Emergence of Probability, Cambridge University Press, 1975; also 'The Leibniz-Carnap Program for Inductive Logic: Journal of Philosophy 68 (1971),597-610. 9 See L. J. Savage, The Foundations of Statistics, John WHey, New York, 1954.

7

QUESTIONING AS A PHILOSOPHICAL METHOD 1. Questioning as a General Knowledge-Seeking Method

Questioning is not only an important philosophical method; it offers a useful model for many different types of knowledge-seeking. For the time being, I shall in fact treat questioning as a process of information-gathering in general. Only later, once the structure of information-seeking by questioning has been discussed, can we see how variants of this method are particularly adept to serve the purposes of philosophical thinking. The best known historical paradigm of questioning as a philosophical method is the Socratic elenchus. 1 It is of interest to see how several aspects of this celebrated technique can be understood and put into a perspective on the basis of my analysis of questioning as a philosophical method. Before doing so, we nevertheless have to look at the logical structure of question-answer sequences. Here the first question that is likely to come up is probably going to be the skeptical one: What's so new about the idea of questioning, anyway, as a knowledge-seeking method? It is one of the first ideas likely to occur to anyone interested in philosophical or scientific or hermeneutical method, and it has in fact occurred to a number of philosophers, such as Plato, Francis Bacon, Kant, Collingwood, Gadamer, and Laudan. 2 Moreover, a large number of different treatments of the logic of questions are on the market. 3 It is surely not realistic to expect new insights to ensue from this old idea-or so it seems. 215

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2. The Logical Structure of Questions. What is new and promising about the approach I am proposing is that it is based on an adequate analysis of the crucial questionanswer relationship. 4 Before we know what counts as an answer (intended, full, conclusive answer) to a given question, we cannot hope to understand how answers to questions one asks can yield information, for we don't really know what an answer to a given question is likely to be. Surprisingly, this crucial question-answer relationship is not analyzed satisfactorily in the earlier discussions of the logic of questions, in spite of the fact that the right analysis follows naturally from the basic idea of considering questions in informational terms. The line of thought-I shall call it, in analogy to Kant's "transcendental deductions," a "model-theoretical deduction" -which yields the right analysis is important enough to be sketched here. 5 It relies on the idea that having information (knowing something) amounts to being able to eliminate certain alternative situations or courses of events ("possible worlds").6 This is the true gist in the often-repeated idea of "information as elimination of uncertainty."7 What it means is that a person's, say b's, knowledge state in a "world" Wo is characterized by reference to the set of all those "worlds" W t that are compatible with what b knows in Wo (and by implication to the set of worlds that are excluded by b's knowledge). These will be called the epistemic balternatives to Wo. Then it will be the case that a sentence of the form (1)

b knows that p

is true in Wo if and only if it is true that p in all the epistemic b-alternatives to wo. Furthermore, a wh-question like (2) Who killed Roger Ackroyd? is to be analysed for my purposes as a request for a certain item of information. What information? Obviously, the information the questioner has when she or he can truly say (3)

I know who killed Roger Ackroyd.

In general, a specification of the informational state that the questioner requests to be brought about is called the desideratum of the question in question. Thus (3) is the desideratum of (2).

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Now (3) is naturally, not to say inevitably, analyzed as (4)

(3x) I know that (x killed Roger Ackroyd)

where "x" ranges over persons. For what more could it conceivably mean to know who did it than to know of some particular person x that x did it? In model-theoretical terms, (4) means that there is some individual x such that, in each world compatible with everything I know, x killed Roger Ackroyd. This is, of course, but saying that I have enough information to rule out x's not having done it. 3. Question-Answer Relation Analyzed. What is now going to count as a conclusive answer to (2)? Let's suppose someone tries to answer the question (2) by saying "d." (I am making no assumptions concerning the logical or grammatical nature of this response, as long as it makes (5) below grammatically acceptable. It may be a proper name, definite description, indefinite description, or what not.) This reply is a conclusive answer if and only if it provides the questioner with the information that was requested. For the sake of argument, I shall assume that the reply is true, honest, and backed up by sufficient information. What information does it then bring to the questioner? Clearly, the information that enables him or her to say, truly, (5)

1 know that d killed Roger Ackroyd.

This is the state of knowledge (information), actually brought about by the reply "d". But it is not necessarily that state of information requested by the speaker, for this requested state is expressed by another proposition, viz. (4). Hence the reply "d" is a conclusive answer, i.e., it provides the requested information, if and only if (5) implies (4).8 But when does this implication hold? First, why should it ever fail? The model-theoretical perspective provides an instant answer. What (5) says that the term "d" picks out, from each world compatible with what I know, an individual who in that world killed Roger Ackroyd. The reason why this does not imply knowing who did it is that those several references of "d" need not be the same person. We may put it as follows: my knowing that someone or other killed Roger Ackroyd means having enough information

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to rule out all courses of events under which someone or other did not kill him. But in order to know who did it, I need further information: I have to have enough information to guarantee that the killer of Roger Ackroyd is one and the same person in all the worlds my knowledge has not yet eliminated. Thus the extra premise one needs to infer (4) from (5) will have to say that the term d picks out the same individual from all the worlds compatible with what I know, i.e., that there exists some one individual x such that in all those worlds d = x. But, according to our observation concerning (I), something is true in all the worlds my knowledge does not rule out if and only if I know that it is true. Hence the extra premise needed to restore'the implication from (5) to (4) is (6)

(3x) I know that (d = x).

This, then, is the criterion of conclusive answerhood. The reply "d" to (1) is a conclusive answer if and only if it satisfies (6). What is remarkable about this result is not the particular condition (6). Indeed, it is precisely the condition one would expect. By the same token as the near synonymy of (3) and (4), (6) can be expressed more colloquially by (7) I know who d is. And this is obviously a necessary and sufficient condition for the repiy "d" lu satisfy the questioner. For if the questioner does not know who d is, this reply does not enable him or her to know who it was who killed Roger Ackroyd. Instead, it would prompt the further question, "But who is d?" or some equivalent response. 9 What is remarkable about the criterion (6) of conclusive answers to (1) is, first of all, that it is generalizable. 1O Even though the technical details of some of the generalizations are messy, the leading idea is clear in all cases. Even more remarkable is the fact that the aptness of my criterion of conclusive answerhood can be proved. The intuitive modeltheoretical argument outlined above can be transformed into a formal argument, which relies on these principles of epistemic logic that codify my model-theoretical assumptions sketched above. Likewise, the generalizations of my criterion likewise can be proved to be correct in the strictest sense of the word in most of the relevant cases. 11

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In view of the crucial importance of the question-answer relationship (criterion of conclusive answerhood) for any study of knowledge-seeking by questioning, a couple of further remarks are in order. The analysis of the question-answer relationship I have offered is an inevitable consequence of a certain way of conceptualizing knowledge (information). Hence those critics have been barking up the wrong tree who have tried to criticize it by reference to the surface phenomena of language, including unanalyzed and ill-understood "intuitions" that the critics profess to have about the logical implications between different natural-language sentences. 12 The only relevant criticism would be to develop an alternative model-theoretical framework for (an alternative way of conceptualizing) information and knowledge, and an alternative way of codifying the idea that a question is a request of information. There is no need for me to respond to self-appointed critics who have not done this. 4. Further Problems The outline account given above leads to further problems in virtually all directions. Here is a sample: (i) Besides being a request for a certain item of information, a question implies certain restraints as to how this request is to be fulfilled. We need an account of these restraints}3 (ii) It is not enough to use logicians' time-honored models as implementations of the idea of alternative states of altering or courses of events. For if we do so, we are led to the paradoxical conclusion that everyone always knows all the logical conclusions of everything he or she knows. What is the appropriate generalization we need here?14 (iii) There is another way of taking a question like (1), viz. to take the requested state of knowledge to be. expressible by (8) (x) (x killed Roger Ackroyd :::> (3z) (z = x & I know that (z killed Roger Ackroyd»). In other words, the speaker wants to be aware of the identity, not just of one person who killed Roger Ackroyd, but of all of them. How are the two representations (4) and (8) related to each other?15 (iv) What are the precise conditions on conclusive answers to more complicated questions? How are such complex questions to be analyzed in the first place?'6

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(v) Many perfectly respectable responses to a question don't satisfy my condition of conclusive answerhood, but nevertheless contribute partial information towards a conclusive answer. How are such partial answers to be defined? How can we measure their distance from a conclusive answer?l? (vi) Such representations as (4) or (8) assume that quantifiers and epistemic operators (e.g., "I know that") are informationally dependent on each other transitively, so that they can be represented in a linear fashion. Can this assumption fail? What happens if it does?18 5. Strategic Aspects of Questioning-Presuppositions of Questions Such questions can easily be multiplied. It would be a serious mistake to take these new problems, and others like it, to constitute evidence against my approach. Here it is in order to anticipate the self-awareness that our discussion of knowledge-seeking by que~tioning can engender. One of the most important advantages, perhaps the most important advantage, of the questioning model is that by its means we can discuss and evaluate, not just someone's state of knowledge at a given time (vis-a-vis the evidence one has at the time) but also entire strategies ofknowledge-seeking}9 Then the value of an answer A to a question Q of mine (or the value of conclusion I draw from such an answer A) cannot be measured in the sole terms of the knowledge (theory) this answer A yieids. Rather, we must also consider the opportunities for further questions and answers that are opened by the original answer A. The basic reason for this is that questions cannot be asked in a vacuum. A question can only be asked after its presupposition has been established. Hence one may need answers to earlier "smaller" questions in order to be able to ask the crucial questions whose answers are likely to yield the information really desired. Here we can also see the usefulness of game-theoretical conceptualizations. From game theory we know that utilities cannot be assigned to individual moves. Utilities, which in my informationseeking games depend essentially on the information (knowledge) sought, can only be assigned to entire strategies. Likewise, we can see here the importance of another feature of my analysis of questions and answers, viz. the role of presuppositions. In the example above, the presupposition of (2) is

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(9) (3 x) (x killed Roger Ackroyd), that is (to)

Someone killed Roger Ackroyd.

Obviously, (2) can be sensibly asked only if (to) is true. Once again, my definition is generalizable beyond our particular example. In general the presupposition of a wh-question is obtained by omitting the outmost epistemic operator or operators "I know that" from the desderatum of the question. The presupposition of a wh-question minus the quantifier is called the matrix of the question 6. Significance of New Problems Self-applied to the knowledge-seeking that is involved in my approach to questions, answers, and question-answer sequences, these observations imply that the approach should not be judged on the basis of the theory it has reached at one time. Even less should the open questions my approach prompts be counted against it. On the contrary, the ability of an approach to lead to interesting problems is a strong reason in its favor. These problems are evidence for its power to give rise to new questions whose answers are likely to essentially increase our knowledge of the subject matter. This illustrates neatly how my general theory of knowledgeseeking by questioning can enhance our self-awareness of our own philosophical enterprise and its methods. 7. Meno Answered The nature of the question-answer relation and of the presuppositions of questions deserves a few comments. Part of the philosophical relevance of my observations on these two subjectsespecially on the former-can be expressed by saying that they provide a solution to Meno's puzzle. 20 On the basis of what we have found, it is in fact easy to see how Meno's paradox comes about. Applied to what is questions, my criterion of answerhood yields the following result: Suppose Socrates asks the definitory question

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(11) What is d? The desideratum of (11) is (12) I know what d is. Then a reply, say "b," is a conclusive answer only if Socrates (i.e., the questioner) can truly say, (13)

(3x) I know that (b = x),

in other words, can truly say, (14) I know what b is. Thus it looks as if the question (11) can be answered conclusively only if the questioner already knows an answer. No wonder poor Meno was perplexed by this paradoxical-looking circularity. The solution to Meno's problem lies in the fallaciousness of the word "already" in my formulation of the problem just given. The right conclusion to draw from my criterion of conclusive answerhood is not that the questioner must already know what the answer (in our example, the term "b") stan"ds for prior to the reply, but rather that it is part of the task of that reply to provide the collateral information that enables the questioner to say, truly, (13) (= (14». The right conclusion here is thus that an adequate response to a wh-question will have to serve two different functions. To put the point in the form of a paradox, it is not enough for a reply to provide (what is usually taken to be) an answer to the question (viz. a true substitution-instance of its matrix). It must also give to the questioner enough supplementary information to bring it about that the conclusiveness condition is satisfied, i.e., that the questioner knows what the reply term refers to after the reply has been given. This double function of replies to whquestions is the true moral of Meno's paradox. It represents an important insight into the role of replies (answers) in discourse. Speaking more generally, by spelling out the presuppositions for asking different kinds of questions as well as the conditions that conclusive answers to them have to satisfy, we can show just what a questioner has to know before he or she can ask a question and receive an answer to it, and thereby solve Meno's problem in its most general form. All this highlights in turn a general truth about questions and answers. They are very much a discourse phenomena, and their

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theory must be developed as an integral part of the logic and semantics of discourse, as distinguished from the logic and semantics of (isolated) sentences. 8. Different Sources of Information One feature of the conceptualizations expounded above is that they are independent of the specific nature of the answerer (source of information). For this reason, the theory of knowledge-seeking by questioning that is based on these conceptualizations is applicable to several different kinds of information-gathering. In order to see one of them, we may borrow a page from Kant's Critique of Pure Reason and think of the experimental inquiry of the physical sciences as a series of questions a scientist puts to nature. 21 (The page in question is B xiii.)22 In this application, we can once again see the crucial role of the question-answer relationship. For Kant's emphasis is on the way in which a scientist can actively guide the course of investigation by choosing correctly the questions put to nature. The mechanism of this control is of course precisely the question-answer relationship. A question Q predetermines its answers in that they have to be answers to this particular Q. I shall not pursue this application here, however. Another interesting application along related lines is to construe observations-be they scientific, clinical, or pretheoretical-as answers to questions put to one's environment. 23 This point is vividly illustrated in Sherlock Holmes's famed "deductions," which I have interpreted as so many questions put to a suitable source of information. (They will be discussed below.) Not only does Sherlock occasionally call his "Science of Deduction and Analysis" also a science of observation and deduction. 24 He repeatedly speaks of the same conclusion as being obtained, now by deduction or "train of reasoning," now by observation or perception. Upon meeting Dr. Watson, Sherlock Holmes says: "You have been in Afganistan, I perceive" (emphasis added). Yet he later describes a long train of thought (c( below) he needed to reach that "conclusion."25 On another occasion, Sherlock is surprised that Watson "actually [was] not able to see [emphasis added] that that man was a sergeant of Marines," even though Dr. Watson had just referred to'this conclusion as a deduction ("How in the world did you deduce that?") and even though Sherlock himself has to use no fewer than thirteen lines to explain the different steps of his train of thought.2 6

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Less anecdotally, assimilating observations to knowledge-seeking questions offers a natural framework for discussing some of the hottest problems in the contemporary philosophy of science, such as the concept-Iadenness and theory-Iadenness of observations. 27 For instance, if an observation is construed as a question, then the information it yields depends on the concepts in terms of which the question is formulated. Likewise, the observation, being a question, depends on the antecedent availability of its presupposition, which ultimately depends on the theory one is presupposing. We are obviously dealing with an extremely promising line of investigation here. 9. Activating Tacit Knowledge The applications I am primarily interested in here are nevertheless in a still different direction. The source of information need not be outside the questioner. It may be addressed to the questioner's own memory or to whatever other sources of "tacit knowledge" he or she may possess. Then the questioning process becomes a process of activating tacit knowledge. 28 It seems to me that there is an especially dire need here of satisfactory semantical and logical analysis, for the process of bringing the relevant items of tacit information to bear on one's reasoning is practically never dealt with by philosophers and methodologists. Likewise, it seems to me that psychologists could profit from a better conceptual framework in dealing with this subject matter. Thus it is an extremely important subject in several respects. 29 In earlier papers, I have argued that much that passes as "inference" or "deduction" in non philosophical jargon really consists in sequences of implicit questions and answers.30 In many of the most striking cases, such questions are answered on the basis of information that the questioner already has available to himself or herself but which the question serves to call attention to. It is precisely this quality of Sherlock Holmes's "deductions" that so frequently made them look "elementary" once they were spelled out. How did Sherlock know that the good Dr. Watson had been to Afganistan when he was introduced to him? Here is a paraphrase of Holmes's "train of reasoning":31 What is the profession of this gentleman? He is of a medical type, but with the air of a military man. Clearly an army doctor,

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then. Where has he been recently? In the tropics, for his face is dark, although it is not the natural tint of his skin, for his wrists are fair. But where in the tropics? He has undergone hardship and sickness, as his haggard face tells clearly. His left hand has been injured, for he holds it in a stiff and unnatural manner. Now where in the tropics could an English army doctor have recently seen so much hardship and got his arm wounded? Clearly in Afganistan.

Apart from the observations that the famous detective is using, he is relying on perfectly commonplace knowledge about sun tan, medical clues to one's past, and recent military history. Actualization of tacit information is also the gist in philosophers' appeals, so prevalent in our days, to what are known as "intuitions."32 I have argued elsewhere that it is a serious mistake to construe them as the data that philosophical theory or explanation has to account for. If they are to have a legitimate role in philosophical reasoning, they must have some other role in philosophical argumentation. But what is that role? We don't find a satisfactory answer in the literature. 10. Analogy Between Interrogation and Deduction On my model, what does guide the choice of questions that activate tacit knowledge? My answer is: largely the same strategic considerations as govern the choice of the best lines of questioning in general. But what are those strategic principles? It is hard to be specific, but a couple of relevant observations can nevertheless be made. The presuppositions of questions must be among the conclusions a questioner has reached. The crucial questions are typically wh-questions, and their presuppositions are existential sentences. (C( (9) above.) The decisive strategic consideration therefore is: Which of the available existential sentences should I use as presuppositions of wh-questions? An answer to such a question will instantiate the matrix of the question, which is an existential sentence. Hence the strategic choice just mentioned is nearly analogous to the choice faced by a deductive strategist. For it has been shown that the crucial consideration in the quest of optimal strategies is the choice of the existential formulas to be instantiated at each stage of the deduction, which is here assumed to be roughly a natural-deduction or tableaux-type procedure. 33 In other words, the principles that govern the choice of optimal questioning strategies are extremely closely related to the choice of the principles

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that govern one's quest of the best deductive methods. In short, deductive logic is likely to yield the best clues to effective questioning. No wonder Sherlock Holmes called his art of investigation, which I have interpreted as a questioning method, "The Science of Deduction." The same road can be traveled in the opposite direction. Because of the parallelism between deduction and questioning, suitable questions can trigger the right deductive conclusions by the answerer, and may thus serve inversely as heuristic guides to the right deductive strategies. 34 Hence a philosophical inquirer should discard the misleading positivistic generalization model and think of his or her task, not as a series of generalizations from the data offered by "intuitions," but on the model of Sherlock Holmes's "Science of Deduction and Analysis." In so far as my questioning model is applicable, i.e., insofar as Kant is right, such generalization from random data plays a much smaller role in science itself than philosophers seem to imagine these days, let alone in philosophical inquiry. Another symptom ofthe insufficiency of the generalization model is that it does not offer any clues as to how our intuitions (the data) have to be changed if they prove unsatisfactory. Here, then, we can see one of the main services that my questioning model can perform when thought of as a paradigm of philosophical method. It can guide a philosopher in activating the tacit knowledge that constitutes the raw materials of a philosopher's inquiry. In particular, it shows that important guidelines for this task are forthcoming from our familiar deductive logic. Successful thinking is colloquially referred to as "thinking logically." Philosophers might be well advised to take this idea more seriously than they are currently doing. 11. Trivial vs. Nontrivial Reasoning Part of the force of the near analogy between questioning and deduction that I have argued for is brought out by the question: What characterizes nontrivial (synthetic) reasoning? I have argued on earlier occasions for an answer to this question applied to deductive reasoning. 35 (It has turned out that this answer was not only anticipated but strongly emphasized by C. S. Peirce, even

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though no one had understood his idea in the interim.)36 Very briefly, and omitting all sorts of technicalities, the idea is that a logical inference is trivial e'corollarial," Peirce would have said) if it does not involve the introduction of any new entities into the argument. An inferen~e is nontrivial ("theorematic," Peirce calls it) if it depends on the introduction of a new object into the purview of the reasoning. The more numerous such auxiliary objects are that a reasoner has to bring in, the more highly nontrivial is the reasoning. Historically, the paradigm case of such introductions of new objects into an argument have been the so-called auxiliary constructions of elementary geometry, a paradigm reflected by Peirce's choice of his terms. The partial analogy between interrogation and deduction explained above allows us to generalize the trivial-non trivial distinction to empirical reasoning relying on questioning over and above deductive reasoning in contemporary philosophers' narrow sense of the term. The extension is neatly illustrated by an example I have used before, viz. "the curious incident of the dog in the night-time" in Conan DoyleY The famous racing horse Silver Blaze has been stolen from its stable in the middle of the night and its trainer, the stablemaster, has been found killed out in the heath. Everybody is puzzled till Sherlock Holmes directs our attention "to the curious incident of the dog in the night-time." "The dog did nothing in the night-time." "That was the curious incident." What Sherlock is doing here is in the first place to ask a few well-chosen questions. Was there a watchdog in the stable during the fateful night? Yes, we know that. Did the dog bark at the horse-thief? No, it did not. ("That was the curious incident.") Now who is it that a trained watchdog is not likely to bark at in the night-time? Its master, the trainer, of course. Each question and its answer may be "elementary," as Sherlock would say, but what makes the entire line of thought nontrivial is that Holmes brings, for the first time in the story, a new factor to bear on the solution of the mystery, viz. the dog. This introduction of a new object into the argument parallels an "auxiliary construction" by a geometer. It doesn't merely add a psychological twist to the tale; it is what logically speaking enables Holmes to carry out his "deduction. " The most famous deduction in the philosophical literature to be conducted in the form of a question-answer dialogue is Socrates's

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conversation with the slave-boy in Plato's Meno. 38 It illustrates forcefully the same power of auxiliary constructions (more generally, auxiliary individuals, in logicians' sense of individual) to facilitate nontrivial conclusions. In the Men 0, Socrates extends the slaveboy's purview by introducing three new squares adjoining the original one. (See Meno 84 d.) The original one is here: D

C

LSJ

A

B

The completed one looks like this: J H

G

C

D~----I----~E

A

B

F

(The lines BE, EH, and HD are likewise introduced by Socrates in so many words in 84 e-85 a.) Once all these constructions have been carried out the conclusion is obvious: the square of BD can be seen to equal twice the square of AB. This argument depends crucially on the "auxiliary constructions" Socrates is allowed to carry out. If the role and nature of such auxiliary constructions is not understood and appreciated, the power of philosophical questioning methods to yield nontrivial conclusions will be an intriguing puzzle. It is a small wonder, it seems to me, that this puzzle should have provoked Plato to. hypothesize in his doctrine of anamnesis, i.e., of a memory-like knowledge of those unexpected conclusions. 39 It would also be interesting to try to consider theories of innate ideas in the same light.

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12. Thinking as Unspoken Discourse One way of bringing out the crucial general significance ofa suitable questioning model for the conceptual analysis of human thinking in general is the following: Time and again in the course of Western thought, philosophers have proposed to consider thinking on the model of speaking. Plato describes "thinking as discourse, and judgment as a statement pronounced, not aloud to someone else but silently to oneself."40 Likewise C. S. Peirce asserts that "all thinking is dialogical in form. Your self of one instant appeals to your deeper self for his assent,"41 and again, "One's thoughts are what he is 'saying to himself,' that is, saying to the other self that is just coming into life in the flow of time."42 One r~ason why this idea is so suggestive is that, if it is right, the extensive and powerful logic that has been developed for the study of spoken or written sentences may be expected to help us to understand the nature of reasoning and thinking. Yet this suggestive idea has never led to major insights into the nature of thinking or reasoning. Why? In our days, Peter Geach has made an interesting effort to use the idea and construe the concept of thinking or "judging," as Geach calls it, "as an analogical extension of the concept saying."43 In spite of Geach's famous ingenuity, the results are rather meager. We can now see why, more generally, the suggestive idea of thinking as internal saying has not proved as useful so far as one might have hoped. The answer is implicit in Plato's and Peirce's formulations. They don't just compare thinking with saying, but with discourse-a discourse between several different selves. Hence it is not any old logic that can be hoped to be useful for understanding reasoning through the Plato-Peirce analogy; only a genuine logic of discourse as distinguished from logic done on the sentence level will do. We could call the latter "sentential logic" in contrast to discourse logic if the term had not been pre-empted. What is striking about most of the usual logical conceptualizations and theories is that they move on the sentence level. They don't take into account differences between different speakers, for instance differences between what they know. Furthermore, most of the conceptualizations concerning the logic of questions in earlier literature have likewise been sentential.

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Characteristically, Geach, too, tries to use the analogy between thinking and saying to examine, not different types of inferences one can make in one's thinking, but the various kinds of judgments one can make, such as "judgments of identification," "judgments about sensible particulars," ets. In other words, his conceptualizations remain predominantly on the sentence level. Now questions and answers offer the simplest example of a discourse phenomenon that cannot be reduced to sentence-level phenomena. Indeed, there would not be any point in asking a question if the speaker and the hearer knew the same things or if epistemic differences between them did not matter. In view of the importance of the respective epistemic states of the parties in a question-answer dialogue, it is not surprising that my criterion of conclusive answerhood (c( (16) above) is formulated in terms of what the questioner knows (i.e., knows after he or she has received a reply). If there is anything remarkable in my criterion, it lies in the fact that there is no need to refer to the other features of the dialogical situation. Hence my theory of questions, answers, and question-answer dialogues offers a handy paradigm case for the study of characteristically discourse phenomena. According to what we have found, this implies that it also promises, via the Plato-Peirce analogy between discourse and thinking, to serve as an analogical model for at least some instructive sample cases of reasoning (thinking). In brief, it offers us the best hope that I can see of vindicating the Plato-Peirce analogy, at least in the case of selected sample problems. Only in terms of a dynamic theory like my theory of question-answer interaction can one hope to bring logical theorizing to bear on the study of reasoning and thinking in the way Plato and Peirce expected. Several of the developments outlined, mentioned, or anticipated above receive their natural places in this overall perspective. It was for instance mentioned earlier that the process of calling the right items of tacit information to active duty can be approached as if it were a questioning procedure. This characteristically thinking process can in other words be handled by means of an analogy with explicit discourse. Likewise, the deep connections between actual deductive strategies in logic and the skills of a Sherlock Holmes-type practical cogitator uncovered above bear witness to the viability of the same analogy. In the last analysis, it is perhaps

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the capacity of the questioning model to throw light on the nature of thinking more generally that makes it so useful a part of a philosopher's methodology. For a philosopher's last but not least task is to enhance our awareness of our own thinking. In philosophy only an examined thought is worth thinking. Acknowledgment: the work on this paper was made possible by NSF Grant #BNS 8119033 (PI: laakko Hintikka). Notes I. For a recent survey, with references to literature, see Santas 1979, especially ch. 2. Of the earlier literature, c( Robinson 1951. 2. For Kant, see Critique of Pure Reason B xii-xiii; tor R.G. Coiiingwood, see An Essay on Metaphysics, Oxford: CIarendon Press, 1940; for Hans-Georg Gadamer, see Truth and Method, New York: Continuum, 1975; for Larry Laudan, see his Progress and Its Problems, Berkeley: University of California Press, 1977, Science and Hypothesis, Dordrecht: D. Reidel, 1981a, and "A Problem-Solving Approach to Scientific Progress," in lan Hacking, ed., Scientific Revolutions, Oxford: Oxford University Press, 1981. 3. See the bibliography in my monograph The Semantics of Questions and the Questions of Semantics, Amsterdam: North-Holland, 1976. The .best known ones are probably Belnap and Steele 1976; Harrah 1963; Katz 1968; Aqvist 1971. 4. For this analysis, see The Semantics of Questions (note 3 above), chs. 2-3, and below, sec. 3. 5. The similarity between Kant's "transcendental deductions" (and "transcendental expositions") and my argument is perhaps not accidental. See my paper "The Paradox of Transcendental Knowledge" (forthcoming). 6. As I have repeatedly pointed out before, the fashionable term "possible world" is highly misleading, and has in fact misled several philosophers. The alternatives considered in the actual applications of my model-theoretical semantics need not be any more comprehensive scenarios than those involved in most applications of probability calculus. I 7. What this adage thus amounts to is to assert the propositional character of information and knowledge. For a proposition can be characterized in terms of the class of worlds it excludes, which is precisely the "uncertainty" eliminated by coming to know it. 8. This question is of course tantamount to a special case of the question as to when existential generalization is valid in epistemic contexts. I have discussed this problem in Knowledge and Belief. !theca, N.Y.: Cornell University Press, 1962; Models for Modalities, Dordrecht: D. Reidel, 1969; The Intentions of Intentionality, Dordrecht: D. Reidel, 1975; and in "New Foundations for a Logic of Questions and Answers," forthcoming. 9. In actual discourse, the likely response is something like, "But what is he like?" The reasons for this are explained in my The Semantics of Questions, note 3 above, pp. 45-46, 50-54. 10. C( here The Semantics of Questions (note 3 above) and "New Foundations for a Theory of Questions and Answers" (forthcoming b). 11. One version of the formal argument is in effect given in my book, Models for Modalities, Dordrecht: D. Reidel, 1969a, pp. 121-27. (In saying this, I am

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relying on the observation made in note 8 above.) The methodological situation is discussed briefly in my paper, "Questions With Outside Quantifiers," in R. Schneider, K. Tuite, and R. Chametzky, eds., Papers From the Parasession on Nondeclaratives, Chicago: Chicago Linguistics Society, 1982, pp. 83-92. 12. These critics are typically victims of a widespread failure by philosophers of language and linguists to understand what a genuine theory or theoretical explanation is in language theory. 13. They have not been discussed satisfactorily in the literature. One main feature here is the relativity of the request to the truth of the presupposition of the question; c( The Semantics of Questions (note 3 above), pp. 28-29. 14. An answer is provided by Veikko Rantala, "Urn Models," Journal of Philosophical Logic, 4 (1975): 455-74; and Jaakko Hintikka, "Impossible Possible Worlds Vindicated," ibid., pp. 475-84. Both are reprinted in Saarinen 1979. The philosophical implications of this answer are studied in my book, Logic. LanguageGames alld iI!formation, Oxford: C1arendon Press, 1973. 15. See The Selllallt ics of Qucst iOIl (note 3 above), chs. 4-5. 16. The most explicit generalization is found in my "New Foundations for a Theory of Questions and Answers" (forthcoming b). 17. See chapter 3 of The Semantics of Questions (note 3 above). 18. See "Questions With Outside Quantifiers" (note 11 above) for a somewhat surprising answer. 19. For the whole subject of questioning strategies, see Jaakko Hintikka, "Rules, Utilities, and Strategies in Dialogical Games," in Hintikka and Vaina 1983. 20. Plato, Mello 80 d-e. 21. This is part and parcel of Kant's "Copernican Revolution" in philosophy, which means focusing on what we do and what conceptual tools we use in acquiring the knowledge we have or can have. 22. C( my essays on Kant, collected partly in Knowledge and the Known. Dordrecht: D. Reidel, 1975a. 23. Ct: here Hintikka and Hintikka, 1982. 24. Arthur Conan Doyle, "A Study in Scarlet," in Baring-Gould 1967, vo!. I, pp. 143-234, especially pp. 159-60. 25. Ibid., pp. ISO, 160. 26. Ibid., pp. 164. 27. The classical, albeit not necessarily definitive, statement of this view on observation is found in Hanson 1958, especially ch. 1. How neatly the theoryladenness of observations fits into the model of knowledge-seeking by questioning was already pointed out in Hintikka and Hintikka 1982. 28. Ct: here laakko Hintikka, "The Logic of Information-Seeking Dialogues: A Model," in W. Essler and W. Becker, eds., Konzepte der Dialektik, Frankfurt a.M.: Vittorio Klostermann, 1981, pp. 212-31. 29. An indication of the problem situation is found by comparing philosophers' accounts of deductive inference with their accounts of inductive (and other nondeductive) inference. In the latter field, one of the prime problems is the reliance of certain promising accounts, especially the so-called Bayesian one, on what is known as the requirement of total evidence. What it means is that the total body of evidence one has at one's disposal is referred to essentially in the account. Of course, that is not only not what one actually does in a scientific inference, but it is arguably impossible to do. Now an analogous problem of total evidence (totality of premises at one's disposal) haunts what philosophers say of people's actual deductive inferences. They have nothing to say of how the deducer selects the appropriate premises from the totality of potentially available premises. In so far

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as an account is attempted of what people actually do when arguing deductively, the current accounts are hence subject to the same objection to reliance on total evidence as their nondeductive cousins. 30. See the papers referred to in notes 19, 23, and 28 above. 31. The paraphrase is very close to the original. Essentially all that I have done is to use the interrogative mode more often that Doyle. See "A Study in Scarlet" (note 24 above), pp. 160-62. 32. CC here my paper, "Intuitions and the Philosophical Method", Revue Internationale de Philosophie 35 (I98Ib): 127-46. 33. These procedures go back to Beth 1955, pp. 309-42. It is reprinted, with further references to the literature, in Jaakko Hintikka, ed., The Philosophy of Mathematics, Oxford: Oxford University Press, 1969. Beth's original paper remains, in spite of several inaccuracies, the freshest exposition of this technique. The tableaux method is closely related to Hiniikka's slightly earlier method of model sets, which goes back to Hintikka 1955, pp. 11-55. A brief exposition of it is found in chapter I of Jaakko Hintikka, Logic, Language-Games and Information, Oxford: C1arendon Press, 1973. A textbook using the Beth-Hintikka techniques is Jetfrey 1967. 34. In"other words, we can in this way understand better the role of questioning in education. See here my paper, "A Dialogical Method of Teaching," Synthese 51 (I982a): 39-59. 35. See my Logic, Language-Games and Information, Oxford: Clarendon Press, 1973; and "Surface Information vs. Depth Information," in Jaakko Hintikka 1969. 36. See my paper, "c. S. Peirce's 'First Real Discovery' and Its Contemporary Relevance," The Monist 63 (1980): 304-15, with references to Peirce. 37. Arthur Conan Doyle, "Silver Blaze", in Baring-Gould 1967, pp. 261-81; see here p. 277. 38. Plato, Meno 82-83. 39. Plato, Meno 81 e. 40. Plato, Theaetetus 190 a; cC Sophist 263 e. 41. C. S. Peirce, Collected Papers. vol. 2, sec. 26. 42. Ibid., vol. 6, sec. 338. 43. Peter Geach 1957, p.75.

INDEX OF SUBJECTS abstract objects. cross-identification of. 80 acquaintance. objects of. xiv. 22. 60. 117. 119.211 acquaintance. reduction to. 144 AI (artificial intelligence). xii altemativeness relation. 1. 2. 8. 17. 46. 64. 99.191 ambiguity. involving quantifiers and intensional notions. 106 ambiguity. resolution of. 106 analytic-synthetic distinction. 75 analyticity, 186 analyticity on a par with modality. 139 answer, ostensive, 144 answerhood problem, xvi. 19 answerhood, criterion of, 122, 144, 149, 211,216,218.221 answerhood criterion of for perspective and public identification, 123 answers, conclusive, 19, 122, 143,216-218 answers. partial. 220 answers, presuppositions of, 220 answers, restrictions on. 30 any, 108 any. not ambiguous, 109 any, semantical behavior of. 107 argumentation. syntactical vs. semalltical (model)-theoretical),37 backwards-looking operators, 9, 46, 196 being. modes of. 114 belief,202 bound variables as a notational device, 179 branching operator structures, 26-28. 34 Brentano's thesis. 186 catastrophe theory. xiv. 87-88. 94 causality, Hume's arguments against. 185 cogito (Descartes). 113 cogito. performatory interpretation of. 113-114.133 cognition. algorithmic approach to. 131 cognitive science. computational approaches to 131-132

cognitive systems. xiv cognitive systems and cortical pathways. 131 color perception. 125 color blindness. 126 compositionality. 75 compositionality. failures of. 108-110 compositionality. in Montague semantics. 97-98 constituent. 68-69 constituent depth. 67 constituent height. 67 constituent. inconsistent. 71 constituent length. 67 constituents as the logically strongest propositions of a given depth. 67 context-dependence. 77 context-dependence. does not imply indexicality. 147 contexts. direct. 48 contexts. episternic. 57-58. 81. 98 contexts. extensional. 48 contexts. indirect. 48 contexts. intensional. 48. 57. 59 contexts. opague. 48. 55 contexts. transparent. 48 continuity. bodily. 138 continuity. of memory. 138 continuity. spaciotemporal. 81 counterparts (Lewis). 161 cross-identification. xii-xiii. xiv. 41. 43. 57-58.77.79-82. 84. 89-90. 151. 159. 191. 196 cross-identification and ontology. 162 cross-identification by acquaintance. 143. 147. 178; see also c.-i .• perspectival cross-identification by continuity. 102. 137-138 cross-identification by functional considerations. 162 cross-identification. by similarity. 161-162 cross-identification. descriptive. 22. 142. 149, 163, 178; see also c.-i., public cross-identification, differential-equation

235

236 model of, 84 cross-identification, modes of, 79, 116, 130-132, 143 cross-identification, perceptual, 22, 143,206 cross-identification, perspectival, 22, 114, 116, 129-130, 163; see also c.-i. by acquaintance cross-identification, public, 114, 120, 129; see also c.-i., descriptive cross-identification, reduces to reidentification, 80, 138 cross-identification, role of origin in, 81 cross-identification, sex-linked differences in,161-162 cross-identification, world lines drawn by ourselves, 137 database theory, xii de re vs. de dicto, 26, 99-100 decision problem, for predicate calculus, 208 decision problem for standard quantified first-order model logic, 7-8 decision problem for standard second-order logic,7 definite descriptions, 168, 170, 173-174 definite descriptions, primary and secondary occurrences of, 165-167 desideratum of a question, 19,216 differential equations, existence of solutions for, 84 differential equations, singularities of their solutions, 85, 87-88 differential equations, stability theory of, xiii discourse phenomena, 230 discourse theory, 30 domain of individuals, 3, 5, 9,137,196 domino games (Hao Wang), 208 doxastic logic, 138-139 doxastic worlds, 146 dual ostension paradox, 142, 144,147 entity, no entity without identity (Quine), 59,114 epistemc concepts in cognitive science, 132 epistemic logic, xii-xvi, 11-12, 18, 21, 23, 31-32,124,131-132,138-141

INDEX OF SUBJECTS

epistemically possible worlds, 64-66, 69, 71, 101 existence and nonexistence, overemphasis on, 199 existence of individuals, conservation of, 189 existential generalization, 57,143,165,172 existential generalization, can fail for reasons other than failure of existence, 42,168-169,179 existential generalization, conditions on, 56, 119,140,176 existential generalization, failures of, 55, 57, 73,169,180,191,211 existential generalization, possible-worlds account of, 55,179 existentially self-verifying sentence, 133 experiments, as questions put to nature, 29, 223 facticity, 189, 193 feminist philosophy, 155 first-order logic, nonstandard models for, 66 game theory, 28 game, normal form of, 28 geometry vs. set theory, 89 global constraints (Lakoff), 107 good and interests, 157 good as involving tacit evaluations, 157-159 good man vs. benevolent man, 158 good, belonging to the referential subsystem oflanguage, 157 Hauptsatz, Gentzen' s first, 32, 35 higher-order logics, 4-5 higher-order logics, nonstandard interpretation of, xii 1,114,117 identification, xiii, 76, 163 identification and individuation, 87, 90 identification and individuation, rooted in the material realities, 90 identification, modes of, 77,120,123,134 identification, perspectival, 77, 114, 115-118,120-121,124,128,132

INDEX OF SUBJECTS

identification, public, 77, 114, 117, 120-121,124,128,132 identification, synunetry between different modes of, 122 identification, visual, 125 identity, criteria of, 20 identity, in modal contexts, 137 identity, in psychology and psychiatry, 151 identity, transititivity of, 195 identity of individuals, conservation of, 189 identity statements, informative, 165 impossible possible worlds, 12, 24, 65-66 individuals, nonexistence of, 42, 100-101, 103,167,174 individuals, number of considered in a sentence, 23 individuals, well-defined, 5, 8, 21, 43, lOO, 103,138,178 individuating function, 76 individuation, xiii, 163 individuation, connection with identification,78,88 inference, logical complexity of, 208 information set, 26 information, as elimination of Wlcertainty, 17,46,216 information, questions as requests of, 18 informational independence, 24, 26-28, 34, 220 informational independence in intensional contexts, 24, 34 informational independence, notation for, 26-27 instantiation rules, in episternic logic, 20 intentionality as intensionality, xv, 183-184, 188 intensionality as multiple referentiality, 50 intentionality, xv, 132, 183-185, 187 intentionality as directness, 183 intentionality of meanings, 186 intentionality, criteria of, 193, 197-198 intentionality, degrees of, 188, 190, 193 intentionality, dimensions of, 189, 197, 201-202 intentionality, symptoms of, xv interrogative derivability, 31-32 interrogative games, 30-31

237 interrogative model of knowledge acquisition, 29-32 intuitions, 139, 152,219,225 intuitions, according to Kant, 89 kinds of identification vs. kinds of knowledge, 121, 130 knowing + direct object, 18-19,22,43, 105, 116, 118, 144 knowing + wh-construction, 18-19, 20-21, 56, 58, 61, 79, 92, 98, 102-103, 115, 118, 140, 142, 147-149, 160, 167, 170, 211 knowing as, 119 knowing that, 18, 121, 145 knowing who, 25, 140, 146, 150, 153, 170, 172 (see also Knowing + wh-construction) knowing who, different criteria of, 150 knowing who, in psychology and psychiatry, 151 knowing who, variability of truth-conditions of,147 knowledge acquisition by questioning, 29, 219-220 knowledge by acquaintance, 22, 122, 130, 133-134 knowledge by description, 22, 122, 130, 133-134, 171 knowledge of identities, 51 knowledge representation, xii knowledge, active, 31 knowledge, objects of, xiii, 45-46, 49-50, 54,57 knowledge, possible-worlds analysis of 63-64,75 knowledge, potential, 31 knowledge, potential deductive, 31 knowledge, spatial knowledge of space, 128 knowledge, tacit, 30-32, 224-225 knowledge, verbal knowledge of space, 128 knowledge, virtual, 31 knowledge, virtual deductive, 31 knowledge, visual, 22 Kripke semantics, xi, 1-9 Kripke semantics, as a nonstandard semantics, 4,7

238 language act, 113 language as calculus, 39-40 language as the universal medium, 39-40 language, referential subsystem of, 156-160 language, structural subsystem of 156-157, 159, 161 logic of questions, xvi, 215 logic, intuitiouistic, 18 logical atomism, 89 logical constants, non standards interpreta. tions of, 65 logical omniscience, xiii, xvi, 24, 63-64, 70-71,75,200-201,219 logical omniscience and situation semantics, 207 logical omniscience, failure of logical omniscience as a criterion of intentionality, 200 logical omniscience, syntactical solution to, 71 logical omniscience, paradox of, xiii, 23,71, 207-209 logical problem, difficulty of, 70 logical standardness of worlds, 190 logical truths, as tautologies, 64 logically possible worlds, totality of, 46 logically possible worlds, 64-66, 69, 71, 194 logically proper name, 116 man, ambiguity of, 158 meaning function, constant, 57 meaning functions, 52, 76, 97, 103, 184,212 meaning functions as abstract entities, 54 meaning functions, operationalisations of, 54 meaning functions, reified, 54 meaning functions, restricted, 53 meaning, humanly graspable, 203 memory, 115,122, 128, 135, 138,202 memory, as a source of answers, 31 memory, continuity of, 137 memory, episodic, 23, 129-130, 135 memory,object-centered, 130 memory, personal, 190 memory, semantic, 23, 129, 130, 135 memory, subject-centered, 130

INDEX OF SUBJECTS

Meno's paradox, 221 mentalese, translations into mentalese as explanations, 131 modal logic, alethic, 1, 3, 6, 9, 11-13, 138-139 modal logic, syntax of, 9 modal logics, nonstandard semantics for,S, 10 modal logics, Quine's criticisms of, 137 modal logics, semantics for xi, 4,138,186 modal logics, standard semantics for, 5, 6, 10-11

modal semantics, standard and nonstandard, 7 modalities, alethic, xi, 1, 3, 6, 9, 11-13, 138-139 modalities, analytic, 1, 139, 185-187, 193, 202-303 modalities, causal, 187, 193, 202 modalities, conceptual, xii modalities, deontic, 193 modalities, in object language, 13 modalities, logical, xi, 1-2,9, 12, 138-139, 185,193 modalities, metaphysical, 12-13 modalities, physical, 184-185, 193 modalities, transcendental, 13 model sets, 206 model theory, presupposes the conception of language as calculus, 39 model-theoretical argumentation, 38 models, nonstandard, 202 Montague semantics, 12,76, 100, 105, 107, 110 Montague semantics, conditionals in, 106 Montague semantics, quantifiers in, 97 name-object relations, 76 nature, as a source of answers, 29 necessity, logical, 1,138,196 necessity, analytic, 196 nonextensionality (Chisholm), 197 object-centered system, 128 objects, as defmed by singularities, 85 objects, incompatible, 40 objects, nonexistent, 37-38, 40-41

INDEX OF SUBJECTS

objects, nonexistent where?, 40-41 objects, of acquaintance, xiv, 22, 60, 117, 119,211 objects, of description, xiv objects, of Wittgenstein' s Tractatus, 39 objects, perceptual, 143-144, 175 objects, physical, 57-58 obligation, 202 observations, as questions put to environment,29 observations, concept-ladenness of,224 observations, theory-ladenness of, 224 omniscience, logical, see logical omniscience omniscience, with respect to individuals, 11 Oracle, 29 ordering principles, 107 ostension, paradox of dual ostension, 142, 144, 147 ostensive questions, 175 paraconsistent logics, 24, 34 partially ordered operators, 28 perceiving a word, 120 perception, 122, 138, 190,202 perception, of shape, 124 perceptual categorization, 124 perceptual space, 127-128 perceptual verbs,' .1 04 personal identity,~51 perspectival identification and "where" system,127 philosophical method, 152 physical necessity, 196 physical space, 127 picture theory oflanguage, 76 possibility, epistemic, 63 possibility, logical, 63 possible worlds, xii, xv, 2, 12, 40-43, 46, 49-50, 60, 63, 78, 89, 115, 134, 139, 146,161,185,216 possible· worlds as totalities of experience, 66, 196 possible worlds in Leibniz, 80, 93 possible worlds, transcendental limitations

on,75 possible worlds, analytical, 12

239 possible worlds, part in common, 80 possible worlds, small worlds, 186 possible worlds, totality of, 53, 74 possible-worlds semantics, xi-xiii, xvii, 18, 41,45,49, 60,71,74-77,90, 104-105, 151,159,183-184,203,206-212 possible-worlds semantics, not restricted to big worlds, 213 possible-worlds semantics, problems prompted by, 74-78 presupposition, of a question, 29, 35 private experiences, 134 probabilities, objective, 202 probabilities, subjective, 187, 202 probability, 187, 203 probability theory as involving possible worlds, 186, 212 probability theory, as intentional, 187 propernames, 104, 116,168 proper names, do not reduce to definite descriptions, 172 propositional attitudes, 50, 59 propositional attitudes, objects of: see knowledge, objects of, 50 prosopagnosia, 126 quantification in natural languages, 97 quantifier phrases, 97 quantifier phrases, on a par with singular terms, 98 quantifiers as ranging over objects of acquaintance, 173-175 quantifiers, as carrying an ontological burden,179 quantifiers, number of layers of, 70 quantifiers, objectual interpretation of, 171, 180 quantifiers, perspectival, 118 quantifiers, public 118 quantifiers, substitutional interpretation of, 171,180 question, desideratum of, 19 question, matrix of,221 question-answer relationship, see answerltood, criterion of questioning, as a knowledge-seeking method 215

240 questions and answers, xvi, 18,21, 144,230 questions and answers, as discourse phenOlnena,150,222 questions and answers,logic of, 29, 75 questions, complex, 219 questions,logical structure of, 216 quotation, 192 range of attention, 32 re-identification, xiii, xiv, 32, 77,80-82,88, 159,196,209 re-identification by continuity, xiii, 80-84 re-identification of physical objects, 84 re-identification, differential-equation model of,84 reasoning about knowledge, 31 reasoning, trivial vs. nontrivial, 226 reducibility to acquaintance, 170, 179 referential opacity (Chisholm), 197 repetition requirement on surface models, 68-69 rigid designator, 116, 134, 140, 162 scenarios, see possible world scope, 25 second-orderlogic, 4, 7-10, 28 seeing + direct object, 116, 118, 123, 134, 144 seeing + wh-question, 115 seeing as, 119 seeing someone, ambiguity of, 119 semantic memory, 129 semantica1 concepts, in cognitive science, 131 semantica1 game, 25 semantica1 tableau, 35 semantics, game-theoretical, 25 semantics, ineffability of, 39 semantics, nonstandard, xi, 4-6,190 semantics, possible-worlds, see possibleworlds semantics semantics, standard vs. nonstandard, xii, 4-5,7,9 sense (Frege), as a meaning function, 57 sense vs. reference, 45, 47-48 sense-data, 60 sense-perception as a way of knowing

INDEX OF SUBJECTS

particulars, 89 senses (Frege), as meaning functions, 52-53 senses (Frege), as objects of knowledge, 49 senses (Frege), identity of, 53 sexist language, xiv, 150, 155-156, 159 situation semantics, xv-xvi, 75, 206, 211-212 situation semantics vs. possible-worlds semantics, 205-207 ' small worlds, 205, 212 Socratic questioning, 215 speech-act, 114 stability and the concept of a physical object, 88 stability theory (of solutions to differential equations), 87 standard interpretation of connectives and quantifiers, 65 standard vs. nonstandard semantics, 10-12 standard vs. nonstandard semantics, in firstorderlogic, 10 standard vs. nonstandard semantics, in higher-orderlogic, 10 standard vs. non~tandard semantics, in modal logic, 10 strategies ofknowl~ge-seeking, 220 strategies, deductive, 226 strategies, importance of, 220 strategies, in questioning, 225 strategy, winning, 25 subfonnula principle, 29, 32 substitutivity of identity, 46, 52, 165 substitutivity of indentity ,conditions on, 51 substitutivity of indentity, failure of, 57, 73, 191,197,211 substitutivity of indentity, Frege's account of, 48-49, 51-53 substitutivity of indentity, possible-worlds account of, 50, 52-53 substitutivity of indentity, for singular tenns, 194 surface models, 65 surface models as model-theoretical counterparts to constituents, 67 surface tautology, 70-71 syntactic argumentation, 38

l

INDEX OF SUBJECTS tautologies, 31, 64 tense logics, 93, 209 text semantics vs. sentence semantics, 150 thinking as unspoken discourse, 229 thougth act, 113-114 transfonnational grammar, 109 transparent context, 49 truncation requirement on surface models, 68--69 truth definitions, Tarski-type, 141 truth -conditions, 20, 147 uniqueness conditions, 140, 143, 145-146, 148, 151 uniqueness conditions for different propositional attitudes, 145 uniqueness conditions, Quine' s criticism of, 145-149 urn models, 24, 66-71, 75,201,209 urn models, invariant, 66-71 urn models, standard models as invariant urn models, 66, 201 utilities, 220 valuation function, 76 viewer-centered visual system, 128 visual cognition, 120, 124 visual identification, 121 visual infonnation, 123 visual infonnation processing, 136 visual object, 22, 123, 127 visual perception, 22, lIS, 132 visual perceptions of one's own body, 126 visual space, 22, 115, 143 visual systems, two kinds of, 23 well-defined individual, see individual, welldefined what- and where-systems and brain anatomy, 124 what questions and memory, 129 what-questions vs. where-questions, 121 what-system, 124-125, 128-129 what system, disturbances of, 126 where system, 124-126, 128-129 where system and geometry, 127 where system and perspectival identifica-

241 tion, 127 where system vs. what system, 127 where system and memOry, 129 where system, disturbances of, 126 where-questions, 120-121 world lines, xiv, 4, 8,20-21, 43, 57-59,76, 83, 100-102, lOS, 130, 138, ISO, 159, 177 world lines can break down, 100-102 world lines, as solutions of differentiated equations,83-S5 world lines, branching, 196 world lines, by acquaintance, 149 world lines, by description, 149 world lines, different ways of drawing, 77 world lines, extendability of, 189 world lines, failure of, xiv, 43,101,104,198 world lines, methods of drawing, 190 world lines, not defmed everywhere, 85 world lines, reified, 59 world lines, split and merge, lOS, 196 world lines, two systems of, xiv, 22 worldbound individuals, 58-59 worldbound individuals vs. world lines, 58 worlds, almost invariant, 201-203

INDEX OF NAMES Abbott, E. 93 Adkins, A. 163, 164 Aqvist, L. 231 Aristotle 75,88,91, 164 Ayer, A. 59

Follesdal, D. 13, 14, 151 Frege, G. xii, 38, 39, 45,48-60,75,98, 153, 165 Gadarner, H.-G. 215,231 Gallin, D. 5,14 Geach,P.lll,229,230,233 Gentzen, G. 32, 35 Goldfarb, W. 121, 179, 181 Guillaume, M. 2, 5, 14

Bacon, F. 215 Bar-Hillel, Y. 156 Barwise,J. xv, 33,206-208,210-213 Belnap, N. 231 Berger, R. 213 Beth, E. W. 13, 35, 233 Boer,S. 140,142.153 Bowen. K. 32 Brandom, R. 34 Brentano,F. 183, 184,186,193 Broad, C. D. 134 Brovernan, D. M. 164 Broveman, 1. K. 164 Butters, N. 128

Haavikko, P. 193 Hacking, I. 93,213, 214,231 Halpern, J. Y. ix, 34,136 Hanson, N. R. 232 Harrah, D. 231 Heidelberger, H. 192 Heijenoort, J. van 49, 61 Henkin, L. xii, 14 Hintikka, J. ix, 2, 5, 13, 14,33, 34,71-73, 75, 78, 80-82, 89-94, 117, 133-135, 152-154, 159, 163-164, 203-204, 208, 214,231-233 Hintikka, M. B. ix, x, xvii, 34, 59, 134, 135, 152,163,183,232 Him, Y. 158, 163 Hii; H. 153 Holmes, G. 127 Homer 101,102 Hume, D. 185, 187 Hussed, E. 45,148,152,183-185,188,193, 203

Cadson, L. 34, 35 Camap,R.39,93.98,III,213 Chisholm, R. xv, 197-200,204 Chomsky, N. xiii. 33,109,112 Cocchiarella, N. xii, xvii, 1,5,7,14 Collingwood, R. 215,231 Cook Wilson, J. 142, 153 Cress well, M. 71 Davidson, D. 141, 153, 154, 186 Democritus 88 Descartes, R. 113, 114, 117, 125, 133, 134 Dewey,J.183,203 Dolev, D. 34 Dowty, D. 90, 163 Duns Scotus 40

Ince, E. 93 Jeffrey, R. 233 Kagan, J. 164 Kalish, D. 15, 111 Kanger, S. xii, 4, 15 Kant, 1. 75, 89, 128, 148, 152, 185, 215, 216,223,231,232 Kaplan, A. 92, 154 Kaplan, D. 154

Falk, G. 136 Feldman, F. 133 Feldman, J. A. 136 Finetti, B. de 187 Fitting, M. 32 Fodor, J. 112, 163

243

244

INDEX OF NAMES

Karttunen, L. 142, 153 Katz, J. 112,231 K1nsbourne,~. 135 Kivi, A. 188 Klirna, E. 112 Kneale, W. 183,203 Knuuttila, S. 164 Kolrnogorov, A. 186,202 Kraut, R. 152 Kries, F. 133 Kripke, S. xiv, 2, 13, 15, 60, 81-82, 84, 92-94, 116, 134, 137, 152, 159, 162, 164,191,195,196,209,213 Kulas, J. 34, 154

Newcombe, F. 125 Nieland,J.14 Nishihara, H. 128, 131,135,136

Lakoff, G. 107, 112 Laplace, P. 60 Laudan, L. 215, 231 Leibniz,G.W.40,41,43,60,73,80,89,93, 163,164,213 Lenzen,W.32 Lewis, C.I. 14 Lewis, C. S. 95, 164 Lewis, D. 60,90,153,161,164,189 Lichtenberg, G. C. 113, 133 Locke, J. 81,93 Loewer, B. 135 Lu, Y.94 Lycan,W. 140,142,153

Quine, W. V. xii, I, 13, 15, 20, 38, 39, 58, 79, 81, 82, 88, 92-94, 114, 118, 126, 135, 137-141, 145-147, 149, 151-153, 159, 161, 164, 168, 179, 186, 187, 191, 192,209,213

~accoby,

E. 164 ~arcus, R. B. 195 ~arr, D. 124, 128, 131, 135, 136 ~ates, B. 93 ~aunsell, J. 134 ~einong, A. von 40 ~eno 221, 222 ~eulen, A. ter 34, 206, 213 ~ishkin, ~. 125 ~ontague, R. xii, xvii, 5, 6, 12, 15,60,61, 90, 97, lOO, 103-112, 137, 152, 163, 191 ~oore, G. E. 59, 158, 163 ~orick, H. 192 ~oses, Y. 34 ~oss, H. A. 164

P~ons,T.xii,37-40,42,44

Partee, B. H. 91, 153,184,204 Paul,R.136 Pears, D. 33, 92, 133,153, 181 Peirce, C. S. 75, 91, 226, 227, 229, 230, 233 Perett, D. 128 Perry, J. xv, 33, 206-208, 210-213 Peters, S. 90, 163 Planting a, A. 60 Plato 215, 228, 229, 230, 232, 233

Rantala, V. 34, 65, 66, 75, 91, 187, 188, 200-202,204,208,232 Rescher, N. 34 Russell, B. xiv, 33, 38, 39, 59, 60, 92, 98, 116, 129, 133, 134, 144, 148, 153, 165-181,211 Ryle, G. 37 Saarinen, E. 34, 81, 91, 93, 146, 152, 154, 213,232 Sallinen, A. 193 Santas, X. 231 Saunders, P. 94 Savage, L xiii, 33,186,187,202-204,214 Scott, D. 60, 152, 187 Sigel, I. E. 164 Socrates 227, 228 Steel, T. B. 231 Stephens, G. L 192 Stich, S. 136 Suppes,P.xvii,71,110 Sussmann, H. 87,94 Tarski, A. 91,92,141,163 Teuber, H. L 126, 128

245

INDEX OF NAMES

Thorn, R. 87, 94 Thomas, J. A. 192 Tulving, E. 33, 129, 130, 135 Vaina,L.33, 124, 125, 128,129, 134, 135 Verdi, G. 38 Vesey, F. N. A. 134 Wall, R. 90, 163 Wang, H. 208,213 Warnock, G. 134

Watson, G. 94 Waugh,E. 150, 160 Whittaker, E. 94 Wilson, J. C., see Cook Wilson, J. Wittgenstein, L. 38, 39, 76, 81, 89,91, 126, 135, 152 Wood,F.135 Wright, G. H. von 32, 94 Zahler, R. 94 Ziff, P. 163