Language and logic: a speculative and condition-theoretic study (Pragmatics and Beyond Companion Series, Vol 2)

LANGUAGE AND LOGIC

Pragmatics & Beyond Companion Series Editors: Jacob L. Mey (Odense University) Herman Parret (Belgian National Science Foundation, Universities of Leuven and Antwerp) Editorial Address: Department of Germanic Languages and Literatures University of Antwerp (UIA) Universiteitsplein 1 B-2610 Wilrijk Belgium Editorial Board: Norbert Dittmar (Free University of Berlin) David Holder oft (University of Leeds) Jerrold M. Sadock (University of Chicago) Emanuel A. Schegloff (University of California at Los Angeles) Daniel Vanderveken (University of Quebec at Trois-Rivières) Teun A. van Dijk (University of Amsterdam) Jef Verschueren (University of Antwerp)

2 Johan Van der Auwera Language and Logic A Speculative and Condition-Theoretic Study

LANGUAGE AND LOGIC A Speculative and Condition-Theoretic Study

Johan Van der Auwera University of Antwerp (UFSIA)

Special editor for this volume: Hubert Cuyckens (Belgian National Science Foundation, University of Antwerp)

JOHN BENJAMINS PUBLISHING COMPANY AMSTERDAM/PHILADELPHIA 1985

Library of Congress Cataloging in Publication Data Auwera, Johan van der. Language and logic. (Pragmatics & beyond companion series; 2) A revision of the author's thesis, University of Antwerp, 1980. Bibliography. Includes index. 1. Language and logic. I. Title. II. Series. P39.A88 1985 160 84-24201 ISBN 90-272-5002-2 (European) ISBN 0-915027-48-8 (U.S.) © Copyright 1985 - John Benjamins B.V. No part of this book may be reproduced in any form, by print, photoprint, microfilm, or any other means, without written permission from the publisher.

"Well, perhaps: you never know: anything can happen. Nature is bountiful, and full of surprises, and there is plenty more ... Think cornucopian." (Seddon 1972: 494) "Thus what is needed is a counterpart of Occam's law—a law stipulating that entities must not be suppressed below sufficiency. This principle used as a methodological tool would separate compounds of various constituents passing for homogeneous into their diverse compo­ nents. It might be called a prism resolving conceptual mixtures into the spectrum on their meanings or, if one wishes to remain in the tonsorial domain of the razor, a comb disentangling and straightening out the various threads of thought. ... In a more general form — as it were, as a Law against Miserliness — the principle might be stated: it is vain to try to do with less what requires more This law may also be construed as a semantic maxim opposing equivocations. And while synonyms are bad, equivocations are worse. " (Menger 1979:106)

TABLE OF CONTENTS

PREFACE SYMBOLS AND ABBREVIATIONS CHAPTER I: METHODOLOGY, CONTENTS, AND RELEVANCE

xi xiii

1

CHAPTER II: FROM POSSIBLE WORLDS TO HUMAN ACTION . 9 1. Philosophy of mind, ontology, and reflection 1.1. Philosophy of mind and reflection 1.2. Ontology and reflection 1.3. Reflection

10 10 14 15

2. The 2.1. 2.2. 2.3.

out-of-mind States of affairs Minimal ontology Possible worlds

18 18 20 22

3. The 3.1. 3.2. 3.3.

mind Beliefs and desires Consciousness and beliefs Intentionality and desires

27 27 31 33

4. Human action CHAPTER III: SPEECH ACTS AND MEANINGS

36 41

1. Meaning and speech acts 42 1.1. Meaning versus intended, natural, and non-natural meaning . 42 1.2. Speech act meaning 43 2. Basic speech acts 2.1. Assertions 2.1.1. ρ

45 45 45

viii

TABLE OF CONTENTS

2.1.2. S believes that p 2.1.3. S speaks as if he or she believes that ρ 2.2. Imperatives, optatives, and interrogatives 2.2.1. The speech acts of non-belief 2.2.2. ...are the speech acts of desire 2.3. Basic speech acts 3. Semantics and pragmatics 3.1. Mental states versus conceptualizations 3.2 Genetic reflection and focus CHAPTERIV: TOWARDS A REFLECTIONIST AND CONDITION-THEORETIC LOGIC

46 47 50 50 52 53 55 55 59

61

1. The basis of logic 1.1. Contemporary logic 1.1.1. What logicians do 1.1.2. What philosophers of logic say 1.2. Reflectionist logic

61 61 61 65 72

2. Intra-logical RL interpretations

76

3. Conditions 3.1. Basic conditions 3.1.1. Sufficient conditions 3.1.2. Necessary conditions 3.1.3. Necessary and sufficient conditionality 3.1.4. Completeness 3.2. Impossibility conditions

87 91 92 94 97 97 98

4. Truth 4.1. Truth and conditionality 4.2. Two-valued 'truth of 4.3. Three-valuedness 4.4. Correspondence and Coherence 4.5. A tinge of holism 4.6. Truth and satisfaction CHAPTER V: PROPOSITIONAL OPERATORS

100 102 105 115 118 121 124 129

1. Conditional and componential analyses

130

2. Conjunction

132

TABLE OF CONTENTS

ix

3. Truth, falsity, and possibility 3.1. Values and supervalues 3.2. Pseudo-monadicness and presupposition 3.3. Truth-value paradoxes

133 133 157 169

4. Modality 4.1. Necessity, contingency, and impossibility 4.2. Iterated modality 4.3. Fatalistic necessity 4.4. The necessity of possible worlds semantics 4.5. Generic modality

177 178 183 184 185 188

5. Implication 5.1. Sufficiency 5.1.1. The connection thesis 5.1.2. Objections 5.1.3. Other implications 5.1.3.1. Material implication 5.1.3.2. Strict implication 5.1.3.3. Variably strict implication 5.2. Possibility 5.2.1. Particular conditionals 5.2.2. Generic conditionals 5.2.3. Objections

189 190 190 193 200 200 200 201 203 204 . 208 211

6. Postliminaries

213

NOTES

217

REFERENCES

229

INDEX

251

PREFACE

This book is in part the reflection of a purely personal problem, viz. my attempts to come to grips with modern logic. Despite my efforts in studying the present-day orthodoxies of logic, I have long felt myself to belong to the uninitiated, described by C.I. Lewis as far back as 1912: "symbolic logic appears to the uninitiated as an enfant terrible which intimi­ dates one with its array of exact demonstrations, and demands the accep­ tance of incomprehensible results." (C.I. Lewis 1912: 522)

As a result I now blame my frustration on logic itself. This book justifies this blame with a philosophical critique of modern logic, and with the program and the partial construction of a new, so-called 'reflectionist' and 'conditiontheoretic' logic. The logic is condition-theoretic because of the importance of conditionality notions. What makes the logic reflectionist is the underlying principle that language reflects both the one constituent of reality called 'mind', and reality at large. As I am more of a linguist than a student of the mind or of reality as such, reflectionist logic will be put into the context of an overall, reflectionist theory of meaning. For the latter enterprise I will reintroduce the term 'Speculative Grammar'. The original reference of this term are the Scholastic treatises written from the perspective that language reflects both mind and reality — Latin 'speculum' means 'mirror'. Language and logic is a revision of three fourths of a doctoral dissertation (Van der Auwera 1980c), presented at the University of Antwerp in July 1980.1 Both the original research and the revision were made possible through a fellowship of the Belgian National Science Foundation and an affiliation with the Germanic Department of the University of Antwerp (U.I. Α.). Part of the revision emanated from courses taught at the Universities of Cologne (Winter 1980-1981) and Antwerp (Fall 1981 and Fall 1982). Among the many people I am grateful to, I must single out Wim A. de Pater, who tested my materials in a course taught at the Catholic University of Louvain (Spring 1981), Herman Parret, Hubert Cuyckens, Jacob Mey for their editorship, Heinz Vater for his hospitality during a stay in Cologne, and Louis Goossens

xii

PREFACE

for the many aspects of the many years of guidance and support. I also thank Alison Woodward, my favorite sociologist, and the Swedish serrila bakers. This book is meant as a proposal. As it lies in the nature of proposals to be judged and amended, I expect that most of what follows calls for further inves­ tigation. Obviously, some of the forthcoming claims will turn out to be false. May this confession be an incentive to further research.

SYMBOLS AND ABBREVIATIONS (references to first occurrences) SOA, 18 OOM, M, SD, ID, 27 H, S, 45 RL, 61 SDL, 73 wff, 76 RSL, 77 RPL, 78 CPL, Λ , ν , → , Τ, F, 79 s, 91 se, s\ se'\ 92 si'e, sei, ne, 94 ni nei, 95 i, ni,e, 96 ns,97 Ts, 103

T

ns'105

F-SOA,T s n s , T s s , 108 F s U s , F s , s , F s , n s ,F s , s , n e , Fs,s,nei, Us,s,ni,Ts,s i, 116 ,  p , B p , 122 !, ~ , ◊,133 ◊*, U*, ◊*, U,s 138 ! 2, ~2,!4,, ~4, 139

xiv

SYMBOLS AND ABBREVIATIONS

CHAPTER I METHODOLOGY, CONTENTS, AND RELEVANCE

I think that it is obvious that language reflects both mind and reality. This idea, which is probably as old as common sense and certainly as old as Aristo­ tle's philosophy, is also vague. In this book I will try to clarify it. More particu­ larly, I will attempt to elucidate the reflection idea by turning it into the cor­ nerstone of a linguistic theory of meaning. Interestingly enough, I am not the first to embark on such a project. In the 13th and 14th centuries, some linguis­ tically minded Schoolmen devised reflectionist or, as they called it, 'Specula­ tive' grammars (see Bursill-Hall 1971; Ashworth 1978; Covington 1982). It is precisely their general outlook, but not the details, that the present study at­ tempts to revive. That the modern meaning of 'speculative' suggests that I will be speculat­ ing a lot is a felicitous pun. Most of what lies ahead is indeed philosophical and conjectural. This study is not an effort to solve a 'puzzle' (Kuhn 1962) gener­ ated by a specific linguistic framework or 'paradigm' by means of a set of paradigmatic routines. It is more an attempt to construct a general framework. I will try to design a model more than to apply one that already exists. The conjectural or speculative nature of the inquiry does not make it unempirical, however. My armchair conjectures are geared towards a com­ prehension of empirical matters such as language, mind, and reality. I do not want to write fiction here. But what their conjectural nature does imply is that some of my claims will not have any deeper justification than my hypothesis that the claims are self-evident. Even though I claim that the speculations whose only vindication consists in an appeal to self-evidence can still be empirical, I am aware that the word 'empirical' is often understood in a different sense, according to which a hypothesis is empirical only if it can be subjected to a paradigmatically defined testing or falsification procedure (see Harré 1972; Parret 1979b). Unless the judgments on what is self-evident and what is not were taken to result from a test or falsification procedure of a paradigm of some sort — I have never seen such a position defended, most of this study would qualify as unempirical.

2

METHODOLOGY, CONTENTS, AND RELEVANCE

I have no fundamental qualms about this definition of the term 'empiri­ cal'. Still, I have some reasons to favor a wider notion. First, it seems clear to me that science is always a blend of the empirical and the unempirical (re­ stricted sense) and that it may furthermore be difficult to separate the two. Thus there is something to be said for the view that all of science has a degree of empiricalness, which amounts to the claim that all of science is empirical in the wider sense (my sense). Second, by calling self-evident claims 'empirical', I want to stress that their subject matter is simply reality and therefore no dif­ ferent from the subject matter of experimentally testable or falsifiable claims. Third, with this notion of empirical self-evidence I want to guard myself against the defeatist and all too comfortable view that the unempirical (re­ stricted sense) fragments of science cannot really be called wrong. My employment of the term 'empirical' is not new. It relates to Quine's usage. One of the keynotes of Quine's work is that logic and philosophy are truly empirical sciences. The terminological similarity should not be overesti­ mated, though. There are large differences of opinion on the question of how empirical science could (or should) be done. In ontology, for example, I am much more conservative than Quine, but in logic, I am much more unor­ thodox. An important point is that I seem to value the role of self-evidence more than Quine does, at least more than the Quine of the earlier, pragmatist writings.2 When in "Two dogmas" (Quine 1961c [1951]) Quine offers advice for the choice between two rival general conceptual schemas, he does not say "Take the one that you find self-evident", for I assume that Quine believes that the defenders of any seriously held conceptual schema take it to be selfevident, but "Take the simplest one" (1961c: 45-46) and "Take the most fruit­ ful one" (44). Self-evidence does not appear in a vacuum. In the present case, it is in­ tended to emerge as a crystallization of my observations and intuitions of the objects of study, as well as of my understanding of some of the commonsense concepts and ordinary language meanings related to the objects of study (cp. Allwood 1978: 1-3). Such a formation process may go astray and the crystal might shatter. In other words, self-evident beliefs are by no means immune from revision. That a self-evident belief is mistaken is the conclusion one might have to draw in the face of recalcitrant experience or of a second selfevident belief inconsistent with the first. In fact, the present work is the result of much refutation of earlier speculation. Furthermore, part of the purpose of making it public is to invite others to falsify and to further speculate. When the meaning of a word is self-evident, the word can be called a

METHODOLOGY, CONTENTS, AND RELEVANCE

3

'primitive'. Every single word of the English language that I have used so far is such a primitive. Some of the ontologicai, psychological, and linguistic ones will later be given a deeper clarification. But for absolutely all of them, I as­ sume that the reader already understands them. This assumption is probably safe. If the reader has reached this very sentence, it is likely that he or she has made sense of what precedes. To repeat, I assume that even the special ontological, psychological, and linguistic primitives that I will later try to clarify are intelligible. They are so basic that they appear everywhere, not, then, as objects of study, but as elements of the language I am now writing in. Given, for instance, that the reader has made sense of expressions like 'I must' and 'If such and such, then so and so', I can assume that he or she knows what I am talking about when I come to a discussion of necessity and implication. Obvi­ ously, this does not mean that the reader can put this knowledge into words.3 A second methodological point concerning primitives is this. Suppose that the study of a primitive has been successful. Doesn't, then, the additional information transform the primitive into a technical concept, something that is much more precise than the one that occurs in my ordinary discourse? In other words, doesn't the description have a stipulative effect? I believe that there is some truth in this. But there is nothing wrong with this technicalization. The investigation of a primitive may transfer it from ordinary English into a var­ iant of jargonese English in the same way as a scientific inquiry may turn con­ glomerates of vague commonsense ideas into scientific models. And this is not unwanted. So much for methodology. Let me now give a preview of what I will be doing with it. The two things that are reflected in language are mind and reality. That is why I will devote some space to the philosophy of mind (philosophical psychology) and to ontology. After a brief consideration of what the philosophy of mind is, Chapter II expounds a very general and partial account of how the mind works. In particular, I investigate the nature of beliefs, de­ sires, consciousness, and intentions. Since the mind is, in some sense, a part of the world, the chapter is embedded in an ontology, and since I am working to­ wards a speech act theory, the chapter ends with some aspects of the philosophy of action. In the ontology, special attention is drawn to its defini­ tional problems and to the concepts of minimal ontology, state of affairs, and possible world. In the section on the theory of action, I am especially con­ cerned about the distinction between actions and events. In Chapter III, the cognitive model of Chapter II is used to develop an ac-

4

METHODOLOGY, CONTENTS, AND RELEVANCE

count of basic speech acts, a reappraisal of the traditional distinction between the assertive, interrogative, imperative, and optative mood. The different basic speech act meanings, largely defined in terms of a reflection of mental states, are looked at in some detail. Another target is the problem of what it is for a speaker to mean something. Finally, a peculiar version of a division of labor between semantics and pragmatics is suggested. In Chapter IV, a characterization and evaluation of present-day logic leads to a manifesto for a 'Reflectionist Logic'. This logic is to have a three-fold empirical interpretation. It must be a partial theory of reality, human reason­ ing, and of natural language. After a general clarification of the nature of these interpretations, I turn to a typology of conditions, a refinement of the traditional distinction between sufficient, necessary, and necessary and suffi­ cient conditions. The next step takes us from condition theory to a theory of truth. The relation between the two theories is so close that the logic as a whole will be called 'condition-theoretic'. The most important features of the truth theory are (a) a radical dyadic interpretation of truth ('all truth is truthof ); (b) the claim that the logic is 'two-supervalued', 'three-valued', and 'many-subvalued'; (c) the attempt to harmonize the Correspondence Theory of Truth with its rival theories, especially the Coherence Theory. Chapter V sets out to construct a 'Reflectionist Condition-Theoretic Propositional Logic'. Propositional operators are defined in terms of the con­ ditional typology. A deeper analysis of truth is offered, as well as of falsity and indeterminacy. The question of whether these operators are fundamentally dyadic or monadic leads to concepts of pseudo-monadicness and presupposi­ tion. The latter notion is also used in an analysis of truth-value paradoxes such as the Liar Paradox. A triadic account is offered for necessity, impossibility, and contingency, and the chapter culminates in an account of different types of conditionals. It is obvious that the preceding agenda will confront us with a large number of problems. Not all of them will be mentioned explicitly. Some will only be hinted at in the margin. More importantly, though, some of the issues that do make it into the text will not get the full-fledged treatment one might have ex­ pected or wanted. There are two reasons for this. First of all, my undertaking is primarily concerned with natural language, which explains why the chapters on the philosophy of mind and ontology are much less developed than could have been the case. I only present those fragments of the respective disciplines that are relevant for my purposes. Secondly, one should not forget that it is my primary intention to design a general framework. It is only to be expected that

METHODOLOGY, CONTENTS, AND RELEVANCE

5

a general conceptual schema generates questions. Delimiting a set of speech act types as basic, for instance, immediately calls for a treatment of the nonbasic ones. Similarly, when one prepares the ground for a modal, non-truthfunctional, two-supervalued, three-valued, many-subvalued, propositional logic, one raises the question of the relation of this logic to other unorthodox and orthodox, n-valued, truth-functional and non-truth-functional, modal and non-modal systems. Conceivably, I could have worked out some of these and other details. But a local gain might have been a loss in the overall picture. A restriction that deserves special attention is that the hypotheses pre­ sented in this book, although emphatically universalist, are based on my un­ derstanding of languages such as English and Dutch. This is a serious risk. It is possible that I only reincarnate Mr. Everyman, 'the natural logician', against whom Benjamin Lee Whorf has warned us. Mr. Everyman's problem is that he mistakes his way of thinking which "is perhaps just a type of syntax natural to Mr. Everyman's daily use of the western Indo-European languages" (Whorf 1956: 238) for the embodiment of the universal laws of thought and, I would add, the reflection of certain universal features of reality. A high-prior­ ity task for future research, therefore, is that of testing my armchair hypoth­ eses against as wide a range of languages as possible. Finally, a word on the relevance of the following 200 pages. If I may presuppose the relevance of linguistics, logic, and philosophy, I hope that my Language and logic will be relevant for two reasons: the answers it provides to old questions and the new questions it generates. First of all, Language and logic should be a new discussion of old issues. The reflection idea itself is truly ancient. I have already expressed my hunch that it is probably as old as common sense. The one application that is re­ flected in the title of this work is the 13th-14th-century tradition of Speculative Grammar. But there are others. For one thing, the reflection idea is closely connected with the so-called 'Correspondence Theory of Truth'. For another, my reflectionism is also reminiscent of the picture theory of logical atomism (see Urmson 1967: 1-98) and of the reflection or copy theory of dialectical materialism (see Cornforth 1954: 27-40; Schaff 1973: 121-139; Lorenz and Wotjak 1977). Furthermore, as 'a reflects b' is more or less the same as 'a is a sign of b', 'a refers to b'., or 'a represents b', the reflection thesis comes close to simply acknowledging that there are such things as intensions and extensions. So, though I do not want to create the impression that everybody has accepted or would accept the reflection thesis — there has been fierce opposition to all ideas listed above (see e.g. Rorty 1979) — it is clear that the reflection idea is a

6

METHODOLOGY, CONTENTS, AND RELEVANCE

persistent theme, and one that is not easily eradicated. This old issue is here approached in a new way. It will become evident, for example, that I am not a proper Scholastic or logical atomist. It will also be­ come clear, I hope, that the theory of meaning presented later is not to be equated with any extensionalist and/or intensionalist acount available. There are other old and important issues. Here are a few: (a) How does the meaning component of a theory of language have to be structured? (b) What is the status of the distinction between assertive, interrogative, imperative, and optative sentences? (c) What is it for somebody to mean something? (d) What is the status of logic? (e) How does the material implication relate to the ordinary language 'if... then'? (f) Is there any point in constructing a non-modal propositional logic? I will attempt to provide new answers. In the course of doing so, I will obvi­ ously draw on old answers, but some of them will be discarded as invalid. It is good to realize that we are living in an era that allows the fundamen­ tal questions to be asked. Not so long ago, in fact, many of them were not quite respectable. The main linguistic paradigms disregarded or neglected the study of meaning. Similarly, much of 20th-century Anglo-Saxon philosophy was dissociated, through positivistic logicism or through Wittgensteinian therapy, from the traditional philosophical task of investigating the general properties of human existence. But now we can once again study the fundamental prob­ lems about meaning and even speculate about ontology and feel sure that these issues are judged relevant. Furthermore, Chomsky has made mentalism respectable again and, as we shall see, there are signs that even 'psychologism' may be losing its depreciatory connotations. My second reason for claiming relevance is that this work will generate new questions. Some examples: (a) How do we deal with non-basic speech acts? (b) How does Reflectionist Propositional Logic relate to, say, Rele­ vance Logic or the Gricean approach to propositional logic? (b) Are there any languages that mark the distinction between what will be called 'particular' and 'generic' conditionals? It is apposite to say something about the relevance of self-evidence, too. It might be asked whether there is any point in advancing claims that are taken to

METHODOLOGY, CONTENTS, AND RELEVANCE

7

be self-evident. In a similar vein, the value of explaining primitives might be questioned, for, after all, everybody should already 'know' the primitives. The answers are easy. First, something that is self-evident for me may not be self-evident for somebody else. Second, perhaps self-evidence is actually one of the more decisive types of evidence there is. Compare, on this score, Kripke's opinion on the value of intuition: "Of course, some philosophers think that something's having intuitive con­ tent is very inconclusive evidence in favor of it. I think it is very heavy evi­ dence in favor of anything, myself. I really don't know in a way what more conclusive evidence one can have about anything, ultimately speaking." (Kripke 1972:265-266)

Third, 'knowing' a primitive does not mean having full knowledge about it. For one thing, it may only be a knowledge-how to deal with, say, the word 'neces­ sary' or with necessary situations, which does not encompass the ability to say what necessity is. For another thing, a knowledge-that about something may not include all that can be known about it. To take necessity again, one may know what necessity is, only in the sense that one can give a characterization that is sufficient to separate it from possibility. Increasing knowledge about primitive concepts, now, will be a matter of acquiring new partial knowledge, i.e. of charting new distinctions and of relating them to other concepts in new ways or to concepts they have not been linked up with so far. Displaying the network of relations surrounding a primitive is its explanation. It is worth stressing, however, that this enterprise is inherently limited. Each of the con­ cepts that enter the explanatory relations of the network is just as much enti­ tled to an explanatory network of its own. In this connection, Castañeda (1975: 57) rightly speaks about an ''unavoidable circularity", ''one of the basic predicaments of philosophy". This makes it all too easy to be a sceptic, of course. The sceptic can deny any relevance on the accusation of vagueness and circularity. Naturally, this argument sounds persuasive, for vagueness and circularity are indeed to be avoided as much as possible. But surely, we cannot avoid them 'more' than is possible. One should not ask for the impossi­ ble. The only remedy against scepticism is to change the sceptic, to turn him or her into a tolerant and even cooperative pragmatist. As Quine (1961b: 19) comments on the choice of an ontology: "the question what ontology actually to adopt still stands open, and the obvi­ ous counsel is tolerance and an experimental spirit."

CHAPTER II FROM POSSIBLE WORLDS TO HUMAN ACTION

If the reflection thesis is taken seriously, it may be instructive to look at the mind, in particular, and at reality, in general, before coming to the linguis­ tic aspects. This is basically the perspective from which most of this chapter, its philosophy of mind and its ontology, has been written. Except for the opening section, which is largely concerned with the defi­ nitions of the philosophy of mind and of ontology, this chapter is perhaps the most constructivist of all. I will build up a model universe, an abstraction from the real one. Into this artificial environment, an homunculus will be intro­ duced. This homunculus is not the real human being, but only a simplified and abstract counterpart. Naturally, the value of these artifacts should still be an empirical one. I assume that the idealizations and simplifications are justified. I take it, that is, that the relations and the entities of my model universe have their direct counterparts in the real universe or that the full-scale study of the latter could profit from the investigation of the former. These assumptions are not themselves in need of any further justification. In other words, their valid­ ity is fallibly self-evident. This does not mean, however, that the model presented in what follows is the only possible one. On the contrary, I have no objection against a transla­ tion of my frame into another one, if the latter can be argued to be more con­ venient. In view of this relativity, I have furthermore tried to present my ac­ count of the structure of the universe and of the mind in a way that should not foreclose any of the great ontological options (realism, conceptualism, nominalism ; idealism, materialism, etc. ). The strategy of doing ontology and mixing in a large dosis of non-commitment, will be called 'minimal ontology'. Thus minimal ontology is a restriction on my enterprise. But that minimal on­ tology is possible at all will be argued to be a significant result. The model is intended to be a substantial component of the linguistic analysis of the following chapter, and of the logic of chapter IV and V. For these purposes, I do not need any fully developed universe or mind models. So this chapter will be incomplete, both in scope and in depth of analysis. For the same reason, I will not trouble myself greatly to compare this account to

10

FROM POSSIBLE WORLDS TO HUMAN ACTION

other accounts. Some parts of the analysis might be taken to be an 'over-jargoned' mystification of common sense or, if the reader is in a better mood, an explication of implicit knowledge. For a reason to be explained in the next few pages, the latter interpretation would not displease me. Connectedly, the reader might feel uneasy for no other reason than that he or she hoped not to have to spend any more time on such truly basic questions (about beliefs, de­ sires, etc.) as the ones to be treated here. He or she might have expected these questions to have been settled a long time ago. If this expectation is not borne out, let me remind this reader of the fact that, for the last two thousand years or more, philosophers have been discussing very similar questions in rather similar ways. Yet philosophical inquiry has not come to an end, nor is this fact considered to be an intellectual scandal. 1.

Philosophy of mind, ontology, and reflection

1.1. Philosophy of mind and reflection What is the philosophy of mind? In one view, it is the study of a few very basic mental phenomena and relations like believing, imagination, emotion, 'willing', the relation between minds and brains, and the general relation be­ tween mind and matter. I will call this the 'realist' view. What the philosopher of mind would speculate on is the complexity of the mental phenomena and relations themselves, of the 'real stuff'. The second approach will be called 'mentalist'. 4 In this approach, the philosopher of mind would not (after all) directly speculate about the mind it­ self, but only about our thoughts and concepts about the mind. A prime exam­ ple of the mentalist approach is Gilbert Ryle's classic The concept of mind (1949). Ryle only aims to "rectify the logic of mental-conduct concepts" (1949: 16). Whether he succeeds in this mentalism, incidentally, is another matter, for he sometimes writes like a realist and he has been interpreted as a realist (see Ayer 1963b: 23-24,27-28). Note also that my description of Ryle as a mentalist forms a paradoxical contrast with the fact that Ryle is usually, be­ cause of his efforts to destroy the mind-body dualism ('the myth of the ghost in the machine'), considered a champion of anti-psychologism. The mentalist easily slips into a 'nominalist'. If the philosopher of mind only deals with mental-conduct concepts, then perhaps he or she really only studies the meanings of our mental-conduct words. It is no coincidence that Ryle fits into a tradition of so-called 'linguistic philosophy' and that he can write that

PHILOSOPHY OF MIND, ONTOLOGY, AND REFLECTION

11

"this [i.e. The concept of mind] as a whole is a discussion of the logical be­ haviour of some of the cardinal terms, dispositional and occurrent, in which we talk about minds". (Ryle 1949: 126; my emphasis; see also Mundle 1970: 41-45,54-55,91-109)

To describe the activity of a linguistic philosopher with the words of one who is disillusioned about it: "due to philosophy's rather recent enlightenment, there seems little left for the subject beyond the analysis of just so many words, beyond the under­ standing of their meanings or, more generally, of various features of their behaviour." (Unger 1975: 318)

Why is it that one can claim to do philosophy of mind in three different ways? I will first discuss the relation between mentalism and nominalism. Realism will be brought in later. I contend that nominalist and mentalist philosophy of mind are simply identical. To see this, let us ask again what nominalism amounts to. Nominalist philosophy of mind is the study of the linguistic conventions of such words as 'belief, 'will', and 'knowledge'. The linguistic conventions, now, that the philosopher of mind is interested in are certainly not the phonological or the morphological ones. How the word 'belief is pronounced, whether it is a com­ plex morpheme or whether it has a declension or not, is not of his or her con­ cern. The conventions he or she is looking for are those of meaning or, what boils down to the same thing, the conventions of the use of the meaning. So the nominalist is interested in meaning. The mentalist philsopher of mind, on the other hand, is analyzing concepts. But are these activities really different? When one philosopher of mind is investigating the meaning of the word 'be­ lief and another one is analyzing the concept of belief, aren't they doing exactly the same thing? I am strongly inclined to a 'Yes' I do not wish to con­ tend that all inquiry of meaning is conceptual analysis, but at least to the ex­ tent that a philosopher of mind is interested in it, the two activities seem to coincide. The fact that they definitely coincide in the particular case of The concept of mind confirms this. It might be objected that the argument is of little avail. What is the use of equating something as obscure as meaning with an equally obscure notion of concept?5 My answer goes as follows. First, if I am accused of obscurantism, then the objector will appreciate the fact that an account with one obscurum, viz. concept-meaning, takes precedence over an account with two entities shrouded in obscurity, viz. concept and meaning. Second,the primitives'con­ cept' and 'meaning' must here be taken in a pretheoretical sense. I have not

12

FROM POSSIBLE WORLDS TO HUMAN ACTION

supplied any theory of concepts or of meaning yet. So the equation of nominalist and mentalist philosophy of mind must rely on ordinary language understanding, which is indeed vague. But remember what it means to give an explanation of primitives. Due to the unavoidable circularity of philosophy, to explain a primitive is to relate it to other primitives. I think that it is there­ fore safe to say that the hypothesis on concepts and meanings argued for above is at least the start of a theory. Whether the hypothesis can be held on to depends on the rest of the theory construction. The claim on the equation of nominalism and mentalism can only be tentative at this stage. Be it a tentative claim, I think that it is a plausible one. Here is another way to reach it. A mentalist philosopher of mind wants to find out how hu­ mans think about matters of the mind. It is a commonplace to say that at least some thought is verbal. If we convince ourselves that the thinking that the mentalist philosopher of mind is interested in is verbal thinking, the case for equat­ ing nominalism and mentalism seems to be a good one (cp. Warnock 1958: 161). Now, to be convinced that the philosopher's attention goes to verbal thought is rather easy, for surely things like unverbalized brainstorms, if they exist, or the preverbal thinking that children might engage in are not his or her concern. So much for the relation between mentalism and nominalism. It warrants emphasis that I have not claimed that mentalism and nominalism always re­ duce to each other, but in the case of the philosophy of mind they do. Hence­ forth, the position describable as the collapse of nominalism and mentalism will be called 'conceptualism'. What is the relation between conceptualism and realism? It is clear that conceptualism and realism cannot be reduced to each other in the way of the reduction of mentalism and nominalism. How do we explain the coexistence of conceptualists and realists then? And how do we explain that realist and conceptualist philosophers of mind, despite their radically different idea of what they are doing, do not seem to have any more communication problems than any group of scientists or philosophers of the same paradigm? The an­ swer is provided by the reflection thesis. Up to a certain point, human con­ cepts (i.e. mind and language) reflect reality. When the realist is studying the mind, and a conceptualist colleague is looking at a concept of the mind, they are therefore, up to a certain point, studying the very same thing. So both realism and conceptualism are correct. When philosophers of mind are under­ taking a realist analysis, they will often, unwittingly, produce a conceptualist one, too.

PHILOSOPHY OF MIND, ONTOLOGY, AND REFLECTION

13

There is no way that I can prove the reflection thesis. As claimed before, however, I believe that it is intuitively sound, and we have just seen how the history of the definitions of the philosophy of mind makes it rather plausible, too. I hasten to add that the 'up to a certain point' of the claim that realism equals conceptualism, but up to a certain point only, hides a very serious prob­ lem. But I will not try to solve it. I intend to steer clear from the cutoff point. In this philosophy of mind, I will only deal with the clear cases of reflection. I will discuss beliefs, for instance, while taking it for granted that there are such things and that the generic human being has both a concept and a word for it. Still, the problem is worthy of a few remarks. Minds do not only reflect reality. Minds also fear reality, want it, mis­ construe it, and mask their ignorance about it. Some of this sinks down (gets reflected) into our concepts, too. Therefore, the study of concepts, which is, once again, a study of both mind and language, cannot be a totally trustworthy clue to the understanding of reality. J.L. Austin is one of the many who is aware of this. On the one hand, he is convinded that the analysis of language is of philosophical interest, for language embodies "the inherited experience and acumen of many generations of men" (Austin 1970c: 185). On the other hand, he issues a warning that is worth quoting in full: "But then, that acumen has been concentrated primarily upon the practical business of life. If a distinction works well for practical purposes in ordinary life (no mean feat, for even ordinary life is full of hard cases), then there is sure to be something in it, it will not mark nothing: yet this is likely enough to be not the best way of arranging things if our interests are more extensive or intellectual than the ordinary. And again, that experience has been derived only from the sources available to ordinary men throughout most of civilized history: it has not been fed from the resources of the microscope and its suc­ cessors. And it must be added too, that superstition and error and fantasy of all kinds do become incorporated in ordinary language and even sometimes stand up to the survival test (only, when they do, why should we not detect it?). Certainly, then, ordinary language is not the last word: in principle it can everywhere be supplemented and improved upon and superseded. Only re­ member, it is the first word." (1970c: 185)

A similar idea can be found in logical atomism, according to which lin­ guistic structure both pictures and conceals the structure of reality. This ten­ sion is also evidenced by the very fact that post-atomist Anglo-Saxon philosophy branched off into Ordinary Language and Ideal Language Philosophy, and by the fact that neither the one nor the other can exist in total purity.6

14

FROM POSSIBLE WORLDS TO HUMAN ACTION

What we are confronted with is the imperfection of the reflection rela­ tion. Sometimes the student of reality will not be able to use ordinary lan­ guage, at least not in the ordinary way, and sometimes the useful bits may not be sufficient. Thus he or she is justified in coining new terms — and concepts — and devising new uses for old ones. Let me introduce one more 'ism' in this connection, viz. 'instrumentahsm'. As instrumentalists, we construct our own instruments.7 As my brief comment on Ordinary and Ideal Language Philosophy has already suggested, instrumentalism can come in large or in small doses. In subatomic physics the instrumentalism is obviously enormous. In my forthcoming remarks on minds, however, the instrumentalism will be rather mild. 1.2. Ontology and reflection In actual fact, the preceding considerations on reflectionism and in­ strumentahsm are very general. They do not just apply to the demarcation problem of the philosophy of mind. They are useful for the definition of philosophy, in general, and of each of its subdisciphnes, in particular. One of the subdisciphnes is metaphysics, and one of the subdisciphnes of metaphysics is ontology. Given the importance of ontology for this study, a brief discussion would not be out of place. What is ontology all about? The classical answer is the realist one: ontol­ ogy is a theory of what exists, of what sorts of things 'really' exist rather than appear to exist. This is different from the mentalist answer implied by Strawson's (1959) definition of metaphysics. Strawson (1959: 9) only aims "to lay bare the most general feature of our conceptual structure". It is interesting to see that Strawson reluctantly disclaims nominalism: "Up to a point, the reliance upon a close examination of the actual use of words is the best, and indeed the only sure, way in philosophy ... The struc­ ture he [i.e. the metaphysician] seeks does not readily display itself on the surface of language, but lies submerged. He must abandon his only sure guide when the guide cannot take him as far as he wishes to go." (1959: 9-10)

Still, critics have thought that ontology is really no more than a study of lin­ guistic structures, i.e. that ontology is nominalist. Benveniste's (1966) attack on Aristotelian ontology is famous: Aristotle might think that he was classify­ ing ontological categories, but in reality he was classifying the linguistic struc­ tures of Greek. My explanation for why we find the three aforementioned views about

PHILOSOPHY OF MIND, ONTOLOGY, AND REFLECTION

15

ontology again consists of merging nominalism and mentalism into concep­ tualism, and conceptualism and realism into reflectionism. Up to a point, therefore, each approach is correct, for some of the general features of reality are reflected in our conceptual apparatus. But only up to a point. Naturally, the question of where to have the cutoff point is again fraught with difficulties. But I think that I can ignore them. The ontological problems to be dealt with in this book will be argued or assumed to be safe in this respect. I will deal with such absolutely general things as objects, states of affairs, conditions, and necessity, and I will claim (a) that these 'things' really exist, and (b) that both the generic human being and his or her language have concepts for them. I must also mention instrumentalism. In ontology, too, investigators can coin their own instruments, and no ontology can wholly embrace instrumen­ talism or totally desist form it. In view of the centrality of the reflection thesis, however, my own attempt is predominantly non-instrumentalist. The in­ strumentalism shows in the unavoidable jargonese. But it is English jargonese. 1.3. Reflection In the second statement of the first chapter, I admit that the reflection thesis is vague. This has not prevented me from applying it to the demarcation problems of the philosophy of mind and ontology. As a matter of fact, this ap­ plication is to count as an attempt to further clarify the reflection thesis. There will be more such application-clarifications. The reflection thesis will be used in the discussion of the boundary problem of semantics and pragmatics and in the definitional analysis of logic. Other, more specific applications concern the nature of possible worlds, truth, and the so-called 'universals issue'. Perhaps the repeated application will be found tedious. Nevertheless, I think that there is ample justification. First of all, the above mentioned issues are often discussed in isolation from each other. The status of possible worlds, for instance, is the subject matter of one debate, and the question of what truth is belongs to another. A viewpoint in the first controversy does not imply a stand in the second. Each controversy deserves to be dealt with on its own terms. So, if I want to take up the same stand in two debates, I still have to argue for it twice. Secondly, it is indeed my purpose to take the very same stand, that of reflectionism, in each of the discussions. I hope, then, that the fact that the same point of view holds good throughout the various controver­ sies will not be found unattractive. Thirdly, each application of the reflection idea is to count (and to be welcomed) as a further clarification.

16

FROM POSSIBLE WORLDS TO HUMAN ACTION

Another way to clarify the reflection thesis is to obviate all possible ob­ jections. Let me here just deal with one objection, an important one. The re­ flection relation is supposed to hold between reality, in general, and two of its constituents, viz. language and mind. It is a fact, though, that I must use both my mind and my language to discuss whichever bits of reality I claim would be reflected. It may further be argued that the fact that my discourse on reality in­ evitably depends on both mind and language shows the reflection thesis to be totally amiss. What I am talking about when I claim to be discussing reality is not really reality; it is something that is just as mental and linguistic as the mental and linguistic entities that are supposed to reflect this alleged reality.8 I think that the problem can be clarified with an appeal to what could be called the principle of the indispensable thinker-talker'. This principle states that there is no way that one can talk or think about reality with an exclusive interest in reality — and not in one's thought or talk about reality — without thinking or talking about it. This is intended as a truism. I will therefore as­ sume its intelligibility and correctness without any further argument.9 When I apply it to the present worry, I admit to the objection that my ontologicai theory is a linguistic and mental construct. I confess, that is, that the ontology that I postulate is a fallible projection from my mind and my language. This does not mean, however, that the ontological theory cannot be about reality. To repeat, though the ontology is undoubtedly constrained by the limits of my imagination and rationality as well as by my language, I, at least (see also Ayer 1963c: 180,186; Mackie 1973b: 54-56), see no reason why its categories cannot be ontological. The contrast between the reflection thesis and the ob­ jection can summarily be phrased as follows: 'some categories are ontological and not psychological or linguistic' versus 'some linguistic and psychological categories are mistaken for ontological ones'. This is a fight between realists and sceptics. Given that common sense as well as the relative success of sci­ ence may well support realism, and given that the present incarnation of the sceptic is inconsistent by not being sceptic about linguistic and psychological categories, I think that the burden of proof lies on the sceptic. Naturally, the mere permission to postulate not only linguistic and psychological categories, but also ontological ones does not give us the reflec­ tion thesis yet. I am also postulating a relation, that of reflection. And it is here that my approach is superficially similar to the one embodied in the objection. To describe the phenomenon for which I need a reflection, the objection in­ vokes a simple identity. According to the latter, the allegedly ontological categories would in fact be psychological and linguistic. I suspect that neither

PHILOSOPHY OF MIND, ONTOLOGY, AND REFLECTION

17

point of view can be proved and that one of them, but only one of them, can be made plausible. One final point and a set of disclaimers. I have admitted that ontologicai categories are mind-and-language-dependent. This does not mean that they cannot be dependent on reality itself anymore. In some cases they are. One's conception of color, for instance, depends on the language that one speaks. Perhaps one's language has two 'basic color terms' (Berlin and Kay 1969) or perhaps it has seven. But color conception is no less determined by physics. Nobody on this planet has so far had any conception of a physically impossible color. On the priority problem of which dimension — reality, mind, or lan­ guage — is the most important one, perhaps so over-important that the others must be seen as aspects of it, I will suspend judgment, except for one 'inno­ cent' claim. That is to say that I will not pause over such deep questions as 'Is all matter really made of spiritual stuff or is the mind fundamentally a matter of matter?' I simply accept that reality, mind, and language are different, to a sufficiently high degree at least.1() As far as the 'innocent' claim goes, I accept a sense in which both minds and languages are somehow parts of reality. In this sense, reality is the more-encompassing entity. But notice two points. First, this inclusion relation does not imply that linguistics or the philosophy of mind are included within ontology. Ontology is only concerned with the general features of reality and not with any questions particular to minds or languages. Second, the acceptance of the sense in which reality includes mind and lan­ guage does not entail any answers to the deep questions I suspend judgment on. Perhaps my intention to remain uncommitted on the priority problem is taken with a grain of salt. Doesn't reflectionism itself imply that ontology is somewhow prior (cp. Parret n.d.b)? What is, is, whether it is mentally or lin­ guistically reflected or not, but there cannot be any linguistic or mental reflec­ tion without there being something (to be reflected). These considerations are serious. Let me make two remarks. First, I will soon develop a notion of reality that comprises both what is and what is not (what is only possible). This notion allows me to hold that even the non-existent can be reflected, in which case I could say it changes status and becomes part of the realm of what is. If it can thus be made acceptable that reflection can create what there is, then the claim that reflectionism implies a priority of reality will be recognized to be mistaken or at least oversimplified.11 A second respect in which the view on the priority of ontology is oversimplified is that, although reality will mostly be given the role of the 'reflected' rather than that of the 'reflecting', there will

18

FROM POSSIBLE WORLDS TO HUMAN ACTION

be an important exception. One essential feature of desires and intentions, so I will claim in II.3.1 and II.3.3, is that reality reflects the mind. 2.

The out-of-mind

2.1. States of affairs Minds are part of the world. Everything outside of any particular mind is this mind's out-of-mind. Both the out-of-mind and the world contain four types of entities: states of affairs (abbreviated as 'SOA'), objects, states, and events. These four terms are ordinary words, but I must narrow down their commonsense understanding somewhat. By definition, the term 'entity' will be the most neutral of all. It is easy to explain: there is nothing in my model that is not an entity. What the three re­ maining terms mean can best be shown with some examples. A stone, for in­ stance, is an object. SAs are constituted by one or more objects that are in one or more states (e.g. the SOA of the mere presence of a stone) or that par­ ticipate in one or more events (e.g. the SOA of the falling of the stone). Perhaps, there are also SO As that have states or events but no objects. The SOA in which it is raining, for instance, might qualify as an object-less event SOA, but then there is the tricky question, to be glossed over here, of whether rain is not really an object, too. SOAs can also be made up of other SO As. An example would be the SOA in which it is warm and in which John takes off his shirt. The world at large as well as the out-of-mind will here be considered to be such complex SO As. Notice the technicality now. The world is not an object, though it is an en­ tity. States of affairs are not states.12 Falling and raining are events and not SO As, but they can be a part of SO As. I will have little more to say about objects, events, and states. I do not wish to imply, however, that the distinction is unproblematic. Yet it is of minor importance here. The ordinary language understanding, slightly technicaiized, will have to do. The notion of states of affairs, on the other hand, will play a major role in this book. So I will try to clarify it a bit more. To some extent, my understanding of SO As is based on that of C.I. Lewis (1946: 48-55). An SOA is a fairly abstract entity. Just how abstract it is, might be appreciated more clearly by a negative demonstration of the following kind. An SOA need not be "a space-time slab of reality with all that it contains" (1946: 53). To take Lewis' example, when Mary is making pies in the kitchen, either it is true that she burns her fingers or it is not true that she burns her fin-

THE OUT-OF-MIND

19

gers. Hence the full chunk of reality either includes the finger accident or it does not include it. It is either true or not true that there is a clock in the kitchen. It is either true or not true that there is a knife on the kitchen table.13 And so on. Still, all of these situations are characterized by Mary's making pies in the kitchen. This characteristic, one of Mary-making-pies-in-thekitchen, is my SOA. For Lewis (1946), an SOA is never a "space-time slab of reality with all that it contains". Since I have claimed that an SOA need not be such a total spacetime slab, I have departed from Lewis. My reason is this. First, it seems obvi­ ous to me that SOAs are ontological categories. It is really the world itself, and not somebody's conception or assertion about it, in which I present Mary as making pies in the kitchen. Lewis would seem to agree, but he also holds that an SOA functions as a peculiar 'mode of meaning', called 'signification', of what he calls a 'proposition' or 'content of assertion'. That is to say that the proposition attributes an SOA to the world (or, better, to a possible world—I will come to this later). The relation to propositions is crucial. A Lewis SOA can only be an attribute of the world if it is the signification of some "formu­ lated or formulatable proposition" (1946: 55). In my model, however, SOAs do not depend on possible contents of assertions. My SOAs are truly chunks of reality, and I am not embarrassed, therefore, to grant SOA status to en­ tities the whole truth of which could never, I suppose, be believed or asserted. Examples of such entities are the world itself and the space-time slabs with ab­ solutely all that they contain. I have a second reason for calling the all-inclusive space-time slabs SOAs. If Mary-making-pies-in-the-kitchen is an SOA and if Mary-making-pies-inthe-kitchen-and-Mary-burning-her-fingers is also an SOA as well as Marymaking-pies-in-the-kitchen-and-Mary-burning-her-fingers-and-there-beinga-clock-on-the-kitchen-table, etc., then I do not see any reason why the set of all characteristics, knowable or not, of either the world or of one full spacetime slab would not also be an SOA. Notice, incidentally, how his decision simplifies the ontology. If I did not allow the total space-time slabs to be SOAs, the model would have five instead of four types of entities. All of this is not to say that Lewis' SOA concept is wrong, only that mine is different. Furthermore, my present plea for an ontological understanding of SOAs will not prevent me from introducing psychological and linguistic SOA-like entities too (see II.3 and III.2.2) or from studying the SOAs and SOA-like entities in abstraction from their ontological or non-ontological nature (see IV.2).

20

FROM POSSIBLE WORLDS TO HUMAN ACTION

The picture of SOAs is still very incomplete. One important feature, for example, is that SOAs can have a dimension of time and place relative to the larger SOAs that incorporate them. In other words, SOAs can obtain some­ where and at some time. I will say a little bit more about the temporal dimen­ sion in II.2.3, but, all in all, questions of time and place will not be dealt with. Another feature of SOAs is that I have used natural language to describe them. For the SOA in which it is warm, for example, I have used the words 'it', 'is', and 'warm'. On the strength of the reflection thesis, I assume that at least some SOAs can be given an ordinary language description. To this assump­ tion, a very important convention must be added. My SOA descriptions are intended to be fully explicit. When I use the description 'it is warm', for in­ stance, I want to speak about an SOA in which it is warm, and not about an SOA in which it is warm and sunny or very warm. Of course, the description does somehow apply to such SOAs, but it is not explicit. The term for this explicitness will be 'completeness'. So, by definition, my SOA descriptions are complete. 2.2. Minimal ontology However vague the ontology of objects, states, events, and SOAs may be, one thing is clear: it is a generous one. It can rightfully be asked whether I really need to attribute a separate existence to, say, John, a taking-off event, a shirt, as well as to the SOA in which John takes off a shirt. My answer is dou­ ble. On the one hand, I confess to realism, for I believe that objects, states, events, and SOAs all exist. But on the other hand, I remain uncommitted about how they exist. This strategy will be termed 'minimal ontology'; it obvi­ ously demands some further comments. First of all, I hope that I am not alone in thinking that objects, states, events, and SOAs are at least somehow involved in the world, that is to say that they all somehow exist. This is enough for me, for myfaçon de parler. It is precisely this 'somehow existing' or 'minimal existence' that my entities all partake in. Second, my realism about minimally existent entities does not preclude mentalism or nominalism. On the contrary, I claim that the ontological categories of objects, states, events, and SOAs are reflected in the conceptual framework of all human languages as well as of the generic human mind. Again, I am here only saying that they are reflected, not how. Third, as far as the ontology of objects, events, states, and SOAs goes, I will restrict myself to the level of minimal existence. I want to be neutral on the 'how' issues. I do not want to answer questions like the following:

THE OUT-OF-MIND

21

Isn't the existence of an object much more basic than that of a state in that the latter would only be involved as something about the object that we, humans, attribute a concept or a word to? Even if a state is indeed only something that humans have given a concept or a word to, it still is something, i.e., it still enjoys its minimal existence. Thus it is possible to be a realist about minimal existence and, say, a nominalist in the in­ vestigation of how my entities non-minimally exist. But the point is that I will not go beyond minimal existence. I plead absolute innocence in the debate be­ tween realism, mentalism, and nominalism, when fought about non-minimal existence. I even set out to remain uncommitted in the preliminary battle against any neo-positivists who would doubt whether the debate about nonminimal ontology has any interest at all. I might be retorted that my minimal ontology totally misses the point. Of course, the objection goes, events, objects, states, and SOAs all somehow exist. This is uncontroversial enough but merely precedes philosophical speculation. Philosophy only starts when one tries to distinguish the derived from the underived, and the real from the shadowy existence. So minimal on­ tology is at most minimally interesting, but certainly not ontology. Against this objection, three considerations can be adduced. First, I doubt whether everybody would accept that each of the entities in question exists, even if only 'somehow'. Second, whether or not minimal ontology is an interesting strategy cannot be decided apriori. I make the aposteriori conten­ tion that it is interesting. Quite a bit of what follows crucially depends on the acceptance of SOAs as ontological entities — as well as supports it. Third, S. Haack (1976b: 471) has remarked that, when an ontologist denies existence to an entity of a certain sort, he or she often does not really mean it. One only wants to deny that the entity in question is what it is generally thought to be. If this is correct, why couldn't we be justified in abstracting form the question of whether the entity is or is not what it is commonly thought to be, and just ac­ cept that it exists. This is what minimal ontology is all about. The peculiar ontological neutrality of minimal ontology may be illumi­ nated further by comparing it to the position defended by Aune (1977:26-49). Aune's non-committal strategy is one of positing events and SOA's, for in­ stance, even though he does not know whether it is necessary to do so, and is inclined to think that it is, in the end, avoidable. Aune thus makes a hesitant choice for an all-or-nothing type of existence. Minimal ontology, however, embodies a decisive choice for a minimal existence. There is one more point that needs to be made. The fact that I do not take

22

FROM POSSIBLE WORLDS TO HUMAN ACTION

a stand on the question of whether the non-minimal existence of either object, state, event, or SOA is the more basic one is not in contradiction with the fact that, on the level of minimal existence, SOAs will be considered to be prior. This category preference may not be self-evident. One could reason as fol­ lows. On the one hand, the model does not allow any SOA that does not con­ tain at least some state or event and (possibly) some object. On the other hand, there are no objects, events, or states outside of SOAs. Considerations like these clearly leave the issue of the priority unresolved. The sense in which an SOA is more basic, though, refers to the fact that SOAs are the direct in­ gredients of the world, whereas objects, states, and events, in virtue of the fact that their involvement in the world only comes through an involvement in its SOAs, are the indirect ones. However trivial this category preference may seem, I hope it is clear that it is a purely ontological one.14 2.3. Possible worlds This section takes me back to the problem of time. SOAs can exist simul­ taneously. Otherwise, they succeed each other. This way, the dimension of time can be said to comprise a past, a simultaneity, and a future. At every mo­ ment in time, the world will be taken to contain lots of SOAs that do not yet or no longer exist. Both the future and the past are determinate, however. Only that which will actually happen or come into existence is part of the modelworld. Only that which did exist, belongs to it. One might also say that the world sub specie aeternitatis, i.e. looked upon from a timeless perspective, contains all and nothing but the existing entities, whether their existence is past, simultaneous, or future relative to any one of them. This is the appropriate moment to enlarge the model. Just as I allow en­ tities not to exist with respect to SOAs, I allow them not to exist with repect to the world. These entities could have existed or exist, but their possibility has never been actualized, nor will it ever be. They do not belong to the realm of 'not yet' or 'no longer', but to that of 'never', to a 'non-world' or 'non-actual world'. A non-world lacks 'worldly' existence. Since there is absolutely no limitation to the ways the world could be or have been, I postulate an infinite number of non-worlds. As could be expected, both the actual world and the non-worlds will be called 'possible worlds'. Once again, I admit that I am ontologically generous. I have, in fact, al­ lowed an infinite plurality of para-worlds. No doubt, this clamors for futher justification. What, then, is the ontological status of possible worlds and of possibilia, in general? Even though the possible worlds idiom is definitely en

THE OUT-OF-MIND

23

vogue these days,15 the philosophical literature does not supply a consistent answer. But the very emergence of the different suggestions is consistent with the reflection idea. First of all, there are the realist views. Stalnaker (1976b),16 Apostel (1974: 145-147), and Nute (1980: 28) seem to be realists, but the present locus classicus has become D. Lewis (1973).17 Since I have a realist palate, Lewis's credo is worth quoting in full: "I believe that there are possible worlds other than the one we happen to in­ habit. If an argument is wanted, it is this. It is uncontroversially true that things might be otherwise than they are. I believe, and so do you, that things could have been different in countless ways. But what does this mean? Ordi­ nary language permits the paraphrase: there are many ways things could have been besides the way they actually are. On the face of it, this sentence is an existential quantification. It says that there are many entities of a certain description, to wit 'ways things could have been'. I believe that things could have been different in countless ways; I believe permissible paraphrases of what I believe; taking the paraphrase at its face value, I therefore believe in the existence of entities that might be called 'ways things could have been'. I prefer to call them 'possible worlds'." (D. Lewis 1973: 84).

It is probably easier to be an anti-realist, though. For one thing, it is no hardship to poke fun at the realist18 or to criticize him (see Richards 1975; S. Haack 1977). For another thing, there are good alternatives, the obvious one being mentalism. This was probably Leibniz's view (see Mates 1968; Ishiguro 1979). It is advocated by Kroy (1978) as well as by Hintikka (1971) and Kripke (1972): "Quine's distinction between ontology and ideology, somewhat modified and put to a new use, is handy here. ... We have to distinguish between what we are committed to in the sense that we believe it to exist in the actual world or in some other possible world, and what we are committed to as part of our conceptual system. The former constitute our ontology, the latter our 'ideol­ ogy'. What I am suggesting is that the possible worlds we have to quantify over are a part of our ideology but not of our ontology." (Hintikka 1971: 153-154)" "A possible world isn't a distant country that we are coming across, or viewing through a telescope. Generally speaking, another possible world is too far away. Even if we travel faster than light, we won't get to it. A possible world is given by the descriptive conditions we associate with it. What do we mean when we say 'In some other possible worlds I might not have given this lecture today'? We just imagine [my emphasis] the situation where I didn't decide to give this lecture or decided to give it some other way." (Kripke 1972: 267)

24

FROM POSSIBLE WORLDS TO HUMAN ACTION

The phrase 'descriptive conditions' suggests that Kripke would accept the peculiar mixture of mentalism and nominalism which I have called 'concep­ tualism'. Conceptualism may be palatable to Mackie (1973a: 90-92) and it is clearly to Rescher's (1973a, 1975) taste. "Nonexistent possiblities thus have an amphibious ontologicai basis: they root in the capability of minds to perform certain operations—to conceive or describe and to hypothesize (assume, conjecture, suppose) —operations to which the use of language is essential, so that both thought processes and lan­ guage enter the picture." (Rescher 1975: 208)

For Rescher, conceptualism is not just a side issue. His 1975 book is one long, but elegant defense of it. I haven't come across any pure nominalism but I have seen a position called 'instrumentalism'. A radically anti-realist instrumentalism is that of Merrill (1978): "The instrumentalist takes it [i.e. the talk of possible worlds] with a grain of salt, just as he would take talk of dragons or theoretical entities in science." (316) "Possible worlds semantics is a fairy tale with explanatory power." (317)

But, as Merrill (1978: 306, 324) holds that the subject matter of semantics is concepts, it seems better to call him a conceptualist. This typology does not quite exhaust the literature. I could also mention the phenomenon of non-commitment. Thus Hazen (1977) considers possible worlds to be abstract entities of the same type as the ones that mathematics is all about, but he (1977: 68) admits that he still has to face the question of what mathematical entities are. Other neutralists are Plantinga (1974: 45; 1977: 140) and, less clearly, Bradley and Swartz (1979).19 Why have I belabored this typology to such an extent? The answer is that each of the positions outlined ends up as constitutive of my own approach. The non-commitment goes into my miminal ontology, and the various 'isms' com­ bine into a reflectionism. As far as the reflectionism goes, I believe that realism, mentalism, and nominalism are all correct. To start with realism, I maintain that an SOA may not be actual; that there is a set of SOAs at least one of which is non-actual; that this set could replace the set of actual SOAs (the world); that there is an infinite number of world-replacing SOA sets. These sets are my non-worlds. I do not doubt, for example, that the reader may put this book aside in exactly one minute from now. In case he or she does not, the last part of the preceding sentence only describes a part of one or

THE OUT-OF-MIND

25

more non-worlds, of one or more ways things could have been but aren't. It is surely an ontologicai feature of my environment that things can be and could have been different. This is not just a matter of my imagination or my lan­ guage. So I am a realist. But this realism does not mean that I cannot be a mentalist or nominalist as well. Now, while nominalism and mentalism might not be objectionable in isolation, the reflectionist way in which they get combined with realism is probably more offensive. It implies that I do not merely hold that my thought and talk about the actual reflects the actual, but also that my thought and talk about the non-actual reflects the non-actual. Doesn't this make mockery of the whole reflectionism thesis? I believe not. Of course, the reflection of the non-actual is a little different from that of the actual. While the reflection of the actual is, to a certain extent, constrained by whatever it is that happens to be actual, viz. this one and very specific possible world that is the actual one, there are almost no ontological constraints in the case of a re­ flection of the non-actual. The latter is, after all, the infinity of ways things could be and could have been. Admittedly, if our ordinary language concept of reflection requires a dependence of the reflection on what is reflected ('the object of reflection'), then my notion of the reflection of the non-actual is largely technical. Yet, even if the object of reflection is the non-actual, there is some dependence. First, the reflection of the non-actual is trivially con­ strained by the fact that the object of reflection may not be the actual. Sec­ ondly, it depends on the object of reflection being the non-actual, that the reflection is almost entirely unconstrained. Three more remarks about reflectionism. First, my phrase 'thought or talk about the actual/non-actual' is somewhat ambiguous. What I have in mind is thought or talk that is really about the actual/non-actual and not just intended or thought to be about the actual/non-actual. The complex issues that the ambiguity points to will be dealt with in III.2.1. Second, my reflectionist understanding of possible worlds is not absolute. In accordance with the gen­ eral reflectionist stand that language and mind reflect reality, but only up to a certain point, I would admit that there could be possible worlds (in the realist sense) that come without linguistic or mental counterparts. In accordance with the strategy of steering clear of the cutoff point of where the reflection thesis does not hold any more, however, I will have nothing to say about such possible worlds. Third, though I hold that the notion of possible worlds can be interpreted ontologically, psychologically as well as linguistically, it seems best, for the sake of convenience, to restrict it to the ontological. On the one occasion (IV.4.5) that I need a non-ontological notion, I will devise a new

26

FROM POSSIBLE WORLDS TO HUMAN ACTION

term. It is appropriate to bring in minimal ontology once more. It cannot be em­ phasized enough that my ontology is restricted to the claim that possible worlds exist. It is clear that there is an ordinary language sense in which only the actual world can be said to 'exist'. But it is equally clear to me that the nonactual is a crucial feature of my environment, not just of what I think or say about it, so that there is also a sense in which even the non-actual worlds can be said to 'exist', 'somehow exist', or 'minimally exist'. It is on the level of min­ imal existence, common to all possible worlds, actual or non-actual, that I am arealist. Note that when I am pleading for an ontological understanding of non-ac­ tual possible worlds and putting them on a par with the actual one, I am im­ plicitly defining yet another notion of world, reality, or 'environment'. I will use a new term for this, viz. 'universe'. By definition, the universe is charac­ terized by both the way things are and by the multitude of ways things could have been. The universe is thus the set of all possible worlds, the actual one and the set of the countless non-actual ones. 20 The analysis possibilia and possible worlds is still a superficial one. The very notion of possibility, for example, is left vague. Is 'possible' the same as 'neither actual nor non-actual' or is it rather a matter of 'possibly actual and possibly non-actual'? Or is the possible that which is neither necessary nor im­ possible? These and other questions will be dealt with in Chapter V. It will then be seen (a) that my emphatic acceptance of possible worlds does not mean that they will play the crucial role that is commonly assigned to them in the analysis of modality and implication, and (b) that possibilia will not be confined to the non-actual possible worlds, but be allowed in the SOAs of the actual world. I have not characterized all possible worlds approaches yet. For some (e.g. Prior 1962; Hintikka 1971), there is no difference between SOAs and possible worlds. In this study, however, all possible worlds are SOAs, but not all SOAs are possible worlds. The distinction is essentially that of C.I. Lewis (1946) and is well expressed by Plantinga (1974: 45; 1977: 140): a possible world is a maximal SOA. Maximality is defined as follows: "a state of affairs S is complete or maximal if for every state of affairs S', S in­ cludes S' or S precludes S'." (Plantinga 1974: 45; 1977: 140)

Without the maximality condition, there does not seem to be a need to distin­ guish between SOAs and possible worlds.

THE MIND

3.

27

The mind

Now that we have had a closer look at the out-of-mind ('OOM'), we will analyze the mind ('M'). The mind will be considered to be an object with two parts: a storing device ('SD') and an interactive device ('ID'). The ID is the part of the M that interacts with the OOM. It will later be argued that the ID interacts with parts of the M too. But, as a first approximation, the claim that the ID is in contact with the OOM has the interesting feature of clearlyseparating it from the SD, for the latter does not interact with the OOM at all. Both the ID and the SD consist of two compartments. The SD believes and desires, and the ID is conscious and intends.

Part of the challenge of this section is to make this four-dimensional model of the mind, which is in part inspired by Artificial Intelligence work, a plausible one. 3.1. Beliefs and desires The cognitive aspect of the SD has to do with the mind's storing a massive number of beliefs. For the purpose of this study, beliefs, opinions, ideas, as­ sumptions, views, prejudices, and bits of knowledge will all be lumped to­ gether under the term 'beliefs'. Dl is a preliminary definition. Though it will be improved on several times, for the moment it will do to distinguish the cog­ nitive from the volitional aspects. D l : A beliefs a result of an effort to reflect a part of the OOM in the M. What the definition does not say is that the effort in question cannot be undertaken by the SD. As mentioned above, the SD does not interact with the OOM. That it is the ID that is responsible here will be integrated in a later version of D l . Another reason, incidentally, for why Dl needs improve­ ment is that not all beliefs originate in the way adumbrated in it.

28

FROM POSSIBLE WORLDS TO HUMAN ACTION

The M does not only contain beliefs, but also desires. For my present purposes, desires will not be different from wishes, wanting, and cravings. In­ tentions, however, will be given a separate analysis. A tentative first attempt to define desires gives ut this: D2: A desire is a cause for an effort to reflect a part of the M in the OOM. The parallels between beliefs and desires are rather striking. Both are somehow stored in the SD. Both involve a reflection relation between M and OOM a well as some kind of effort. But beliefs and desires are of the inverse type (cause versus result). Futhermore, the function of the M and OOM is a different one: in the case of the belief, the M contains the 'map' and the OOM the 'original', while in the case of the desire it is the other way round. To use Searle's (1979c: 254) terms, for a belief the 'direction of fit' is M-to-OOM and for a desire it is OOM-to-M.21 Notice that the direction of fit that characterizes desires runs counter to the directionality inherent in the Speculative Gram­ marian viewpoint. While from the Speculative perspective, reality is the origi­ nal, in the present model of desires, reality is the map. Yet, despite the fact that the direction of fit for a desire is OOM-to-M, I will soon claim that the conceptual building bricks of desires (the so-called 'conceptualizations') have an M-to-OOM orientation. Definitions Dl and D2 contain a notion of effort. It indicates that no re­ flection is necessarily successful. Suppose, for instance, that somebody be­ lieves that the earth is flat, though the earth of his or her actual OOM is really round. For this sort of situation I will say that the belief does not reflect the OOM. The belief is false, while in a successful reflection the belief is true. De­ sires are no less liable to misreflection. Imagine that somebody wants to go form Brussels to Paris and that the desire is only followed up by his going from Brussels to Amsterdam — in the most direct way. All of this illustrates the basic fallibility of the human being. I will have more to say about the success and failure of reflection, about truth and falsity, in Chapters IV and V. Beliefs and desires are entities. This is trivial; in the present model, noth­ ing fails to be an entity. I have not made clear yet whether beliefs and desires are SOAs, states, events, or objects. Within the purview of this study, they will be objects. A belief and a desire will therefore be put on a par with a tree, but not with the growing of a tree or with the SOA of the-tree-is-growing. Be­ lieving and desiring, however, will be regarded as states, more specifically, mental states.

THE MIND

29

It is good to stress how very little I am actually claiming and how much I am — or hope to be — relying on a common understanding of primitive con­ cepts. Take the decision to consider beliefs as objects, for instance. I do not make clear what type of objects they are. It is obvious that beliefs and trees are different types of objects. But it is equally self-evident to me that beliefs, given the four-way typology of objects, states, events, and SOAs, are to be clas­ sified as objects. This is not a deep or new finding. But, at least, it indicates that I am seriously committed to the idea that there really are such objects as beliefs. Beliefs, just like my non-worlds and just like states, events, and SOAs, enjoy a minimal existence. I have no qualms about this minimal ontological commitment, for I think that everybody agrees that beliefs, what­ ever they may be, are at least somehow involved in the operation of a mind. If one retorts that 'existence' is too strong a term for this involvement and that my universe of 'existing' entities is overpopulated, then one does not ap­ preciate the function of the qualifier 'minimal'. I do not deny that ontological parsimony may be quite appropriate for the level of non-minimal existence, however. The following point brings in SOAs or, at least, SOA-like entities. One never believes a stone, rain or warmth, or raining or being warm. One be­ lieves that there is a stone, that the stone is falling, that it is raining, and that it is warm. One believes in SOAs, not in objects, events, or states. This view is not contradicted by the fact that English allows one to say that one believes in a person, for instance. Expressions of that type are always a shorthand for ex­ pressions of a belief in an SOA in which that person is involved somehow. A belief in God is a belief that God exists or that God is trustworthy. Similarly for desires. One does not really desire objects, states, or events. One desires that one would own an object, that the event would take place, or that the state would obtain. The belief and desire dependent SOA-like structures will be called 'conceptualizations'. Conceptualizations are not the same as on­ tological SOAs, though. When one believes or desires that Antwerp is, respec­ tively, were full of flowers, it is not the real Antwerp or the real flowers that enter the belief or the desire, but only the believer's or the desirer 's concept of Antwerp and his or her concept of flowers. A conceptualization is an amalga­ mation of concepts. A conceptualization is just like an SOA, except that it does not obtain in the OOM but in the M. We are hitting upon an important factor in the explanation of why the M and the OOM can be said to reflect each other: somehow the M and the OOM contain the same sorts of entities, viz. conceptualizations and SOAs. They are the original relata of the reflection re-

30

FROM POSSIBLE WORLDS TO HUMAN ACTION

lation. It is really the conceptualization of a belief that is supposed to reflect an SOA. It is only in a derivative way that the belief as a whole is to reflect an SOA. Similarly, it is primarily the conceptualization of a desire rather than the desire itself that is supposed to be reflected in an SOA. It might also be asked whether the mere possibility of certain concep­ tualizations or the mere availability of certain concepts can be looked upon in reflectionist terms, too. My answer is positive, but carries a risk.22 Concepts and their amalgamations reflect ontological universals. Once they are inte­ grated in beliefs or desires, however, the ontological entities a successful reflec­ tion connects them to are particulars. A belief about a horse, for example, as well as its conceptualization, refers to a particular SOA with a horse in it. Yet, the concept of horse by itself refers to the universal of horsehood, and a con­ ceptualization that is unattached to any belief or desire of, say, a-horse-isdrinking refers to a universal of a-horse-is-drinking-hood.23 I will not develop this idea any further here. Let me just bring in minimal ontology again. To the extent that my position on the universals issue is a realist one — because of the reflectionism, I am no less of a conceptualist, though — the realism is a minimally ontological one. When I am claiming that there are such ontological universals as horsehood, I do not proceed to clarify what their existence amounts to. I support this strategy with the observation that everybody seems to agree that horsehood is at least somehow involved in reality. As to a level of non-minimal ontology, however, I do not rule out that the existence of particulars is somehow much more basic than that of univer­ sals, to the point even that universals cannot be said to exist except through particulars. Yet, I do not exclude that universals are more basic than particu­ lars either. So concepts, I suggest, reflect ontological universals. Yet, in another sense, they also reflect beliefs. Take an Eskimo with seven snow concepts. About snow number seven, for example, the Eskimo believes that it is the kind that calls for heavily waxed skis. It sound natural to say that the snow concept reflects the belief about just what kind of snow it is. I am touching on a truly simple idea: concepts can be explained and the explanation is the reflected be­ lief. Applied to scientific concepts, this is also the meaning of the phrase that no concept is theory-independent. Often, the belief has a role in the genesis of the concept, too. Roughly, it is only because generations of Eskimos have been holding beliefs about a kind of snow that asks for heavily waxed skis, that they have developed a concept for it. Some concepts can therefore be seen as the result of beliefs. Now, what

THE MIND

31

is interesting but also confusing about this, is that the word 'reflection' can be used as a (near) synonym for 'result'. Henceforth, this idea of reflection will be termed 'genetic reflection'. Thus snow concept number seven genetically reflects the beliefs of generations of Eskimos.24 So much for a partial account of concepts and conceptualizations and what it is that they can be said to reflect. I can 'update' the definitions of beliefs and desires as follows: D3: A belief is an SD-object resulting from an effort to reflect an SOA in a con­ ceptualization. D4: A desire is an SD-object causing an effort to reflect a conceptualization in an SOA. The new definitions bring in conceptualizations and SOAs. They also expli­ cate that beliefs and desires are objects, and, to separate them from other types of objects, I can call them 'SD-objects'. 3.2. Consciousness and beliefs A human being whose mind is only a storehouse of beliefs and desires could not survive. He or she would have the space for what is meant to be con­ nected with the OOM, both the world and the non-worlds, but would not have anything to establish the connections. The SD does not do it. Although the SD is disposed to be acted upon and to generate action, it does not itself act. Men­ tal action is the function of the ID. The part of the ID that provides the SD with a belief on the OOM is con­ sciousness (awareness). Consciousness produces momentary reflections of the OOM. Some of them get recorded, i.e., they are transferred to the SD where they get stored as beliefs. The essence of the conscious ID is that it acts. From the point of view of the ID, consciousness can therefore be regarded as an event. When we report on this event, however, we normally take the point of view of the human being the ID 'belongs' to and we say that he or she is in a state of consciousness. I will follow ordinary parlance and consider being conscious, just like believing and desiring, to be a mental state. For lack of a good one-word name, the object that is involved in con­ sciousness will simply be called 'object of consciousness'. Objects of con­ sciousness are close to beliefs: for both of them conceptualizations reflect

32

FROM POSSIBLE WORLDS TO HUMAN ACTION

SOAs. A definition of an object of consciousness could run as follows: D5 : An object of consciousness is a momentary ID-object resulting from an effort to reflect an SOA in a conceptualization. The claim that the conceptualization is supposed to reflect an SOA rather than an object, a star, or an event is not falsified by the fact that one can say that one is conscious of somebody or something. Such phrases seem to be shorter ways of expressing that one is conscious of, say, the presence of some­ body or something. I can now describe the role of the ID in the formation of beliefs as one of losing an object of consciousness but passing on its conceptualization to the SD, thus creating a belief. Connectedly, a belief can now be redefined as fol­ lows: D6: A belief is a lasting SD-object resulting from an effort of the ID to reflect an SOA by creating a momentary object of consciousness and trans­ mitting its conceptualization to the SD. The qualifiers 'lasting' and 'momentary' are supposed to contrast with each other, but the distinction between them is not unproblematic. Furthermore, saying that a belief is something that lasts raises the questions of how long it lasts and whether it changes. These problems and the related one of how to re­ trieve and of how to forget are not dealt with here. So far, the model of beliefs and objects of consciousness is such that every belief results from an object of consciousness, but that not all objects of con­ sciousness give rise to beliefs. This will now be changed. The human being is allowed to believe, be it under special circumstances, things he or she has never been conscious of. Beliefs that do not come from a prior consciousness have to be implied by one or more other beliefs. As the issue of what an impli­ cation is will not be addressed before Chapter V, an example must suffice. Suppose that I believe that Priam's fifty daughters are all intelligent. Suppose, furthermore, that I also believe that one of the fifty daughters is called 'Polyx­ ena'. The final assumption is that I have never thought about Polyxena in iso­ lation — except, precisely, for thinking that Polyxena is one of Priam's daughters. In these circumstances it has never occurred to me that Polyxena is intelligent. Still, I would want to say that I believe that Polyxena is intelli­ gent. I have never been conscious of Polyxena's intelligence, but the belief in question is implied by the belief that Priam's daughters are all intelligent and

THE MIND

33

the belief that Polyxena is one of Priam's daughters. This leads me to redefine beliefs once more: D7: (a) A belief is a lasting SD-object resulting from an attempt of the ID to re­ flect a SOA in a conceptualization by creating a momentary object of consciousness and transmitting its conceptualization to the SD. (b) Any implication of a set of beliefs is also a belief. Perhaps there are also innate beliefs, but I do not take a stand on this issue. 3.3. Intentionality and desires So far, the homunculus is equipped with a mind full of beliefs and desires and the ability to be conscious. The only events we have seen so far are those of creating and moving mental objects and conceptualizations. But the M, in particular the ID, can take part in a second event, that of intending. Some of the homunculus' desires are oriented towards his or her future accomplishments. The desire to raise a hand or to go away are of this type. The desire that the sun would stop shining is not. Desires are stored in the SD, and there is nothing the SD will do except storing them. If the desire relates to the human being 's own behavior, the M can actually influence this behavior by having its ID 'intending' the behavior. In that case, the ID reactivates the de­ sire such that the organism is in a state of readiness to perform the desired ac­ tion. When the ID intends to act, it does not itself perform the act. It does not guarantee success either. Perhaps the desire is unrealistic to start with, or perhaps the execution is a misfire. The intending only puts the human being in an activated disposition to act in the desired way.25 Note that I do not claim that the desired action can only take place if one in­ tends it. Perhaps one can 'give in to a desire' without intending some­ thing. I will have more to say about this when I come to human action itself (in II.4). From the point of view of the ID, intending is an event. Predicated about the human being, however, intending will be taken as a state. This way, 'in­ tending' will be used in the same way as 'being conscious', and I will have four mental states: believing, desiring, being conscious, and intending. The ob­ jects of intendings are the 'intentions'. They share the particularity of the ob­ jects of consciousness of being momentary. In the same way as objects of con­ sciousness are close to beliefs, intentions are close to desires:

34

FROM POSSIBLE WORLDS TO HUMAN ACTION

D8: An intention is a momentary ID-object causing an effort to reflect a conceptuali­ zation in an SOA. Yet, different from a desire, an intention imposes severe limitations on the type of SOA and on the effort. To start with the latter, it has to be the intender who makes the effort. This is a point where my technical notion departs from ordinary language. The ordinary 'intending' is sometimes more like 'wishing' and 'wanting', and we get sentences like 'I intend you to do this'. There are two limitations on the type of SOA. First, the SOA in which the intender in­ tends to act must belong to what he or she conceives to be the actual world. Through its being intended, the intended action is made to belong to the realm of what is supposed to be real or realistic. Thus there is no intention corre­ sponding to the desire for past happiness, for example. What I am getting at here is only the commonsense idea, cropping up in most accounts of intentionality, that one can only intend to do things one believes to be in one's power. Another restriction is that the SOA has to come later than the one in which one is intending. One cannot carry out the intention at the moment of the intending or before it. When I symbolize the latter two restrictions by call­ ing such SOAs 'future W-SOAs', and when I explicitly mention that the ef­ fort has to be undertaken by the intender, definition D9 resuts: D9: An intention is a momentary ID-object causing an effort of the intender to reflect a conceptualization in a future W-SOA. To intentionally activate a desire is not the same as being conscious of it. One can be conscious of a desire to cut down a tree without in the least intend­ ing to. This shows that a consciousness of a desire does not imply an intention. But what about the opposite? Does the intention necessarily involve a con­ sciousness of the underlying desire? Is somebody who intends to cut down a tree necessarily also conscious of the desire to cut down a tree? Again my an­ swer would be 'No'. A readiness to perform is simply different from being conscious of the desire that underlies the readiness. In a similar vein, I feel like arguing that an intention does not necessarily occur with a consciousness of the intention. In other words, intenders need not be conscious of their inten­ tions.26 Consciousness is not necessarily intentional either; if such were the case, it could be taken to mean that consciousness would itself be a readiness to perform. As the description of consciousness necessitated a change in the defini-

THE MIND

35

tion of beliefs, this account of intentionality should make us look at desires once more. Yet the relation between intentions and desires is different from the one between beliefs and objects of consciousness: if we analyze the rela­ tion between beliefs and consciousness, we get a limited account of the origins of beliefs, but if we analyze the relation between desires and intentions, we do not get any account of the origins of desires. Instead, we learn something about the origin of intentions. So we really have to make the definition of in­ tentions a bit more complex. D10: An intention is a momentary ID-object causing an effort of the intender to reflect a conceptualization in a future W-SOA and resulting from a desire with the same conceptualization. My final point concerns both desires and intentions. It is implied in the preceding discussion that a readiness to perform does not guarantee an at­ tempt to perform. Similarly, not all desires actually cause an attempt to reflect their conceptualization. Both intentions and desires, that is, may remain caus­ ally quiescent. Our definitions cannot be silent on this. So I will no longer speak about an intention or a desire causing something, but only about them possibly causing something. This amendment is a very poor one. It is almost trivial, for what, indeed, is not a possible cause? As I have nothing better to offer at present, 'possibly causing' should only function as a pointer towards a better solution. D11: A desire is a lasting SD-object possibly causing an effort to reflect a concep­ tualization in an SOA. D12: An intention is a momentary ID-object possibly causing an effort of the intender to reflect a conceptualization in a future W-SOA and resulting from a desire with the same conceptualization. This completes my philosophy of mind. The trouble with 'possibly caus­ ing' illustrates that the analysis slurs over a good many important questions. Still, however halting and infirm the understanding we have reached, the cen­ tral points should be clear. I have endorsed the view that beliefs and desires stand in an inverse relationship to each other. I have furthermore suggested that, fine detail aside, objects of consciousness are inversely related to inten­ tions, and that the relation between beliefs and objects of consciousness is the

36

FROM POSSIBLE WORLDS TO HUMAN ACTION

inverse of the relation between desires and intentions. With these paral­ lelisms, the account should have made it plausible that believing, desiring, being conscious, and intending are four important, if not the important mental states. It should not shock anybody when, in the next chapter, a crucial dis­ tinction in the theory of meaning will refer to precisely those four — and no other—mental states. This theory of meaning will also refer to a peculiar type of human action, viz. speech acts. That is why the philosophy of mind will now turn into a philosophy of action. 4.

Human action "I think that the problem of the relation of action and intention is one of the messiest tangles of puzzles in contemporary philosophy" (Searle 1979c: 253)

A human being does not live by mental states alone. He or she has to act. Actions (acts) are events that have to do something with consciousness and intentionality. Let me first look at intentionality again. It will be recalled that the intention puts the organism in a state of readiness. It is clear that not all human events require an intentional readiness. Certain biological events of the body never happen with an intentional preparation. It is perhaps less clear that there is not a single 'intendable' event that could not occur withoutthe in­ tention. All intendable events could just as well come off as automatisms or as results of unconscious drives, or they could happen when one is asleep or hyp­ notized. There is, therefore, a category of human events that groups together the events that may or may not be preceded by an intention. This group, I be­ lieve, splits up in two subclasses, and the criterion is a cultural one. There is a set of social conventions that say that some types of events count as events that are intended and conscious, and that certain other types do not have this value. The events that do not count as intended and conscious constitute mere behavior or doings. The others constitute a subtype of behavior called 'action' or'acts'. For illustration, consider the event of moving one's fingers. Since we can­ not sit still all the time, our fingers are continually moving. In most cir­ cumstances and, I presume, for most cultures, this will be regarded as be­ havior. In the setting of Thai temple dancing, however, or when the doing functions as signaling or thimblerigging, finger movements will be considered an action. An example of a culture in which the finger movements of a temple dance would not count as action is one in which the dancers are thought to be

HUMAN ACTION

37

completely possessed by the gods. When the event counts as one that is in­ tended and conscious, it does not matter whether or not the dancer, the sig­ naler, or the thimblerigger have actually intended to move their fingers or are in fact conscious of it. Even when it is very likely that the movement is nei­ ther conscious nor intended — when the finger movements have become routine, for instance — the event can be taken as an act, i.e., it can still have the social value, meaning, and consequences of the intended and conscious version. So action does not require the actual presence of consciousness and intentionality, but only a conventional presence. To approach action in terms of consciousness and intentionality is very common, both in philosophy and in sociology.27 In many cases, intention—or some psychological state not too different from it—is considered to cause the action. This approach has been called 'The Causal Theory of Action'. The po­ sition that I am advocating here is a mixture of this and of the 'Contextualist Theory of Action' (see Rubinstein 1977). It is contextualist in that action is considered a function of the social context. But what the social conventions do is more than picking out a set of doings and labeling them 'actions'; they give them the value of conscious and intended doings.28 A helpful concept is that of responsibility. I will say that the human being is responsible for his or her actions but not for what is mere behavior. That is to say that when the human being is held responsible, there is a convention in play according to which his or her ID is taken to be in control, both qua con­ sciousness and qua intentionality. That the ID might not be in control does not really matter, for responsibility is a social notion. Since one is not responsible for mere behavior, one might find oneself moving one's fingers and hitting somebody in the eye, and not be held responsible for it — at least as far as the behavioral aspects of finger movements go. Unfortunately, human beings are often expected to be careful, in which case following the maxim of caution is regarded as a basso contìnuo action accompanying everything one is doing. With respect to this underlying action, it becomes difficult to escape respon­ sibilities. It is undoubtedly true, as Allwood (1978: 6) contends, that our ordinary concept of action is not clear. To some extent, then, my definition of action is stipulative. Still, I hope that it captures the kernel elements of the ordinary language notion. I even hope that it is universal and I am inclined to think that it can somehow be 'derived' from the conditio humana. An argument might go along the following lines. Step one: The fact that a human being can intend to do something and be conscious of this is far from irrelevant. Such doings ac-

38

FROM POSSIBLE WORLDS TO HUMAN ACTION

quire a social value or effect different from the ones that happen spontane­ ously. That is to say that if an observer assumes the presence of consciousness and intentionality on the part of the doer, this assumption will influence his or her reaction. Precisely because some observer supposes that the doer intended to hit and that the finger movement was not an accident, the observer will take it ill and hit back. So intended and conscious doings get associated with a set of typical responses. Step two: It seems to be a fact about human beings that they can learn to do things automaticaly and — which is equally important — that this private automatization process does not cause the doings to lose their typ­ ical public value. This greatly facilitates life. Take the example of somebody who is learning to type. In the beginning most or even all the movements are conscious and intended. At the stage of the 'blind' typist, however, typing has become an automatism. Still, whatever social value the conscious and in­ tended typing has — it justifies the expectation that the typescript is not a ran­ dom sequence of symbols—it is 'inherited' by the automatic typing. Step three (which concludes the argument for the universality of my action concept): I am not disinclined to claim that the process of automatization and retention of social value is so absolutely basic that human beings have conceptulized it. The concept of a doing which may or may not be intended and conscious, but which has the social value of the intended and conscious occurrence is that of action. Perhaps, one might object, this claim to universality is too strong, and perhaps the definition only deals with a Western, common parlance concept of action. So the action concept would be culture-dependent anyway. My reaction is one of doubt. I admit that the importance of this action concept may differ from culture to culture. But I suppose that action is such a basic fact of life that it may well be reflected in the conceptual framework of all cultures. Yet I may be mistaken. Even then I could argue for a universality however, an instrumentalist one. This is to say that all cultures could be investigated with my action concept as an instrument. Such a study would not necessarily reveal what the members of a culture call 'action'. Furthermore, what might vary from culture to culture is not only the meaning of their own action concepts, but also the extension of mine, i.e. the question of which events do and which do not get counted as actions. A final remark, intended as a prelude to the next chapter, is this: I have been speaking about people who take events as actions. I could just as well have said that they interpret the events as actions, that an occurrence of an event may mean that a doer performed an action. So even though the pres-

HUMAN ACTION

39

ent chapter is only preparatory to a theory of meaning for natural language and even though it does not explicitly deal with language or meaning, yet it im­ plicitly harbors a general notion of meaning. This general notion will be the starting point for the theory of meaning to be developed in Chapter III.

CHAPTER III SPEECH ACTS AND MEANINGS

"On this view the philosophy of language is a branch of the philosophy of mind." (Searle 1979b: 190)

In this chapter I will develop a 'Neo-Speculative' theory of meaning for natural language, in the context of which I will later engage in a logic. The theory will comprise both a semantics and a pragmatics, and the division of labor will be dependent on the way meanings reflect mental entities. Thus the theory of meaning will be grafted on the theory of mind (more so than on on­ tology). I will devote special attention to the pragmatic entities that the logic will operate with, viz. the so-called 'basic speech acts'. Before I come to all this, however, I will establish a direct link with the end of the preceding chap­ ter. I am by no means the first to anchor a linguistic account onto a general theory of the mind. Despite the anti-psychologism among logicians and among the more syntax-oriented linguists, this strategy has been gaining cur­ rency. The present-day locus classicus is Grice's "Meaning" (1957), in which linguistic meaning is analyzed in terms of intentions. Grice's work — and not just the one paper mentioned — has had an enormous influence (see e.g. Allwood 1976 and Bennett 1976). As the chapter's introductory citation may suggest, Searle has pushed his version of speech act theory into the direction of the philosophy of mind, too, a strategy in which he is partially paralleled by Parret.29 Yet the road of inquiry opened up (or reopened) by Grice and others has many undiscovered turns and byways, an occasional dead end, and too many conflicting road signs.

42

1.

SPEECH ACTS AND MEANINGS

Meaning and speech acts

1.1. Meaning versus intended, natural, and non-natural meaning Sometimes an event is interpreted as an action. An occurrence of an event then means an occurrence of an action. As we have seen, this meaning is entirely conventional. The fact that an event has action status depends on a convention and not on what the doer of the event might intend. The latter de­ termines the 'intended meaning', not the meaning proper. The intended meaning is the meaning that a human being actually intends. Thus, when a doer intends his or her event as an action, actionhood is an intended meaning, whether or not the event is conventionally interpreted to be an action. The distinction between meaning and intended meaning resembles that of Grice (1957) between 'natural meaning' (abbreviated as 'MN ') and 'nonnatural meaning' (abbreviated as 'M NN '), which is largely a rephrasing of the venerable philosophical division between 'natural' and 'conventional signs' (see Rollin 1976: 15-32). Because of the age-old prominence of this dualism, its present Gricean actuality, and the danger of confusing the two classifica­ tions, it is worth going into the differences between them. Grice (1957: 377-378) contrasts sentences of the following type (italics and capitals mine) : (1) (2)

Those spots mean MEASLES. Those three rings on the bell mean THAT THE BUS IS FULL.

The italicized fragments of (1) and (2) are meant to exemplify natural and conventional signs, respectively. More importantly, the capitalized con­ stituents are examples of MN and MNN (in that order). The major difference in meaning seems to be this: in the intended, most normal reading of (2) there is somebody in the situation who means or should mean that the bus is full; there is no such individual in the situation described in the intended, most normal reading of (1).30 What is the relation between MNN and MN, on the one hand, and meaning and intended meaning, on the other? First of all, MNN cannot be the same as the intended meaning, since Grice allows that the situation that is normally described by (2) includes somebody who should mean that the bus is full and who may, therefore, mean something entirely different. Only in case the con­ ductor does mean that the bus is full does the MNN correspond to the intended meaning. In case he or she means something else, the MNN may be the mean­ ing proper, yet only when the three rings conventionally mean that the bus is full (but this is probably what Grice has in mind with his 'should mean'). Sec-

MEANING AND SPEECH ACTS

43

ondly, all the MNs of the type exemplified with the normal reading of (1) are meanings proper. That the relation between spots and measles is not mediated by any intention like that of (2) is obvious. That it is dependent on a convention is less obvious. But there is no denying that it is ultimately only the possibly inappropriate convention of modern Western medicine that is re­ sponsible for it. In a hundred years from now, Western doctors may have to­ tally changed their opinions about spots, and for a Chinese acupuncturist those very same spots may have a completely different significance even now. All of this is not to deny that either present-day Western medicine or Chinese acupuncture is correct somehow. The beliefs about the relation between spots and measles may be true. And, in fact, I am personally convinced that some of our beliefs about spots, measles, stars, language, and all the rest of the uni­ verse are true. This is why I am a realist, after all. But there is no certainty about these beliefs. The natural meaning relation between spots and measles is, therefore, a conventional or culture-dependent one. In the spots-measles case, MN is truly a meaning proper. But not all of Grice's MNs are of the spotsmeasles type. Grice (1957: 378) has decided to treat a case of somebody mean­ ing to do something as exemplifying an MN, too. This 'meaning' involves an in­ tention, and I see no obstacle to considering the intended doing as an intended meaning and not as a meaning proper. Conclusion: Despite the similarities, there is no congruence between my notions of meaning and intended meaning, and Grice's MNN and MN. When Grice talks about MNN, he could be discussing a meaning proper or an in­ tended meaning. The same goes for when Grice talks about M . The distinction between MN and MNN, it might be mentioned, is not the only or even the most influential contribution Grice has made to the study of the relation between meaning and intention. Grice (1957, 1968, 1969, n.d.) has also analyzed the nature of the intention that is responsible for what I have called 'the intended meaning'. In other words, he has offered an acount of what it is for a speaker to mean something. This issue will be discussed in a later section (III.2.1.3). 1.2. Speech act meaning The meanings that I am interested in here are not those of spots or rings, events or actions in general, but those of linguistic actions, better known as 'speech acts'. Before I come to speech act meanings, though, it behooves to point out that linguistic actions are more worthy of discussion than mere lin­ guistic doings. Most of the linguistic events that we are confronted with in our

44

SPEECH ACTS AND MEANINGS

day-to-day experience are indeed linguistic actions. In most circumstances, speakers are held responsible both for the fact that they have said something and for what they have said. The speaker's behavior counts as (has the social value of) something he or she has intended and is conscious of. It is good to spell out two implications of this account. First, I do not deny that there are circumstances in which speaking is not considered an action. One can think about talking in one's dream and about certain sessions in the psychiatrist's room. Second, I claim that speech acts often lack intentionality and consciousness. Many times we find ourselves saying something which we did not really intend at all or which we did not really intend to put in the terms we ended up with. Notice that in neutral contexts, i.e. in situations that do not themselves suggest that we could not have meant what we said or that we could not have been conscious of our talk, our speech events will be taken as if they were intended and conscious. If it is important enough to annul this all too natural interpretation, we have to resort to explicit suspension formulae like Ί did not really mean that', 'I didn't really express myself that well' or 'My God, what did I say?' I have now justified my decision to focus on speech acts rather than mere speech behavior. What interests me about them is their meaning, and not their intended, natural, or non-natural meaning. Let me now have a look at what it means for a speech act meaning to be (ir)refutable. To the question of what it means to say that a certain event occurred, there is, as we have seen, no simple single answer. I have already given two: either there was an action or there was a doing. Similarly, there is no one sim­ ple answer to the question of what it means that a certain speech act occurred. Speech acts can have all sorts of meanings. The account that follows will be structured as a search for things that could sensibly be called central, essential, or 'irrefutable' speech act meanings. But as a result of the discovery that some candidates for irrefutable meaning status are not, in fact, irrefutable, the analysis also counts as a description of refutable speech act meanings. My reasons for adopting this peculiar approach are the following. First, I assume that the approach is interesting in its own right. Second, it will be seen that it is a neat way of separating the ontologicai, the mental, and the linguistic strands, and of discussing the reflection relations holding between them. Third, it will also turn out to be an appropriate framework for arguing for the existence of a closed class of so-called 'basic speech acts'. Fourth, the analysis will automatically bring forth an account of what it is to mean something. Notice that I have not spoken about the meanings of morphemes, words,

BASIC SPEECH ACTS

45

phrases, or syntactic patterns yet. Such meanings are simply different from what I take to be speech act meanings. Of course, there is a relation. This will make itself felt in the analysis of speech act meaning, but it will not be singled out for special treatment except for the sketch of the division between seman­ tics and pragmatics (in III.3). 2.

Basic speech acts

2.1. Assertions Suppose that somebody makes the following speech act: (3)

I love pheasant.

On purely formal criteria (word order, intonation, word choice), the action represented in (3) can be called an 'assertion'. So 'assertion' is a formal cate­ gory. Yet I also hold that it is a category of meaning. That is to say that I argue that all assertions always carry their typical 'assertive' meaning. This is a stronger claim than it would seem. It is perhaps not self-evident that such for­ mally assertive speech acts as the 'promise' of (4) and the 'order' of (5) still contain assertive meaning. (4) (5)

I promise to let you go. I order you to go home.

The forthcoming analysis is supposed to back up this somewhat radical posi­ tion. Of course, I am by no means saying that the analysis of the meanings of (4) and (5) is completed with saying that they carry assertive meanings. For ease of exposition, I will sometimes discuss a speech act meaning in terms of an interpretation of a hearer (Ή'). To render the conventionality of the speech act meaning, this hearer will be idealized: H will both know and apply the linguistic conventions. In this way I can alternate between saying that a speech act means such-and-such and saying that the hearer interprets it as such-and-such. 2.1.1. ρ The speech act in (3) may simply mean that the speaker ('S') really loves pheasant. In that case, the speech act is taken to reflect the world. I will call this meaning 'ontological'. In general terms, the ontological meaning of an as­ sertion that ρ is simply p. Hopefully, the intuitive idea behind this definition is both simple and obvious. I confess, however, that the definition is somewhat sloppy. The two occurrences of the symbol 'p' do not refer to the same thing.

46

SPEECH ACTS AND MEANINGS

The second occurrence represents a randomly chosen SOA, but the first oc­ currence, the one in 'the assertion that p', does not. My phrasing is meant to suggest that there is an SOA-like entity, something that is structurally much like an SOA and that reflects it, that somehow 'lives' a linguistic existence. Note that this is not the first non-ontological SOA-like entity that crops up in this book. We have already introduced the conceptualization, the mental re­ flection of the SOA. For the linguistic reflection of the SOA, the 'p' of the as­ sertion that p, I will use Hare's term 'phrastic' (see Hare 1952, 1970; Lyons 1977). Just what phrastics are and how they relate to SOAs, conceptualiza­ tions, and to what will be called 'propositions' is not of my concern yet. These issues are reserved for a later section (III.3) and a later chapter (IV). The decision to assign an ontological meaning may seem rather naive. Saying that one loves pheasant by no means proves that one loves pheasant. If an irrefutable meaning is wanted, the ontological one is a poor candidate. A meaning assignment that is less vulnerable is the one in which H decides that (3) only means that S believes that he or she loves pheasant. This is the second layer of refutable meaning to be discussed, the 'psychological meaning'. In general, the ontological meaning assignment is dependent on the psychological meaning assignment: H interprets the assertion that p to mean that ρ because Η interprets the assertion to mean that S believes that p, and H further accepts that S's belief is true. At present, I have nothing to say about this. For one thing, it concerns that concept of truth, the discussion of which I have already (in 1.3.1) deferred to Chapter IV. For another thing, it brings in one of the key problems of epistemology, viz. the relation between belief, true belief, justified true belief, and knowledge, a problem that lies outside the purview of the present inquiry. 2.1.2. S believes that ρ On the psychological interpretation the speaker of (3) is taken to believe that he or she loves pheasant. This is not an irrefutable meaning. S could be lying, for instance. If H is aware of this, H does not assign the psychological meaning. This is not to say that the speech act becomes meaningless. H might still attribute the ontological meaning. H might also come to hold that S does not believe that p. Suppose that H is questioning S and that H is absolutely convinced that S is going to lie. If S then replies that he or she loves pheasant, H might interpret the answer to mean that S does not love pheasant. S's lying seems to be a matter of not believing that p and of wanting H to attribute the psychological meaning anyway. Different from lies are stylistic

BASIC SPEECH ACTS

47

devices such as irony, metaphor, and hyperbole, with which S can also assert that p, and yet not believe it. The difference with the lie is that S does not want H to attribute the psychological meaning, but desires to 'be seen through'. H is supposed to figure out both that S does not believe that p and what it is that S does believe. There is yet a third situation in which an assertion that/? may coexist with an absence of a belief that p. Suppose that S believes that 'pheas­ ant' is the English word for what S and H know to be a turkey. S furthermore believes that his or her opinion on the name of a turkey is shared by H and that he or she does not love pheasant, be it that S does not know how to name this animal. If this is the context for S's assertion that he or she loves pheasant, then S is not a liar, and S is not playing a stylistic trick either. And yet, S does not believe thatp. In the case at hand, S actually believes that not-p. A fourth and final situation that allows S to assert that/? and not believe it is the one in which S does not feel responsible for the assertion. If only S realized what he or she asserted, S would not want to consider it as one of his or her actions. But S does not realize it. So S does not produce a repair statement of the type 'Oh, what did I say? I didn't really mean that.' The above remarks should suffice as a suggestive and rudimentary de­ scription of the compatibility of asserting thatp and not believing it (see, for a related discussion, Pollock 1982). Interestingly, in actual life, the possible dis­ crepancy between believing and asserting does not cause too many problems. Ceteris paribus, hearers simply assume that speakers are honest, non-rhetori­ cal, linguistically competent, minimally idiolectical, and responsible. So psychological meanings are the norm more than the exception. But they are not irrefutable. What is irrefutable, however, is that whenever S asserts that he or she loves pheasant, S speaks as if he or she believes that he or she loves pheasant. 2.1.3. S speaks as if he or she believes that ρ That S speaks as if he or she believes that ρ will be called a 'linguistic meaning'. Both 'speaking as if' and 'linguistic meaning' are technical terms that might be found objectionable. The problem with 'speaking as if/?' is that it carries a connotation of 'not-/?'. By definition, this connotation will be ab­ sent in my usage. Otherwise, I could not maintain that an assertion means that S speaks as if he or she believes that/?, whether or notthe assertion also means that S believes that/?. The trouble with 'linguistic meaning' is that one might doubt whether S's speaking-as-if should really be considered a meaning. Perhaps assertions are speakings-as-if. Speakings-as-if are the sorts of entities

48

SPEECH ACTS AND MEANINGS

that carry the meanings; they themselves are no meanings. My answer to this objection is threefold. First, granted that speakings-as-if are assertions, this fact does not yet preclude that speakings-as-if are meanings. To see this, re­ member the claim that when an event is an action, the event is interpreted as an action. Second, the idea that S speaks as if he or she believes thatp seems to develop naturally out of a consideration of what the meaning of an assertion would be at a level of generality that is one step higher than that of the psychological interpretation. This should make one think twice before dismiss­ ing something that one might not, at first sight, consider to be a meaning. Third, that there really is a point in maintaining that an assertion means that S speaks as if he or she believes that p becomes all too clear, when one considers an unknown language. Consider (6): (6)

phǒmậchôopphasǎathai 'I do not like the Thai language'

For those that do not know Thai, the speech act represented in (6) is impossi­ ble to interpret. Now I do not think that it is all that counterintuitive to say that it is an interpretative step, a true discoveryoFmeaning, should one find out that the sounds of (6) are used to speak as if one believes that one does not like the Thai language. When one confronts a familiar language, however, the deci­ sion that some configuration of sounds is to be taken as a speaking-as-if one believes thatp is a matter of course. Such decision taking has become our sec­ ond nature. One immediately jumps to the more problematical decision of whether S believes that/? and of whether/? is actually the case. There are two further reasons why linguistic meanings are interesting. First of all, if the speaking-as-if is defined in terms of grammar, the linguistic meaning is irrefutable. Thus the speech act of (3) irrefutably means that S speaks as if he or she believes that he or she loves pheasant. Of course, in a context where S mistakenly holds that turkeys are called 'pheasants', (3) may also mean that S speaks as if he or she believes that he or she loves turkey. But here the linguistic meaning is defined in terms of grammar and context rather than grammar alone (see Van der Auwera 1980b for some considerations on the (ir)refutable meanings ofUNgrammaticalutterances). Second, I claim that the linguistic meaning forms the conceptualization of the intention that speak­ ers have whenever they use assertions to mean something. In other words, I propose that when an asserter means /?, he or she intends to speak as if he or she believes that/?. This analysis is markedly different from analyses proffered by Grice (1957, 1968, 1969, n.d.) and Griceans (e.g. Schiffer 1972; Bennett

BASIC SPEECH ACTS

49

1976). Though a full-scale comparison is outside the scope of this study, some hints may be helpful. Grice's original idea is this: when S means something, he or she intends the utterance to produce some effect in an audience by means of the recogni­ tion of this intention. In the case of an assertion, the effect would seem to be a belief about a belief of S (. Grice 1971: 59), which one can argue to be noth­ ing but the understanding of what the assertion means (cp. Searle 1969: 47). Now, whatever the details of the description of the effect may be, I do not think that it enters the description of what it is for somebody to mean some­ thing. I do not deny, of course, that speakers often intend to produce an effect on their real or imaginary audience. But I believe that this is beside the point. I do not think that it is necessary to intend to produce an effect in order to mean something. Whether or not S uses an assertion to mean something depends on whether or not S intends to act in a linguistically meaningful way, where 'lin­ guistically meaningful' is a technical term referring to speaking-as-if one be­ lieves something. Another point of comparison concerns the roles assigned to S's meaning something. For Grice, S's meaning something is the pivot of the theory; it is logically prior to all the rest. In my model, however, S's meaning ρ can be re­ garded as just one more speech act meaning. Note that it is a refutable one, for speech acts never really require intentions. As S's meaning something thus only figures as one of a set of refutable speech act meaning, its role is much less crucial than in Grice's rnodel. Notice three more points. First, the analysis of what it is for S to mean something takes us back to the distinction between meaning proper and in­ tended meaning. What S means is nothing else than the intended meaning. But, paradoxically perhaps, that S means is a meaning proper. Second, there is an interesting analogy between the analysis of assertion and the general theory of action. What makes an event an action is the presence of mental states, viz. consciousness and intentionality. But this presence need not be ac­ tual. Even without consciousness and intentionality an event can have the meaning of an action. The event is an action if it is taken as if'it is accompanied by consciousness and intentionality. Similarly, the individuating characteris­ tic of an assertion is the mental state of belief. But the belief need not really be present for the speech act to qualify as an assertion. It is sufficient that the asserter speaks as if he or she believes. Third, it should sound acceptable by now to say that an assertion reflects a belief. But note that this claim is ambiguous. It could refer to the psychological or to the linguistic meaning. In the first case,

50

SPEECH ACTS AND MEANINGS

the reflected belief is truly present, independent of whether S speaks in order to reflect it. In the second case, the reflected belief only exists as a reflection, as the content of a speaking-as-if, independent of whether S truly believes it. 2.2. Imperatives, optatives, and interrogatives 2.2.1. The speech acts of non-belief... The preceding discussion has clarified how assertions can be said to re­ flect a belief. There are also speech acts that can be said to reflect the absence of a belief. Their psychological meaning has speakers not believe that p. To­ gether with assertions, these speech acts will be called 'basic speech acts'. As there are two ways of not believing that p, viz. believing that not-p and believ­ ing that possible/indeterminate-p (which amounts to the absence of the beliefs that p and not-p), there are also two basic speech act types other than asser­ tions, interrogatives and optative-imperatives. Yet the correspondence is not quite as perfect as the above phrasing suggests. An interrogative speech act al­ ways reflects a belief that it is indeterminate whether/?. An optative-impera­ tive speech act can reflect an indeterminacy belief as well as a belief that not-p. This calls for some examples. (7)

Is John going home?

(7) is an interrogative. S speaks as if he or she does not believe that John is going home. To be more precise, S speaks as if he or she believes it to be inde­ terminate whether John is going home or not. A different type of interroga­ tive is shown in (8): (8)

Who is going home?

The analysis of this example is more complicated: (8) means that S does not be­ lieve that the one or more individuals that might be going home are in fact going home. More precisely, S speaks as if he or she believes that it is indeter­ minate whether the one or more individuals that might be going home, are going home. The optative-imperative can be illustrated with (9) : (9)

John, go home.

The speech act in (9) means that its S speaks as if he or she does not believe that John is going home. It is left open whether S's speaking-as-if concerns a belief that John is not going home or a belief that it is indeterminate whether John is going home or not. Different subtypes of optative-imperatives are il-

BASIC SPEECH ACTS

51

lustrated below: (10) ( 11 ) ( 12)

Long live the king! If only the king lived now. If only the king had lived.

These speech acts all mean that their speakers speak as if they do not believe that p. (10) means that S speaks as if he or she believes it to be indeterminate whether or not the monarch will live to grow old. (11) is vague: it can reflect the belief that it is indeterminate whether the king is still alive, but it can also reflect the belief that the king is dead.31 In (12), S is interpreted to be speaking as if he or she believes that the king was no longer alive. I confess that the preceding analysis is perverse. One symptom of this perversity is that I have purposely missed the obvious point that (9) does not only reflect a non-belief, but also, and even primarily, a desire. Another symptom is that I have collapsed imperatives and optatives into one category, while the terminology clearly indicates that optatives and imperatives are dif­ ferent. But the perversity is strategic. I want to show just how surprisingly far one can get with the analysis of imperatives, optatives, and interrogatives, when one starts form the unorthodox view that they reflect the absence of a belief. But it is clear that the analysis must be supplemented. For one thing, the knowledge that a speech act is a speaking-as-if about an indeterminacy be­ lief does not yet distinguish between interrogatives and optative-imperatives. For another thing, the distinction between optatives and imperatives has been left vague. Before I come to a second analysis, one easy objection must be dealt with. Suppose one accepts that (7) means that S speaks as if he or she believes that it is indeterminate whether or not John is going home. But isn't this the meaning of the assertion in (13), too? (13)

It is indeterminate whether John is going home or not.

If this were the case, nothing would be said yet about the distinction between assertives and interrogatives. Yet the answer is a 'No'. Precisely because (13) is an assertion, it does not mean that S speaks as if he or she believes it to be in­ determinate whether p. It means that S speaks as if he or she believes that/7. Of course, the phrastic of (13) happens to express the very indeterminacy that (7) is all about. So (7) and (13) end up with a closely resembling meaning any­ way. But a close resemblance is not an identity. Mutatis mutandis, the same must be said about the relation between the assertion of (14) and the corre­ sponding optative-imperatives.

52

SPEECH ACTS AND MEANINGS

(14)

I believe that John is not going home.

2.2.2. ... are the speech acts of desire The preceding chapter has shown that a desire is in more than one way the converse of a belief. This makes it understandable why optative-imperatives and interrogatives cannot only be given a 'negative' characterization in terms of the absence of a belief, but also a 'positive' one in terms of the presence of a desire. Thus optative-imperatives mean that S speaks as if he or she desires something. Consider (15) and (16): (15) (16)

Stop! If only he would stop!

Both utterances mean that S speaks as if he of she desires somebody to stop. Interrogatives, too, mean that S speaks as if he or she desires something, and what S desires is nothing else than the converse of a desire, viz. a belief. The event represented in (17), for instance, (17)

Is the food good?

means that S speaks as if he or she desires to hold a belief about the quality of the food or, in informal terms, as if he or she wants to know whether or not the food is good. We also have a vocabulary for the secondary difference between impera­ tives and optatives. The crucial factors are desires and hearers. An imperative means that S speaks as if he or she desires something from the hearer. In other words, imperatives always convey an appeal to the hearer. Optatives do not express any appeal, neither to the hearer nor to anybody else. This approach should leave no doubt about the status of utterances of the types exemplified in (18) and (19). ( 18) (19)

I want to know whether John went home. I wish that John went home.

These speech acts show the assertive expression of what is reflected by the speech act type in interrogative and optative-imperative speech acts. In claim­ ing that (18) and (19) are assertions, I do not deny that they can fulfill the func­ tion of the related interrogatives and optative-imperatives. In many contexts, (19) is interchangeable with (20), for instance. (20)

If only John went home.

But notice that there are circumstances in which (19) can be used and (20) would be inappropriate. Only (19) can report on a habit, as in (21):

BASIC SPEECH ACTS (21)

53

Every single night I wish that John went home.

Notice also that this account is not invalidated by the fact that the characteris­ tic function of the optative of reflecting a desire may well be served more fre­ quently by the indirect means of asserting that one desires. 2.3. Basic speech acts Optative-imperatives, interrogatives, and assertives are basic in a very special sense. Their 'basicness' refers to some aspects of the meaning of speech acts, but not to all. If one maintains that (19) is an assertion, one is cor­ rect, but one also misses the important point that it often functions the way the optative in (20) does. Yet, as mentioned above, this is due to the particularity of the phrastic of the assertion. To recast the essential idea in terms of the refutability analysis: (19) and (20) may have the same refutable meaning that S desires John to go home. But their irrefutable linguistic meanings are differ­ ent. (19) irrefutably means that S speaks as if he or she believes that he or she wishes that John went home. (20) irrefutably means that S speaks as if he or she desires John to go home. This gives us the first characteristic of basic speech acts: their 'basicness' is defined in terms of an irrefutable linguistic meaning. The second property concerns mental states. The only mental states that the irrefutable linguistic meaning of the basic speech act may refer to are those of believing and desiring. This excludes speech acts like (22), (23), and (24). (22) (23) (24)

Hello! Thanks! Ouch!

(22), (23), and (24) may well be irrefutable as reflections of gratitude, plea­ sure, and pain. Yet, whatever their proper analysis is, it clearly cannot be put in terms of speakings-as-if, beliefs, and desires (alone). One could look for a third property by investigating whether basic speech acts are on a par with speech acts of greeting, thanking, congratulating, and many others, or whether a non-basic speech act always includes a basic one. If one opts for the first alternative, one ends up with what could be called the 'weak' version of the basic speech act concept. Many, but by no means all, ut­ terances would then involve basic speech acts. The second alternative yields the 'strong' version according to which every speech act is to be classified as either assertive, interrogative, or optative-imperative. In this perspective, (22), (23), and (24) would be considered to be assertives, admittedly peculiar

54

SPEECH ACTS AND MEANINGS

ones, rather than interrogatives or optative-imperatives. I am inclined to ac­ cept the strong version, but I will leave the matter unsolved. A somewhat related issue is that of the so-called 'explicit performatives', such as (25) and (26). (25) (26)

I order you to go home. I promise to go home.

Are they sufficiently different form basic speech acts, notable from asser­ tions, to claim that there is no level of description at which their S's assert something. Contrary to orthodox speech act theory, as represented by Austin (1975 [1962]) and Searle (1969), the only appropriate answer is that explicit performatives are assertions. But, of course, they are rather peculiar asser­ tions, just like (18) and (19). This completes my effort to dust off the assertive-interrogative-optativeimperative distinction. This distinction, I have argued, is not only a formal one. It is not an uninteresting remnant of traditional grammar either, viz. the distinction of mood. This distinction or, as I prefer to call it, this typology of basic speech acts should be a part of any serious account of meaning. I am by no means the first to propose a typology of speech acts, however, and I have not even shown that my typology is any better than the others (e.g. Austin 1975: 148-164; Searle 1975, 1976; Wunderlich 1976: 75-86). I further confess that my typology may be incomplete, the pending issue being that of 'Hello', 'Thanks', and 'Ouch'. And ultimately, its value can only be judged when it is tested as a valuable starting point for the study of the hundreds of things people do with language besides making basic speech acts. In other words, this hypothesis on basic speech acts can only prove its mettle when it is coupled to a theory of non-basic speech acts. So, if the language of the preced­ ing analysis sounded 'assertive', I have now added some words of caution. At present, the proposed typology is unorthodox for a couple of reasons. First, the number of speech acts is rather small.32 Of course, no great innova­ tive thrills are offered here: other work has been done with more or less the same orientation (e.g. Hare 1952, 1970; Tugendhat 1976: 510-512; Allwood 1976: 124-127; Lyons 1977: 745 ff.; Parret 1979b, n.d.a). Second, and more importantly, the non-assertives are not only characterized in terms of a desire, but also in terms of a non-belief. To reemphasize this point, I maintain that the absence of the belief that ρ belongs to the meaning of the non-assertive. When issuing an imperative, for instance, S must be taken to speak as if he or she does not believe that p. This characterization is not redundant. It cannot be de-

SEMANTICS AND PRAGMATICS

55

duced from the fact that S, when issuing an imperative, speaks as if he or she desires H to bring it about that ρ, for there is no incompatibility between desir­ ing and believing that/?. Incidentally, as non-assertives must be described in terms of a non-belief, one might expect that assertives need the converse analysis in terms of a non-desire. It is an intriguing feature of language that this parallel does not hold. Assertions that p do not mean that S speaks as if he or she does not desire that/?. Assertions that/? are simply non-committal about desires that/?. Some other general, unusual features of the typology are the explicit reflectionism, the refutability perspective, the notion of the speaking-as-if, and the ease with which the typology leads to an account of what it is for speakers to mean something. 3.

Semantics and pragmatics

The preceding pages have shown that a typology of basic speech acts is partially based on an understanding of the mental states of believing and de­ siring. In this way, speech act theoy is intimately connected with the theory of mind. There is nothing like 'autonomous linguistics' here. We have to think in an interdisciplinary frame of mind. In the same frame of mind, I will now make some general remarks on the structure of the theory of meaning. More par­ ticularly, I will make a proposal for a distinction between semantics and prag­ matics. The distinction will be argued for by taking certain issues which are generally agreed to be either semantic or pragmatic and by showing how the proposed delimitation both agrees with and justifies the communis opinio (for a comparison with other delimitation proposals, see Van der Auwera 1981a: 20-25). 3.1. Mental states versus conceptualizations The division I propose depends on whether or not it is essential to refer to a reflection of a speaker's mental state. If the answer is positive, then one is doing pragmatics. If the answer is negative, i.e. if one can abstract from the mental state reflection, then one is on semantic ground. Thus it is the job of the semanticist to describe how the meaning of the whole of a sentence like (27) depends on the meanings of its parts. (27)

Yesterday morning John slept late.

Typical questions are the following: What is the meaning of an adverbial

56

SPEECH ACTS AND MEANINGS

like 'yesterday morning' an immediate contribution to? How is the meaning of the adverbial itself composed? How does its composition and its contribution differ from those of other adverbials and other types of constituents? This composition problem can easily be studied without reference to a speaker's mental state. It is entirely irrelevant, for example, to know whether the speaker of (27) would believe and/or desire that John slept late or whether he or she only speaks as if. A second semantic problem is that of cases (or case roles). I am doing se­ mantics when I am discussing whether John is an agent, a patient, or an experiencer. Again, case-theoretical questions can be answered in abstraction from the mental states of speakers. The same goes for most lexicological problems. In other words, a lot of lexicology is semantic. It is a semanticist's duty to de­ scribe the differences in meaning between, for instance, 'sleep', 'doze', 'snore', 'nap', 'hibernate', and 'drowse'. A fourth semantic task, which is (largely) a disguised blend of the preceding ones, is to provide a theory of what sentences semantically imply and—if one believes in presuppositions—what sentences semantically presuppose. (27), for instance, semantically implies (28) and (29). (28) (29)

Yesterday John slept late. Yesterday morning John was sleeping.

I have stressed that the semanticist does not mention a speaker's mental state. He or she is not prohibited from doing so, however. I might say, for example, that whenever the speaker believes (27), he or she also believes (28). But the introduction of the speaker's belief is not all that revealing. In the same way that the belief of (27) is a 'refinement' of the belief of (28), the desire for knowledge represented in (30) is a refinement of the desire for knowledge represented in (31). (30) (31)

Did John sleep late yesterday morning? Did John sleep late yesterday?

The implication relation is independent of the type of mental state associated with the speech act. Similarly, the contribution of the adverbial 'yesterday morning', the meaning of 'sleep', and the case role of the one who sleeps are independent of whether the speech act reflects a belief, as in (27), or a desire for knowledge, as in (30). Each of the meaning phenomena is also indepen­ dent of any intention or consciousness that the speaker might experience or express while saying either (27) or (30). To sum up: A substantial part of the

SEMANTICS AND PRAGMATICS

57

theory of meaning of linguistic action can abstract from mental states. Let this be semantics. In pragmatics, however, mental states play a central role. Consider the problem of speech act typology once more. What does it mean to say (27) rather than (30)? Any answer, so I have argued in III.2, must somehow say that (27) generally means that the speaker believes that such-and-such, and that (30) generally means that the speaker desires to know something. As this difference in meaning concerns the linguistic reflection of mental states, it will be called a 'pragmatic' one. It is of interest to see that this perspective brings in a concept of action. I have just claimed that (27) and (30) generally mean that the speaker either be­ lieves or desires something. But 'generally' is not the same as 'necessarily'. The speaker may well say that John slept late and believe the opposite, be­ cause he or she does not know what 'sleep' means, for example. Yet, as I have amply argued before, even if the speaker does not believe that John slept late, the assertion still means that the speaker speaks as if he or she believes that John slept late. This speaking-as-if, an acting-as-if, is the link between the mere physical event and the mental state. Sounds only reflect mental states when mediated through an acting-as-if. Thus we see that the notion of action plays a central role in pragmatics, even though I do not — as is sometimes done in order to reflect that 'pragma' can mean 'action' — set out to define pragmatics in terms of an action concept. The mental state interpretation of pragmatics is helpful in dealing with other commonly called 'pragmatic' problems, too, among others that of prag­ matic presuppositions — these have to do with what speakers ('speak-as-ifly') believe to be shared knowledge (see Van der Auwera 1978b, 1979a). Another issue is that of the intended meanings (conversational implicatures). Here the pragmaticist studies the phenomenon that speakers often ('speakas-if-ly') intend to convey much more than is semantically implied by what they say (see Van der Auwera 1978a, for an overview of this type of research). It is important to see that the fact that pragmatics is defined in terms of a reflection of the mind, and that semantics does not have to refer to mental states does not imply that semantics does not describe a reflection of the mind at all. Indeed, there is more to the human mind that mental states. Somehow, a mind also houses concepts and conceptual patterns. These are precisely the sorts of things that semantics may be said to reflect. Take the assertion of (27) and the question of (30):

SPEECH ACTS AND MEANINGS

58 (27) (30)

Yesterday morning John slept late. Did John sleep late yesterday morning?

We have seen (in Chapter II) that mental states essentially involve a concep­ tualization. As far as one can tell from the speech acts, the conceptualizations of the mental states reflected in (27) and (30) are identical. The choice and the organization of the concepts seem to be the same. In both cases a concept of sleeping appears, and not of snoring or hibernating, and it is put in relation to a person called 'John' and to a time. That there is a very close relation with se­ mantics here does not need belaboring. Just what the relation is can be analyzed in two steps. First, I hold that the semantic struture of a language is a conceptual struc­ ture. Describing the meanings of 'sleep', 'snore', and 'nap', for instance, is conceptual analysis. Agenthood and patienthood are concepts, and the se­ mantic contribution of the adverbial 'yesterday morning' is a conceptual one. Second, for any particular speech act, the semantic aspects reflect conceptual aspects, but there need not be an identity. For assertion (27) and question (30), a conceptualization of John sleeping late is normal but by no means necessary. Perhaps, the speaker does not know the meaning of the word 'sleep'. Perhaps he or she associates 'sleep' with a concept of napping, which is really the meaning of 'napping'. Perhaps the conceptualization is indeed one of John sleeping late yesterday morning, but whereas the English language concept of a morning leaves it relatively vague when mornings start, the speaker's personal concept of a morning may include the specification that mornings start at six. Yet, whatever the precise conceptualization of the speaker's mental state might be, the speaker cannot help speaking as if he or she conceives of John sleeping late yesterday morning. So John's sleeping late need not 'fill up' the conceptualization itself, but it must be contained in the speaking-as-if of the conceptualization, which is nothing else than what was earlier called the 'phrastic'. So the phrastic of a speech act reflects the concep­ tualization of a mental state. But, to bring in my first point again, though phrastics are different from conceptualizations at the level of the individual speech act, at the level of the language the organizational principles of phras­ tics are the same as those of conceptualizations. The meaning of the word 'sleeping' is the concept of sleeping, although when speakers utter the word 'sleeping', there may not be a concept of sleeping in their minds at all, and even if there is one, it may be totally idiosyncratic.

SEMANTICS AND PRAGMATICS

59

3.2. Genetic reflection and focus I will now argue that the delimitation squares well with presently held views that the meaning embodied in the notion of subject is semantic and that of topic is pragmatic. To this purpose, I will first bring in the notion of genetic reflection again. In II.3.1,1 have claimed that concepts genetically reflect be­ liefs. That the Eskimos have their seven snow concepts could be due to the fact that generations of Eskimos have found it necessary to differentiate, in their beliefs, between seven kinds of snow. Connectedly, they have also been speaking about seven different types of snow. This explains the genesis of vari­ ous snow words, and the meanings of these words genetically reflect the speaking-as-if about different types of snow. Briefly — if I may be allowed to use the name of a discipline for what it studies—semantics genetically reflects pragmatics. To illustrate this slogan-like contention in a totally different way, the interpretation of a newly conceived metaphor concerns a conjecture about an intended meaning and is therefore pragmatic. But the metaphor can get genetically reflected in the semantic structure of the language: the metaphor 'catches on', and we eventually find the 'dead' metaphor as part of the vocabulary. To some extent, then, the semantic structure of a language is the conceptual sediment of the speech behavior of generations of its speakers. So much for genetic reflection; I now come to consciousness. Of the four mental states, consciousness is the only one that has not gone into the characterization of pragmatics yet. Furthermore, one may wonder what is so peculiarly interesting about it from a linguistic point of view. Psychology, confirming common sense, tells us that one cannot pay any atten­ tion to something without focalizing one's attention. William James' The prin­ ciples of psychology (1890) is by no means outdated in this respect: "Everyone knows what attention is. It is the taking possession by the mind, in clear and vivid form, of one out of what seems several simultaneously possi­ ble objects or trains of thought. Focalization, concentration, of conscious­ ness are of its essence." (James 1890: 403-404; my emphasis)

The very state of consciousness divides the object of consciousness into a focus (center, figure) and background (frame, ground). The psychological de­ tails need not detain us here. The assurance that focalization exists and is im­ portant, and a common sense understanding of what it is are sufficient. A speech act usually reflects what one is conscious of. If one says that John is in the kitchen, for instance, one speaks as if one is conscious of John's being in the kitchen. If focalization is really that essential a feature of con-

60

SPEECH ACTS AND MEANINGS

sciousness, it is not unreasonable to expect language to reflect focalization, too. This expectation, I believe, is borne out, and, given a framework in which the study of meaning in terms of mental state reflection is labeled 'pragma­ tics', this linguistically reflected focus could be called 'pragmatic focus'. The more common term is 'topic'. Thus, in (32), (32)

Speaking about John, did you see him at the show?

the 'speaking about' construction tells us what the speaker's alleged focus of attention is. It would seem that a pragmatic focus is entirely at the discretion of the speaker. So, in a simple speech act about an agent and a patient, the pragmatic focus may be put on either. Yet it is not inconceivable that speakers of a cer­ tain language fall into a habit of focussing on the agent more than on the pa­ tient, or conversely. Such pragmatic preference may eventually sink down into the semantic structure. The result is a language with a conceptual bias in favor of, say, agents and against patients. Ceteris paribus, its speakers will conceive of an action from the perspective of the agent. If pressed for an example of such a language, we do not have to look very far. English will do. That a speaker of English normally conceives of an action from the point of view of the agent is another way of saying that the active voice is unmarked, and the passive voice marked. It must be emphasized that I am no longer speaking about the real, psychological focus, nor even about its pragmatic re­ flection, the pragmatic focus. My concern is with the semantic, genetic reflec­ tion of the pragmatic focus, the proper name for which is therefore 'semantic focus' or, more traditionally, 'subject'. In its essential thrust, this is the argument that is detailed and tested against a range of languages in Van der Auwera (1981a, 1981b, 1983). For my present purpose, I only seek to suggest that my delimitation proposal is not only consistent with the present trend of semanticizing subject talk and pragmaticizing topic talk, but that it justifies that trend. If the mental states of be­ lief, desire, and intention are relevant for pragmatics, why isn't consciousness, the remaining member of the mental quadruplet? If focalization is that essen­ tial a characteristic of consciousness, why couldn't it be relevant for pragma­ tics, too? If the semantic structure of a language genetically reflects the prag­ matic facts, why could't it reflect the pragmatics of focalization?

CHAPTER IV TOWARDS A REFLECTIONIST AND CONDITIONTHEORETIC LOGIC

"The foundations of logic should be obvious and compelling." (Ellis 1976: 187)

In the preceding chapters, I have laid some of the foundations of 'NeoSpeculative Grammar', in particular of its 'Reflectionist Logic' (henceforth 'RL'). These foundations comprise an ontology (Chapter II), a reflectionist philosophy of mind (Chapter II), and some general considerations on the se­ mantics and pragmatics of language (Chapter III). The present chapter is con­ cerned with the properly 'logical' foundations of RL. It starts out with the socalled 'philosophical' question of what logic is all about. My own, reflectionist answer will be used both as an instrument to understand the emergence of the various non-reflectionist answers and as the backbone of RL. These founda­ tional issues will then feed into a so-called 'condition-theoretic' theory of truth and truth-value. 1.

The basis of logic

'What is logic?' is the philosophical question of the present section. Note that the question is somewhat ambiguous. It could mean 'What is this thing that is called "logic"?' or 'What is logic for meV ('What do I want logic to be?'). Both issues will be dealt with here, but in strict separation. An issue that will not be taken up, however — though some of its terminology and ar­ gumentation is also used for the questions that concern us here—is the prob­ lem of the acquisition of logical knowledge (see, for some discussion, Pollock 1974: 302-340). 1.1. Contemporary logic 1.1.1. What logicians do There is a sense in which it is unclear for any discipline what it is about. Within every discipline there are usually competing paradigms defining dif-

62

REFLECTIONIST AND CONDITION-THEORETIC LOGIC

ferent routines and goals. Furthermore, these paradigms change all the time. Also, the amount of so-called 'knowledge' amassed within a certain paradigm is usually taken to grow. Since the answer to the question of what a discipline is about is a function of paradigmatic competition and change as well as of growth of knowledge, it necessarily involves a measure of vagueness. This is perfectly acceptable. Of course, the measure of vagueness should not be too large. There should be sufficient agreement between the paradigms about the basic goals and the ways to reach those goals. Just when the vagueness be­ comes unacceptable is unclear, but the following correlation seems to be obvi­ ous: the higher the vagueness, the more unacceptable the state of the disci­ pline. A completely inadmissible situation is that of a discipline whose subject matter can only be defined as whatever its supposed experts happen to be in­ terested in. An example of such an empty definition would be to say that sociology is the investigation of what so-called 'sociologists' study. This is only an example: I make no claims about the state of sociology. Let me make a claim about logic though: I believe that the answer to the question of what logic is about, approaches the empty definition that logic is what 'logicians' do. This is not to say that there are no theories dealing with the question of what logic is about; there are, but there does not seem to be a sufficient over­ lap. The casual observer, the linguist 'who wants to know all about logic but is ashamed to ask' (cp. the title of McCawley 1981), and the logician who is too immersed in present-day orthodoxies may well find my judgment overly and unjustifiable severe. Let me therefore support it with a small anthology of ci­ tations: "logicians themselves continue to differ widely as to the nature, the function, the value, and even the existence of their science." (Schiller 1912: vii) "Though the content of almost all logic books follows (even in many of the il­ lustrations) the standards set by Aristotle's Organon — terms, propositions, syllogism and allied forms of inference, scientific method, probability and fallacies — there is a bewildering Babel of tongues as to what logic is about. The different schools, the traditional, the linguistic, the psychological, the epistemological, and the mathematical, speak different languages, and each regards the other as not really dealing with logic at all." (Cohen and Nagel: 1934: iii; cp. M.R. Cohen 1944: ix) "Whether one looks at different treatments of modern logic or at textbooks of the subject since they first began to appear about thirty years ago, one is left without any explanation of the goal of the whole subject. There are vari-

THE BASIS OF LOGIC

63

cms bits and pieces but their interconnectedness is not always evident, nor is it clear what are the central problems to which logic is devoted." (Wisdom 1964: 116) "The great developments in what is justly called 'non-quantitative mathema­ tics' ... during the last hundred years have obscured what must surely be re­ garded as the continuing crisis in the foundations of formal logic. This crisis is most visible in the simple fact that among the best minds in the field there is radical, categorical disagreement upon what things are mentioned and analyzed in the field, and upon what their essential properties and relations are. Between some investigators the divergence is strong enough to warrant a parallel in imagination with, for example, theoreticians in music who are un­ able to agree upon whether they were theorizing about tones and their inter­ relations or black marks on staff lined paper." (Willard 1979: 158; . 144145,152-160)

Before I try to substantiate my point any further, I will adduce some reasons — not all of them philosophical33 — for why relatively few people seem to worry about "the continuing crisis in the foundations of formal logic" (Willard). In doing this, I will be impartial to any particular theory about the basis of logic. First of all, the definition of the subject matter of a science always in­ volves some vagueness. Moreover, the distinction between acceptable and un­ acceptable degrees of vagueness is a fuzzy one. This may excuse some of logic's defects. Another extenuating circumstance may be found in the fact that the de­ finitional problems of logic are rather similar to those of other disciplines. Just like the philosophy of mind and ontology, for example, logic can be defined in realist, mentalist, or nominalist ways. Now, if philosophers of mind and ontologists do not seem to bother too much about the lack of agreement of what they are doing, why should logicians be troubled? Third, among logicians there is a considerable degree of agreement about how to do logic or, more specifically, about the formal, mathematical aspects of their business, despite the divided opinions on the 'what' questions. Mates (1972: 3) has noticed this too: "Yet at the same time it is necessary to acknowledge the fact that logicians do not agree among themselves on how to answer the seemingly fundamental questions here treated. As concerns the formal developments there is re­ markably close agreement, but any question bearing on 'what it's all about', tends to bring forth accounts that are very diverse."

In my view, this agreement may have clouded some of the real issues. Coupled

64

REFLECTIONIST AND CONDITION-THEORETIC LOGIC

with an inevitable conservatism,34 it can easily give logicians the feeling that they are moving in the right direction and that they should continue whatever they were doing, even if there is anything but agreement on what they are doing. Another point, to be elaborated later, is that the communis opinio on formal matters may have given rise to the minimalist view of formalism, ac­ cording to which logicians should only deal with formal matters. The very emergence of formalism then consolidates the formal agreement even more. Fourth, a possible result of the consensus on the formal matters and the emergence of formalism could have been that the discussions about what logic is are usually confined to introductory or concluding chapters, or to ancillary papers, none of which are felt to be dealing with logic itself, but only with the philosophy of logic. Of course, there is nothing inherently wrong in consider­ ing the question 'What is logic?' to be a philosophical one. In actual fact, however, this boils down to 'solving' the problem by moving it into another discipline. Fifth, the consensus on formal developments implies that there is a part of the logical enterprise that is independent of the empirical question of what logic is about. Since this part is quite large, it puts the logician in the comfort­ able but delusive situation where many of his or her claims are simply irrefut­ able by any kind of empirical considerations. Logicians have thus largely im­ munized themselves against all but formal mistakes; empirical uncertainty has become empirical immunity.35 Sixth, the fact that the logician is impregnable against empirical attack contrasts sharply with the extreme vulnerability of those of us that are empiri­ cally preoccupied. Another shrill contrast is that between a logical language, constructed according to the logician's canons of precision and beauty, and a natural language, which is continually rising out of its own ruin and which con­ fronts the linguist with its vagueness and opaque complexities. It is easy to see how such contrast could contribute to the logicians' superiority complex. Seventh, many of the logicians' claims are actually intuitively plausible, irrespective of their views (if indeed they have any) on the basis of their logic. In most, if not all varieties of sentential logic, for example, the logician defines something that is very much like the ordinary language 'and'. This operator, combining simple sentences into a complex one, lets the complex sentence be true if and only if the simple sentences are true. Such a definition, one will admit, is intuitively sound.

THE BASIS OF LOGIC

65

1.1.2. What philosophers of logic say The empty definition of the subject matter of logic — logic as whatever the logicians use their routines on—was claimed to be related to the impossi­ bility of finding a relevant, common denominator for the available view­ points. These viewpoints are those of realism, mentalism, nominalism, in­ strumentalism, and formalism. Let us now have a closer look at them. For a realist, the logical laws tell us something about the nature of the uni­ verse.36 Some logicians associated with this view are Frege — at least in his later period (see Resnik 1979) —, the early Russell, M.R. Cohen in combi­ nation with the early Nagel, and Quine. "Logic is concerned with the real world, just as truly as zoology, though with its more abstract and general features." (Russell 1919:169)37 "From this point of view, logic may be regarded as the study of the most gen­ eral, the most pervasive character of both whatever is and whatever maybe." (Cohen and Nagel 1934: 185-186) "The quest of the simplest, clearest overall pattern of canonical notation is not to be distinguished from a quest of the ultimate categories, a limning of the most general traits of reality." (Quine 1960:161)

Mentalism, which is usually called 'psychologism', comes in two versions. According to its descriptive variety, which was one of the standard views from Antiquity till the end of the 19th century, logic describes the laws of thought, the principles according to which our mental processes are normally or­ ganized. Here is an unambiguous statement: "In this perspective logic is the physics of thought or nothing at all." (Lipps 1880:531; my translation)

It must be mentioned that my definition of descriptive mentalism is unusally wide. It is not uncommon to find an 'anti-psychologism' according to which logic is not really about thinking itself but only about what is thought, about the contents of thought (cp. Blanché 1967: 127-128). I see no reason not to consider this a descriptive mentalism. What is truly different, however, is the prescriptive variety of mentalism. For the prescriptivist (e.g. Freeman 1967; S. Haack 1978), logic is about the norm of thinking: it does not describe, but only prescribes; it tells us how to think. All this is not to say that descriptive and prescriptive mentalism are in­ compatible. Harré (1972: 2) combines them as follows:

66

REFLECTIONIST AND CONDITION-THEORETIC LOGIC "once the principles of logic have been extracted from examples it is inevita­ ble that they should be used as canons, that is to express the standards to which reasoning should conform."

Another example of the closeness of descriptive and prescriptive mentalism is furnished by Peirce. Though Peirce has been claimed to espouse prescriptivism (see S. Haack 1978:238), Michael and Michael (1979:87) have recently concluded that Peirce held that logic is normative, though not prescriptive. The point of this distinction becomes clear once we find out what Peirce has to say about logical norms: "we all have in our minds certain norms or general patterns of right reason­ ing, and we can compare (any) inference with one of those and ask ourselves whether it satisfies that rule." (1974: 332)

and about norms in general: "I never use the word norm in the sense of a precept, but only in that of a pat­ tern which is copied, this being the original metaphor." (1974: 323)

Norms certainly guide us, but they are not merely prescriptions. They are somehow part of the mind and they are 'waiting' to be described. Ever since the Greeks, for whom 'logos' meant both 'thought' and 'lan­ guage', mentalism has been competing with or complemented by nominalism.38 Nominalism may be combined with mentalism in a concep­ tualism (see e.g. Ellis 1979). When logicians subscribe to a pure nominalism, they hold that the logical principles are to be regarded as descriptive of the meanings (or parts of the meanings) of certain words. Clear nominalist cre­ dentials are offered by the Soviet philosopher Zinov'ev: "The conventions of logic are considered as explanations of the conventions that have developed in language."(Zinov'ev 1970:114; my translation)

According to the instrumentalist39 position, logic is fundamentally the in­ strument of the sciences, constructed by the logician, and deviating therefore, at least in part, from ordinary parlance. The most prominent spokesman of in­ strumentalism nowadays is Quine, who combines it with his realism. The later Nagel (1949) is a partisan of an anti-realist instrumentalism. Note that this four-way typology of the definitions of logic is related to, but also different from the three-way typologies of the definitions of the philosophy of mind and of ontology. For the latter two disciplines, even though they are both to some extent instrumentalist, there is no instrumen­ talist definition: ontology and philosophy of mind are by no means defined as instruments of the sciences. A second difference is that the mentalism of logic

THE BASIS OF LOGIC

67

— by contrast to that of the philosophy of mind and of ontology — splits up into a descriptive and a prescriptive variety. A third difference, already adum­ brated above, has to do with the lack of convergence of the logical positions. While the philosophy of mind gets defined as a study of the mind, of our think­ ing about the mind, or even of our talking about the mind, logic is not similarly defined as the study of the general features of reality, of our thinking about these general features, or of our talking about them. Instead of being a theory about our thinking about the most pervasive traits of reality, a mentalistically conceived logic is a theory about thinking as such. And the meanings of the words that form the subject matter of a nominalist logic are not taken to refer to the general traits of reality either. Some of them, called 'syncategorematic', are even thought to have no meaning at all when they occur in isolation. What­ ever meaning they have would only come from combining them with words that do have a meaning in isolation. A fourth difference separating the de­ bates about the status of ontology and the philosophy of mind from those on logic is that the latter involves yet a fifth position, viz. thatoFformalism. For the formalist, logic only deals with the symbols, the manipulations, and the systems that it defines. Logic does not refer to anything outside itself, just as abstract art, for some critics and artists, does not refer to anything beside art itself either — I owe this comparison to Nauta (1974: 12). I suspect that there is an interesting historical connection between the emergence of formalism and the fact that actual logics are largely invariant under the different answers to the question of what logic is all about. For­ malism can be regarded both as an explanation and as a canonization of this situation. Its explanatory potential stems from the formalist assumption that logic fundamentally is not concerned about either reality, mind, language, or science, but only about itself. Thus it is no longer surprising that realists, mentalists, nominalists, and instrumentalists find themselves agreeing on the question of how to do logic, for, as formalism explains, the proper business of logic is 'how' business. Yet, the roles of explanans and explanandum might well have to be reversed. This is where canonization comes in. I have a hunch that logicians just happened to find themselves disagreeing on the substantive side and agreeing on the formal side, and that this situation was then canonized. When the 'is' of the formal agreement combined with a disregard for the substantive disagreement into an 'ought', the result was formalism. Rather than explaining this historical situation, formalism derives its expla­ nation from it. This may look like a chicken-and-egg problem, but it is an utterly serious and decidable one.

68

REFLECTIONIST AND CONDITION-THEORETIC LOGIC

There are other factors that may have contributed to the emergence of formalism. Blanché (1967: 20-23) has drawn attention to the phenomenon that a scientific methodology, originally defined in terms of an independently conceived subject matter, may gradually redefine that subject matter as what the methodology can deal with. Applied to logic, the process produces a logic whose subject matter consists of what the logical routines can cope with. Perhaps the formalist view that logic is about logic is due, at least in part, to a 'perverse professional modesty', as M.R. Cohen (1944: ix) has suggested. Yet another important factor for the appearance of formalism may have been the close link between logic and mathematics. Notice, though, that merely declar­ ing that logic is mathematics or at least the same sort of thing as mathematics does not yet imply a formalist outlook. One still has to say what mathematics is about, and, not surprisingly, the debate on the foundations of mathematics features versions of realism and mentalism, too. In any case, formalism seems to be a paradoxical position. The point of the 'about' question, one might say, is to find out whether there is anything outside of logic that logic can be considered to be about. Still, if this is an ob­ jection to formalism, it is not strong enough, for self-reference is after all a form of reference, too. A second, and really devastating objection to for­ malism, however, is this. An abstract painting is always made up of plain ter­ restrial colors and patterns. So, even though it may not refer to a concrete ob­ ject like a tree, it at least necessarily refers to shapes and shades. It also neces­ sarily involves a reflection of the artist's conception of these shapes and shades, a conception which, furthermore, is expressed in an artistic language of some sort. So purely abstract ('cutoff') art does not exist. It always reflects a language, a mind, and a reality. In the same way, I would claim that there is no abstract or formalist logic. Formalism, being untenable, reduces to a combi­ nation of realism, mentalism, and nominalism. Realism comes in because the structures the logician defines are the possible structures of his or her own uni­ verse and not, by any means, those of another universe. But mentalism comes in, too. Despite the fact that the formal structures of the would-be formalist logician are not intended as a description of valid reasoning, a weak men­ talism is inevitably involved, in the sense that the formal structures are after all, concocted in the logician's own mind. Therefore, the study of the formal structures is also a study of the mind, of the thinkable. In the same way, for­ malism floats on a weak nominalism. All of logic is necessarily represented through the medium of a language, be it a technical one. So, in a sense — a very weak sense — would-be formalist logic reflects what can exist, what the

THE BASIS OF LOGIC

69

logician can think about, and even what he or she can talk about. This peculiar mixture of realism, mentalism, and nominalism will be termed 'weak descrip­ tivism' ; 'weak', because it is only an unwanted consequence of the simple fact that logic is a mental activity expressed in a language about something. 'Weak' captures the weak sense in which a logician who does not want to describe re­ ality, mind, or language cannot escape doing it anyway. However trivial and uninteresting the idea of weak descriptivism may seem, I think that it wins over the idea that logic is about logic. Furthermore, I believe that it proves valu­ able for characterizing the sum total of the other positions. Before I de­ monstrate this, however, I will have a closer look at an attitude that is some­ what akin to formalism, and that is sometimes embraced by instrumentalists and prescriptive mentalists alike, viz. anti-descriptivism. Anti-descriptivism denies that prescriptivist or instrumentalist logic de­ scribes anything that exists independently of, and prior to the construction of the logic. At first sight, the case for anti-descriptivism seems to be a plausible one. Ordinary language, the logician will point out, is too vague, ambiguous, and incomplete to be considered the subject matter of the fully precise and explicit canons of inference that logicians would like to establish. Nagel puts it as follows: "No known recent system of formal logic is or can be just a faithful transcrip­ tion of those inferential canons which are embodied in common discourse, though in the construction of these systems hints may be taken from current usage; for the entire raison d'être for such systems is the need for precision and inclusiveness where common discourse is vague or incomplete, even if as a consequence their adoption as regulative principles involves a modification of our inferential habits." (Nagel 1949: 205)

That ordinary language is vague cannot be denied. But that does not force us to trade description for prescription. Why couldn't the vagueness, ambiguity, and incompleteness of ordinary language be given an explicit and precise description? Why couldn't we provide its ambiguous and incomplete constructions with various unambiguous and complete readings? I do not see any reason why the rules of inference that the prescriptive mentalist or the in­ strumentalist is interested in could not be stated in relation to just such read­ ings. It is true, for example, that the word 'and' has different meanings and uses. But why couldn't we give an accurate account of the one meaning or use (or set of meanings or uses) that is involved in the inference form 'p and q' to 'q and p'? Conclusion: Even if one worries about vagueness and ambiguity, and if one sets oneself prescriptive or instrumentalist goals, one need not let

70

REFLECTIONIST AND CONDITION-THEORETIC LOGIC

go of descriptivism. But this conclusion may not have fitted the historical con­ text. Until recently, many linguists had barely started to investigate meanings; some had even made a point of not investigating them. No wonder, then, that ambiguity and vagueness remained outside the logician's purview as well. Nowadays, some logicians no doubt embrace the anti-descriptivist attitude for no other reason than that it has become an orthodox one. But an historical excuse, even when canonized, is not a rational justification.40 Yet, as the last lines of the quote from Nagel already suggest, one may also rely on the vagueness and even inconsistency of actual reasoning rather than language to validate one's anti-descriptivism. Here is a recent spokes­ man: "The initial 'practice of reasoning' with whose systematization logic com­ mences is very diversified, variegated, and largely inconsistent (perhaps even less uniform than linguistic practice)." (Rescher 1977: 244) "The construction of a logic to systematize inferential practice is not a purely descriptive project. Logic makes emphatically normative claims about right and wrong in the context of inference and argumentation ... Accordingly, logic does not slavishly summarize the presystematic practice which provides its basis. At every stage of its development it criticizes its practice, rejecting some of it as unworthy of serious attention (exactly as grammarians of the old school reject some sectors of actual linguistic practice as improper). Thus logic does not simply reflect our inferential intuitions, it also re-educates them." (Rescher 1977: 260)41

There is undoubtedly a lot of consistent or muddled thinking in this world, and not just because of the way we use language. How can a descriptive logic account for this? For S. Haack (1978: 241-242), the existence of logical error is the difficulty for descriptive mentalism. But is the problem really that formidable? I do not think so. For one thing, the logician can learn something from psychology, at least from psychology that does not pay lip service to logi­ cal anti-psychologism. Henle (1962), for instance, has persuasively suggested that many so-called 'logical' mistakes do not result from faulty reasoning at all, but only from a misunderstanding of, or an influence from what is to be reasoned about. For another thing, if logicians, instead of comparing them­ selves to the prescriptive grammarians of the old school, turned to some rep­ resentatives of the newer schools, they might learn or be reminded of a very simple idea.42 In the wake of Chomsky, many linguists have maintained that one must not confuse linguistic competence with linguistic performance, and that both of these are empirical objects. Analogously, I suggest that one could distinguish between a competence to reason (logical competence) and the

THE BASIS OF LOGIC

71

acutal performance of reasoning (logical performance),43 both of which are conceived of as empirical objects. But only one of them, to wit, logical compe­ tence, provides logic with a subject matter. Thus we have a partial solution to the problem of logical error, for the distinction between competence and per­ formance implies that not all performance happens in full accordance with competence. I admit, however, that the solution may only be partial. It is not impossible that the internalized system of logical rules which makes up the logical competence is inconsistent, such that a strict adherence to one set of rules may lead to breaches of another set. This is a problem for empirical in­ vestigation. At present, I only want to argue that the existence of logical mis­ takes does not warrant any apriori dismissal of descriptivism. So apriori anti-descriptivism fails. Yet it is very pervasive. It can even be found when logicians seem to take up a descriptive stance. Zinov'ev is not atypical. I have earlier described him as a nominalist. Yet, if I embed his nominalist credentials (italicized in the following) in their context, his descrip­ tivism becomes doubtful. The science of logic investigates those signs [the logical words of natural lan­ guage] and their rules; it makes corrections and distinctions; it takes away ambiguities, discovers hidden properties, establishes connections between signs, etc. ... The conventions of logic are considered as explanations of the conventions that have developed in language. How close the two convention types really are is another question, and a difficult one (one of the problems is that of the 'paradoxes of material and strict implication')." (Zinon'ev 1970: 114; translation and emphasis mine)

Here is another citation documenting Zinov'ev's ambivalence: "One shouldn't simply consider the results of logic as descriptions of the ordi­ nary instruments of language {although logic does fulfill such a function)". (Zinov'ev 1970: 91; translation and emphasis mine) 44

The Zinov'ev case also serves to reintroduce the problem of logic's in­ variance under the question 'What is logic?' We have already discussed a number of reasons why logicians have seldom worried about this problem. There is one more reason, however, that needs mentioning. I have claimed that a would-be formalist logic is weakly descriptive of reality, mind, and lan­ guage, even if it professes to talk only about things logical. At the weakly de­ scriptive level, therefore, the debate between realism, mentalism, and nominalism is pointless, for, in a weak sense, each of them is correct. Now, if even logics that are supposed to describe or prescribe nothing except them­ selves are weakly descriptivist, then surely all of modern logic is weakly de-

72

REFLECTIONIST AND CONDITION-THEORETIC LOGIC

scriptivist. But again, only weakly descriptivist. Any normal, strong descrip­ tivism is invalid. It is easy to see that full-bodied nominalism falls short of the mark as a description of the whole of modern logic. Indeed, much of modern logic is to­ tally irrelevant for the study of language, and even the bits that are relevant often turn out to be descriptively inadequate. The same goes for mentalism. 20th-century logic hasn't provided us with an adequate theory of valid infer­ ence: just think about the paradoxes of implication and the unsuccessful at­ tempts to solve them. By contrast, realism may seem to fare a little better. In­ deed, present-day logic can plausibly be interpreted as the study of the possi­ ble structures of reality. Yet, this interpretation is hampered by the vagueness of the word 'possible': what is, in fact, not possible, when even the impossible is, in a sense, possible? Furthermore, this near-trivial realist interpretation al­ lows for the watered-down mentalism and nominalism that combine into a weak descriptivism. Again, we conclude that modern logic can be charac­ terized as weak descriptivism, only weak descriptivism. This general conclusion, by its emphasis on the weakness of the descrip­ tivism and by its explicit reference to reality, mind, as well as to language, parallels the tenor of De Pater's view on the nature of logical laws: "The most reasonable thing to say, so it seems to me,... is this: one can hardly or perhaps one cannot express what logical laws say; yet they somehow show something — the vagueness is deliberate — which has to do with the formal, structural characteristics of the world, which are reflected in both language and thought". (De Pater 1979: 641; my translation)

Notice that De Pater claims that both language and thought reflect the world. He is thus preparing the ground for the type of logic that interests me most, viz. reflectionist logic. 1.2. Reflectionist logic Logic is a product of a human cognitive and linguistic activity that is es­ sentially about something other than itself. This is what 'weak descriptivism' is all about. 'Strong descriptivism', on the other hand, I take to be a combination of full-bodied realism, descriptive mentalism, and nominalism, where each of these is taken at its full and original value. This is to say that a logic engendered by strong descriptivism should be descriptive of certain general traits of real­ ity, of the canons of valid inference, as well as of the meanings of certain ordi­ nary language words. It is strongly descriptive logic that I want to engage in. Let it be clear that my advocacy of Strongly Descriptive Logic (hence-

THE BASIS OF LOGIC

73

forth 'SDL') does not imply that I want to redefine logic as such. However slightingly I have spoken about modern logic as a whole, its weak descrip­ tivism is justified in its own right; besides, it houses many interesting schools. Since, furthermore, I am committed to fallibilism and pluralism, as a fallibilist, I am fully aware that my strongly descriptivist project may fail, and as a pluralist, I fully accept that other people try out different roads. In the totality of modern logic, SDL represents an addition. Of course, SDL is not altogether new; for one thing, it endorses realism. Now, realism as such is not new, but perhaps its combination with a full-bodied descriptive mentalism and nominalism is. As for descriptive mentalism, I have already mentioned that it was one of the dominant views until the breakthrough of modern logic at the end of the 19th century. Though our century has so far been dominated by such anti-mentalist giants as Frege, Husserl, Wittgen­ stein, Ryle, and Popper, the mentalist tow has always been present, both in theory and in practice. More importantly, we are now witnessing a new up­ surge of mentalism. It is due not only to the intuitive appeal of the mentalist idea itself, but also to the new respectability of all kinds of non-extensionalist logics and to recent, beginning (and fast spreading) criticisms of the anti-mentalists.45 Further, one can point to today's generation of psychologists, who have been testing out logic in experimental work on how people actually reason,46 and to the influence of Chomskyan and post-Chomsky an linguistics. SDL also reinstates nominalism. The latter has its contemporary follow­ ers, too; view the strong nominalist streak in some very recent logic. Since the late sixties, certain logicians and linguists — Montague Grammarians, for example — have been engaged in a joint effort to refine the standard systems in view of an application to the study of natural language. If these workers are willing to not only enrich the orthodox systems but to modify them, however thorough a modification the norm of descriptive adequacy will call for, then these attempts may ultimately lead to the same results that work on SDL is supposed to lead to. It is necessary to stress that the starting points are differ­ ent, however. The sophisticated logical systems in question start off from logi­ cal orthodoxy. SDL does not. There seem to be three possible ways to justify the SDL idea. One could try to giveapositive reason for setting up an SDL program. One could also at­ tempt to refute all possible objections against it. A third justification strategy could consist of actually constructing an SDL. The latter strategy will occupy me later. The second has been given some consideration in the preceding subsection. Let me now turn to the first type.

74

REFLECTIONIST AND CONDITION-THEORETIC LOGIC

My positive reason for suggesting SDL is this: I believe that realism, de­ scriptive mentalism, and nominalism are all correct, but only partially so, and that they are fully correct, but only jointly so. The means to join them is noth­ ing but the reflection thesis. I claim, then, that the subject matter of SDL consists of certain structures of reality that are reflected in the principles of valid reasoning as well as in the meanings of certain words. As a tribute to reflectionism, SDL will also be called 'Reflectionist Logic' ('RL'). So reflectionism is my positive reason for adopting theSDL/RL ap­ proach. But do I have any (positive) reason for reflectionism? My answer is double. A priori, I cannot help finding it plausible that certain general charac­ teristics of our universe are reflected in the canons of valid reasoning and in the meaning of certain words. This a priori judgment then functions as a re­ search program, as a hypothesis to be verified or falsified. A posteriori, after the research conducted so far, I can report corroborating evidence and no in­ dications to the contrary. I will not try to persuade anybody to share my a priori intuitions on the feasibility of RL, but part of what follows can count as a defense of my a posteriori grounds. Notice that the reflection thesis provides RL mentalism with realist foun­ dations. This is an important feature of RL mentalism, for one of the main anti-mentalist lines of attack, championed by Husserl, has been that the logi­ cal laws are too stringent to rely on habits of thinking only, even when re­ stricted to certain habits of thinking.47 The rejoinder to this objection is that RL does not make logical laws rely on habits alone. These laws are just as basic and rigid as the general characteristics of reality that they reflect. A further, interesting consequence of these realist foundations is that the differ­ ence between performance that accords with competence, and performance that does not, has a normative connotation. Invalid reasoning is an improper use of language and mind. In this way, RL allows me to have prescriptivist leanings, too. I fully subscribe to the combination of descriptive and prescrip­ tive mentalism as advocated by Harre and Peirce, and presented in IV. 1.1.2.1 also espouse instrumentalism; after all, science can be characterized as wellreasoned (mentalism) language (nominalism) about the universe (realism). It is implicit in the preceding considerations that I insist on the continuity between the philosophy of the subject matter of RL, and RL itself. In con­ tradistinction to much contemporary work, our foundational discussions are not confined to the philosophy of logic, but are expected to guide the con­ struction of the logic. Nevertheless, there is a sense in which RL, just like weakly descriptivist logic, is independent of its realist, mentalist, and

THE BASIS OF LOGIC

75

nominalist, in short, of its empirical interpretations. By force of the reflection thesis, RL is such that when it meets one of its empirical interpretations, it necessarily meets all of them. Suppose, for example, that RL can indeed be in­ terpreted as a partial theory of valid reasoning. The structures that it accounts for then can also be interpreted as linguistic structures and as structures of re­ ality. This peculiarity, the fact that the subject matter of RL is really invariant under all three interpretations, gives it a delusive independence. RL does not depend on any one interpretation more than on another. It is misleading, however, to conclude that it does not therefore depend on any interpretations at all. The conception of RL advanced above is profoundly absolutist, monis­ tic, and universalist. In other words, I hold that the principles of logic are unal­ terable and universal. This is not in contradiction with my earlier avowed pluralism. One must be careful with 'pluralism'; the term has been applied to logic in at least three different ways. The pluralism represented by R. Haack (1978) and called 'local pluralism' by S. Haack (1978: 223ff.) is one that I do not advocate; it embodies the thesis that we should not look for one basic logic. There would not be one set of logical principles, but different sets applicable to different aspects of the universe, cognition, discourse, and sci­ ence. Though I do not subscribe to this, I naturally admit that the universe in which we are living, which we are thinking and talking about, could have been a different one, and also that it may change. However, it is our present uni­ verse that is the standard for my universalism. In this respect, my views are ut­ terly conservative. There is another type of pluralism, which has affinities with what S. Haack (1978: 233ff.) calls 'global pluralism', viz. the view that a set of logical principles can be classified in various ways. Each of these subgroupings would be the subject of a separate 'logic'. So there could indeed be many logics — to name just a few: propositional logic, predicate logic, and epistemic logic. In this respect, every modern logician is probably a pluralist. Finally, there is an epistemological pluralism, one that is closely wedded to fallibilism and which I whole-heartedly endorse. It says that one should have an open and experimental mind. There are no monopolies, and we are all allowed to try. All our proposals are (based on) fallible conjectures. A beautiful, though over-optimistic declaration that shows how an epistemolog­ ical pluralism can go hand in hand with absolutism as well as with an empirical perspective has been issued by Lukasiewicz (1970: 233 [1936]):48

76

REFLECTIONIST AND CONDITION-THEORETIC LOGIC

"I am convinced that one and only one of these logical systems is valid in the real world, that is, is real, in the same way as one and only one system of geometry is real. Today, it is true, we do not yet know which system that is, but I do not doubt that empirical research will sometime demonstrate whether the space of the universe is Euclidean or non-Euclidean, and whether relationships between facts correspond to two-valued logic or to one of the many-valued logics."

So much for a general, programmatic statement on reflectionist and strongly descriptive logic. The programmatic tenor suggests that we are on to something new. However, as I have already documented, the idea of an RL depends on many old ideas. Thus my logical reflectionsim is not entirely new. In its essence, it is not too remote from the underlying ideas of the Scholastic Speculative Grammars. As noted at the close of IV. 1.1.2, the reflection idea also occurs in De Pater (1979). Further, it makes a casual appearance in the work of Hasenjaeger (1962: especially 6) and allows the latter to combine realism and nominalism but not mentalism. Close, too, is the view of Cornforth (1954: 61-64). His 'principles of reflection' are principles about lan­ guage as well as about thought — not, interestingly enough, about reality, for his principles do not arise from reality itself, but only from the way reality is re­ flected in language and thought. Still, although the reflection idea itself is an­ cient, and although it has earlier been associated with the question of what logic is, it is by no means the case that everybody agrees that logical reflectionism is an important or even moderately important conception. What re­ mains to be done then is to actually construct an RL or at least to start constructing one. 2.

Intra-logical RL interpretations

The previous section dealt with the problem of the proper interpretation of logic. It was made clear that this is usually considered to be a philosophical and extra-logical issue. Modern logics also harbor an intra-logical interpretation. Usually, a logic is defined by the combination of a 'syntax' or 'uninterpreted system' consist­ ing of a 'vocabulary' and 'formation rules', and an 'interpretation' or 'seman­ tics'. The latter specifies what the vocabulary items mean and what the for­ mulae allowed by the formation rules (the 'well-formed formulae' or 'wffs') stand for. The semantic interpretation makes clear, for example, whether the wffs of classical sentential logic refer to ordinary sentences, to electric switches or, more abstractly, whether they are to be associated with an abstract object such as 'Γ, belonging to a set of two such abstract objects, viz.

INTRA-LOGICAL RL INTERPRETATIONS

77

{1,0}. The intra-logical interpretation echoes the philosophical interpretation, but only partially so. First of all, not every intra-logical interpretation has a philosophical counterpart. There is no philosopher of logic who would say that logic is basically about electronics, for instance. But more importantly, an 'in­ side' look at the question of what logic is allows for a more detailed view, which is why I now come to it. The thesis that RL is a theory about reality, mind, and language will be concretized in an analysis of just which aspects of reality, mind, and language RL is supposed to deal with. The core of logic is so-called 'sentential logic'. Informally speaking, sen­ tential logic is concerned with sentential connectives such as 'and', 'or', and 'if ... then', and with sentences. Sentences are the entities that the sentential con­ nectives connect. Each wff represents a sentence. Unfortunately, in such an interpretation, just what the relation between classical sentential logic and real life sentences and sentential connectives amounts to is often left vague. This particular vagueness need not bother us here, for our own interests lie in a strongly descriptivist Reflectionist Sentential Logic, and there should not be any doubt that the latter is to be a description of the meanings of normal sen­ tences and sentential connectives. Thus Reflectionist Sentential Logic ('RSL') becomes a natural part of a linguistic theory of meaning. Before I proceed to clarify whether the theory of meaning is semantic or pragmatic (whether the unspecified sentence talk gets changed into talk about either phrastics or speech acts) and before reflectionism takes the logic to the realms of mind and reality, I must make an important terminological remark. Sentential logics are commonly called 'propositional logics'. I will follow this practice, as RSL will soon be termed 'Reflectionist PropositionalLbogie', but only up to a certain point. To be more exact, sentential RL will not be called 'propositional' because sentential logics have always been called 'propositio­ nal'. The terms 'proposition' and 'propositional' will be given a special sense, and the claim that RSL is propositional in my own, new sense of 'proposi­ tional' is an empirical contention rather than a terminological stipulation. By definition, RSL is a semantic theory of meaning. This means that its wffs stand for phrastics. This semantic point of view should not come as a sur­ prise. RSL is concerned with the meanings of such lexical items as 'not', 'or', and 'if ... then'. I have argued in III.3.1 that most of lexicology belongs to se­ mantics. So why shouldn't one start with the hypothesis that the study of the meanings of 'not', 'or', and 'if... then' is semantic? Actually, the matter is not quite that simple. First of all, I do not deny that some aspects of the meanings in

78

REFLECTIONIST AND CONDITION-THEORETIC LOGIC

question may be purely pragmatic. Secondly, the claim that RSL is to be a se­ mantic theory does not imply that it cannot be given a pragmatic interpreta­ tion. I have claimed earlier (III.3.1) that all of semantics can be stated in prag­ matic terms. Thirdly, it is not only possible to do semantics in a pragmatic dis­ guise; as we will see below, in section IV.4, it is also useful. For the moment, this suffices for the nominalist, semantic side of RSL. I now come to its mentalist and realist sides. As for mentalism, RSL is a theory about just those inferential operations that involve the mental counterparts of the phrastics and the phrastic connectives of the nominalist interpretation. Thus RSL comes out as a theory about conceptualizations and the way they are connected. As for realism, RSL is a theory about just those general traits of our universe that have to do with whatever is reflected by the inferential op­ erations of the mentalist, respectively, the meanings of the nominalist in­ terpretation. As conceptualizations reflect SOAs, RSL is a theory about SOAs and SOA connections. So far RSL has three intra-logical interpretations. For the sake of general­ ity and economy, however, it is handy to define yet a fourth one. A conse­ quence of the reflection thesis is that if one of the three RSL interpretations applies, necessarily all three of them apply. It follows that we could abstract from what is properly speaking linguistic in the nominalist interpretation, psychological in the mentalist interpretation, and ontologicai in the realist one as long as we do not abstract from what is common to all of them. Let the result of this abstraction be the 'propositional interpretation'. Its basic unit is the 'proposition'. A proposition is what an SOA, a conceptualization, and a phrastic have in common. A proposition is an abstract entity that equals an SOA minus its ontological properties, a conceptualization minus its psychological properties, and a phrastic minus its linguistic properties. Clearly, this definition of 'proposition' is quite unorthodox. But it is in accor­ dance with my views on the philosophy of mind, ontology, logic, and possible worlds. The definitional history of 'propositions' is one of a succession and a coexistence of realist, mentalist, and nominalist points of view. My own defi­ nition validates them all. Because of the vagueness of the term 'sentence' and the importance of as­ signing it a propositional interpretation, Reflectionist Sentential Logic will henceforth be called 'Reflectionist Propositional Logic' ('RPL'). What we know about the structure of RPL and, by extension, about the structure of the embedding RL can be summarily represented in Figure 2.

INTRA-LOGICAL RL INTERPRETATIONS

79

Figure 2 Figure 3 recapitulates the interpretation of wffs.

Figure 3 A propositional interpretation bears some resemblance to what has been called a 'formal' interpretation. A formal interpretation or, as Plantinga (1974: 126-128) and S. Haack (1978: 30,188ff.) call it, a 'pure semantics' is to be understood in contrast with its empirical interpretation or, again, in terms of Plantinga and Haack, a 'depraved' or 'applied' semantics, or 'patter'.49 Just what this contrast amounts to can best be explained using the example of Classical Propositional Logic ('CPL'). The CPL vocabulary has two types of items: variables ('p', 'q, V, etc.) and constants ('A\ ' V ' , '~>',etc). In a formal interpretation, the variables get paired off with one and only one member of a certain set, which could be called a 'value set'. Such a value set can be {1,0} or {T,F} or even, to show the arbitrary nature of such sets, {Adam, Eve}. The formal interpretation of the CPL constants involves matrices, standardly called 'truth-tables'. These de­ fine operations over the values of the variables. The matrix in (33), for exam­ ple, shows that while there are no limitations on the valuation of 'p' and 'q'

80

REFLECTIONIST AND CONDITION-THEORETIC LOGIC

the valuation of the wff 'p^ q' is limited by the operation of the constant '  '. The first line, for instance, is read as follows: both 'p' and 'q' have '1' and in that case 'p^q' has '1', too. Using the matrix definitions, each CPL wff can be evaluated in terms of ' and '0'. An interesting result is that we can thus define a sublanguage made up of just those CPL wffs that always get Ί ' . The sublan­ guage in question is that of the so-called CPL 'theorems'. So much for the formal interpretation. Essential for any non-formalist logic, however, is the empirical interpretation, which makes one decide, for example, that '1 represents truth and '0' falsehood, that '  ' stands for the or­ dinary language 'and', and that the variables refer to assertions. This makes the logic into 'some kind of theory about natural language—notice the vague­ ness. Theoremhood, furthermore, can be related to the validity of infer­ ences, in which case the logic becomes 'a kind of' theory about the mind. If Ί ' gets defined as 'on' and '0' as 'off' and the variables as electric switches, then one is on one's way to a theory about electrical switching circuits. The resulting picture is that an uninterpreted CPL system is given a for­ mal, non-empirical interpretation, which, in its turn, is assigned an empirical interpretation (see Figure 4).

Figure 4 If we now compare the orthodox CPL division of labor to that of RPL, we immediately see the similarity. Both CPL and RPL have three levels. In both cases the lowermost level is empirical. It is also plausible to hold that the mid­ dle levels are abstractions from the lowermost ones. But there are differences, and they outweigh the parallels. That the empirical level of RPL is different

INTRA-LOGICAL RL INTERPRETATIONS

81

from that of CPL has been stated above. Let me just repeat that RPL is sup­ posed to be a full-blooded empirical science with three empirical domains, whereas CPL is not. Another difference is that the propositional interpreta­ tion of RPL is not a formal, non-empirical interpretation. It is true that a prop­ osition is an abstraction from an SOA, a conceptualization, and a phrastic, but this does not make it less empirical. A proposition is what is common to an SOA, a conceptualization, and a phrastic, and it is this empirical entity and, especially, the relations between such entities that RPL is all about. Note that the empirical status of the propositional interpretation is independent from its actual formal organization. It is not a priori impossible that the RPL proposi­ tional interpretation evaluates RPL wffs in terms of two values, defining a sub-language of theorems in a way similar to that of CPL. Notice also that I do not claim that a formal RPL interpretation is impossible. There is no apriori reason why a schema such as that of Figure 5 could not be implemented.

Figure 5 But there is also no a priori reason why such a formal interpretation level would be interesting. One more, important claim about formal interpretations. Up to now, I have assumed that the difference between formal and empirical interpreta­ tions is a genuine one. Yet I believe that this assumption is actually incorrect, and that the idea of a formal interpretation is an emanation from formalism. Perhaps, the formalists have tried to integrate the undeniable fact that a lan­ guage is always about something in their allegedly non-empirical 'aboutness'. Now, just as formalism is only a cover for descriptivism, be it a weak one, a formal interpretation is really empirical, be it minimally so. Notice, for in­ stance, that the value set of CPL is not totally arbitrary. The set {Adam, Adam} will not do. The set must at least incorporate a difference; and differ-

82

REFLECTIONIST AND CONDITION-THEORETIC LOGIC

ence, surely, is something empirical. My last point takes me back to the non-propositional interpretations. I contend that each of them can be carried out in two ways. Let me take the nominalist interpretation first. I have earlier defined it as a semantic one. To illustrate this, suppose that (34) is an RPL law. (34)

(p^q)→p

As (34) is intended to be a trivial example, the details of the propositional in­ terpretation need not concern us. (34) symbolizes the sense in which a propos­ itional conjunction of '/?' and 'q' implies the proposition '/?' or, in a semiabbreviated form, it says that whenever the proposition that ρ and q, then also the proposition that p. Interpreted semantically, (34) means that the phrastic that p and q implies the phrastic that/?. In other words, whenever a speaker (S) speaks as if he or she is in a mental state concerning the conceptualization that p and q, then S also speaks as if he or she is in a mental state concerning the conceptualization that/?. If the essential idea of the phrastic interpretation is clear, it should not be hard to see that the 'p' and the 'q' can also be interpreted pragmatically. Re­ member that the whole of semantics can be rendered in pragmatic terms. Here is one pragmatic interpretation of (34) : whenever S speaks as if he or she believes that p and q, then S also speaks as if he or she believes that/?. In other words, an assertion that p and q implies the assertion that/?. Here is another pragmatic interpretation: an optative that p and q implies an optative that/?. The conclusion that the linguistic or nominalist interpretation can be both semantic and pragmatic is diagrammed in Figure 6.

INTRA-LOGICAL RL INTERPRETATIONS

83

Evidently, if the nominalist interpretation can be split up, so can the mentalist one. A mental interpretation either refers to mental states or to concep­ tualizations. Applied to (34), a mentalist interpretation allows me to claim, first, that a conceptualization that ρ and q implies the conceptualization that /?; and, second, that the mental state of, say, desiring that p and q implies the mental state of desiring thatp. Thus the bifurcation in the mentalist interpre­ tation is completely analogous to the one dividing the semantic from the prag­ matic interpretation. See Figure 7.

Figure 7 What about the realist interpretation? Does it also split up? The reflec­ tion thesis suggests a positive answer, and, in fact, section 3.1 of Chapter II has hinted at a very specific proposal. There, it was claimed that conceptualiza­ tions, when integrated in mental states, reflect particulars. Outside mental states, however, they would reflect universals. Notice also that just as speech acts involve the instantiation of phrastics and mental states that of concep­ tualizations, particulars involve the instantiation of universals. With these parallels in mind, it would seem to make sense to have a realist interpretation for universal SOAs as well as for particular SOAs. With respect to (34), then, I am claiming that the universal SOA of 'p-and-q-hood' implies the universal SOA of 'p-hood', and that a particular 'p and q' SOA implies a particular 'p' SOA. My realist interpretations may sound trivial. But remember that (34) was chosen for its triviality. Some may feel that the universal interpretation im­ plies the particular one. To see that this is not the case, it pays to go back to

84

REFLECTIONIST AND CONDITION-THEORETIC LOGIC

some mentalist interpretations. (35) is the conceptual interpretation of (34). (35)

the conceptualization that ρ and q implies the conceptualization that ρ

The existence of a valid conceptual interpretation such as (35) does not ensure that all possible mental state interpretations are valid. (36), for example, is valid, while (37) and (38) are not. (36) the belief that ρ and q implies the belief that ρ (37) *the belief that ρ and q implies the desire that ρ (38) * the intention that ρ and q implies the belief that ρ A condition for the validity of the mental state interpretations of (34) is that the mental state of the implicans is of the same type as that of the implicandum. All of which goes to say that we need a similar condition in the case of particular, realist interpretations. Let me illustrate this with the possible worlds j argon. A particular SOA always obtains in a possible world, either the actual one or one of the many non-worlds. So both (39) and (40) are particular realist interpretations of (34). (39)

the universal SOAοfρ and q particularized in the actual world im­ plies the universal SOA of ρ particularized in the actual world

(40) *the universal SOA of ρ and q particularized in the actual world implies the universal SOA of ρ particularized in non-world w1 Yet clearly, (40) is invalid. The possible worlds of implicans and implicandum must be the same. The resulting structure of RPL and of all RL to the extent that it em­ bodies a propositional logic is represented in Figure 8. Some concluding remarks. There are logicians who prefer to construct sys­ tems and worry about interpretations later. More commonly, though, logi­ cians devise logics with, as the phrase goes, 'an interpretation in mind'. In the same vein, the present section is a projective statement about the RPL in­ terpretation I have in mind. What I do not envisage is a so-called 'formal in­ terpretation'. Instead, I want to work towards a complex, empirical interpre­ tation according to which RPL wffs refer to propositions, which in turn can be interpreted as phrastics, speech act types, conceptualizations, mental states, and universal and particular SOAs. Any RPL wff that can be interpreted as a description of the structure of phrastics, speech acts, conceptualizations, etc. and of the way phrastics, speech acts, etc. relate to each other, belongs to the sublanguage of the RPL wffs that makes up the descriptive theory of reality,

INTRA-LOGICAL RL INTERPRETATIONS

85

Figure 8 mind, and language that I am interested in. I have suggested that the RPL wff of (34), for example, is a likely part of this sublanguage. That is to say that the prospects for a theory of conjunction (' ^ ') and implication ('→') that allows (34) to pass the 'six-fold reality-mind-language test' outlined above look rather good. But notice the careful tone. It is the tone appropriate for a projection of an interpretation which I have not given and of an uninterpreted system which I have not given either. It is further of interest to note that some of the foundations of RPL were laid in the earlier chapters. These foundations concern the relation between conceptualizations and mental states, the distinction between semantics and pragmatics, the acceptance of both universals and particulars, and the idea that many of the postulated entities are connected through reflection rela­ tions. All entities, it will be remembered, are allowed a minimal existence. For most of them, I have been at pains to defend their minimal existence in the face of the accusation of creating an unjustifiedly overpopulated universe. No doubt, this defense has not been totally effective. Notice now how the projec­ tion of RPL supplies me with a rather powerful argument for getting back at the Scrooges of ontology. The argument is powerful because it expresses the same desire for simplicity and economy as the one that lies behind the reduc­ tionist accusations. My point is this: much of what I have to say about phrastics is no less valid for assertions, for instance, for desires and conceptualizations, and for SOAs, both universal and particular. For many aspects of reality,

86

REFLECTIONIST AND CONDITION-THEORETIC LOGIC

mind, and language, I do not need three theories. One is enough. At its level of propositional interpretation, this one theory is freed from bondage to the uniquely ontological, the uniquely psychological, and the uniquely linguistic. Since I am really all in favor of simplicity and economy, I am willing to take the relevant characteristics common to six minimally existing entities and unite them in one theory. Paradoxically, this does not reduce the number of en­ tities; it economizes the description by creating a new one, viz. the proposi­ tion. The activity that goes on at the level of the propositional interpretation, it may be pointed out, is not just one of translating linguistic, psychological, or ontological findings into a more abstract terminology. It is also a matter of original research. Let me illustrate this as follows. Suppose again that (34)

(34)

(pAq)^p

passes the 'sixfold reality-mind-language test'. It certainly is no extravagancy to let RPL also have some kind of substitution rule according to which all the occurrences of a variable thoughout a wff may be substituted by another wff. According to such a rule, something like (41) should be derivable: (41)

((^r)^q)→(p^r)

Obviously, (41) passes the reality-mind-language test with flying colors. And the interesting thing is that it does not even have to take the test. We simply know that if both (34) and the substitution rule are empirically adequate, then (41) is, too. What is more, this particular bit of knowledge can be acquired en­ tirely mechanically. We simply take (34) and start substituting according to the rule; the results are guaranteed to be interpretable as valid claims about language, mind, and reality. The fact that we can do linguistically, psychologically, and ontologically relevant work without having to leave the abstract level of the propositional interpretation, merely by drawing consequences and getting organized, is an extremely attractive feature of RPL. But this attraction is also its biggest danger. If one gets carried away by the organizational problems of the proposi­ tional interpretation, one may lose interest in its descriptive adequacy. If that happens — reverting to Strawson's metaphor (see note 35) — the RPL geog­ rapher of language, mind, and reality who is "passionately addicted to geometry, and insists on using in his drawings only geometrical figures for which rules of construction can be given" (Strawson 1952: 58) is no longer a good geographer.

CONDITIONS

3.

87

Conditions "A satisfactory logical theory of conditions is still very much of a de­ sideratum." (von Wright 1970: 161)

Though the discussion of the intra-logical interpretation was more con­ crete than that of the extra-logical interpretation, it was still rather general. We didn't get much further than sketching the various components of RPL. I will now start looking at the finer details of RPL interpretations, more par­ ticularly at the kind of 'values' that are involved. If RPL is like CPL in this re­ spect, then it will involve only two values, {1,0} or {T,F}, where Ί ' and 'T' usually stand for 'true' and '0' and 'F' for 'false'. Because of their association with truth and falsity, the CPL values are usually called 'truth-values'. These truth-values get matched with wffs according to specific rules or conditions, called 'truth conditions'. When one says that CPL is 'truth-conditional', one thus means that CPL is essentially a definition of the conditions under which wffs get their truth-values. RPL has one propositional interpretation and six non-propositional ones. It should be clear that they cannot all be truth-conditional. It makes sense for an assertion and a belief to be true of false; one could thus imagine that at least one pragmatic and one mental state interpretation could be phrased in truth-conditional terms. However, it makes no sense to say that particular SOAs, desires, or phrastics are true or false. A particular SOA is not true; it is actual, it obtains or prevails. A desire is satisfied rather than true.50 A phrastic as such, i.e. taken in abstraction from the speech act it supplies with a conceptual content, cannot really be true or false either. Not even propositions, at least when defined as what is common to particular and universal SOAs, to mental states and conceptualizations, and to speech acts and phrastics are truly true or false. So we need other values/conditions in ad­ dition to truth values/conditions. In the case of particular SOAs, for example, one could speak about actuality conditions. For desires, one could introduce satisfaction conditions. What is at issue in the present section is not, however, the identification of the conditions appropriate to each non-propositional level, but rather the more abstract machinery that would fit the propositional interpretation. I am thus looking for conditions that abstract from what estab­ lishes truth conditions as being appropriate for assertions and beliefs, and from what makes satisfaction conditions and actuality conditions the right types of conditions for, respectively, desires and particular SOAs. In other

88

REFLECTIONIST AND CONDITION-THEORETIC LOGIC

Figure 9 words, I want to know what it is that relates to truth, satisfaction, and actuality conditions in the same way that propositions relate to, respectively, beliefs and assertions, desires, and particular SOAs (see Figure 9). My answer is very simple. What I need in order to deal with propositional interpretation are conditions as such. This is not overly surprising: obviously, what conditions of truth, satisfaction, and actuality have in common is that they are all conditions. If it is true that the propositional RPL interpretation should be organized in terms of conditions as such, we want to know more about conditions and about types of conditions. But unfortunately, our understanding of conditions is relatively poor (cp. the citation from von Wright at the onset of this section). The theory of conditions (conditionality) is underdeveloped. Yet, such con­ cepts as necessary, sufficient, and necessary and sufficient conditionality be­ long to the central parts of the philosopher's machinery. Some would even de­ fine philosophical analysis as the investigation of certain necessary and suffi­ cient conditions, viz. those that establish the appropriateness of philosophical

CONDITIONS

89

concepts (. Bennett 1976: 22; Searle 1979a: 90). So one most certainly uses the notion of conditionality, even if one seldom studies it explicitly. Note that I do not object to the everyday use of such notions as necessary, sufficient, and necessary and sufficient conditionality. These are primitive notions and we all understand what they mean. But precisely because of our incomplete working knowledge and unreflected usage of these notions,51 it is a good idea to try and reach a deeper understanding. In my view, the underdevelopedness of the theory of conditions is an his­ torical accident, connected with the fact that most research has been under­ taken from the perspective of so-called 'inductive logic'. Whatever the status of this discipline may be — is 'inductive logic' really 'logic'? — it can safely be said to be the study of induction. Induction itself can be characterized, in many contexts, as a search for causes. As the latter term is somewhat vague, it calls for further analysis, and this is where conditionality comes in. It has in­ deed become standard practice to analyze causality in terms of condition types (see Sosa 1975). Of course, this does not by itself lead to a study of condition­ ality for its own sake, for one is interested in causality, not in conditions. Thus many causality theorists take their conditionality notions for granted or con­ tent themselves with an isolated definition (e.g. Ayer 1956:193; Taylor 1966: 28-30). But there are exceptions, such as Broad (1930), Marc-Wogau (1962), Scriven (1964), and Mackie (1965). The most important exception is von Wright. For the last forty years (i.e. since von Wright 1941,1942), he has been emphasizing the need for and the usefulness of an adequate theory of condi­ tions. For the analysis of causality, von Wright (1975: 96) claims: "the theory of conditions ... opened new prospects which are only beginning to be explored". Conditionality theory could further, according to von Wright (1970), provide a novel conception for deontic logic. It could also contribute to our understanding of determinism (see von Wright 1971: 39) and " it seems ... eminently suited as a propedeutics to logic and the methodology of sci­ ence" (von Wright 1971: 40; cp. von Wright 1951: 77). As to its nature, com­ pared to its uses, von Wright (1974, 1975) has suggested that the theory of conditions should be incorporated in some already existing modal logic. It is this suggestion, together with the mini-logics he constructed earlier (von Wright 1941,1942,1951: 66-74) as well as those inspired by him (Tranøy 1970; possibly Skyrms 1966: 80-83), that I take to be von Wright's most important contribution to the theory of conditionality. Here von Wright purports to give conditionality a place in logic proper. Unfortunately, few logicians have fol­ lowed von Wright in this respect. For most of them, the study of conditionality

90

REFLECTIONIST AND CONDITION-THEORETIC LOGIC

remains an optional exercise in causality theory (see also, V.5.1.1 below). 52 In what follows, I will develop a partial theory of conditions. More pre­ cisely, I will commit myself to the thesis that sufficient conditionality is the converse of necessary conditionality, and I will distinguish between various subtypes of sufficient and of necessary conditions. My general aims are not those of the causality theorist, but those of the logician. As claimed above, condition theory is relevant to RPL in that the RPL propositional interpreta­ tion is organized in terms of conditions. But the relation between condition theory and RPL is closer still. While the condition-theoretic nature of the RPL propositional interpretation only shows that condition theory is relevant to the RPL metalanguage, the development of the next chapter will document the relevance of condition theory to the RPL object language. This is in gen­ eral agreement with von Wright's logical work on conditions, but we go about our analysis in quite different ways. Von Wright wants to construct a logic of necessary and sufficient conditions on the basis of the existing modal logics. I will do the opposite. Thus I will claim in Chapter V that such modal operators as 'it is necessary that' must be understood in terms of conditions. The same goes for 'if ... then', which I contend must be taken as modal, too. In what follows, the various types and subtypes of conditions will be illus­ trated using structural contrasts between pairs of propositions. Thus the struc­ tural contrast between (42) and (43), for example, (42) (43)

John and Mary come home John comes home

is such that (42) is a sufficient condition for (43). However, the illustration may need some further clarification. First, the notion of structural contrast al­ lows us to identify the type of condition only as far as the structure of the prop­ ositions is concerned. It is quite possible, for instance, that the John of (43) is different from the one of (42), in which case (42) is not a sufficient condition for (43). Yet, as far as one can tell from the structure of the propositions, (42) is sufficient for (43). Such structure-dependent sufficient conditions have been called 'logically sufficient conditions' (see Flew 1975: 37-42). Second, the claim that (42) is sufficient for (43) concerns propositions. If this is felt to be too abstract a procedure, it can easily be given non-propositional interpreta­ tions. Here are two: a particular SOA in which John and Mary come home is a sufficient condition for a particular SOA in which John comes home ; an asser­ tion that John and Mary come home is sufficient for an assertion that John comes home. My third point may seem trivial. I am obviously using language

CONDITIONS

91

to describe propositions. By definition, my propositional descriptions are complete, just as SOA descriptions are definitionally complete (see II.2.1). Thus the words 'John', 'comes', and 'home', arranged in that order, are only used to speak about a proposition in which John comes home. Note that I am not speaking about a proposition in which John and Mary come home. For such a proposition, I need the phrase 'John and Mary come home'. It will be handy to represent the condition types as functions. When a proposition χ is a condition of type y for a proposition z, then y will be a func­ tion which has ζ as its argument and χ as its value. Symbolically: (44)

y(z) = x

If s stands for 'sufficient condition', then the relation between (42) and (43) could be formalized as: (45) s(John comes home) = John and Mary come home Actually, (45) is not quite correct. By definition, a function provides an argu­ ment with a unique value. The value of s(John comes home) is not unique, however. A proposition in which John comes home with Fred is just as sufficient. To straighten out the formalism, it suffices to give s subscripts. s1 could then stand for just that sufficiency that picks out John and Mary's homecoming, while s2 would do the same for John and Fred. (46) s1(John comes home) = John and Mary come home (47) s2(John comes home) = John and Fred come home For expository convenience, my propositions will be kept extremely sim­ ple. Every proposition will be about one or more animals and will 'say' no more than that the animal(s) is/are present. To simplify matters even more, the name of the animal will be used as an abbreviation for the whole proposi­ tion. Thus z1 for instance, is the proposition of the presence of one non­ specific cat and one equally non-specific mouse: (48)

z1 = cat, mouse

3.1. Basic conditions Necessary, sufficient, and necessary and sufficient conditions could be called 'basic conditions' to distinguish them from conditions for conditions, which would then be 'non-basic'. In this book, we will only concern ourselves with basic conditions (see Van der Auwera 1980c: 185-196 for a general ac­ count of non-basic conditions, and Van der Auwera 1981c for an analysis of

92

REFLECTIONIST AND CONDITION-THEORETIC LOGIC

the so-called 'inus' conditions (msuffient and necessary conditions for unnecessary and sufficient conditions)) A terminological point of importance is that I will abbreviate the phrases 'sufficient but unnecessary condition' and 'necessary but insufficient condi­ tion' as, respectively, 'sufficient condition' and'necessary condition'. The one exception to this practice will be the phrase 'necessary and sufficient condi­ tion'. 3.1.1. Sufficient conditions The first type of condition to be investigated is that of sufficient conditionality. Three subtypes will be distinguished. The first is that of 'quantita­ tive' or 'expansion' sufficiency (s6). (49)

se(z) = χ

χ is se for z iff χ and z are identical except for the fact that χ contains more en­ tities than ζ. χ is an expansion of z. For the presence of a cat and a mouse(z1— see (48)), for instance, it is se that there is a cat, a mouse, and a dog. Formally: (50) se2 (z1)=cat,mouse, dog A different se condition is shown in: (51)

se2(z1)=

mouse, cow

The second type of sufficiency will be called 'qualitative' or 'instantiation' sufficiency (s1). In this case, χ and ζ are identical except for the fact that one or more entities of ζ are instantiated or exemplified by one or more entities in x. White cats, for example, instantiate cats. Thus a white cat and a mouse are si for a cat and a mouse. (52) si1(z1)

=

white cat, mouse

Here are some other sufficiencies: (53) (54)

si2(z1)=catwhite mouse sl3(Z1)= white cat, white mouse

The third type of sufficient condition is partially se and partially si. One way to 'construct' such a condition is to take an se value and change it such that (a) it does not become insufficient; (b) it does not lose its se characteristics; (c) it acquires some si properties. As an instantiation of a z-entity is independent of whether something is added to z, we can easily obtain the value of the de­ sired s function by replacing the part of the se(z) that is identical with z, with an si(z). Let the resulting value be called 'se,i(z)' and the condition an 's e,icondi-

CONDITIONS

93

tion'. (The order of the superscripts symbolizes that we have started out from an se condition.) (55) se1(z1)=cat, mouse, dog si1(z1) = white cat, mouse se1,i1(z1) = white cat, mouse, dog The subscripts identify the new se,i function by referring to those of the original se and sl functions. Here is another illustration: (56)se,2i2(z1)=cat, mouse, cow The part of the se(z) that needs to be replaced with an si(z) does not have to comprise all that is identical with z. Suppose that I just replace the cat of the se1(z) rather than both the cat and the mouse. The result is: (57) se,i1,1(z1) = white cat, mouse, mouse, dog But what does (57) mean? Does the description of χ call for two mice or is it a redundant way of requiring just one mouse? I opt for the latter interpretation. The redundancy must be explained as resulting from the fact that the presence of this one mouse can be due to the se character of the se,i function as well as to its si character. To avoid confusion, redundancy will be prohibited. We simplify the value of (57) into that of (55). The substitution of the se(z) with the si(z) may even involve the part of the e s (z) that is not identical with z, as long as it does not involve all of it, for then the resulting value would lose all its se characteristics. se3(z2) = cat, mouse, dog, cow si1(z1) = white cat, mouse se,i3,1(z1) = white cat, mouse, dog (59) se3(z1) = cat, mouse, dog, cow si1(z1) = white cat, mouse *se,i(z1) = white cat, mouse

(58)

Notice, incidentally, that the subscriptive identification of the functions is far from perfect. In (58), the cat, the mouse, and the cow are replaced. If one re­ places the cat, the mouse, and the dog, one still gets an se3i1 function. (60)

se3'z;(z1) = white cat, mouse, cow

Furthermore, the value of the se,i3,1 function of (58) is identical with that of the se,i1,1function of (55). This identification problem is too marginal for our in­ terests, however, to demand further attention.

94

REFLECTIONIST AND CONDITION-THEORETIC LOGIC

So far, I have constructed the functions that are partially se and partially si by starting out from se. But there can be no objection to doing it the other way around. One takes an si(z) and replaces parts of it with an se(z). As long as one leaves some entities that instantiate entities of z, the result will retain an si characteristic. The value in question could be called si,e(z), and the order of the superscripts could symbolize the difference from an se,i(z). (61)

si

= white cat, mouse 1(z1) e s 1(z1) = cat, mouse, dog si,e1,1(z1)= white cat, cat, mouse,

dog

= white cat, mouse, dog Notice that the value of the si,e function is identical to that of the se,i1.1 function. In fact, this observation can be generalized: for each si,e function there is an se,i' function with the same value. This makes clear (clear enough anyway) thats i,e and se,i functions are not really different and that I have only constructed things in different ways. Henceforth, I will speak about seiconditions. The order of the superscripts is no longer symbolic; it is just the alphabetical order. 3.1.2. Necesssary conditions Not surprisingly, just like sufficient conditions, necessary conditions can be subcategorized in three groups. It has long been held that necessary and sufficient conditions are interdefinable:x:is a sufficient condition for z iff z is a necessary condition for x. This symmetry has been challenged (see Wertheimer 1968; Sanford 1976; Nerlich 1979; Sharvy 1979; Mackie 1979). There are two ways to argue that these challenges are unsuccessful. The first is to scrutinize the challenges themselves and to show that they are implausible (that they confuse the a-temporal notions of sufficiency and necessity with considerations of time, for example). The second is to document the plausibil­ ity of the symmetry itself. I will opt for the second strategy. χ is ne for z iff z is se for x. (62)

ne(z) = xise(x)

=z

e

z1 has two obvious n values: (63) (64)

ne1(z1)= cat ne2(z1) = mouse

The problem of whether z1 has more ne conditions is very tricky. It might be suggested, at first sight, that it is ne for a cat that it has a tail, a head, claws, whiskers, feet, a belly, etc. However, it would be a bit naive to disqualify an

CONDITIONS

95

animal that is just like a prototypical cat except that it has lost its tail. Poi­ gnantly, does a cat cease to be a cat if it loses its tail? The problem that confronts us is that of essentialism. I won't pause over it. It is sufficient for me to make the point that there are ne conditions. Some ri conditions are jointly sufficient. Others are not. Consider the case of z2'. (65)

z2 = cat, mouse, dog

(66) lists all the unproblematic ri vlaues: (66) ne1(z2) = cat ne2(z2)= mouse ne3(z2) = dog ne4(z2) = cat, mouse ne5(z2) = cat, dog ne6(z2) — mouse, dog The combination of ne1(z2),ne2(z2), and ne3(z2), for instance, yields z2 So the conditions in question will be called 'jointly sufficient'. Another set of jointly sufficient and individually ri conditions is that ofne1(z2)and ne6(z2). What about the combination ofne1(z2),ne6(z2),and z3 though? (67)

z3 = cow

z3 is individually unnecessary for z2. But this does not make ne1(z2), ne6(z2), and z3 any less jointly sufficient. Thus we see that jointly sufficient conditions may or may not be individually necessary. I can be brief about ni conditions. For any z,x is ri iff ζ is sl for x. (68) ni(z) = xiffsi(x)

=z

Here are some examples: (69) ni1(z1) = cat, rodent (70) ni2(z1) = feline, mouse (71) ni3(z1) = a pair of animals Just like ne conditions, ni conditions may be jointly sufficient. An example is the combination of ni1(z) and ni2(z1). Notice that it is not the union of ni1(z1) andni2(z1) that yields z1 It is the fact that z1 is a common instantiation. As might be expected, there are also neiconditions. Since they are par­ tially ne and partially ni, they are necessary, but neither fully ne nor fully ni. They relate to ne and ni conditions in the same way that sei conditions relate

96

REFLECTIONIST AND CONDITION-THEORETIC LOGIC

to se and si ones. They relate to sei conditions in the same way that rf and ni conditions relate to se and si ones. Recall our approach to sei conditions. We first took an se value and changed it to the effect that it acquired some si characteristics. Then we did the same for si. I will now use the same method to derive nei conditions. Again, I will have recourse to two intermediate categories, viz. ne,i and ni,e. Let us take an ni condition first. The steps leading to the ni,e condition are illustrated in (72). (72)

ni1(Z1)= cat, rodent ne2(Z1) = mouse

ni,e2(z1) — rodent The idea is to drop something from the ni(z) to the effect that what is left is in­ stantiated by an ne(z). The second ni,e subscript indicates that one is working towards a particular ne(z), ne2(z1) in (72). The result of this change, ni,e1,2(z1) for example, is indeed partially n1 and partially ηe . ni,e1,2(z1) is partially rf be­ cause it does not match every entity of z1 with an entity that is either identical with it or that is instantiated by it (for ni values we do get this matching). Yet ni,e1,2 is partly ni for it is at least a part of an ni(z1) which cannot be a part of an ne(z1). The description of ni,e conditions calls for one more refinement. (72) may give the impression that the entire ni,e(z) has to be instantiated by an ne(z). In actual fact, only part of the ni,e(z) needs this instantiation. Consider the con­ struction below: (73)

z2 = cat, mouse, dog ni1(z2) = cat, rodent, dog ne6(z2) = mouse, dog ni,e1,6(z2) = rodent, dog

Clearly, ni,e1,6(z2) is as good an ni,e(z2) as we can get. It is still necessary for there to be a cat, a mouse, and a dog that there is a rodent and a dog. But this par­ ticular necessary condition is neither ni nor ne. Rather, it is a mixture. This mixture can also be reached if one starts off from rf conditions by simply following the construction method in the opposite direction. This gives us the ne,i conditions. So we get both ne,i and ni,e conditions, but again, such conditions are really identical. I will henceforth refer to them by the label 'nei condition'. This completes the description of nei conditions in terms of ne and ni con-

CONDITIONS

97

ditions. Notice two more points. First, nei conditions can also be defined in terms of sei conditions: nei(z)=xiffsei(x)

(74)

=z

ei

Second, n conditions may or may not be jointly sufficient. This is illustrated in (75), which lists three jointly sufficient nei conditions for zr (For conve­ nience, the subscripts only serve to distinguish between the three conditions. They do not refer to the composition.) (75) nei1(z2) = cat, rodent ne2i(z2)= feline, mouse nei3(z2) = rodent, dog 3.1.3. Necessary and sufficient conditionality Individually necessary conditions may or may not be jointly sufficient. Now just in case the set of individually necessary and jointly sufficient condi­ tions has only one member, the latter is both necessary and sufficient. As al­ ready indicated in IV.3.1, 'necessary' and 'sufficient' in the phrase 'necessary and sufficient' do not mean 'only necessary and not sufficient', respectively 'only sufficient and not necessary', but rather 'at least necessary' and 'at least sufficient'. This variation remains at the stipulative stage for the moment, but will be dealt with descriptively before long (IV.4.2, below). It should also be pointed out that the phrase 'necessary and sufficient' is often used as a (sloppy) shorthand for 'individually necessary and jointly sufficient'. Otherwise, the discussion of necessary and sufficient conditionality (ns) can be brief. For any z, the ns condition is always simply z. (76)

ns(z) — ζ

There is no need to subcategorize in terms of expansion or instantiation. 3.1.4. Completeness The preceding sections have yielded some insights into the seven-way typology diagrammed in figure 10.

98

REFLECTIONIST AND CONDITION-THEORETIC LOGIC

I contend that this typology is complete in the sense that there cannot be a con­ dition that is either necessary, sufficient, or necessary and sufficient and that does not fall into one of these categories. It is not possible, for example, for a sufficient condition to be neither se, si nor sei. This completeness claim is not quite self-evident. Imagine that some χ is sei for some proposition that is itself si for a z. Now, while it seems self-evident that the conditional relation from χ to z is one of sufficiency, I think it is far from obvious that this sufficiency is also either se, si or ei.The problem we meet here has to be dealt with in a theory of non-basic conditions. The completeness claim does not imply that one could not find any further parameters to divide the realm of n, s, and ns conditions. Further­ more, I do not deny that a condition may fall into more than one category. I have not been able to show this, in part because my illustrations have involved only definite numbers of animals. Consider z4, however: (77)

z4 = cats, white cat

zA contains two or more cats as well as a white cat, in other words: three or more cats one of which is white. For zA it is ne that there are two or more cats. 4

(78) ne1(z4) = cats But, since the presence of three or more cats one of which is white is just as much an instantiation of the presence of two or more cats as the earlier, more obvious cases, the latter presence is no less an ni condition. (79)

ni1(z4) = cats

3.2. Impossibility conditions Implicitly, the preceding analysis has only allowed 'positive propositions', i.e. propositions about something being the case. The moment we let in 'nega­ tive' propositions, we see some of the limitations of the basic condition typol­ ogy. To characterize the conditional relation in (80), for example, (80) y(z1) = no cat, no mouse one would want to say that the proposition that has neither cat nor mouse is sufficient for z1 not to 'obtain' .53 The sufficiency and the 'not' can be combined to form the term 'impossible', and we could say that the 'no cat, no mouse' proposition is impossible for z1 or that the 'no cat, no mouse' proposition is an impossibility condition for z1. The notion of impossibility condition is a little different from that of suffi-

CONDITIONS

99

ciency and necessity condition. While the latter two have a long-standing usage in philosophical language, the former hasn't. I have just created it. What is more, I have created it out of a 'not' and a sufficiency. So the closer analysis of impossibility conditions depends on that of sufficient conditions. But it also depends on a analysis of necessary and sufficient conditions, for there are in fact two subtypes of impossibility conditions. A proposition may be sufficient for another proposition not to 'obtain', like in (80), or it may be necessary and sufficient, like in (81). (81)

y(Z1) = it is not the case that there is a cat and a mouse

So the notion of impossibility condition appears to be more artificial and less basic than that of necessary and of sufficient conditionality. This is one reason why I will not study it any further. The other reason is that it will not be as cen­ tral to my later interests as the others. There is one more point about impossibility conditions that I want to draw attention to. The definition of impossibility as a sufficiency or a necessity and sufficiency for something not to 'obtain', in other words, for it to be false that it obtains, clearly shows that conditionality theory implicitly houses a no­ tion of non-actuality or falsity. Furthermore, the introduction of impossibility conditions has made us aware of the fact that all the other condition types are conditions for something to 'obtain', for it to be true that it obtains. So condi­ tionality somehow hides truth and actuality too.54 Doesn't this falsify the claim that things like truth and actuality only belong to a non-propositional level of RPL and that they are to be defined in terms of condition types? In a way, yes, but only if one forgets that our conditionality, truth, and actuality notions are all primitives, and that any explanation of them is inherently li­ mited and unavoidably circular (see Chapter I). If one keeps these points in mind, it becomes clear that the explanation of conditionality requires some notions of truth and actuality just as much as the explanation of truth and actu­ ality requires conditionality notions. But as truth, actuality, and conditionality are primitives, we already understand them. So we can assume them to be known. Or better, we can assume one of them, say, conditionality, to be known and see what this conditionality-assumptive perspective shows about truth and actuality. Better still, we can offer a partial analysis of one of them, say, conditionality, an analysis that stops short of the explicit demonstration that one cannot fully understand conditionality without drawing in actuality and truth, and see what perspective the strategic priority of conditionality gives us on actuality and truth. I claim that the strategic priority of condition-

100

REFLECTIONIST AND CONDITION-THEORETIC LOGIC

ality is very fruitful or, to use the metaphor that is most appropriate for the de­ fense of circularity, that the circular explanation of truth and actuality in terms of conditionality is a three-dimensional spiral rather than a two-dimensional circle. The strategy chosen shows some very important features of the truth and actuality dimensions, which would be hard to detect if we did not consider conditionality notions as given. To illustrate this for the truth dimension, I contend that a condition-theoretic account of truth-values shows that RPL is 'many-subvalued' and that these 'subvalues' can be grouped together under three 'values' — so that RPL is also 'three-valued'. I will argue these claims in the next section. 4.

Truth "There are moments when we need to remember the First Maxim for Balliol Men: 'Even a truism may be true.'" (Flew 1975: 73)

In the preceding section, I have argued that truth, truth-values, and truth conditions are not as central to RPL as they are to orthodox logic (cp. Tugend­ hat 1976: 505-510).55 Truth is only a special case, a non-propositional in­ terpretation of something more basic to be described at the condition-theore­ tic propositional level. Even so, truth is at least a very important special case. This is one reason why I now embark upon a relatively thorough analysis of truth and truth-value. There are other reasons, too. First of all, a high degree of abstraction can be a hindrance to understanding. One way to study an abstract phenomenon in a clearer way, therefore, is to concretize it. Applied to the present issue, this means that the upcoming study of truth does not just aim at elucidating truth alone. It must also be seen as an indirect but profitable — because of the lower degree of abstractness — study of the conditionality that underlies truth. Second, so far the very claim that truth is a non-proposi­ tional interpretation of a more basic propositional and condition-theoretic notion has not really got much attention. A closer study of truth will fortify this claim, and by the same token, it should clarify the nature of such 'truth parallels' as satisfaction and actuality. Third, it pays to concentrate on truth, since one may want to compare some of the details of RPL to some of the de­ tails of other logics. As the latter are usually phrased in terms of truth, the comparison can be made a lot easier if the present considerations on RPL are put forward in terms of truth, too. With these objectives in mind, I want to start on what is often called a 'theory of truth'. Unfortunately, this term is vague. Following Ayer (1963c)

TRUTH

101

and Platts (1979: 9-10) (see also Puntel 1978: 1-5), one should distinguish be­ tween at least three types of 'truth theories': (a) a descriptive analysis of the meaning of words like 'true' and 'truth' ; (b) an account of how truth conditions depend on certain logical operators (e.g. conjunction and disjunction); (c) an account of the foundations of truth, including, for example, a dis­ cussion of the debate between 'Correspondence' and 'Coherence' theorists. The second sense will concern us in the next chapter. For now, I will turn to problems (a) and (c). Since the meaning of the word 'true' reflects what truth itself is, these problems do not differ all that much, at least not for our present purposes. I believe that many present-day foundationalist inquiries into truth are too minimalistic. One fears that the problem is too obscure to be dealt with and one certainly does not want to be confronted with the abstract noun 'truth', that "camel... of a logical construction, which cannot get past the eye even of a grammarian" (Austin 1970b: 117) (cp. Mackie 1973b: 17; Platts 1979: 10). There are, no doubt, various reasons for this lack of enterprise. It may, first of all, be a reaction of sobriety to overadventurous metaphysics such as F.H. Bradley's. It may also have to do with the logician's indifference to the question of what logic is all about. Indeed, for many logic(ian)s that employ a notion of truth, it does not really matter what truth is. A third reason is that truth is normally taken to be a primitive notion. Fourth, some truth talk has a truistic flavor about it. If one claims that 'p' is true iff p, it is by no means clear that such a claim is not a trivial one.56 Furthermore, since this formula seems to specify the necessary and sufficient condi­ tion for an application of the predicate 'true', one may have the impression that everything that has to be said about truth has in fact been said. A final and related point is that certain philosophers (e.g. Ramsey 1978 [1927]; Ayer 1963c; Mackie 1973b; Williams 1976) have seen it as their task to show that truth is something much more simple than other philosophers have thought. The locus classicus is Ramsey (1978: 44 [1927]): "it is necessary to say something about truth and falsehood, in order to show that there is really no separate problem of truth but merely a linguistic mud­ dle."

No doubt it is laudable to try and ban unnecessary complexity, but one must take care not to oversimply. While it may to some extent be self-evident what

102

REFLECTIONIST AND CONDITION-THEORETIC LOGIC

truth is, our understanding can be improved. 4.1. Truth and conditionality My understanding of truth and of truth-values is based on a typology of conditionality. To see this, let us first take a look at a case of sufficient condi­ tionality: (82)

a proposition that there is a chair and a table is sufficient for a proposition that there is a chair

Propositions can be interpreted in a variety of linguistic, psychological, and ontologicai ways. Here are just two interpretations of (82): (83)

a desire that there be a chair and a table is sufficient for a desire that there be a chair

(84)

a particular SOA in which there is a chair and a table is sufficient for a particular SOA in which there is a chair

In both (83) and (84), both propositions have been given the same type of interpretation. (85) is an example of a mixed interpretation: (85)

a phrastic that there is a chair and a table is sufficient for a desire that there be a chair

(85) is clearly farcical. Yet not all mixed interpretations have a similar, disas­ trous effect. Consider (86): (86)

a particular SOA in which there is a chair and a table is sufficient for an assertion that there is a chair

Perhaps (86) sounds acceptable, but it is still elliptical. It does not say what as­ pect of the assertion the particular SOA is sufficient for. It is by no means suf­ ficient for the grammaticality of the assertion, for example, or for its beauty or appropriateness. What I am getting at, of course, is that the particular SOA is sufficient for the truth of the assertion. (87)

a particular SOA in which there is a chair and a table is sufficient for the truth of an assertion that there is a chair

(87) is still not good enough. If the assertion concerns the chair that stood in my kitchen on May 1st, 1980 and if the SOA in question obtained in my dining room on April 30th, 1980, then the SOA does not suffice for the truth of the assertion, not, at least, as far as one can tell from the structural comparison be­ tween the propositions of the assertion and the SOA.57 In order for the gen-

TRUTH

103

eral truth sufficiency statement of (87) to hold, the assertion must be asserted about the SOA.58 (88)

if an assertion that there is a chair is asserted about a particular SOA in which there is a chair and a table, then the particular SOA is sufficient for the truth of the assertion

Let (89) be the shorter formulation of this idea: (89)

an assertion that there is a chair is Τ relative to a particular SOA in which there is a chair and a table

'T' abbreviates 'true' and the subscript's' refers to the sufficiency of the prop­ osition of the particular SOA for the proposition of the truth-value bearer, which is an assertion in this case. There are other types of truth-value bearers than assertions, e.g. beliefs. This leads us to (90): (90)

a belief that there is a chair is Τ relative to a particular SOA in which there is a chair and a table

One might also propose that questions are truth-value bearers. Whatever the value of such proposal, I claim that it stretches our ordinary concept of truth. Questions are not normally the kind of things we think of as true. We do not ordinarily think of sentences as truth-value bearers either, unless we speak about their uses and exclude things like interrogative sentences. With the ap­ propriate qualifications, sentence talk may thus reduce to assertion talk. And if it does not, one can still define a purely technical notion of truth. Perhaps one would object that a restriction to assertions and beliefs is in conflict with the common practice of attributing the ability to be true to what are usually termed 'propositions' — which I have called 'phrastics' and 'conceptualiza­ tions'. Yet this disagreement may be superficial only. If a 'proposition' is de­ fined as that what is expressed by either an assertion or a belief, i.e. as the 'content' of an assertion or a belief, then the claim that propositions are truthvalue bearers comes close — close enough for my present purposes — to say­ ing that only assertions and beliefs qualify as truth-value bearers. If 'proposi­ tion' is defined as that which can serve as the content of an assertion or a be­ lief, or as the content of a desire, a question, an order, etc., then the disagree­ ment is substantive. But, here again, I grant that one can get away by defining a technical sense of truth. An issue that looms large in disputes about truth-value bearers is whether beliefs have the same standing as assertions. Both have been argued to be the

104

REFLECTIONIST AND CONDITION-THEORETIC LOGIC

primary bearer of truth. I have no desire to take part in this debate, however. A more interesting question is whether the SOA with respect to which an asser­ tion or a belief is true can be universal. The basis of the answer has already been supplied. One always believes or asserts something particular. Of course, one draws on universals to conceive the conceptualization and to ex­ press the phrastic, but both these objects are particularized as soon as they enter into a mental state or a speech act. Now, just as belief and assertion-de­ pendent propositions are particular, ontologicalones, the SOAs, must be par­ ticular, too. Up to now, I have argued that the words 'true' and 'truth' refer to aconditionality whose relata have been given certain specific linguistic, psychologi­ cal, and ontologicai interpretations. My next move is to interpret the truth re­ lation itself. Even truth can be interpreted in three different ways. When we say that some assertion or belief is true, we ordinarily mean one of three things: the assertion or belief is (a) ontologically true; (b) believed to be ontologically true; (c) asserted to be ontologically true.59 In the preceding discussion, I have implicitly adopted the realist (or ontological) stance. In this interpreta­ tion, assertions and beliefs are true, independent of any other mental state or speech act. The realist conception of truth has been considered rather impractical. Indeed, we humans can never really know whether a belief or an assertion is ontologically true. From here, a sceptic like Unger (1975) goes on, saying that nothing is ever true, that there is no such thing as truth, and that our language should be purged of 'truth' words. Such sweeping concusions need not be ac­ cepted, though. The fact that I can never know whether something is on­ tologically true or not will not prevent me from believing or asserting that something is ontologically true rather than merely believed or asserted to be ontologically true. Anyway, in logic proper, the realist conception of truth seems to need little defense. It is so common that there exists a logical theory based on it, called 'realism' (see e.g. Platts 1979). The terminology is some­ what dangerous, however, for a realism of truth is not the same as the realism of the view that logic as such 'is about' certain general characteristics of the uni­ verse (see IV.1.1.2, above). Other logics — a minority — have chosen a mentalist notion of truth as their basis. This decision is not without consequences. While logics that adopt a realist truth conception are usually two-valued, logics based on the mentalist truth conception may be three-valued (or 'more-valued'). The reasoning be­ hind this has a prima facie plausibility. As soon as one lets truth be dependent

TRUTH

105

on the human mind, one brings in a fallibility factor. This factor allows for a truth-value 'gap', or a truth-value of the indeterminate, the 'neither false nor true', the unknown or the undecided. In the rest of this study, I will continue to employ a realist notion of truth; however, I claim that nothing essential depends on this choice. Thus all further claims about truth, though framed in a realist language, could be given a mentalist or nominalist interpretation as well. This will be of special impor­ tance when considering the number of truth-values (IV.4.3). Let me stress, finally, that the decision to disregard the differences be­ tween realism, mentalism, and nominalism in matters of truth does not imply that such differences are not important.60 Recall in this connection the refutability analysis of assertions (see III.2.1),.which distinguished between the ontological meaning that ρ, the psychological meaning that a speaker believes that p, and the linguistic meaning that the speaker speaks as if he or she be­ lieves that ρ. What is of interest here is that this analysis can be interpreted as a partial account of the distinction between the realism, mentalism, and nominalism of truth. 4.2. Two-subvalued 'truth-of If one accepts that truth can be defined in terms of sufficient conditional­ ­­y ('T '), then one will also accept that there is a second definition, viz. one that involves necessary and sufficient conditions ('T '). Examples (91) and (92) illustrate the two cases. (91)

an assertion or belief that there is a chair is Τ relative to a particu­ lar SOA in which there is a chair and a table

(92)

an assertion or belief that there is a chair and a table is Τ relative to a particular SOA in which there is a chair and a table

One is forced to admit, on this account, that truth comes in two versions and, consequently, that we have two truth-values of truth. This conclusion is a simple one, yet it may be both overestimated and underestimated. As far as overestimation goes, one should not interpret the conclusion as implying that a conception of the one and only type of truth is necessarily mistaken and/or a mix-up of two totally different types of truth. On the contrary, although there are two types, they are related and may be taken to represent a sub-categori­ zation of a 'one and only' type of truth. Henceforth, I will call them 'subtypes', letting the one value of truth subsume its two 'subvalues'. The point about the two subtypes could also be mistaken for a trivial one.

106

REFLECTIONIST AND CONDITION-THEORETIC LOGIC

The assertion or belief of (92) can be said to imply that of (91). Now, whenever an assertion or belief is true, its implications are true, too. So claiming that the assertion or belief of (91) is true, when one also claims that of (92) to be true, shouldn't boggle anybody's mind. I have no qualms about this argument; yet I would like to take this train of thought to its 'terminal'. What I mean is that the truth of (92) is one thing and that of (91), to some extent, another. Again, both are truths, but they are different subtypes of truth. Of course, I still have to show that this subclassification is relevant. My subcategorization of truth depends on a distinction between two sub­ types of linguistic and psychological propositions. Consider (91) and (92) again. Their particular SOAs are identical. The propositions of the assertions or beliefs, though, are not, and it is this difference that subcategorizes truth. I will now have a closer look at the ontological side. As a preliminary, I will apply the thesis about the two subtypes of truth to my own theoretical dis­ course. So far, I have followed the convention, the origin of which lies in II.2.1, that the descriptions of propositions or 'propositional descriptions' are com­ plete (see the introduction to IV.3). I have adopted this convention for no other purpose than to ensure the clarity of the exposition and to prevent cer­ tain issues from unnecessarily complicating the account. It certainly seemed to be a straightforward idea to have a propositional description to '/?' refer to the proposition that p. I am now in a position to clarify my notion of complete­ ness. A propositional description can be regarded as a kind of assertion. When I am discussing the proposition that there is a chair and a table, there is some obvious sense in which I am asserting that the proposition in question is such that there is a chair and a table. What is equally obvious is that the prop­ ositional descriptions are true by definition. Given that propositional descrip­ tions are true then, they can be true in two ways : they can be Τ and Τ . If Τ , the proposition contains what is both necessary and sufficient for/?; the prop­ osition is an ns(p). If Τ , the proposition contains what is sufficient for/?; the proposition is an s(p). The relation between the subtypes of truth and the completeness of propositional descriptions should be clear: a propositional description is complete iff it is Τ . True propositional descriptions are Τ by convention. As I have claimed that'T ' is just one subtype of truth, which is in no way more true or more fun­ damental than 'T ', a problem of justification appears. Why does my conven­ tion refer to 'T ' rather than to Τs '? To some extent, the choice is indeed arns

s

'

bitrary. Yet, for the purpose of coming to grips with the notion of truth itself,

TRUTH

107

my choice is worth scrutinizing. Whenever an assertion or belief is true, it is not just true of the particular ns(p) SOA alone: I claim that it is true of the whole of reality. Take the assertion that there is a chair. If this is true, it is obvi­ ously true of the particular SOA in which there is a chair. But chairs are always somewhere. So if the chair in question is in a church, the assertion is also true of the particular SOA in which the chair is in a church. But again, chairs in churches do not exist in isolation. If there is a hotel near the church, the asser­ tion is no less true of the particular SOA in which the chair is in the church near the hotel. And so on. Clearly, the true assertion is true of the whole possible world in which the chair is in the church near the hotel. But the chair might not have been in a church, in which case the assertion is still true of the infinity of possible worlds defined by the presence of a chair outside of a church. In the end, it is nothing short of the whole universe that assertions or beliefs are true of. The universe now seems to be a huge, particular SOA of the 's(p)' type. It follows that the propositional descriptions of the particular SOAs that are in­ volved in the evaluation of truth must be understood as being Τs So propositional descriptions of particular SOAs associated with true as­ sertions or beliefs are read as Τ . But doesn't this amount to a revision of the s

convention on the completeness of propositional descriptions? Such a revi­ sion is neither wanted nor necessary. First of all, it is not desirable as it would only be partial. From linguistic and psychological viewpoints, the proposi­ tional descriptions would still have to be Tns. What I want to evaluate is an as­ sertion or belief that ns(p). When discussing the assertion that there is a chair, for instance, I am definitely not interested in the assertion that there is a chair and a table. Second, the revision can be avoided. Instead of changing the in­ terpretation of the propositional descriptions of particular SOAs, we can also change the propositional descriptions themselves. To be more specific, in­ stead of starting with a 'p' and giving it a 'T ' reading, we could start with an 's(p)' and give it a 'Tns ' interpretation. It is the second strategy that I will adopt. What cannot be avoided, however, is the task of once more defining the truth-subvalues on the basis of conditionality types. Indeed, the earlier de­ finitions were framed in terms of particular SOAs of the 'ns(p)' type. The obvious task is to inquire whether it still makes sense to distinguish between 'T ' and'T '. The answer is not obvious. A distinction that is defined ns

s

in terms of a mapping to particular ns(p) SOAs is not necessarily valid when the mapping involves particular s(p) SOAs. In fact, this distinction might be taken to be wholly invalidated. The subtype of truth involved in a pairing be­ tween a true assertion or belief and a particular s(p) SOA isalways'Ts'. What

108

REFLECTIONIST AND CONDITION-THEORETIC LOGIC

could be the point of maintaining a distinction between 'T ' and Τs ' if asser­ tions or beliefs, if true, can only be Τ ? Yet, the essence ofthe'T ns'-'T s' distinction can be saved, if it can be argued that truth, though fundamentally a matter of''Ts ', does split up into the two subtypescalled'T ns'and'T s'. This brings up the question of focalization. Though all assertions or beliefs are about the whole universe, there is al­ ways a part of the universe that they focus on. The true assertion that Alfred bakes cookies, for example, is true about a universe that includes the particu­ lar SOA in which the Indians lost the battle of Wounded Knee. The speaker making the assertion about Alfred, however, is probably not at all concerned about Wounded Knee. Perhaps, he or she is only interested in what comes out of Alfred's baking efforts or who among the speaker's friends bakes cookies. The speaker's interest or focus can be associated with a certain cut of the uni­ verse. Let me call this focus-relative particular SOA the 'F-SOA'. Thus, the speaker's focus on what it is that Alfred bakes could be associated with an FSOA in which Alfred bakes cookies and bagels, for example, or with an FSOA in which Alfred only bakes cookies. What has this got to do with the subcategorization of truth? Consider again the assertion that Alfred bakes cookies. If this is true, it is clearly Τ , for it is true about the whole universe, which was taken to be a particular SOA of th 's(p)' type. Suppose now that the assertion is associated with an F-SOA of Alfred baking cookies. With respect to this F-SOA, the assertion is clearly Tns . With respect to any other F-SOA, however, the assertion is, if true, T . If I now relativize the evaluation to both the universe and the F-SOA, then I ob­ tain a categorization of truth as 'T ' and a subcategorization in terms of T ' and 'T '. The subtypes of the one basic T will be called 'T ' and 'T '. The distinction between 'T ' and T ' is a claim about our intuitive notion of truth and the meanings of the words 'true' and 'truth'. Before I come to some general remarks on focalization and on its role in logic, I will try to ease some possible anxieties and gather some fairly straightforward support. First, I want to stress that F-SOAs are ontologicai entities. It must not be thought, therefore, that the introduction of the psychological phenomenon of focalization reduces truth to a relation between assertions or beliefs and psychological entities. Of course, my subcategorization does depend on the focalization phenomenon, but the reason for this is that the truth-value bearer is a psychological entity or the 'speaking-as-if of one. Secondly, if this F-SOA focalization is really as important for assertions or beliefs as I claim it to be, why is it then that for many assertions or beliefs

TRUTH

109

focus and F-SOA are completely vague? So vague, in fact, that it is impossible to determine whether the assertion or belief, when true, isΤs,nsorΤs,s? The answer is simply that Ts, ns' and 'T s,s' are only subtypes of truth. Thus, in many contexts, the subtype is totally irrelevant, the predominant question being whether the assertion or belief is true at all. In others, this is not so. Consider the following conversation: (93)

A - How many children do you have?  -- Three.

Suppose that  answers the question and focuses on the exact number of chil­ dren . If  ' s reply is true, its truth will be interpretedas'T s , n s'. Or consider the following scene. A is a city welfare worker who wants to know whether a par­ ticular couple, wife  and husband C, have at least three children. In this A-BC world parents get a special family allowance for three or more children.  knows what A wants to know;  and  have four children. The conversation starts as follows: (94a) A -- Do you have three children?  -- Yes, we have three children. At this very moment,  comes in. He hears B's reply but not A's question, and he does not have any idea what A is interested in.  can't believe his own ears when he hears his wife declare that they have three children and im­ mediately corrects her as follows: (94b)  - That is not true. We have four children.  reassures him: (94c)  — Oh well. Of course, we have four children. But then we have three, too, don't we? You see, the gentleman wants to know if we have three because of the family allowance. If you have three or more children, you get an allowance; other­ wise, you don't, see? What happens here is that  takes B's answer as an attempt to make a T as­ sertion about the number of their children, meaning that they have exactly or only three children. As an attempt at a T assertion, B's answer obviously fails, which explains why  accuses  of not telling the truth. Of course,  only wants to convey that they have at least three children and this, I now claim, can be characterized as an attempt to make a T or a Ts statement. If B's state­ ment is meant to be Τ , it is made relative to an F-SOA with four children; the

110

REFLECTIONIST AND CONDITION-THEORETIC LOGIC

subtype sufficiency is due to the fact that four is sufficient for three; we get an 'at least' because 'four' qualifies for 'at least three'. If B's statement is meant to be Τ only, then the F-SOA contains three or four (or five or six, etc., as long as there are at least three) children. Here, too, there is a type of suffi­ ciency, but it is neither the 'sufficient but unnecessary' of a T s,s ' reading nor the 'sufficient and necessary' of a Ts,ns ' reading; rather, it is indeterminate as to these two types. Like 'T ', however, and unlike 'T ', this 'T ' can be paraphrased with 'at least': when there are either three or four children, then there are at least three children. The 'at least' of the'Ts,' reading is the 'at least' that allows one to say that 'exactly three' implies 'at least three'. The other sense of 'at least' does not allow 'exactly three' to imply 'at least three'; this is the 'at least' of the 'T s,s ' reading. The 'T s,s ' 'at least' implies the 'Ts' 'at least', but the converse does not hold (see also V.3.1). The claims that the 'exactly' ofa'T s , n s' and the 'at least' ofa'T s , s' imply the 'at least' of a'T ', but not conversely, clarify my earlier claims that'T ' stands for the one truth type and that'T ' and 'T ' represent subtypes. To further clarify the distinction between'T s 'on the one hand,and'T s,ns'and'T s , s'on the other, I will make use of the notion of an assertion's literal meaning. Let the literal meaning of an assertion be the combination of its phrastic meaning and its assertive meaning, i.e. the 'speaking-as-if-one-believes' ele­ ment. A non-literal meaning of an assertion, on the other hand, is a combina­ tion of phrastic meaning, assertive meaning, and yet some other, extra mean­ ing which is dependent on the context. A ' T s ' reading, it seems to me, is a lit­ eral meaning, and the Τs,ns ' and Τs,s ' readings are non-literal. Thus I would claim that the literal meaning of the assertion that  and  have three children is just the combination of the speaking-as-if-one-believes meaning and the phrastic meaning that says that  and  have three children, leaving it unde­ cided whether they have exactly three children or more than three. We get 'Ts,ns ' and 'Ts,s ' readings if the context is taken to resolve the 'three or more' vagueness. In the context of the question how many children  and  have, the assertion will be given a'T s n s ' reading. In the context of an argument that derives this assertion from an assertion that  and  have four children, it will be given a 'Ts,s ' reading. I will leave unanswered the question ofwhether'T s,ns' and 'T s,s ' readings exemplify the type of non-literal meanings that Grice (1975, n.d.) has called 'conversational implicatures' (see also Horn 1972). In any case, one big difference between a 'classical' Gricean account and mine is that I distinguish between two types of 'at least' and that the Gricean one does not. So much for sorting out literal and non-literal meanings. I will now return

TRUTH

111

to a more general matter. The very idea that an understanding of truth has something to do with focahzation is bound to be met with scepticism. In our contemporary climate of thought, it is customary to consider truth as an unanalyzed primitive and to be suspicious of anything coming from psychology. Let me now meet the logicians on their own ground. I will attempt to show that even an orthodox CPL interpretation must ultimately rest on employing focahzation and on a subcategorization of truth. Consider the classical truth-tables for conjunction and disjunction:

Let me interpret these tables in a harmless way. Let 'p' and 'q' stand for ran­ domly chosen assertions or, at least, assertion type objects, which can be true or false. I claim now that if 'p', 'q', 'p ^ q', and 'ρ ν q' are true at all, they must be true of the whole universe. Classical logicians — though agreeing, I hope — might retort that it has never been the task of truth tables to show this, which I fully acknowledge; but it does not make the truth of 'p', 'q','p ^ q', and 'ρ ν q'' any less a matter of 'Ts '.

112

REFLECTIONIST AND CONDITION-THEORETIC LOGIC

(98)

I will now bring in the subtypes of truth. Consider (97). On each line, the interpretation of the conjunction is made to depend on a different segment of reality. On the first line, for example, the interpretation is relativized to the universe — trivially so — as well as to a particular SOA in which both 'p' and 'q' are true. This particular SOA is nothing else than my F-SOA. On the sec­ ond line the logician's focus has shifted. The reference frame still involves the universe, but the F-SOA is one of the truth of 'p' and of the falsity of 'q' On the third and fourth lines the focus shifts again. I conclude that the truth-table procedure most perfectly illustrates the focalization phenomenon as well as its relevance for truth. It also illustrates that my distinction between 'Ts,ns 'and'T s , s' is not as unfamiliar as the terms suggest. Since the CPL truth-table procedure is based on focus, and since focus defines two subtypes of truth, it may be possible to subcategorize the 'T s ' of tables (97) and (98). To start with (97), if one accepts the premise of CPL that tables (97) and (98) catalogue all the possible distribu­ tions of the truth-values of the components 'p' and 'q' then it is clear that the circumstances of the first line of (97) are both necessary and sufficient for the truth of 'p ^ q' The 'T s ' of 'p ^ q' must therefore be a 'T,sns '.See table (99). (99)

The situation is markedly different for the disjunction. Here the truth-table informs us about three types of circumstances that are all sufficient and un­ necessary for the truth of'pvq'.It follows that the truth of 'ρ ν q' is, each time, 'T '. '

s,s

TRUTH

(100)

ρ

ν

q

Τs

Τs,s

Τs

Τs

Τs,s

F

F

Τ s,s

Τs

F

F

F

11

Let me emphasize that what I have been doing so far is showing that the notion of focus and the focus-relative two-subvaluedness of truth is not as foreign to present-day logic as they seem to be. They are an implicit ingredient of such simple endeavors as that of the CPL interpretation of '^' and ' v ' . They are essential to them. If logicians didn't accept my characterization of the 'T' of 'p ν q' as 'Ts,s ', for example, I would have to admit that I haven't properly understood what CPL is about. Logicians might again retort that they are not really interested in the distinction between Τ 'and'T s , s', just as they confessed no interest in clarifying that all truth is 'T '. This time around, however, a lack of interest is less excusable. Logicians can afford not to let themselves be disturbed by the fact that all truth is Τ ', since this has no dis­ criminative value for the study of propositional operators. The case is dramat­ ically different for the 'T ' - 'T ' distinction, however. 'T ' seems to characterize conj unctionand'T s , s' disj unction. Logicians cannot neglect to in­ vestigate this in more detail. By now, I hope my readers grant me that a proposal for a focus-relative subcategorization of truth deserves some credit. I will deal with one more objection. Some might want to say that I have totally missed the point. I have not analyzed 'true', but only 'true of and, as Platts (1979: 23) has it — and Quine (1961d: 130), who takes 'truth of as a synonym of 'denotation', might have it — 'true' and 'true of' just aren't the same. My rejoinder is the following. It is not the case that I am not aware of the distinction between 'true' and 'true of, and that I mix them up unconsciously. Quite to the contrary, I am most conscious of 'mixing them up'. It is a hallmark of my approach that 'true' is analyzed as 'true of' and that all truth is 'truth of. Of course, I know that when we call something true, we often do not mention the ontological relatum. The reasons for this are simple. Either the ontological relatum is obvious or it is irrelevant. Thus, the universe is obvious. It is always the final reference frame. So why bother mentioning it? The other ontological relata are the F-SOAs. But, as the distinction between Ts,ns ' and

114

REFLECONIST AND CONDITION-THEORETIC LOGIC

'Ts,s ' is often either contextually irrelevant or obvious, there is again no point in spelling out what some assertion or belief, when true, is true of. What I am doing here is regarding 'true' as a dyadic and pseudo-monadic predicate. By 'pseudo-monadic predicate' I will understand a dyadic predicate that is often used as if it were monadic. I will have a more detailed look at pseudomonadics in the next chapter. The proposal to regard 'true' as a dyadic and pseudo-monadic predicate is relatively new. The common view is that 'true' is a monadic. This view is forcefully expressed by Frege (1967:18): "the word 'true', which is not a relation-word and contains no reference to anything else to which something must correspond."

Yet, though the view that 'true' is only abbreviatory for 'true of is unor­ thodox, the idea that there is something relational about 'true' is not. It is the essential ingredient of the widely held 'Correspondence Theory of Truth', ac­ cording to which truth consists of a correspondence with the facts61 (see also IV.4.4). Still closer to my 'true of' thesis comes possible worlds semantics. The least one can say is that the possible worlds semanticist has a use for the phrase 'true of'. Here, again (see note 17), is Lewis's definition of a possible world: "Anything which could appropriately be called a world, must be such that one or another of every pair of contradictory propositions would apply to or be true of it". (Lewis 1946: 56; my emphasis)

Officially, Lewis espouses the monadic conception of truth, but occasionally, he slips into 'truth of' talk, without theorizing about it. An example of some­ one who theorizes about it, however, but insufficiently so, is Mates. In his Leibnizian semantics, Mates (1968: 525) formally defines a notion of 'true of', but he remains silent on the relation between 'true' and 'true of'. All this is not to say that logicians have not theorized about both 'true' and 'true of' or even proposed to derive the one from the other; yet, much to my surprise, the more primitive of the two predicates is more commonly thought to be that of 'true'. 62 Consider Plantinga (1977: 141): "Truth-in-W [W = possible world] is to be explained in terms of truth simpliciter; not vice versa. A proposition is true in the actual world if it is true; it is true in W if it would have been true had W been actual. "

Some implicit support for the claim that all truth is 'truth of' may also be gathered from Mackie's (1973b) 'simple theory of truth'. First of all, Mackie (1973b: 19) allows predicate expressions to be 'true of objects and subject ex-

TRUTH

115

pressions to be 'sub-true' of concepts. Secondly, although sentences and statements are just 'true' (1973b: 19), Mackie occasionally employs 'truth of: "But what is the closed sentence 'Dolores loves Dagmar' true of? Presumably the universe at the time in question." (43; my emphasis) and "But what satisfies a closed sentence, what it is true of and therefore true, is the universe, all sets of objects. " (48 ; my emphasis)

With "true of, and therefore true", Mackie has unconsciously expressed one of the essential points of the theory of truth defended here. But he does not capitalize on it. Notice two other things about these quotations. First, Mackie is quite aware of the fact that, in the end, everything that is true, is true of the universe.63 Second, Mackie connects 'true' and 'true of with 'satisfies'. This will be singled out for special attention in IV.4.6. 4.3. Three-valuedness64 The fact that truth can be defined in terms of sufficient and of necessary and sufficient conditions invites us to try and define other values in terms of necessary conditions. In order to do this, it makes sense to distinguish be­ tween the three subtypes of necessity. (101) to (103) exemplify ne, ni, and nei conditionalities. I have not filled in any truth-values yet. (101) an assertion or belief that there is a chair and a table is ... relative to the universe and an F-SOA in which there is a chair (102) an assertion or belief that there is a chair and a table is ... relative to the universe and an F-SOA in which there is some furniture (103) an assertion or belief that there is a chair and a table is ... relative to the universe and an F-SOA in which there is one piece of furni­ ture None of the above F-SOAs is sufficient for the truth of an assertion or belief that there is a chair and a table. That much is both obvious and uncontroversial. So is the contention that both (101) and (103) render the value 'false' ('F'). Surely, when the F-SOA only contains a chair or one piece of furniture, it is false that it contains both a chair and a table. What is perhaps less obvious and definitely less uncontroversial is the claim that the value of (102) is not one of falsity. It seems to me that an F-SOA with furniture in it does not exclude the possibility that the furniture in question consists of a chair and a table. So the truth-value of (102) is one of possibility, indeterminacy, or undetermined-

116

REFLECnONIST AND CONDITION-THEORETIC LOGIC

ness CU'). Since 'F' and 'U' are always conceived of as relative to the universe, they come out as 'F ' and 'Us ', just as 'T' always comes out as Τ '. Just like truth, both falsity and indeterminacy can be categorized in terms of a choice be­ tween sufficient and necessary and sufficient conditions. Take the falsity of (101). A universe with an F-SOA of a chair is not necessary for the falsity of the 'chair and table' assertion or belief. It is only sufficient. So what is needed in (101) is Τs,s ' rather than 'Fs,ns '. However, whereas in the case of truth, the 'ns' and 's' subscripts also capture the conditionality relation between the proposition of the assertion or belief and that of the F-SOA, for falsity and in­ determinacy we need an additional index. In (101), for example, the condi­ tionality relation is one of expansion necessity. So the second subscript is 'ne', and the subvalue of (101) can be symbolized as 'Fs,s,ne' (104) an assertion or belief that there is a chair and a table is F ssn e relative to the universe and an F-SOA in which there is a chair The same type of argument gives us Έ

ei s,sn '

for (103) and 'Us,sni' for (102):

(105) an assertion or belief that there is a chair and a table is F s,snei relative to the universe and an F-SOA in which there is one piece of furniture (106) an assertion or belief that there is a chair and a table is Us,s,ni relative to the universe and an F-SOA in which there is some furniture If we look closer at the list of subvalues described so far, it becomes clear there are other ways to expand it. For one thing, we could bring in non-basic conditions, such as impossibility conditions: (107) an assertion or belief that there is a chair and a table is F relative to the universe and an F-SOA in which it is not the case that there is a chair and a table For another thing, if a subcategorization in terms of expansion and instantia­ tion is allowed for necessity, there is no reason why it could not be undertaken for sufficiency. Thus one can easily define a subvalue like T s,s i ', for instance. (108) an assertion or belief that there is a chair and a table isTs,si relative to the universe and an F-SOA in which there is an armchair and a table And one could investigate whether the second sufficiency of 'Fs,s ' and 'Us,s ' splits up into three groups, too, and even whether it makes sense to sub-

TRUTH

117

categorize the 's' of 'Τs,' 'F s ' and 'U s '. But I will not go into such matters here. The main purpose of this paragraph is to give an idea of the available subvalues. Yet in most of what follows, I will abstract from many-subvaluedness. I will use Quine's (1960: 160) 'Maxim of Shallow Analysis' ('Do not expose more logical structure than required') and restrict myself to three-valuedness. It is worthy of emphasis that my third truth-value is not prompted by 'epistemological' considerations. It is not specifically designed to capture the fact that people can be in doubt as to whether something is true or false. Of course, it does capture this fact, too, but only because 'U ' can be interpreted mentalistically, just like'T '. But 'U ' can also be interpreted linguistically and ontologically, like in the interpretation adopted above. The real explanation why RPL is a three-valued system is that its truth-valuations are effected rela­ tive to abstract segments of the universe called 'F-SOAs', and that not all FSOAs guarantee truth or falsity. The connection between three-valuedness and F-SOA-relativization also helps to explain some of the intuitive appeal of the claim that logic is basi­ cally two-valued. Though an F-SOA is an ontological entity and truly contains a cut of 'what there is' rather than of 'what there is said or thought to be', the 'location' of the cut is dependent on what the asserter or believer wants to focus on. Notice here the appearance of an asserter or believer. The only thing that we must do to filter a two-valued logic out of a three-valued one is to put a restriction on the asserter's or believer's focalization. If the latter only wants to focus on something that guarantees truth of falsity, there is no need for any third value. The bivalence thesis sounds attractive because asserters and be­ lievers do in fact often restrict their focus on what should guarantee either truth or falsity. Put into this perspective, I can see a justification for two-val­ uedness: a two-valued logic is just a pragmatically and mentalistically defend­ able simplification of a three-valued one. Observe that my striking down the number of truth-values from the basic set of three to only two has been based on a non-ontological argument. The complementary reasoning is offered by such proponents of two-valuedness who would reject to enlarging the set of values to three on the argument that doing so would mean that one is no longer dealing with 'what there is'. A lot more could be said about the question how many values a logic should have. In particular, it remains to be discussed whether the description of words, concepts, and ontological categories needs a three-valued logic, or if its two-valued simplification will suffice. The next chapter will indicate that it is the three-valued one. It will also introduce the notion of 'supervalue'

118

REFLECTIONIST AND CONDITION-THEORETIC LOGIC

(in V.3.1), which will allow us to state that RPL is two-supervalued. 4.4. Correspondence and Coherence I wholeheartedly embrace a Correspondence Theory of Truth. That is to say that my account is intended to elucidate the rather commonsensical view — which one may even believe to be "founded upon and drawn from the un­ iform consent of the human race and the practical needs of humanity" (Poland 1896: 66) — that an assertion or belief is true iff it 'corresponds' to reality. The fact that I endorse the Correspondence Theory is not accidental. It parallels the acceptance of the Correspondence Theory by the modern reflectionist schools of thought, such as logical atomism or dialectical materialism (see Petrovic 1967: 190-198; Puntel 1978: 31-36). There are different types of Correspondence Theories. Some (e.g. Wittgenstein 1922; Sellars 1962) claim a structural similarity between truthvalue bearer and reality. Others (e.g. Austin 1970b [1950]; Unger 1975) do not. My views on propositional abstraction should make it clear that I count myself among the first group. It should also be clear that my account is open to the usual objection that the notion of correspondence is as much in need of ex­ planation as the notion of truth itself. To which I agree: the notion of corres­ pondence is indeed vague. This is why I have embedded my version of the Correspondence Theory in a larger enterprise of clarifying what it means to say that language and mind reflect reality. The chief competitor to the Correspondence Theory is the Coherence Theory. The latter defines an assertion or belief, or a set of assertions or be­ liefs, as true iff it is coherent or consistent in some sense. Let us have a closer look at the notion of coherence itself. At first glance, there appear to be two types of coherence, viz. coherence with something to the outside ('external coherence') and coherence within ('internal coherence'). These notions are interdefinable. The internal coher­ ence of an entity χ can be understood in terms of the external coherence of the parts of x. Conversely, when two entities χ and y are coherent with each other, the conjunction of χ and y can be said to be internally coherent. On the relation between internal coherence and truth I will be brief. Can internal coherence be the basis of truth? In my opinion, such a view is self-evidently false. For, if it were true, a scientific theory could not be distinguished from a consistent fairy tale posing as a theory. But what about external coher­ ence? This is a harder nut to crack. It seems to me that assertions or beliefs can be consistent with each other or with reality. Coherence theorists prefer to

TRUTH

119

discuss the first case (only); I will start with the second. It seems to me that coherence with reality must be described in terms of'T s ' and 'Us ' : whenever an assertion or belief is either Τ or U relative to the universe and to some Fs

s

SOA, the assertion or belief, on the one hand, and the universe and the FSOA, on the other, are consistent with each other. In the 'F ' case, they are in­ consistent. Thus 'consistent with reality' means 'not false of reality'. Though every true assertion or belief is consistent with reality, not every assertion or belief that is consistent with reality is true. So the external consistency be­ tween assertions or beliefs, and reality does not define truth. The external consistency between assertions or beliefs and other assertions or beliefs does not fare any better, for it can be defined in terms of the first type of external consistency. An assertion or belief that p is consistent with an assertion or be­ lief that q iff the assertion or belief that ρ is consistent with reality and the FSOA of q. Another matter is that an external consistency among assertions or beliefs can be defined in terms of internal consistency. When the internally consistent fairy tale consist of the assertions 'p' and 'q', then the assertions 'p' and 'q' are externally consistent with each other, and conversely. Somebody might retort that I have thus far only characterized consis­ tency and that coherence is a much richer notion (cp. Rescher 1973b: 169-175; Puntel 1978: 179,191). This may be correct, but I cannot help feeling that no notion of coherence gives us truth, unless what is added to consistency to reach coherence and therefore truth eliminates the 'U ' of the 'T -or-U ' consistency. However, this would only extend our ordinary notion of coherence, making it synonymous with 'correspondence'. Going one step further, one could extend the notion of coherence as well as that of truth. This was practiced in Hegelian versions of the Coherence Theory (see L.J. Cohen 1978), held by such philosophers as F.H. Bradley (1911), Blanshard (1939), and Joachim (1939). Under this extension, coherence is meant to include comprehensive­ ness, in the sense that the true theory of reality implies an answer to absolutely all possible questions. It should be clear that such a conception is very artifi­ cial. The one and only comprehensive set of assertions or beliefs and, in a sec­ ondary sense, any assertion or belief that is a member of this set, is not the kind of entity most humans ascribe their notion of truth to. My appraisal of the Coherence Theory has been negative. Yet I believe that it is partially correct. My definition of truth involves a correspondence with particular SOAs. In a sense, those particular SOAs are out of human reach: they are actual or non-actual whether or not we think or talk about them. But there is another sense in which they are not out of our reach: after

120

REFLECTIONIST AND CONDITION-THEORETIC LOGIC

all, we can make assertions or hold beliefs about them. For what else could it mean, in this connection, for something to be within our reach than that we, the 'indispensable thinker-talkers' (see 1.1.3), can think or talk about it? Of course, to the extent that particular SOAs are within reach, we are no longer dealing with the particular SOAs as such, but only with beliefs and assertions about them. From the 'indispensable thinker-talker' perspective, the corres­ pondence that defines truth no longer holds between assertions or beliefs and particular SOAs, but between assertions/beliefs and assertions/beliefs (cp. Neurath 1931: 396-397; Puntel 1978:208-209). Why, now, does the indispens­ able thinker-talker think or say that some assertion or belief that ρ is true? Surely not because he or she says or thinks that the assertion or belief that ρ corresponds with another assertion or belief that p . It is here, I believe, that the Coherence Theory is partially right when it claims that truth is a matter of coherence. In part, the indispensable thinker-talker will think or say that the assertion or belief that/? is true because it is coherent with what is already held or said to be true. But the Coherence Theory is only partially correct. The in­ dispensable thinker-talker may have other reasons to say or hold that an asser­ tion or belief is true. He or she may judge the truth-value of the assertion or belief by evaluating its effects upon action, the way it 'works' or 'pays off' (a pragmatist view), its acceptance by society or (scientific) authorities, or by consulting his or her intuitions. Such are the criteria, good or bad, which the indispensable thinker-talker uses in saying or thinking that an assertion or be­ lief is true. Each of these criteria defines a subtype of 'thinker-talker-relative truth' 65 : 'true' as 'what is coherent', as 'what guides our action', as 'the hypothesis that works', as 'what is generally accepted', etc. My view about these subtypes of thinker-talker-relative truth is not in­ compatible with the thesis that all truth is a matter of correspondence. To clarify this, let me first point out that the above typology of thinker-talker-rel­ ative truth is not the first typology of truth that I have supplied in this book. I have distinguished earlier between the ontologically true, what is believed to be ontologically true, and what is asserted to be ontologically true. I claim that the typology of thinker-talker-relative truth is basically a refinement of what is believed and what is asserted to be ontologically true, but not of ontological truth. Ontological truth, I further claim, is definitely a matter of correspon­ dence. If both these claims are correct, then it follows that the Correspon­ dence thesis applies to the subtypes of ţhinker-talker-relative truth, too. Spelled out in more detail, my reasoning goes like this: Correspondence Theory describes ontological truth; as thinker-talker-relative truth is a matter

TRUTH

121

of asserting and believing an ontological truth, ontological truth is one of the components of thinker-talker-relative truth; hence Correspondence Theory is one of the components of thinker-talker-relative truth theories, and all truth is a matter of correspondence, Q.E.D. 4.5. Λ tinge of holism The bearer of a truth-value is an individual assertion or belief. This is cor­ rect, but it is not (correct) enough. Consider the discrepancy between the lin­ guistic or mental and the ontological relata of the truth relation (Figure 11). assertion belief

that

linguistic psychological

p

SOA of ns(p)

F-SOA

possible world

universe

ontological Figure 11

On the ontological side, there are four entities. I have concentrated on the F-SOA and the universe so far. It is clear, however, that there is always a par­ ticular ns(p) SOA; it may, of course, be identical to the F-SOA. Given our on­ tology, it is furthermore clear that there is a possible world mediating F-SOA and universe. On the linguistic and psychological side, however, we really have one entity. This discrepancy poses a problem for the reflection thesis. Two solutions suggest themselves: (a) the reflection thesis simply does not apply here; (b) there is more to the issue of truth-value bearers than claiming that they involve individual assertions or beliefs. I will argue for the second solution. Is it the case that only individual assertions and beliefs can be true, unde­ termined, or false? My answer is negative. Take the beliefs represented in (109) and (110): (109) Stockholm is beautiful and cold. (110) Stockholm is beautiful. Whatever an implication really is (see V.5), to say that the belief of (109) im­ plies that of (110) is fairly uncontroversial. If the first is Τ , then so is the sec­ ond. If the first is U or F , then the second is either Τ , Us, or F§. This clearly illustrates that the truth-value of a belief is related to the truth-values of the

122

REFLECTIONIST AND CONDITION-THEORETIC LOGIC

beliefs implied by it. In fact, this truth-value relation is a property of all be­ liefs, not just of the ones that imply each other. Consider the belief of (111) in relation to that of (109): ( 111 ) John bought two tulips. Even if John's tulips have nothing to do with the beauty or the climate of Stock­ holm, there is still a truth-value relation. This relation, a seemingly trivial one, is such that the belief of (111) may be Ts, Us , or F , independently of the truth-value of the belief of (109). This illustration establishes that there exists no belief whose truth-value is not related to that0ofall other beliefs. This awareness of the essential interrelatedness of the truth-values of all beliefs leads us to venture the conclusion that it is always the system of all beliefs, and never only an individual belief, that is evaluated. This conclusion is a bold one, but as a first approximation it is perfect. Our diagram of the truth relation can now be enriched with the psychological counterpart to the universe, viz. the set of all beliefs. Let me call this belief set B.'. (See Figure 12) belief that p psychological

SOA of ns(p)

F-SOA

possible world

universe

1 ontologi cal Figure 12

The sketch in Figure 12 amounts to a crude holism.66 It has to be refined in various ways. For a start, the belief set  must be split up in two subsets, in the same way as the universe divides up into a world and a set of non-worlds. The first subset includes the belief that ρ, and it is internally consistent. It will be symbolized as 'B p '. The second subset contains belief sets that are all inter­ nally consistent, but inconsistent with the belief that p. Each of these will be called 'B" p '. The distinction between B p and B p is prompted by the fact that the effect of the truth-value of the belief that ρ on the truth-value of B p is dif­ ferent from its effect on the truth-value of B- p . If the belief that p isΤs, then B p is Us, and B-P is Fs. If the belief that p is Fs, however, then B" p is u s , a n d B p is F . If the belief is Us , finally, then both BpS and B _ p are U . (See Figure 13)

TRUTH

then Bp

If

belief that ρ

Us

Τss

Us Fs

Us

123

B-p

Fs Us

Us Fs Figure13

One should note the following points. First, the claim that the truthvalue of a belief that ρ implies a certain truth-value for the set of all beliefs is misleading. The truth-value of the belief that p only implies a truth-value for the subsets B p and B- p . Perhaps the irrelevance of the truth-value of the belief that ρ for the truth-value of  may be considered a sufficient ground for drop­ ping the term 'holism'. But I do not have any adequate one-word '-ism' to re­ place it with. It is remarkable, second, that the truth-value of the belief that p can imply both the falsity and the indeterminacy of B p and  p ; but it can never imply their truth. This points to a possible justification of the existence of falsificationist schools in the philosophy of science. Third, there is an interesting sense in which the truth-value of B p and B~ p , when implied by the truth-value of the individual belief that/?, could be called 'vague'. Suppose that the belief that p is a belief of physics and suppose that it is false. This means that B p is false, too. But B p also contains beliefs about mathematics, logic, theology, linguistics, our day-to-day existence, and so on. While this giant 'web of belief is in fact false, it is unlikely that any of the frag­ ments of theology, linguistics, and ordinary life knowledge are falsified. It seems entirely correct, therefore, to postulate an intermediate entity between the belief that ρ and B p . Its extension is essentially vague, but minimally, it equals the belief that/?. Now, there already exists such an intermediate entity on the ontologicai side, viz. that of the F-SOA. So we have the machinery for defining the intermediate belief. Beliefs are not only about a certain possible world and about the universe; they always focus on a F-SOA. Let me call the set of beliefs that aim to describe an F-SOA an 'F-belief. Thus, the F-belief for some belief about a physical problem is either just this one belief or a clus­ ter of beliefs that all have something to do with the problem in question. When the individual belief is false, both B p and the F-belief are false, too ; but it is un­ likely that the giant set of beliefs that do not belong to the F-belief is false.

124

REFLECTIONIST AND CONDITION-THEORETIC LOGIC

Interestingly, Quine, one of the more radical defenders of holism, is quite aware of the F-beief phenomenon (see Gochet 1978: 26-27), but his treatment is an 'isolated' one. In the present analysis, however, it follows from a general thesis about focalization, it has an ontological counterpart (involv­ ing the F-SO A), and I see no reason why there should not also be a linguistic as well as a propositional one. To sum up, while I pleaded earlier (IV.4.2) for an ontological holism ac­ cording to which the truth-value of an assertion or belief is relativized to a pos­ sible world and the universe, and while this holism was refined with a notion of focalization, in this section, I argued for a similar and similarly refined holism with regard to truth-value bearers. Through its emphasis on the interrelatedness of all assertions and beliefs, this holism may capture some of the intuitive appeal of the Coherence Theory. Hopefully, it also integrates some elements of holistic proposals such as Quine's. Above all, the very parallel­ ism between the ontological holism and the one about assertions and beliefs should be seen as an unexpected, but forceful corroboration of the reflection thesis. 4.6. Truth and satisfaction It would be improper to pass over Tarski's celebrated 'semantic' theory of truth (Tarski 1936,1944,1969). Still, this is not the appropriate place for a thorough assessment of Tarski's contribution or of the work it has engen­ dered. Tarski's writings have little (new) to offer on the subject matter of the present sections, i.e. on questions about the fundamental properties of our or­ dinary notion of truth and about the number of truth-values. Therefore, I will restrict myself to some brief remarks on Tarski's proposal to define truth in terms of a more general concept of satisfaction. Before I come to this, how­ ever, I will make two controversial assumptions. First, I assume that it is valid to interpret Tarski's truth theory as a Correspondence Theory (cp. S. Haack 1976a: 324-325,1978: 110-114; Puntel 1978: 44-47, 63-65). Second, I assume that Tarski's theory applies to our ordinary language notion of truth. Tarski himself, incidentally, didn't think so. Tarski wants to show how the truth conditions of a sentence depend on the properties of the components of the sentence. If the components are sen­ tences, it is the interplay of the truth conditions of the component sentences that determines the truth conditions of the compound sentence. But what in case the components are not sentences? Tarski's answer is that some compo­ nents can be satisfied. The truth conditions of sentences are thus determined

TRUTH

125

by the satisfaction conditions of components. What is more, even sentences, when true, can be said to be satisfied, be it in a somewhat peculiar way. Thus satisfaction is a more general notion than truth; truth gets defined in terms of satisfaction. The analysis of the sentence is performed according to Standard Predi­ cate Calculus, turning out expressions like (112), (113), and (114): (112) Ha (113) χ (Hx) (114) χ (Hx) Sentence components that can be satisfied are predicates (such as '.H'), open sentences or sentential functions (such as 'Hx'), and (closed) sentences. To understand the workings of satisfaction, it is sufficient to study the satisfac­ tion of predicates. So let us turn to (112). Let '' be the name of an object, say a. It is precisely this object which can satisfy the predicate. The satisfaction condition is set out below: (115) α satisfies 'H' iff α is Η (116) exemplifies this: (116) Hamlet satisfies 'sees a ghost' iff Hamlet sees a ghost So much for the exposition. As to the assessment,I want to deny that truth, at least when understood in the ordinary way, is to be defined in terms of satisfaction for the simple reason that satisfaction talk is only a terminologi­ cal variation of truth talk. My argument is simple. Tarski's 'satisfaction' is a term of art. So I feel justified to translate it into a familiar idiom. Now, if I am not allowed to translate (116) into (117), I confess that I do not understand what (116) is all about. (117) 'sees a ghost' is true of Hamlet iff Hamlet sees a ghost The step from the 'true of' of (117) to my own 'true of is an easy one. Since the word order in 'sees a ghost' is to have a significance, since there is a point in writing 'sees a ghost' rather than 'a ghost sees', 'sees a ghost' must be elliptical for 'somebody or something sees a ghost'. To have an RPL 'true of' applied to it, 'somebody or something sees a ghost' is either an assertion or a belief. In RPL, assertions and beliefs are true of SOAs. Though the 'true of of (117) applies to an object, this can easily be translated into SOA talk: after all, ob­ jects only exist in SOAs. More concretely, 'Hamlet' defines the F-SOA in which there is a Hamlet.

126

REFLECTIONIST AND CONDITION-THEORETIC LOGIC

(118) an assertion or belief that somebody or something sees a ghost is true relative to the universe and an F-SOA with Hamlet in it iff this SOA is one in which Hamlet sees a ghost Again, if I cannot interpret (117) as (118), then I do not know what (117) means. The moral of this exercise is obvious. The idea that truth is definable in terms of satisfaction must be laid to rest. Truth is fundamentally 'truth of and so is satisfaction. The literature contains implicit support for this thesis as well as coun­ terarguments. One bit of support has already been mentioned. At the close of IV.4.3.1 quoted Mackie saying that: "what satisfies a closed sentence, what it is true of, and therefore true, is the universe, all sets of objects." (1973b: 48)

Other implicit support concerns the notion of 'satisfiability'. Brody offers a typical definition (cp. Blumberg 1967: 30; Massey 1970: 248-249): "A well-formed formula is satisfiable in a given domain of individuals if and only if it has the value truth for at least one system of possible values of its free variables." (Brody 1967: 74)

Although Brody doesn't say so explicitly, satisfiability and satisfation seem to administer the same intuition. If satisfiability is defined in terms of truth, the conclusion is that satisfiability/satisfaction is not more basic than truth.67 Platts (1979: 22-23) offers the following counterarguments: "Of course, you could gloss any of these occurrences of satisfaction in terms of truth; you could say, for example, that 'x2 = 4' is true of +2 and —2. But, first, why should we so gloss it? Second, is true of is not the same as is true, which is what we are defining. 'Is true of', 'is satisfied by', is a two-place rela­ tion, while 'is true', the truth-predicate, is a one-place predicate. Third, not all occurrences of satisfaction are so readily glossed: we can talk, by the defi­ nition, of closed sentences being satisfied, but it is not clear that we can talk of what they are true of."

My answers should not need belaboring. First, we gloss satisfaction in terms of truth because satisfaction is basically the same as truth. Second, all truth is 'truth of. Third, we can in fact translate all satisfaction talk into truth talk. Closed sentences, i.e. assertions that p, are true of the universe, of a possible world, of an F-SOA of ns(p) or s(p), as well as of a particular SOA of ns(p). By arguing against the basicness of satisfaction I do not mean to deny that 'satisfaction' can be a useful technical term. More importantly, I do not object to the idea underlying Tarski's work that the truth conditions of a sentence de-

TRUTH

127

pend on what the sentence parts say. My only point is that using Tarskian satis­ faction to make a component of a sentence that is not itself a sentence contrib­ ute to the truth conditions of the whole sentence is secretely invoking truth (cp. Juhos 1967: 183-184; Danto 1968: 255; Sommers 1969: 267; Tugendhat 1976: 321-322).

CHAPTER V PROPOSITIONAL OPERATORS

The preliminaries to this chapter will be kept in a low key. I will continue to pave the way towards the fulfillment of at least some of the promises of the Reflectionist and Condition-Theoretic Logic program. More particularly, I will study the propositional (RPL) operators 'it is true that', 'it is false that' or 'not', 'it is possible that', 'it is necessary that', 'it is impossible that', and 'if... then'. The analysis of 'if... then' will be the culmination point of the chapter. There are two reasons for this. First of all, it is clear that 'if... then' and 'if... then'-like constants belong to the core of logic. M.R. Cohen, for example, leaves no doubt about it (see also Quine 1950: xv-xvi, 33; Anderson and Belnap 1975:3): "the distinctive subject matter of logic may be said to be the relations ex­ pressed by if — then necessarily." (MR. Cohen 1944: 4) I hope, therefore, that if I succeed in providing a plausible account for 'if... then', the RPL program as such will gain some plausibility, too. The second reason is that an RPL account of 'if ... then is a convergence point of a fair number of independently argued hypotheses: (a) (b) (c)

(d) (e) (f) (g)

the determination to make the most out of the notions of suffi­ cient and necessary conditionality (Chapters IV and V,passim)', the distinction between SOAs and possible worlds (see II. 2.1 and II.2.3); the thesis that all truth is 'truth of (see IV.4.2) and the dyadic, presuppositionalist approach to truth, falsity, and indeterminacy operators (see V.3); the triadic, presuppositionalist approach to necessity, con­ tingency, and impossibility (see V.4); the claim that the above mentioned indeterminacy and con­ tingency are possibility types (see V.3.1 and V.4.1); the scalarity approach to possibility (see V.3.1 and V.4.1); the view on generic modality (see V.4.5).

130

PROPOSITIONAL OPERATORS

The following discussions could be cast in an abstract propositional, i.e. non-nominalist, non-mentalist, and non-realist frame. Yet, for the sake of vividness, the overall primacy of my linguistic aims, and the desire to ease the comparison with other types of logics, most of what follows is written in a nominalist mode, more particularly a pragmatic one, which centers on asser­ tions and their truth-values. I will try to distinguish between literal and non-literal assertive meanings, i.e. between those assertive meanings that merely combine the assertivity with the phrastic meaning, and those that combine assertivity, phrastic mean­ ing, and yet some context-dependent meaning (see IV.4.2). All the forthcom­ ing proposals on this distinction are tentative, however. At the present stage of the investigation, I do not have any good method — with regard to the words and phrases to be studied — for distinguishing between an assertion that has one literal meaning and various non-literal ones, and an assertion that has a plurality of literal meanings, which goes back to a plurality of phrastic meanings. In more common terms, for the operators at hand, I am not sure how to distinguish between (essentially pragmatic) vagueness and (essentially semantic) ambiguity. It should be emphasized again (see also Chapter I) that, although I am in­ terested in human language as such and have universalist aims, my analysis will be restricted to English. This makes the analysis language-particular, but only to some extent. I do not think that the basic meaning of the 'if... then' of English, for example, is drastically different from that of similar expressions of (many) other languages. This speculation is based on a reflection thesis: I believe that English 'if... then' reflects both an aspect of human thought and a feature of the universe, which are so basic that all human languages will have a linguistic reflection of it. 1.

Conditional and componential analyses

In the preceding chapter, I developed a theory about the interpretation of propositional variables and truth-values. We are not sufficiently equipped, however, to embark on an analysis of the corresponding operators. Suppose that we have a dyadic operator '$', 'generating' well-formed formulas (wffs) of the type ' p $ q ' There are at least three types of questions that one could ask about 'p $ q' with an eye towards defining '$': (a)

When is 'p $ q' true? What are the individually necessary and jointly sufficient conditions for 'p $ q' to be true?

CONDITIONAL AND COMPONENTIAL ANALYSES

131

(b) When is 'p $ q' true, false, undetermined? What are the individu­ ally necessary and jointly sufficient conditions for 'p $ q' to be true, false, or undetermined? (c) What is the relation between the truth-values of 'p' and 'q', on the one hand, and those of 'p$q' on the other? The analysis engendered by the first two questions will be called 'conditional' and the one that is associated with the third 'componential. The difference be­ tween the two types of conditional analyses is that the first only inquires into truth conditions, whereas the second inquires into truth-value conditions. Truth conditions are only one of the three types of truth-value conditions, next to falsity conditions and undeterminedness conditions. That both the conditional and the componential approach are valuable is not hard to see. To start with the componential approach, in a wff such as 'p $ q', two of the components have truth-values. Since the compound has a truthvalue, too, it seems natural to inquire into the relations between these truthvalues. Notice, however, that a componential analysis does not automatically do justice to the contribution of the operator. There is nothing to prevent there being two operators, '$ 1 ' and '$ 2 ', for which the relation between the truth-values of 'p' and 'q', on the one hand, and 'p $1 q' and 'p $2 q',on the other, is identical, but where 'ρ $1 q' and 'ρ $2 q' have different truth-valueconditions. The componential analysis is definitionally limited. It only con­ cerns those components of 'p $ q' that have truth-values. While it is true that '$' influences the way in which the truth-values of 'p' and 'q' combine into those of ' p $ q ' , ' $ ' itself does not have a truth-value. Whatever is typical and important for '$' that goes beyond its mapping the truth-values of the compo­ nents 'p' and 'q' into those of the compound, falls outside the scope of a com­ ponential analysis. Note that conditional analyses do not have this limitation. For CPL, there is only one kind of analysis. It is simultaneously truthconditional, truth-value-conditional, and componential. The fact that there is no difference between truth conditionality and truth-value conditionality is due to bivalence. That CPL analysis is both conditional and componential means that all that is necessary and sufficient for a truth-value of a CPL com­ pound is a constellation of the truth-values of the components. Both the CPL analysis and its operators are called 'truth-functional'. RPL, however, be­ longs to the class of non-truth-functional logics.68 Non-truth-functional logics house non-truth-functional operators, while they may also have truth-func­ tional ones. Non-truth-functional logics are usually subjected to conditional analyses only. RPL, however, will be given both a conditional and a compo-

PROPOSITIONAL OPERATORS

132

nential description. The motivation for giving a componential analysis is that there is always some dependence of the truth-value of the compound on the truth-values of the components, even if it is not absolute. RPL componential analyses will be presented in the usual tabular fashion. Of the two types of conditional analyses I choose the truth-value-conditional one, since its claims are stronger than those of the truth-conditional analysis. Such descriptive strength is called for: we will be confronting operators that have identical truth conditions but different truth-value conditions (V.3.1), as well as state­ ments that have truth-value conditions yet no truth conditions (V.3.3). 2.

Conjunction

Very little will be said about conjunctions here. Clearly, there is such a thing as a truth-functional conjunction (' ^'). Perhaps there is also a non-truthfunctional one, paraphrasable with 'and then', but I shall not go into this question, as the conjunction that I need later on is definitely the truth-func­ tional one. The classical truth-functional conjunction is dyadic. Within the three-valued RPL frame, it gets truth-table 1. Ρ

 q

Ts

Us Fs

Ts

Ts Us Fs

Us

Fs

Ts Us

Fs

Fs

Fs Fs

Table 1 The only problem is that conjunction is not realy dyadic but n-adic (cp. Braine 1978:9; McCawley 1981:78-81). I will reflect this in a natural language sort of way, viz. by repeating the conjunction between each pair of arguments. (119)

(^q^r)

I think that it is counterintuitive to render what is meant in (119) using either (120) or (121). (120) ((p^q)^r) (121) (ρ^ (q ^R))

TRUTH, FALSITY, AND POSSIBILITY

133

One may object that there is no real need for (119), as we would want it to have the same truth-value conditions as (120) and (121). This objection is partly correct. But even if (119), (120), and (121) have identical truth-value condi­ tions, that does not prove that conjunction is not n-adic. However close (119) may be to (120) and (121), if (120) and (121) are to represent (119), an element of structure is added which (119) simply lacks. Admittedly, this structural ele­ ment does not have any effect on the truth-values. So n-adic conjunction does not need a truth-functional analysis of its own. 3.

Truth, falsity, and possibility

Assertions can be true, false, or undetermined. But we can also assert that something is true, false, or undetermined. Some of the metalinguistic as­ pects of truth, falsity, and undeterminedness were dealt with in Chapter IV. In this section, I will translate some of these metalinguistic considerations into the object language. That is to say that some of the theses about the truthvalue 'true', etc. will be translated into theses about the operator 'it is true that', etc. This translation may appear to carry a great risk, viz. that of mixing object language and metalanguage and, possibly, generating paradoxes. However, I believe the translation itself to be safe; the next few pages consti­ tute an ad hominem proof of this. As to the appearance of paradoxes, I will de­ vote a whole subsection to it (V.3.3). Other issues on the agenda are the bivalence-trivalence debate, the so-called 'Redundancy Theory of Truth', scalarity, pseudo-monadicness, pseudo-dyadicness, and presupposition. 3.1. Values and supervalues Let '!', '~', and '≤≥' be our truth, falsity, and indeterminacy operators, re­ spectively. That indeterminacy is symbolized with a diamond, a symbol as­ sociated with possibility, is not a coincidence. What is here called 'indetermi­ nacy' and 'undeterminedness' is one side of possibility. (The other side must be understood in terms of necessity and impossibility and will be studied in V.4.) So I can read ' 0 ' as 'it is possible that', or even as 'it is possibly true and possibly false that'. Alternative, realist readings for '!', '~', and ' 0 ' are 'it is the case that', '(it is) not (the case that)', and '(it is) perhaps (the case and it is perhaps not the case that)'. Using a possibility that p, defined as a possibility that 'p' is true and a pos­ sibility that 'p' is false,69I propose the three-valued componential analysis of Table 2.

PROPOSITIONAL OPERATORS

134

!Ρ

Ρ Ts

Ts

Us

Us

Fs

~P

Op

Fs

Fs

Fs

Us

Ts

Ts

Fs

Table 2 Let me put Table 2 in prose, starting with the last column. When the value of '/?' is undetermined, '/?' is obviously true (it is true that it is undetermined whether p—middle cell). When the value of '/?' is not undetermined, i.e. when it is determined as either'T 'or 'F ', '≤≥p' is false (top and bottom cells). I now come to the top and bottom cells of thefirstand second column. When 'p' isΤs, it is clearly true that it is true that/? ('!/?' is true) and false that it is false that/? ('~p' is false). Conversely, when the value of '~' is 'Fs ', it is false that it is true that p ('!p' is false) and it is true that it is false that ρ ('~p' is true). As to the two remaining middle cells, they only render the fact that a possibility that ρ is taken to mean that it is possible that 'p' is true ('!p' is U ), and that it is possible that '/?' is false ('~p' isUs). Table 2 has a number of interesting features. First of all, it incorporates that version of the 'Redundancy Theory of Truth' that says that the assertion that/? and the assertion that it is true that/? have identical truth-value condi­ tions.70 It is worth noticing, however, that '/?' and '!/?' do not have identical subvalue conditions. Let me illustrate this for truth. If I subcategorize truth, the left-hand top corner of Table 2 gets 'mag­ nified'in Table 3. Ρ

!p

Ts

Ts,

ns

Tsn s

Ts,

s

Ts,s

Ts,

s

Table 3 This operation is not too self-evident. Here is the reasoning behind it.

TRUTH, FALSITY, AND POSSIBILITY

135

Another way of saying that ' !p' is evaluated with respect to 'p' being Τ , Τ , and Τ is to say that the truth-values of ' !p' are relative to F-SOAs in which 'p' is either Τs ,Τs,ns,, or Τs,s . Take the first line of Table 3: here the F-SOA is one in which 'p' is true, with 'true' taken in the general'T s sense. From this F-SOA I can abstract the proposition that 'p' is true (in the general sense). What is being evaluated relative to this F-SOA is the assertion '!p'. It has the phrastic that 'p' is true, where 'true' is again understood in the general sense. From this phrastic I can abstract a proposition, viz. the proposition that 'p' is true (in the general sense). To find out, finally, whether the assertion is true and, if true, whether it is Τ , Τ , or Ts,s I need to compare the proposition of the phras­ tic with that the F-SOA. In the case at hand, these propositions are identical. Conclusion: the assertion is Ts,ns The further conclusion is, quite surprisingly, that when 'p' isΤs, '!p' is Τs,ns . As to the second and third lines, the F-SOA propositions have a true 'p', where 'true' is to be taken in a subtype sense. The proposition for the assertion '!p', however, has a true 'p', in the general sense of 'true'. As it is sufficient but unnecessary for the presence of the type that it is manifested by a subtype, I can say that the F-SOA propositions are sufficient for the propositions of the assertions. Hence the assertions are Τ . The second interesting feature of Table 2 is the asymmetry between the columns for ' !p' and ' ~ p ' and the column for '≤≥p'. The former have an occur­ rence of each of the three values, while the latter only employs Fs 'and'T s'. The absence of 'U ' can be interpreted in at least two ways. Either it means that the 'logic' of 'Op' statements is only two-valued, that 'Op' is either true or false, and that the possibility of 'p' cannot itself be possible. Or it means that the table is incomplete. In V. 3.2,1 will defend the second interpretation, but even at this stage it may be pointed out that it is the more plausible of the two. If RPL is three-valued, why shouldn't this entail that all RPL wff's are 'threevaluable'? The asymmetry question brings up another point. So far, I have defined the possibility that ρ as a possibility that 'p' is true and as a possibility that 'p' is false. I believe that this captures some of the meaning of our ordinary (lan­ guage) notion of possibility. Yet there is another definition of ordinary (lan­ guage) possibility, which sounds equally acceptable but seems incompatible with the first. When 'p' is possible, doesn't this mean that 'p' is neither true nor false? Given my three values, what else could it mean that 'p' is possible, than that it is false that 'p' is true and false that 'p' is false?

PROPOSITIONAL OPERATORS

136 Ρ

Ts Us Fs

≤≥

!Ρ

~P

Τs

Fs

FS

Fs

Fs

Τs

Fs

Ts

Fs

Table 4 It is easy to see that the change in the definition of possibility has no effect on the truth-values of ' p' nor on those in the top and bottom cells of '!p' and ' ~ p ' . The difference between Tables 2 and 4 lies in the middle cells of the ' p' and ' p ' columns. When 'possible' means 'neither true nor false', then, obvi­ ously, when 'p' is Us, it is false that 'p' is true (' !p' is Fs) and it is false that 'p' is false ('~p' is F s ). Table 4 does not have the asymmetry of Table 2. Each column employs the same number of truth-values. But what makes us somewhat suspicious is that this number is not three, as one would expect in a logic that is declared to be three-valued. Even more suspicious is the fact that Table 4 confronts us with a notion of truth that does not obey any Redundancy Principle. The ' !p' of Table 4 does not have the truth-value conditions of 'p'. A third point of suspicion is that if both tables are correct, we seem to get two types of truth and two types of falsity, for the '!p' and ' ~ p ' truth-value conditions of Table 2 are different from those of Table 4. And yet there would be only one possibil­ ity, whether it is defined as 'possibly true and possibly false' or 'neither true nor false'. I will now start working towards the claim that Table 4 is not just suspicious but mistaken. The reason for constructing Table 4 was that possibility allows of two, seemingly incompatible definitions. But are these definitions incompatible? How can they be incompatible when they apply to one and the same notion of possibility? Possibility, it seems to me, is always a possibility of truth as well as of falsity, and nothing can forbid me to say that possibility is neither truth nor falsity. The fact that 'possible' may simultaneously mean 'possibly true and possibly false' and 'neither true nor false' seems to indicate that we operate with something like a hybrid between falsity and possibility, a possibility such that when 'p' is possible, 'p' can also be false, and a falsity such that when 'p' is false, 'p' can also be possible. This may seem bizarre, but it isn't. As we shall see, hybrid notions are extremely important and they form the subject matter of an

TRUTH, FALSITY, AND POSSIBILITY

137

independently argued theory, the so-called 'scalaritytheory'.71Scalarity theory deals with scales and with 'at least' meanings — with 'at least' in the Τ ' sense (see IV.4.2). Let us take a finite scale with the numbers 1,2, and 3. A scale al­ ways has an orientation. The 1-2-3-scale can go from 1 to 3 or from 3 to 1. In Figure 14 the scale has a l-to-3 orientation.

Figure 14 Given this orientation, an 'at least 2' with a 'T ' 'at least' can only mean '2 or more'. Moreover, given the finiteness of the scale, it can only mean '2 or 3'. What, now, does '2 or 3' mean? The sense of the disjunction that I am in­ terested in here is the classical truth-functional one: the fact that there are 2 in­ stances of something implies that there are 2 or 3, and so does the fact that there are 3. Semi-formally: (122) '2'implies'2 or 3' (123) '3' implies '2 or 3' '2 or 3' could be entered on the scale, too ; it becomes a hybrid between 2 and 3. This is represented in Figure 15.

Figure 15 In Figure 16, the scale has the less common, more marked72 orientation from 3 to 1, and 'at least 2' obviously means '2 or 1'.

Figure 16

138

PROPOSITIONAL OPERATORS

My final point is that when we reverse the direction yet again, the '2 or Γ can also be characterized as 'at most 2' (see Figure 17).

Figure 17 The relevance of this digression should be clear. Truth, possibility, and falsity define a three-point scale much like 1,2, and 3. Possibility takes up the middle rung. The unmarked direction goes from falsity to truth. This is rep­ resented in Figure 18.

Figure 18 'possible' has special scalar meanings just like '2'. The hybrid with 'true', 'pos­ sible or true', or 'at least possible' will be represented with a diamond (operator) or a 'Us ' (value) with an superscript asterisk (' '' and 'U* '). The hybrid with 'false', 'possible or false', or 'at most possible' gets a diamond or 'U s ' with a subscript asterisk (' ¿ and 'U* '). Figure 19 has the full scales.

Figure 19 The reason for using a diamond or 'U ' for the scalar notions is that they both represent aspects of possibility. Whether 'p' is at least possible or at most pos­ sible, 'p' remains possible, though its possibility is not that of < ' V'U '. ' VU ' is what has been called 'bilateral' or 'two-sided':73 if '!p' is U , so is '~p'', and, conversely, if ' ~ p ' is Us , so is '! p' — this holds good whether the '!' and ' ~ '

TRUTH, FALSITY, AND POSSIBILITY

139

come from Table 2 ('!2' and '~ 2 ') or from Table 4 ('!4' and '~4') Consider the tables in (124) : though I have not yet determined whether such tables are com­ plete— notice the absence of 'U ' for the ' ◊ ' of the first two tables, and the ab­ sence of Τ ' and 'Us ' for the ' ◊ ' of the last two — and the tables cannot, therefore, prove the thesis that ' ◊ ' is bilateral, they at least confirm it. (124) FS

!2

Ρ

◊

Τs

Τs

FS

Us

Us

Τs Fs

Fs

Fs

!

'4

Ρ

Fs

Τs

τ

F

F s

s

Fs

Fs

~2

Us Fs

Ts

Fs

ΤS

Us

Fs

Ts

F

s

Ρ

Us Fs

~4

Ρ

F

τ

s

s

Fs

Fs

Fs

Τs

s

Us Fs

Now, while '◊'/'U s 'is bilateral, '◊*7'U* s ' and '◊ * '/'U* s ' are 'unilateral' or 'one-sided': when '!p' is either U*s or U*s , ' ~ p ' is not, and conversely. This is shown in the tables in (125). (125) ΤS

i2

Ρ

Ts

Τs

τs Fs

Fs

Ts Ts

Us

~2

Us

Fs

Fs

!2

Ρ

Ts

Us Fs

Fs

Ts

Ts

Ts

Ts

Ts

Ts

Us

Ts

Fs

Ts

Fs

~

Fs

Ρ

2

Fs

Us Ts

Us Fs

Ρ Ts Us Fs

PROPOSITIONAL OPERATORS

140

◊* !4

Ρ

◊*

τs

Τs

τs

FS

Fs

Ts

Fs

Fs

Fs

Fs

Us

Fs

Fs

Fs

Τs

Τs

Fs

◊* !4

Ρ

◊*

~

Ρ

FS

Τs

Ts

Ts Fs Fs

Us

4

4

Ρ

Ts

Ts

Fs

Ts

Us

Ts

Fs

Us

Fs

Fs

Τs

Fs

To distinguish '◊*'/u* S ' from '◊*'/'u*s', the former will be called 'upperbound' and the latter lowerbound'. Notice that 'T ', 'U ', and 'F ' get sub­ sumed under 'U* ' and 'U *s 'in the same way as the subvalues 'Ts,ns, ', 'Ts,s ', etc. get subsumed under 'Ts,', 'U s ', and 'Fs,'. To indicate both the parallels and the differences, 'U *s ' and 'U *s ' will be called 'supervalues'. Paradoxically perhaps, upperboundness and lowerboundness do not exclude each other. To show this, I first need to define the notion of a 'Janus scale'. A Janus scale has something like a turning point. Every value above the turning point is mirrored by a value below it. The clearest example of a Janus scale is that of the positive and negative numbers (Figure 20)

Figure 20 Within the one Janus scale going from -8 to + 8, there are two subscales, the first going from 0 to + 8 and the second from 0 to - 8 . Thus the subscales have

TRUTH, FALSITY, AND POSSIBILITY

141

opposite orientations, as shown by the interrupted lines. I claim now that the possibility scale is actually a Janus scale, too (Figure 21).

Relative to the double, subscalar orientation, 'at least possible' means 'either true or possible or false'. I will call it 'double-bound' and represent it as '◊*'/ 'U* s '(Figure 22).

(126) is its truth-table. (126)

◊*

Ρ

Τs

Ts

Ts Us s

Τ

s

F s

s

Clearly, double-bound possibility is bilateral. For the moment, I only need one of the three supervalues described above. Remember that the reason for embarking on scalarity theory was a need to define a hybrid between possibility and falsity such that (a) when 'p' is possible, 'p' can still be false; and (b) when 'p' is false, 'p' can still be possible. The obvious candidate is 'U*s '. So far, I have shown that 'U *s ' is a possibilityfalsity hybrid in a double sense. First, whenever 'p' isU*s', 'p' is either Us orFs. Second, 'U*s ' is a possibility type with the property that when 'p' is possible, in this lowerbound sense of 'possible', 'p' can also be false (as well as possible in

142

PROPOSITIONAL OPERATORS

the neutral, 'unbound' sense). I will now argue that 'U *s ' can also be seen as a hybrid type of falsity, in particular, as a falsity that allows a possibility. This point takes me back to the bivalence issue. Everyone involved in the bivalence debate agrees on the so-called 'Univalence Principle'. In terms of the values 'T ', 'U ', and 'F ', univalence means that whenever 'p' has one value, it cannot simultaneously have another. So, when 'p' is Τ , for instance, 'p' cannot be U or F . Thus univalence operates a cleavage between the one value that is assigned and those that are not. If we subsume the values that do not get assigned under a supervalue, such that this subsuming supervalue is assigned whenever a subsumed value is assigned, then we get a bivalence of sorts. Given that there are three values, one would expect that they define three such 'bivalences'. In actual fact, however, one of the three is excluded, and of the remaining two only one is interesting. As to the excluded bivalence, it is impossible to subsume Τ ' and 'F s ' under a supervalue and not to subsume 'U '. Saying that 'p' has a value for which it is sufficient that 'p' is Τ and equally sufficient that 'p' is F is not different from saying that 'p' is possible and that this possibility is doublebound. Hence it is sufficient that 'p' is Us . The interesting bivalence is thatbetween'T s' and the supervalue subsum­ ing 'U ' and 'F '. As this supervalue is assigned whenever either 'U 'or 'F ' is assigned, it must be 'U*s '. Within the bivalent framework, the ordinary (lan­ guage) name for 'U * ' is 'false'—I will soon substantiate this claim. Of course, within the trivalent framework, only 'F ' is called 'false', and 'U *s ' is actually read as 'at most possible', 'at least possible', or 'possible or false'. If this is cor­ rect, then there are at least two notions of falsity, a narrow one, 'F ', function­ ing in trivalent logic, and a broad one, 'U *s ', a supervalue which functions in a bivalent logic and which covers both the 'F ' and the 'U ' of trivalent logic. A word on the uninteresting bivalence. It is possible to subsume 'Us ' and 'T ' under a 'U*s'. Within a trivalent logic, this 'U* 'is called 'at least possible', 'at most possible', or 'possible or true', but what makes it uninteresting for my present purposes is that the bivalent 'U* '-'F ' framework does not have an or­ dinary (language) one-word name for it. If truth and falsity were symmetrical in all respects, then it would be possible to read 'U* ' as 'true'. But this is not the case. It is high time to provide evidence that 'U*s ' can indeed be read as 'false'. Consider the following conversations: (127) ~ John is in the kitchen now. -- No. It is merely possible that he is in the kitchen.

TRUTH, FALSITY, AND POSSIBILITY

143

(128) - John is in the kitchen now. -- No. He is in the living room. In my view, the best way to account for the above uses of 'No' is to hypothesize that 'No' can express a wide sense of falsity that allows 'p' to be possible ('Us') as well as false in the narrow 'F ' sense. So 'U *s ' can be read as 'false'. If this result is put together with the findings from scalarity theory, we can conclude that 'U *s ' is both a possibility of a peculiar type and a falsity of a peculiar type. This means that 'U *s ' is the tool that is needed to express that 'possible' in its ' ◊ ' sense means 'not/possibly true and not/possibly false'. Just like the two earlier definitions of 'possible', which employ either possibility ('possible' as 'possibly true and possibly false') or falsity ('possible' as 'neither true nor false') but not both, the present definition can be incorporated into a truth-table (Table 5). As can be expected, the only places in which this definition renders the new table different from the two other tables are the middle cells of the '!p' and '—p' columns. Ρ Ts

!Ρ

~P

◊P

Τs

Fs

FS

Us Fs

Fs

U*s

Τs

Ts

Fs

Table 5 We now have three tables, three '!' and three ' ~ ' operators, one operator for unbound possibility ('0') and three for bound possibilities ('◊*'> '◊*'> '◊*'), one of which ('◊*') can also be read as 'false'. All these operators are summarily represented in Table 6. Ρ Ts Us Fs

!2p

~2P

!4p

τs

FS

τs

FS

Fs

Fs

Fs

τs

Us Fs

Us τs

~4P

!5P ~5P τs

FS

U*s

Fs

Table 6

τs

◊P

◊*p ◊V ◊*p

FS

Fs

Τs

Ts

Τs

Τs

Ts

Τs

Fs

τs

Fs

Τs

PROPOSITIONAL OPERATORS

144

Occam would not like this. Yet he might like what comes now. I will more or less discard Table 4 and prove an equivalence between Tables 2 and 5. This en­ terprise is expected to give a double result: (a) the partial rejection and the proof of the equivalence between Tables 2 and 5 leaves me with just a single set of ' ! ' and ' ~ ' operators ; (b) the 'more or less' of the rejection of Table 4 still allows me to retain at least one of its positive features, more particularly, its '!' operator. The layout of the argument is the following. In a first step, I will as­ sume that Table 4 is wrong and show that we can get by without it. The second stage will justify this assumption. In the third step, I will discuss the value of keeping the '!' operator. Remember, first, that Table 4 was designed to capture the sense in which 'possible' means 'nottrue and not false'. The point of Table 5 is not all that dif­ ferent: it is meant to incorporate a sense in which 'possible' means 'not true and not false', the only difference being that the 'not' of Table 5 is such that when 'p' is false, 'p' can still be possible. Thus Table 5 equates 'not' with broad falsity ('◊ * ') while Table 4 equates it with narrow falsity ('~'), Let us assume that the 'not' of 'not true and not false', in the sense that is synonymous with 'possible', can only represent a broad falsity. This would mean (a) that Table 4 is empirically inadequate, and (b) that all the relevant facts about '!', '~', and ' ◊ ' must be describable using Tables 2 and 5. To start with (b), one such rele­ vant fact is that the truth-value conditions of ' ◊ p ' and the object language rep­ resentation of 'not true and not false', where the 'not' stands for broad falsity, should be identical. Before we can compare the respective truth-value condi­ tions, however, we must decide on what the required object language rep­ resentation of 'not true and not false' looks like. This decision has an obvious and a disturbing side to it. It should be obvious that the object language symbolization is '◊* ! ρ Λ◊*~ P' ; the disturbing factor is that we have two types of '!' and ' ~ ' operators, those of Table 2 ('!2' and '~ 2') and those of Table 5 ('!5' and '~ 5 ')· (Under the assumption that Table 4 is mistaken, '!4 ' and '~ 4 ' are no longer in the picture.) So we have four representations of 'not true and not false': (129) ◊* !2 Ρ Λ ◊* ~ 2 Ρ ◊* !2 

Λ

◊* ~5 Ρ

◊* !5 Ρ

Λ

◊* ~ 2 Ρ

◊* !5 Ρ

Λ

◊* ~ 5 ρ

I claim now that these four 'not true and not false' expressions have identical

TRUTH, FALSITY, AND POSSIBILITY

145

truth-value conditions, which, moreover, are identical with those of ◊ ρ'. This is confirmed in (130).

◊*

!2

Ρ

Λ

◊*

FS

FS

Τs

Τs

Fs

τs

ΤS

Τ

Fs

τs

Fs

Fs

Fs

Fs

τs

Fs

◊*

!2

Ρ

Λ

◊*

~5

Ρ

Fs

τs

Τs

Fs

Τs

FS

Τs

Ρ

◊P

τs Us Fs

Us

Us Us Τs F F

Τs

F

τ 0*

f '5

F

τ

s s

◊* Fs

s

Ρ

Λ

Τ

F s

s *s

Τ

τ

s

s

s

s

Us Τs

F

Τ

Fs

F

s

s

s

s

Fs

τs U*s F τ s

s ~2

Ρ

Τ

F

Τ

s

τ Fs s

S

s

~5

τs

Τs

Fs

Τs

Fs

τs

UsΤs Fs

s

  s s τ Fs

!5

Fs

s

0*

◊*

Fs

Us

Us

Λ

U*s

τs

F

Ρ

Τs

Ρ

Us

Ts

s



~2

Τs U*s Fs τ

s

Ρ

τs Us Fs

The claim that each of the four 'not true and not false' symbolizations has the ' ◊ p ' truth-value conditions might lead one to think that it does not matter how 'not true and not false' is represented for it to have the same truth-value conditions as ' ◊ p ' . However, this would be a mistake. Given the options be­ tween '!2' and '!5', and between '~ 2 ', '~ 5 ' and '0*', there are exactly forty-six ways to represent 'not true and not false', besides the four mentioned in (129), none of which has the truth-value conditions of 'Op'. This can be shown as fol­ lows. For any 'not true and not false' expression to have the truth-value condì-

PROPOSITIONAL OPERATORS

146

tions of ◊p', both conjuncts must be Τs when 'p' is Us. Now, two of the fortysix 'not true and not false' expressions, viz. '◊* !2p Λ ◊*◊*p' and '◊*!5pΛ◊* ◊*p', represent the 'not false' by iterated broad falsity, which is F s when 'p' is U.s

(131)

◊*

◊*

Ρ

τs

Fs

τs

Fs

τs

Fs

τs

Us Fs

The forty-four remaining expressions have narrow falsity for at least one 'not'. Either the expression in the scope of this narrow falsity is '◊* p', which is Τs when 'p' isUs, and the conjunct is F . Or the expression in the scope of the nar­ row falsity is '!p' or '~p' both of which are either U s or U*s when 'p' is U s , and then the conjunct is either U s , U*s or U*s. These cases are illustrated in (132). (132)

'2

!

Ρ

τs

τs

~2

◊*

Ρ

τs

FS

Τs

Fs

Τs

Fs

τs

Fs

τs

Fs

Fs

~2

!5

Ρ

~

~

Ρ

Fs

Τs

τs

u*s τs

~2

Us

Us Fs

Fs

Fs

Us Us

Us

5

Τs

5

Fs

U*s Fs

τs Us

τs

Fs

Notice the appearance of the supervalues'U* 'and U* ', which I have not explicitly accounted for yet. For this purpose, I need a table where '/?' is shown as being U*s, U*s, and U*s (Table 7).

TRUTH, FALSITY, AND POSSIBILITY

Ρ

!2Ρ

~2Ρ

!5P

◊P

~5P

◊*ρ

147

◊*Ρ

Table 7 Basically, however, supervalue table 7 contains no more information than value table 6. Take the valuation of ' ~ 2 p ' where 'p' is U *s . For 'p' to be U*s, either the narrow falsity of 'p' or its unbound possibility will suffice. If 'p' isFs, ' ~ 2 p ' is T s ; if 'p' is U s , ' ~ 2 p ' is U s . For 'p' to be U*s, it is therefore sufficient that ' ~ 2 p ' is Ts; it is equally sufficient that ' ~ 2 p ' is U s . We conclude that when 'p' is U*s, ' ~ 2 p ' is U*s. The only tricky point in the supervalue table is that when Table 6 shows that both the truth and the narrow falsity of one expres­ sion are sufficient for the truth of another, the latter is U*s. As I have argued above, there is no way of having a supervalue subsume truth and falsity, and exclude possibility. In what sense is it immaterial whether we take '!2' and '~ 2 ' or ' !5' and '~ 5 ', in order to let '◊* ! ρ Λ◊* ~p' have the same truth-value conditions as ' ◊ p ' ? The answer is simple. '!2' and '!5' refer to the same thing and so do '~ 2 ' and ' ~ ', the only difference being that Table 5 supplies a more general descrip­ tion than Table 2. In particular, Table 5 only says that both '!p' and ' ~ p ' are U*3 when 'p' is Us . This indicates that '!p' and ' ~ p' are either U or F , but it does not decide which. Table 2 shows that the '◊*' possibility is actually a neutral possibility. Another way to'show that my trivalent RPL only houses one set of '!' and ' ~ ' operators is this. Iff 'p' is both U*s and U*s, 'p' is merely Us — and not, as might have been thought, U*s. (133)

◊*

pΛ

F

Τs

Fs

S

τs

Us τs Fs

Fs

◊*

P

τs

τs

τs

Us

Fs τs Fs Hence, '◊* ! 2 P Λ ◊* ·!2Ρ' has the truth-value conditions of ' ◊ p ' · '◊*! 2 P'

PROPOSITIONAL OPERATORS

148

has the same truth-value conditions as ' ◊ * ~ 2 P'; if we replace falsity by truth, boundness is switched around. (134)

◊*

!2

Ρ

◊*

~2

Ρ

τs

Τs

Τs

τs

Fs

Τs

τs

Us

Us Fs

Fs

Fs

τs

Us Us

Fs

Τs

Fs

So, '◊* !2 Λ ◊* ~ 2 p ' has the truth-value conditions of '◊p'· Translating part of my claims into the metalanguage, I can say that there is a '!' and a ' ~ ' operator such that iff 'p' is U s , both '!p' and ' ~ p' are U*s. This is precisely what the middle cells of the ' ! ' and ' ~ ' columns of Table 5 say about ' ! ' and ' ~ '. I now come back to Table 4 again. When I showed that the 'not' of 'not true and not false' can be represented with a broad falsity, and when I argued for the identity of '!2' and '!5', and '~ 2 ' and '~ 5 ', I assumed that Table 4 was wrong. Yet the prima facie evidence in favor of this table seems strong. Table 4 does, after all, incorporate the sense in which 'possible' means 'not true and not false'. Moreover, the claim that the 'not' of 'not true and not false' must be a narrow falsity does allow for a truth-table that confirms that 'not true and not false' has the truth-value conditions of '◊p'. 7 4 (135)

!

Ρ

Λ

Fs

Τs

Τs

Fs

Τs

Fs

Τs

Fs

UsΤs

Τs

Fs

τs Us

τs

Fs

Fs

Τs

Fs

~4

4

Fs

Fs

~4

~4

Ρ

Yet, the identity in truth-value conditions between ' ◊ p ' and 'not true and not false' where the 'not' is represented with '~ 4 ', only holds when both the inner 'true' and the inner 'false' are interpreted with Table 4. (136)

~4

Fs Fs Τs

!2

Ρ

Λ

Τs

Τs

Fs

Τs

Us UsFs

Fs

Fs

Fs

Fs

Fs

~4

~2

Ρ

τs Us Us Fs τs

Fs

TRUTH, FALSITY, AND POSSIBILITY

, 'S

p

/\

Fs

Ts

Ts

Fs

Ts

Fs

Ts

Fs

U*S U s Fs Fs

Fs

Fs

Us

Fs

Fs

U*S Ts (>*

p

4

Ts

,

P

4

Fs

'4

P

/\

Fs

Ts

Ts

Fs

Ts

Fs

Ts

Ts

Fs

Us

Fs

Fs

Ts

Us

Ts

Fs

Fs

Fs

Fs

Ts

Fs

4

4

149

Furthermore, as long as the inner truth and falsity are symbolized with '! 4' and '-4', it does not matter whether we represent the outer falsity with '-4'. (137)

,

'4

P

/\

Fs

Ts

Ts

Fs

Ts

Fs

Ts

Ts

Fs

Us

Ts

Ts

Fs

Us

Ts

Fs

Fs

Fs

Fs

Ts

Fs

'4

P

/\

(>*

-

P

Fs

Ts

Ts

Fs

Ts

Fs

Ts

Ts

Fs

U s Ts

Ts

Fs

Us

Ts

Fs

Fs

Fs

Ts

Fs

2

(>*

,

Fs

2

4

4

P

I see no explanation for why the 'not true and not false' seems to have the truth-value conditions of '(>p' in the cases exemplified in (137), and why it does not in the cases exemplified in (136). This is the first argument against Table4. My second counterargument concerns the correspondence between values and operators. I have not yet explicitly dealt with the question which and 'F; correspond to. Let me do this now. When 'p' operators the values is U s ' it obviously is notTs or F s ' and yet, it must still be possible for 'p' to be T s

'T;

150

PROPOSITIONAL OPERATORS

and F . Hence 'Ts ' and 'F ' must be thought of in a way that permits 'Us ' to be defined as 'not true and not false' as well as 'possibly true and possibly false'. This makes it clear that Τ ' and 'Fs ' correspond to ' !5' and '~ 5 ' and, as the argu­ ment establishing the identity of Tables 2 and 5 is valid independently of our verdict on Table 4, 'T s ' and Fs' also correspond to '!2' and '~ 2 '. This means that we do not need any value that would correspond to ' !4' and '~ 4 '. It would even be hard to conceive what such values and their tables would look like. So, if I cannot imagine any '!4' and '~ 4 ' values, why should I accommodate ' !4' and '~ 4 ' operators! And yet, Table 4 has some validity. As it was alleged to incorporate a def­ inition of 'possible' as 'not true and not false', Table 4 was a statement on three-valued logic. This trivalence statement, so I have argued in the preced­ ing pages, is wrong. I will now save some of it in the form of a statement on a two-supervalued logic that is embedded in the trivalent one. As explained above, we already have a supervalue for falsity, viz. 'U*s '. What we lack is one for truth. In bivalent logic, a double falsity yields truth. So truth can be de­ fined as '◊* ◊* p'· (138) gives its truth-table: (138)

0* ◊*

0* ◊*

Ρ

τs

FS

τs

Fs

ΤS

Fs

Τs

Us Fs

This means that the bivalent truth operator is nothing else than ' ! '. There is no such salvation for*~4', however. I wil now give the two-supervalued truth operator a new symbol, viz. a re­ versed truth symbol ('¡'). In part, I am doing this only to get rid of the indices and to be able to use an index-free ' ! ' and ' ~ ' for trivalent truth and falsity. But my reasons go a little deeper than that. ' ¡ ' is different from all the other (super)value operators in that it neither corresponds to any of the three basic truth-values, Τ ', 'U ', and 'F ', nor to any of the bound possibilities. If we need a matching truth-value, symbolized by ' 1 ' , we will have to define an en­ tirely new one. This could be done as follows: let 'p' be 1 iff 'p' has the truthvalue conditions of 'ip' Notice that, although '¡' does not corresponditoeither T s ', ' U , 'F s ', 'U* s ', 'U* s ', or 'U* s ', its truth-table (Table 8) shows that it can still be defined in terms of Τ ', 'U ', etc.

TRUTH, FALSITY, AND POSSIBILITY

i

Ρ

τs

Τs

Fs Fs

151

Us Fs

Table 8 Notice also that ' !' and ' ¡ ' seem to have identical truth conditions, but different truth-value conditions. (139)

! Τs Us

Fs

Ρ

i

Ρ

Τs

τs

Τs

Us Fs

Fs Fs

Us Fs

Perhaps it is appropriate to take stock of the operators and (super)values that we have defined so far. In RPL, a basically three-valued logic, the truthvalues are T s ', 'U s ', and 'F s ', and the corresponding operators are '!', '◊', and '~'. This three-valued logic also houses three bound possibility supervalues and operators: 'U* s '/'◊ * ', 'U* s '/'◊*', and 'U*s7'/'◊*'· Lowerbound possibility can also be read as falsity, and together with the falsity of this falsity, viz. the ' ¡ ' operator and the '1' value, it defines a two-supervalued logic. One might, at this point, hope that we have sufficiently disentangled the various notions passing under the terms 'true', 'false', and 'possible', and that we can now set the formalism to work. One might want the symbolism to prove or, at least, confirm that 'true' and 'false' mean, respectively, 'neither possible nor false' and 'neither true nor possible'. Unfortunately, our under­ standing is not good enough yet. Not that we do not have enough operators and (super)values; but we must still show that there is a second bound possi­ bility, besides '◊**'/'U*s ', that can be interpreted as 'false'. Let us take 'not possible and not false' first. If 'not possible and not false' were like 'not true and not false', then we could symbolize the 'not' with a broad falsity. But this interpretation only yields nonsense. Broad falsity does not make ' ◊ * ◊p Λ ◊* ~ p' exclude that 'p' is neutrally possible or false. No wonder that the truth-tables do not show any identity.

152

PROPOSITIONAL OPERATORS

(140)

◊

Ρ

Λ

◊*

~

Ρ

τs

FS

τs

Τs

τs

Fs

Τs

Fs

Τs

UsFs

τs

τs

Fs

!

Ρ

◊*

Τs

Τs

Us Us Fs

Fs

Fs

Fs

Fs

Us τs

Us Fs

So we naturally lean towards the hypothesis that the 'not' is to be represented by narrow falsity. Yet, as the table in (141) shows, this hypothesis is not cor­ rect either. (141)

~

◊

Ρ

Λ

~

~

Ρ

Τs

FS

τs

Τs

τs

Fs

τs

Us Fs

Τs Τs

Fs

Fs

Fs

Us

Us

τs

Fs

Us Fs

The fact that the table in (141) does not give the desired result finds its expla­ nation in the circled entry. The first ' ~ ◊ p ' column says that both the truth of 'p' and the falsity of 'p' are sufficient for the truth of '~ ◊p'. As I have pointed out before, this is the same as saying that it is sufficient for the truth of ' ~ ◊ p ' that 'p' is U§. Hence, the circled Τ ' must be changed into a 'Τs ' and the ' ~ ' must be changed into  '◊*'. (142)

◊

Ρ

Λ

~

~

Ρ

τs

FS

τs

Τs

τs

Fs

τs

τs

Τs

Τs

Fs

Us Us Fs

Fs

Us Fs

Us τs

Us Fs

These changes have an important consequence. If we accept the table in (142), then we are forced to admit that a double-bound possibility can be in­ terpreted as falsity. Is this a welcome consequence? I think that it is and I be­ lieve to have sufficient backing for this hypothesis. One element of evidence is, of course, the very fact that 'not possible and not false' will only come out with the truth-value conditions of '!p' if we symbolize the first 'not' with a '0* '. An equally strong indication is that '◊ *' falsity is also needed to define 'it

TRUTH, FALSITY, AND POSSIBILITY

153

is false' as 'it is neither possible nor true'. (143)

~

ρ

◊

Fs

τs

τs

Fs

Us Us

τs

τs

τs

Fs

τs

Fs

ρ



~

!

ρ

τs

Fs

Fs

τs

τs

Us Us Fs

τs

Us τs

Us Fs

Us Fs

But there is evidence of an entirely different sort, too. First, consider again the conversation of (127). (127) -- John is in the kitchen now. -- No. It is merely possible that he is in the kitchen. (127) was used to argue that there is a broad sense of falsity such that when 'p' is false, 'p' can still be possible. I took it for granted that this is an unbound pos­ sibility and so I identified the broad falsity with '◊*'. Yet nothing prevents us from interpreting the possibility as upperbound or even double-bound. The paraphrases in (144) and (145) are necessarily long-winded, but they should make their point. (144) -- No. It is merely possible that he is in the kitchen, although it is sufficient for it to be possible that John is in the kitchen that John is in fact in the kitchen, as you claim he is. It is, however, equally sufficient that it is merely possible — in the 'possibly true, possibly false' sense — that John is in the kitchen. (145) - No. It is merely possible that he is in the kitchen, although it is sufficient for it to be possible that John is in the kitchen that John is in fact in the kitchen, as you claim he is. It is, however, equally sufficient that he is not in the kitchen, and it is no less sufficient that it is merely possible — in the 'possibly true, pos­ sibly false' sense — that he is in the kitchen. The 'No' of both (144) and (145) can be argued to represent a ' ', for the suf­ ficiency of the upperbound or double-bound possibility does not affect the sufficiency of narrow falsity, illustrated in (128). (128) ~ John is in the kitchen now. ~ No. He is in the living room.

154

PROPOSITIONAL OPERATORS

Thus the word 'false' can mean 'either true or possible ('◊') or false ('~')'· Another piece of evidence takes us back into scalarity theory. Figure 23 represents the possibility scale with its unmarked orientation.

Figure 23 So far, '◊*', ' ◊ * ' , and were seen as variations on possibility. But why can't we interpret them as variations on truth and falsity? Then '◊*' would have to be interpreted as 'at most true', ' ◊ * ' as 'at least false', and could be read as 'at most true' and as 'at least false'. When 'p' is atmosttrue, 'p' is not true but only possibly true. So neither '◊*' nor can be read as 'true'. When 'p' is at least false, however, '?' is false albeit in a special way. Hence both ' ◊ * ' and can be read as 'false'. In other words, not only lower-bound possibility can be interpreted as falsity, the same goes for double-bound possi­ bility, Q.E.D. The upshot of our analysis is that we have three falsity operators ' * ' , and ' ~ ' ) , four possibility operators ◊*', '◊*', and ' ◊ ' ) , and two truth operators (' ! ' and ' ¡ '). Truth, falsity, and possibility all come in three-val­ ued, neutral or 'narrow', unbound varieties. Three-valued, 'narrow' falsity is flanked by broad, two-supervalued falsity and by a very broad, 'one-hypervalued' one (Figure 24).

!p

! Ρ

◊p ~P neutral

broad

'very' broad Figure 24: FALSITY TYPES

TRUTH, FALSITY, AND POSSIBILITY

155

Unbound, bilateral, three-valued possibility alternates with unilateral, twosupervalued, lowerbound and upperbound possibilities, and with a bilateral, double-bound, 'one-hypervalued' one (Figure 25).

!

p

! Ρ

-ρ neutral

~ lowerbound

P

upperbound

doublebound

Figure 25: POSSIBILITY TYPES Narrow, unbound, three-valued truth is flanked by an equally narrow and un­ bound, but two-supervalued variety (Figure 26).

Figure 26: TRUTH TYPES The claim that 'it is true that p', 'it is false that p', and 'it is possible that p' can be interpreted in a variety of ways brings up the question of what their lit­ eral interpretations are. Is either ' ~ p ' , '◊ * P'> o r P' the literal meaning of 'it is false that p', for example? Are they all literal meanings? Or is there yet another, more abstract reading common to ' ~ p ' , ' ◊ * p ' , a n d »andcould this be the 'real' literal meaning? The latter possibility can easily be discarded. We do not need to dream up yet another, fourth reading to find out what ' ~ p ' , ' ◊ * p ' , and have in common. is the common element: both when

156

PROPOSITIONAL OPERATORS

'p' is false in the three-valued 'Fs ' sense and when 'p' is false in the two-supervalued 'U* ' sense, 'p' is false in the sense. This might suggest that is the literal meaning, something that sounds implausible but that could get some support from the fact that it would allow for an attractive explanation of ' ~ p ' and ' ◊ * p ' as non-literal meanings, more specifically, as conversational implicatures. A Gricean argument could go as follows. Speakers are supposed to be informative ('Quantity Maxim'; Grice 1975: 45). If the thesis that 'it is false that ρ ' literally means is correct, then the literal contents of an 'it is false that ρ ' statement must be judged very uninformative, as a falsity still allows 'p' to be either true, false ('~'), or possible ('◊')· So, saying that 'p' is generally amounts to a violation of the Quantity Maxim. How should a hearer interpret this? One explanation would be to assume that the speaker flouts the maxim in order to convey something more than just the literal mean­ ing. The most obvious candidate for this extra meaning, the conversational implicature, would be a more stringent and more informative notion of falsity. In other words, the speaker would be taken to implicate that 'p' is either U*s or F . Of these two potential implicatures, the ' ~ p ' implicature is the more infor­ mative and, therefore, the more likely one. Another element of support is that p' is an 'at least' meaning of the 'T ' variety and that I have claimed earlier (IV.4.2) that every assertion is vague between 'T ' ('at least'), 'T ' (another 'at least'),and'T s , n s' (exactly') readings, and that the Τ ' reading is the literal one. But even so, the above proposal should be considered a tentative one. In case it can be confirmed, however, we can also use it, mutatis mutandis, to show that 'it is possible that p' literally means p ' and that ◊ρ', '◊ * ', and '◊*p' are non-literal meanings (see also Van der Auwera n.d.e.). For truth, the situation is a different one. I do not see how either ' !p' or '¡p' is any more informative than the other, given that they have identical truth conditions. So perhaps '!p' and '¡p' are both lit­ eral meanings. With the tentativeness of the preceding considerations suggesting the need tor future research, I will close off this section with a look at some past scholarship. My analysis of truth, falsity, and possibility is new, but, like all novelty, it has its roots in the past. To start with the truth operator, I am not the first to suggest that there is a trivalent variety as well as a bivalent one. Smiley (1960), for example, defines a truth operator which is similar to my '¡ '. He takes no interest in its corresponding truth-value, however. Interestingly enough, he admits of a trivalent 'Τs' value, but he has no corresponding '!' operator. Kripke (1975: 714-715) mentions the 'alternate' intuitions behind

TRUTH, FALSITY, AND POSSIBILITY

157

what seem to be '!' and ' ¡ ' , but he does not really settle the issue of whether they are both acceptable. Neither does McCawley (1981: 259), who discusses 'T ' and values but does not mention the corresponding operators. I am not the first to suggest that there is more than one type of falsity. A classic distinction, which seems to go back to Aristotle, is that between 'choice negation' and 'exclusion negation' (cp. von Wright 1959; Herzberger 1970). It is common to argue for this distinction on the basis of so-called presupposi­ tion failure. Consider the utterance in (146): (146) The King of France is bald. Suppose that there is no King of France. Then he cannot be bald. One might want to argue that this makes (146) suffer a presupposition failure such that (146) would be neither true nor false. As to (147), (147) The King of France is not bald. in one sense, this utterance, too, should be neither true nor false, since the non-existence of the King of France makes it just as impossible for him to be not bald as to be bald. Yet, in another sense, (147) could be said to be true; if the King of France does not even exist, then surely, he is not bald. The 'not' of the first sense is the choice negation, and that of the second sense the exclusion negation. When 'p' is choice-negated and 'p' is neither true nor false,then 'not p' is also neither true nor false. When 'p' is exclusion-negated and 'p' is neither true nor false, then 'not p ' is true. It is most appealing, therefore, to think that my ' ~ ' and '◊*' merely recapture the choice and exclusion negations. Moreover, the truth-tables offered for the choice and exclusion negations (cp. Herzberger 1970:27; McCawley 1981:259) are similar to those offered for ' ~ ' and ' ◊ * ' . And yet, these similarities are only superficial. Given the framework developed so far, when 'p' is neither true nor false, then it is still possible for 'p' to be true, while it is equally possible for 'p' to be false. When the presupposition theorists say that (146) and (147) are neither true nor false, however, they mean that it is impossible for (146) and (147) to be true or false. Indeed, they would claim that when there is no King of France, it is not possi­ ble that he is bald or not bald. As the next section will show, the ' ~ ' — ' ◊ * ' dis­ tinction is unlikely to be justifiable on the basis of presupposition failure. 3.2. Pseudo-monadicness and presupposition In the preceding section, we have distinguished between various (super/ hyper)value operators and assigned them componential analyses. Using these operators, we were able to express intuitions like the following:

158

PROPOSITIONAL OPERATORS

(a) (b) (c)

when 'p' is possible, 'p' is possibly true and possibly false; when 'p' is possible, 'p' is neither true nor false; when 'p' is true, 'p' is neither possible nor false.

Once formalized, such statements count as truth-value-conditional analyses. Thus (148), for example, (148)

!p=

◊Λ~~

says that ' !p' has the truth, falsity, and indeterminacy conditions of '◊**◊pΛ

~~P There is no pretense that the account is complete. As a matter of fact, I have already indicated that it is not. Consider again the componential analysis of ' 0 ' possibility: (149)

Ρ

◊P

Τs

FS

Us Fs

Τs Fs

Though ' ◊ ' is supposed to function in a trivalent logic, the componential analysis does not show how '◊p' can be Us . This could mean three things: (a) 'Op' cannot be U ; (b) 'Op' can be U , but this undeterminedness does not de­ pend on the truth-value of 'p'; (c) the componential analysis is mistaken. I be­ lieve that (a) is wrong; if ' ◊ ' is to function in a trivalent logic, it must be possi­ ble that 'Op' is U . The solution that I advocate is a mixture of (b) and (c). I will claim that the componential analysis is incomplete, but that it is as complete as possible with respect to the truth-value of 'p' The undeterminedness of ' ◊ p ' will be argued to depend on the truth-value of a 'hidden' component. This takes me back to the pseudo-monadicness thesis. In IV.4.2,1 claimed that the truth predicate is fundamentally dyadic, but that it can be used as if it were monadic when the second relatum is either taken for granted or judged irrelevant. On the strength of this claim, we can assume the supposedly monadic ' ! ' and ' ¡ ' operators to be pseudo-monadic ap­ pearances of dyadic truth operators. If this assumption holds water, we can further assume that there are pseudo-monadic falsity and possibility operators. To represent such operators, I will not invent any new symbols but, instead, keep on using '!', '~', ' ◊ ' , etc. In their dyadic appearance, the

TRUTH, FALSITY, AND POSSIBILITY

159

Operators will follow the symbols for what is true, false, or possible, and pre­ cede the symbols of what this truth, falsity, or possibility is relative to. Thus we get wffs like: (150) ρ ! q (151) ρ ~ q (152) ρ ◊ q As we have seen above, the 'q' slot can be filled by a variety of entities. If 'p' is T , for example, q can be the particular SOA that 'p' is Ts,ns of, the F-SOA that 'p' is Ts, of (either Ts,s or Ts,ns ), the possible world that the F-SOA is part of, or even the universe. There are at least two ways to read these formulas. I will call them the 'conditional and the 'presuppositional' way. Let me illustrate these notions with 'p!q'. When 'p' is conditionally true of q, it means that if q is the case, 'p' is true of q. The conditional truth of 'p' relative to q is non-committal about the actuality of q. When 'p' is presuppositionally true of q, on the other hand, the q is taken to be the case. Then '"p' is true of q' means as much as 'given that q is the case, 'p' is true of q'. As the term 'presuppositional' suggests, I will ren­ der the peculiar givenness of q with the notion of presupposition. The details and the justification of this enterprise are reserved for the second half of this subsection. If the distinction between conditional and presuppositional readings is as important as I think it is, then it will be good to symbolize them in different ways. From now on, all the truth-value operators introduced so far — includ­ ing those for supervalues and hypervalues — will be given presuppositional readings. A conditional reading will be symbolized as a combination of a pre­ suppositional reading and a sufficient conditionality. The latter will be sym­ bolized by an arrow with a superscript asterisk ('→)· (153) q→(p!q) (153) is read as follows: for 'p' to be true of q, given that q is the case, it is suffi­ cient, if not necessary, that q is the case. The sufficiency symbolized by'*→is upperbound. This needs to be justified. Sufficiency and necessity fit on a finite bifurcate scale (Figure 27).

160

PROPOSITIONAL OPERATORS

The 's' and the 'n' of the scale's lower rung mean, respectively, 'sufficient and unnecessary' and 'necessary and insufficient'. Like all scalar notions, they have bound varieties. Figure 28 represents the upperbound varieties 'n*' and '5*'.

When something is s*, it is either sufficient and unnecessary or it is necessary and sufficient; it is at least sufficient, 'n*' is interpreted in an analogous way. As it is customary to represent conditionality with arrows in logic, the un­ bound sufficiency of 'n' for 'q' will be represented with '→'. This way, . gets to denote upperbound sufficiency. What remains to be shown is that the arrow needed to express conditional truth is rather than '→'. Remember that the slot for q can be filled with the particular SOA that 'p' is T of. In that case, q is necessary and sufficient for the truth of 'ρ'. In case q is a possible world or the universe, however, q is only sufficient. In case q is the F-SOA, then q is either merely sufficient, or necessary and sufficient. I conclude that the sufficiency needed in the definition of (153) must allow both for necessity and sufficiency and for unbound sufficiency. Hence I need upperbound sufficiency. (153) defines conditional truth in terms of presuppositional truth. In (154) we get the opposite. (154) (q

(p!q))Λq

Reintroducing 'q' out of the scope of the arrow undoes the latter's conditionalizing effect, just as a deletion of the arrow would. So the expression in (154) is synonymous with 'p!q'. (155) (tø

(ρ ! q)) Λ q)

=

(ρ ! q)

(155) is an interesting equivalence. On the one hand, it helps clarifying the re­ lation between conditional and presuppositional readings. On the other hand, it will be helpful for solving the next problem, that of giving 'p ! q' a truthtable. If the idea of a dyadic ' ! ' operator is to be more than a formalist fancy, we should be able to provide it with a truth-table. Assuming that dyadic truth is

TRUTH, FALSITY, AND POSSIBILITY

161

truth-functional, we could try to replace the question marks of the empty table in (156) with truth-values. (156)

!

Ρ

q

Τs

Us Fs

τs

Us Fs

?

?

?

?

?

?

?

?

?

Yet, it might be argued that this exercise simply cannot be done. The question marks would have to be substituted by truth-values. The 'q' that appears in (156), however, has been taken to refer to an entity that cannot have truthvalues. Only beliefs and assertions have truth-values; q, which is what the as­ sertion 'p' is supposedly about, is an SOA. The objection is formally correct, but incorrect in spirit. It was largely for the sake of a more concrete exposé that I decided to interpret the abstract val­ ues that would be suited for the propositional level RPL interpretation as truth-values (see the introductions to IV.4 and V). I could have chosen satis­ faction values (for desires and optative-imperatives) or actuality values (for SOAs) or I could have stuck to abstract propositional values. At this point, the decision to work with truth-values presents a problem, for the values that are needed for the 'q' of (156) cannot be truth-values. The problem can easily be solved, though, by asking the reader to interpret the truth-values to appear in column 'q' as the corresponding ontological values. This is a relatively at­ tractive escape, but there is still a simpler one. I could stipulate that a 'q' that appears in tables such as (156) is an assertion that is Τ s,ns of the SOA q that 'p' is said to be true of. I will adopt the second solution. So much for the groundwork. We can now start filling in the table. As a first move, I propose to take the monadic ' !' table and place it under the T ' of the dyadic table. (157)

Ρ

!

ΤS

Us Fs

q

Us Fs

Τs

τs ? Us ?

?

?

?

Fs

?

162

PROPOSTIONAL OPERATORS

The rationale is straightforward, 'P' ! q' is to mean 'given that q is the case, 'P' is true of q' ; the truth-value correlate to something being the case is truth. What if 'q' isFs? Does this imply that 'p', which is said to be true of q, is F , too? Or must it be U ? One thing seems beyond dispute: if 'q' is Fs or, informally, if there is no q, then 'p' cannot be true of it. But on the question whether the fal­ sity of 'q' makes 'p ! q' U rather than F , or F rather than U , our intuitions seem to be shaky. It is at this point that the equivalence of (155) proves its value.

(155)((q

(p!q))Λq)

=

(p!q)

Suppose now that 'q' isFs. The left-hand wff of (155) is a conjunction; hence it is F if one of its conjuncts is F s . Thus, if (155) is correct and if 'q' is F s , then '((q (P!4)) Λ q)' is Fs and so is 'p ! q'. Ρ

τs Us Fs

!

q

τs

Us Fs

τs ? Us ? Fs

?

Fs Fs Fs

What is left is the case of the Us 'q'. The rules for conjunction tell us that if one conjunct is U , the conjunction as a whole is U , unless another conjunct is F . In the case of '((q (p ! q)) Λ q)' the second conjunct is U . What we need to find out, then, is whether the first conjunct can ever be F . This first con­ junct is a type of conditional expression, viz. 'q (p!q)'. Its antecedent ('q') is U . Thus our question becomes the following: Can the value of a consequent ever be sufficient to make a conditional whose antecedent is Us becomeFs? Though I have not provided with a truth-table yet (see V.5.1.1), a mo­ ment's reflection should suffice for a straightforward 'No'. The arrow stands for a sufficient conditionality. Clearly, the statement that 'q' is sufficient for 'p ! q' cannot be proved false when 'q' is only undetermined. So 'q (p! q)' can­ not be F s . As 'q (p ! q)' is the first conjunct of a conjunction whose second conjunct is U s , the conjunction itself is also U . This is precisely what we need to know. Given the equivalence of (155), we now know that if 'q' isUs, 'p !q'is Us , too.

TRUTH, FALSITY, AND POSSIBILITY

Ρ

!

q

ΤS

Us

τs

Us

Fs

τs

Us

Fs

Us

Fs

Us

Fs

Us

Fs

Fs

163

Table 9 So much for M' truth. Mutatis mutandis, the same argument can be given for transferring the monadic ' ~ ' falsity and ' ◊ ' possibility tables into the lefthand columns of the dyadic tables and for assigning 'Us ' and 'Fs ' values to their middle and right-hand columns, respectively.

◊

ρ

q

τs Us Fs

τs

Us

Fs

Fs

Us

Fs

Τs

Us

Fs

Fs

Us

Fs

Table 10 Ρ

τs υs Fs

~

q

τs

Us Fs

Fs

Us Fs Us Fs Us Fs

Us τs Table 11

Similar arguments could also be given for ' ¡ ' , '◊*', '◊*'> and operators, but I will not pursue this matter further. Tables 9,10, and 11 are, of course, very similar. Their second and third columns are exactly identical, and it is a necessary and insufficient condition for 'p !q ' , p ◊ q ' ,as well as for 'p ~ q' to be true that 'q is true. Bearing in mind that necessity is the converse of sufficiency, this aspect can be represented in the object language with the help of the '→' operator:

164

PROPOSmONAL OPERATORS (159) (ρ ! q)→q (160) (p ◊q)→q (161) (p~q)→q

At this point, the notion of presupposition comes in. From its reintroduction in 1950 (Strawson 1950) onwards until the midseventies, the relation of presupposition was generally understood in truthconditional terms. Classically, 'p' is held to presuppose 'q' iff both 'p' and 'notp ' imply 'q'. The evolution of the last decade, however, convinced most inves­ tigators that not all allegedly presuppositional phenomena can be presuppositional in the classical truth-conditional sense (see Kempson 1975; Wilson 1975; Karttunen and Peters 1977; Reis 1977). Instead, most of these phenomena are now understood in terms of shared knowledge between speaker and hearer. Shared knowledge accounts may still have room for a no­ tion of presupposition, but then the latter is no longer a truth-conditional but a pragmatic notion (see Allwood 1972; Kempson 1975; Reis 1977; Gazdar 1977, 1979). What I would like to do now is to restore the classical notion, though in an unusual way. Since my own RPL framework is unclassical, one cannot expect that my use of presupposition will turn out to be exactly the same as the traditional one. Furthermore, though RPL presupposition gives credit to some of the in­ tuitions behind the classical notion, it does not follow that the former can be used to account for all the phenomena accounted for by the latter, such as fac­ tives and definite descriptions. Quite to the contrary, I do not think that the phenomena discussed in this section have ever been described in presuppositionalist terms; neither will RPL presupposition be put to use in an analysis of the allegedly presuppositional phenomena of the classical tradi­ tion. In the classical conception, a presupposition is a type of implication that is constant under the negation of the antecedent. Consider again the 'implica­ tions' of (159), (160), and (161). (159) (p!q)→q (160) (p◊q)→q (161) (p~q)→q Here, too, we meet a constancy of implication under an operation on the ante­ cedent, 'q' is implied whether we have 'p!q','p◊q', or ' p ~ q ' The obvious differences between presuppositional constancy in RPL and in the traditional account are, first, that constancy in classical presupposition only holds for ne-

TRUTH, FALSITY, AND POSSIBILITY

165

gation, while in RPL implication is constant under negation as well as under neutral possibility — and, for that matter, under all subtypes of truth, possi­ bility, and falsity: second, that RPL operations are unambiguously dyadic. Even so, the similarity deserves to be noticed. Another analogy is found in the following. It is often said that when 'p' classically presupposes 'q' and when 'q' is false, then the question of the truth or falsity of 'p' does not even arise. 'p' would then be neither true nor false. For some, this means that 'p' is to be assigned a third truth-value. For others, 'p' falls into a 'truth-value gap', i.e. an absence of truth-values. Yet others consider 'p' to be false. I will now show that what happens when 'q' is false in 'p ! q', 'p ◊ q', and 'p ~q' is quite analogous. Consider (162): (162) ~q→q(~(p!q)Λ~(p◊)Λ~(p~q)) (162) is an object language representation of the fact that when 'q' is false, 'p ! q', 'p ◊q', and ' p ~ q' are also false. Whether or not (162) is fully adequate — for example, whether the sufficiency is really unbound — does not matter here. It is the characteristic falsity of the consequent that attracts our atten­ tion, as being reminiscent of the 'neither true nor false' talk: in fact, the con­ sequent says that it is neither true nor false, nor even undetermined that ρ, given that q. And it is similarities like these that justify our saying that the 'p' of 'p ! q',p ◊ q\ and 'ρ ~ q' presupposes 'q/ This presupposition will be represented by the operator symbol ' > ' : (163) ρ > q It should now be clear why ' ! ' , ' ◊ ' , a n d ' ~ 'were called 'presuppositional'. ' p ! q ' , ' p ◊ q ' , and 'ρ ~ q' can only be true if 'p > q' is true, too. Interestingly enough, the ' > ' operator itself need not be presuppositional. Indeed, nothing in the preceding discussion has made it necessary for the truth of 'p > q' that 'q' be true. Therefore, 'p > q' will mean that if'q' is true, then either 'p ! q', 'p 0 q', or 'ρ ~ q' is true. So the ' > ' operator is conditional. There is nothing strange about this; after all, classical presupposition was supposed to be a type of implication, too. The fact that the ' > ' operator is conditional does not mean that we cannot define a presuppositional presupposition operator. What we want is some­ thing that is to 'p > q' what 'p ! q' is to 'q → (p ! q)', i.e. something like ' p > q ' , except for the fact that 'q1' is true. The operator that we are looking for is actu­ ally rather familiar; it is merely the dyadic version of the double-bound possi­ bility operator '◊ *'·

166

PROPOSITIONAL OPERATORS

Ρ

τs

Us Fs

τs

τs

Us Fs

τs

Us Fs

τs

Us Fs

Us Fs

Table 12 The relation between ' > ' and

' is made explicit in (164) and (165):

(164) (p q) = ((p>q) Λ (165) (ρ >q) = (q (p

q) q))

Now that we have a better idea of RPL presupposition, we can return to the idea that originally motivated our foray into presuppositional territory, viz. pseudo-monadicness. '!', ' ◊ ' , and ' ~ ' were called pseudo-monadic be­ cause they were claimed to be basically dyadic operators that can occur in a 'p '◊p'? or '~p' format rather than a 'p ! q', 'p ◊ q', or 'ρ ~ q' one. What ex­ plains pseudo-monadicness is the fact that 'q' is taken to be obvious or irrele­ vant. Let me now explicitly connect the pseudo-monadicness and presupposi­ tion ideas: I claim that the only operators that allow pseudo-monadicness are the presuppositional ones. This claim should be a straightforward one. To take truth again: above I distinguished between a conditional operator, as in 'if 'q' is true, then 'p' is true', and a presuppositional one, as in 'given that 'q' is true, 'p' is true'. It is only the 'given that 'q' is true, 'p' is true' that may be ren­ dered as "p' is true'. In this case, the givenness of 'q' is taken to be so obvious or irrelevant that it needs no overt expression. Notice how the relation be­ tween presupposition and pseudo-monadicness reflects the history of presup­ position research. While the RPL account of the presupposition rehabilitates some elements of the classical, truth-conditional presupposition theory, the claim that presuppositional operators can be pseudo-monadic takes up the thesis underlying the 'shared knowledge' accounts, viz. that what is presup­ posed can be left unexpressed and taken as shared knowledge. Perhaps the preceding considerations have raised more problems than they have solved. One of such problems will start off the next section. Three others will be given a brief, tentative treatment now. First, the fact that presup­ positional operators can be used in two ways, an overtly dyadic and a pseudomonadic one. This makes us wonder what the literal meaning of a statement

TRUTH, FALSITY, AND POSSIBILITY

167

like '!p' is. On the one hand, I have been claiming that '!' is fundamentally dyadic. So it is tempting to say that '!p' literally means 'p ! q'. On the other hand, '!p' clearly does not express any 'q' Do we really want to claim that something that is unexpressed can be part of a literal meaning? I believe that the answer is neither 'Yes' nor 'No', but lies somewhere in the middle. It does belong to the literal meaning of ' !p' that there is a q relative to which 'p' is or is not true. To this extent, ' !p' and 'p ! q' are synonymous. ' !p' can be considered as a rough and handy symbolization of 'p ! q'; in this sense the truth-table for ' !p' must be called incomplete. It also belongs to the literal meaning of ' !p' that there are various entities that can make up q, viz. an F-SOA, a possible world, or the universe. But it does not belong to its literal meaning just what the par­ ticular F-SOA and possible world are. The second problem is that of infinite regress. In a statement such as 'p ! q', the truth of 'p' is relative to that of 'q' Unfortunately, if 'q' is true, its truth is itself relative to that of some V', the truth of which is, in turn, relative to that of some 's', etc... It seems that nothing will stop this regression, not even the claim that the most comprehensive entity with respect to which any statement if true, false, or possible, is the universe, defined as an infinity of possible worlds (see II.2.3). Compare this regression to the one that is involved in the definition of the word 'child'. It is essential to this definition that every child is the child of two parents. But these parents are themselves the children of some parents, and so on — until the term 'child' loses its applicability (see Darwin or the Holy Scripture). I believe that both the truth-value and the 'child' regressions are real as well as unproblematic. Ontologically speaking, all truths are 'truths of' and all children are 'children of'. On the level of lan­ guage and thought, however, the regression is halted by pseudo-monadicness. When we speak or think about 'truth of' or 'child of, we may abstract from the dyadicness and present 'truth of' as just 'truth' and 'child of as just 'child'. Notice also that the infinite regress does not turn the truth operator into a n-adic one. The truth operator itself only has two arguments. The sec­ ond argument, however , involves a second truth operator, the second argu­ ment of which involves yet a third truth operator, etc. The third open question concerns the interpretation of 'U ' and 'F ' in dyadic truth-tables. Take Table 9 again.

168

PROPOSITIONAL OPERATORS

Ρ

!

q

τs

Us

Fs

τs

ΤS

Us Fs

Us Fs

Table 9 There is a clear difference between the 'U ' and Τ ' values that are circled and s

s

those that are not. The circled ones cancel the presupposition; the uncircled ' or ' sense, ones do not. When 'p ! q' is undetermined or false in the then ' p ! q' is neither true, nor undetermined, nor false in the Τs', 'u's, or 'Fs' sense. The presupposition-canceling values will be called 'external', while the uncircled, presupposition-preserving ones will be termed 'internar. Parallel to the external ' ' and ' ' values, there are also external and ' operators. Their use is illustrated in (166) and (167), which form an object lan­ ' valuations of Table 9. guage representation of the and (166) (p ! q) (167) (p ! q) Of course, (166) and (167) only illustrate a pseudo-monadic use. The overtly dyadic statements with identical meanings are: (168) (p! (169) (p!q)

q ) r r

When the Τ operator appears pseudo-monadically or when we drop it al­ together— '! p' and 'p' have identical truth-value conditions — then we get: (170) (!p) (171) (\p)

r

Finally, when the and ' monadic disguise, we get:

of (172) and (173) operate in a pseudo-

(174)ρ(175) ρ (174) and (175) are deceptively short. They express only one argument, while

TRUTH, FALSITY, AND POSSIBILITY

169

there are really three. To reflect this, I will say that and ' ' are essen­ tially 'triadic' operators. Triadic operators allow 'pseudo-monadic uses' (as in (174) and (175)) but also 'pseudo-dyadic' ones (as in (172) and (173)). I will also say that ' ' and ' ' are 'bipresuppositional' and not 'monopresuppositional', as are '!', ' ◊ ' , and ' ~ ' . (174) and (175) have an outer presupposition (V) and an inner one ('q'). Note that the inner presupposition is actually false or indeterminate. This is not a feature of bipresuppositionality as such, but only of the bipresuppositionality found in ' ' and ' ' . I n section V.4 we will be confronted with bipresuppositional operators both of whose presup­ positions are true. The explication of the distinction between external and internal values and operators hints at the possibilities of further study. First of all, it is clear that Table 9 is no longer complete: there is no reason why its ' ' and 'q' could not be or as well asΤs, Us , or F . A full, dyadic 'p ! q' table would have 25 cells instead of 9. (176)

!

Ρ

q

Τs

Τ s

Us

F s

Τs

Us Fs

s

Us Fs

? ?

?

?

?

?

?

?

?

?

?

7

?

7

?

7

Second, we also need to provide analyses for the ' ' and ' ' operators. Third, one could envisage an analysis in terms of an indeterminacy and a fal­ sity that abstract from the external-internal distinction. Fourth, it should be investigated how the external-internal distinction relates to that of literal vs. non-literal meaning. None of these questions will be taken up, however. 3.3. Truth-value paradoxes The discussion of presupposition has shown how the truth-value of a statement like 'p ! q' depends on that of 'q' Therefore, the truth-values of ' !p' and 'p' depend on that of some 'q', too. Yet, if one takes a closer look at the truth-table of 'p ! q' (Table 9), one will notice that 'p' varies independently of

170

PROPOSmONAL OPERATORS

!

Ρ

q

T s

T

T

s

s

U

F

s

s

U s

s

F

U

F

s Table 9 Even if this is not altogether wrong, it may seem somewhat absurd, or at any rate superfluous. Take the ' ' column. The first line says that if 'P' is T s and if the '¿7' on which the truth-value of '/?' depends is F , then 'p ! q' is 1 . The superfluity of this claim lies in the fact that if 'q* is F , the independent variation of the truth-value of 'p' is immaterial. And there seems to be a good measure of absurdity, too: (a) if '/?' is T s and if 'q' is F , then 'p ! ¿7' is (; (b) if 'p ! ¿7' is s

, then '/?' is , too, for 'p ! q' and '/?' have identical truth-value condi­ tions; (c) so 'p' is ( , if 'p' is Τ . Yet how can a statement be both Τ and Isn't there a contradiction here? Answer: it is only an apparent contradiction to say that '/?' is simultane­ ously Τ and While the 'T ' valuation is really relative to some 'q\ the ' valuation involves the truth-value of either 'p ! ¿7', 'p ~ q', or 'p #' rel­ ' has a con­ ative to some V. Of course, the claim that '/?' is both Τ and tradictory ring to it, but that is only because we are tricked   me pseudomonadicness. So an independent valuation of '/?' does not necessarily lead to any contradiction. I will now suggest that it is not superfluous either. It is correct that in 'p ! ¿7' the truth-value of '/?' depends on that of 'q\ It is equally correct that the truth-value of '#' does not depend on that of '/?'. These two claims are not equally harmless, however. There are complications with the second one. The problem is that the truth-value of '¿7' is pseudo-monadic and depends on that of some V'; V' is totally arbitrary, and so there is nothing preventing V' from being the truth-value specification of '/?'. In this one case, then, the truth-value of '¿7' seems to depend on that of 'p\ and it seems to make sense, therefore, to try and vary the truth-value of 'p' independently of that of 'q\ This is all very abstract. I will continue the argument while illustrating it with some real, though bizarre language data. Consider the following state­ ments: (177) Statement (177) is true. (178) Statement (178) is false ('F ' sense).

TRUTH, FALSITY, AND POSSIBILITY

171

(179) Statement (179) is undetermined ('U ' sense). (178) is not only bizarre, but famous. It is the key example of what has been called the 'Liar Paradox'. (177) is less famous; it has been said to exhibit a Truth-Teller Paradox' (cp. Mackie 1973a: 240). (179) has not attracted much attention. I have called it a manifestation of a 'Doubter Paradox' (see Van der Auwera n.d.d). Because of its long-standing prominence, I will concentrate on the Liar Paradox. (178) says that a statement 'p' is Fs . 'Fs ' is a pseudo-monadic operator. So there is some 'q' with respect to which 'p' is said to be F . Whether 'p' is really F rather than just said to be F depends on 'q'. Like for any other statement, the truth-value of '¿7' is not unconditional; it depends on that of some V. But, what makes (178) paradoxical, V takes us back to 'p': to find the truth-value of the '¿7' that guarantees either the truth, the internal falsity, or the internal indeterminacy of 'p', one must know whether 'p' is Τ , U , or F . So the 'p' of (178) does not have any '¿7' whose truth-value is independent from that of 'p'. Consider now, with the preceding analysis in mind, the 'ρ ~ q' table; its present version incorporates the distinction between external and internal values. Ρ

~

τs Us Fs

q

T s

Us FS

FS

Us τs Table 11

I contend that the actuality value statement that there is no 'q' — in the case of (178) — whose truth-value is independent of that of 'p' translates into the truth-value statement that 'q' is false. If this is correct, 75 then the third column of Table 11 tells us that 'p ~ q' is . Thus my proposal on the Liar statement is that it is This proposal can be argued for in another way, too. Because the truthvalue of the 'q' of (178) depends on that of 'p', we can try and evaluate 'p' inde­ pendently of 'q' As pointed out above, I have followed this procedure all along ; while it is somewhat preposterous and redundant for non-paradoxical state­ ments, we will now see how it can be useful for paradoxical ones. Suppose

172

PROPOSITIONAL OPERATORS

that (the 'ρ' of) (178) is Ts As (178) says that (178) is F s , it should be Ts that (178) is F . So (178) should be F . But this conclusion must be false somehow, for I have been taking (178) to be Τ , and (178) cannot be both Τ and F . If a conclusion is (178) is false, then it is due to the incorrectness of the inference principles or to the falsity of the premises. As there is nothing in the preceding argument that I can find fault with, I conclude that it is the supposition that (178) is Τ that is false somehow. Of course, this 'somehow false' cannot be 'F ', for this takes us back to the paradox. If 'somehow false' is not 'F ', what is it then? The answer is suggested on the first line of Table 11 : if one varies 'p' in­ , or dependently of 'q' and one gives ita ' T s', then 'p ~ q' is either F , In the paradoxical case of (178), 'p' and 'p~q' have identical trutthvalue con­ ditions. So the non-'F s ' falsity of the 'p' of (178) we are looking for is! , In less formal terms, my stand on the Again, I am claiming that the Liar is( Liar is that it is false because there isnothing (no q) that it could possibly be true of, i.e. because of an unavoidable presupposition failure. (178) has no truth conditions; it can only be The preceding argument started off from the assumption that (178) was true. Let us now see what happens if we assume (178) to be false or possible. The assumption that (178) is false is easily dealt with. If (178) is F , then it should be F that (178) is F . But that is impossible. As there is nothing wrong with the reasoning, the premise must be false somehow. This 'false somehow' '. So once again can't be a 'F '. The third line of Table 11 tells us that it is Ί we conclude that (178) is (178) has no 'F ' conditions. One could think that the fact that (178) has no 'F s ' conditions merely follows from the fact that (178) is ( F ) and one could further think that it also follows that (178) has no 'U ' conditions. The argument below will show that this is not correct. Suppose that (178) is U . This means that it is U that (178) is F . Surpris­ ingly perhaps, this is quite correct. 'U s ' indeterminacy is bilateral: when a statement is U , then its 'F ' negation is U , too. Thus, by contrast to the sup­ position that (178) is Ts or Fs , the supposition that (178) is U s does not lead to a contradiction. So we cannot conclude that it is that (178) is U . Nor have that (178) is U . The only thing we we established that it is Τ , F , U , or know is that the supposition that (178) is Us does not lead to a contradiction: if (178) is U , then the internal negation of (178) is U , too. This is a 'U ' condi­ tion, but it is a totally vacuous one, for the internal negation of (178) happens to be (178) itself. The reason for this vacuousness is not hard to find. We know, on independent grounds, that (178) will never be U , for it is inevitably

TRUTH, FALSITY, AND POSSIBILITY

173

Thus my proposal for the Liar Paradox still stands. There is a lot more to means that I be said, however. Note, first of all, that the claim that (178) is postulate a 'something' with respect to which (178) is Let (180) be an object language representation of my 'Liar Paradox'. (180)

(p~q)

is triadic. So there is a 'hidden' r' with respect to which 'p ~ q' is (181)

(p~q)

r

Or, what amounts to the same, there is an V with respect to which (180) is true. (182)

(p~q))!r

It is not difficult to exemplify the V in question. It is true of the universe that the Liar statement is false because of a presupposition failure. It is also true of the possible world that I take to be the actual one, and of each particular SOA that is part of it. A second, further point is this. So far, I have analyzed (178) as a 'p ~ q' with an F s 'q' and I have investigated the suppositions that 'p' isΤs,Fs, and Us . Clearly, I could further test the ' h y p o t h e s i s by looking at the supposi­ tions that 'p' is and , and1 could refine the hypothesis by claiming that 'q' is not really F , but As to the refinement, thêself-reference of (178) is such that the 'q' that 'p' is supposed to be relative to must have the same truth-value conditions as 'p'. So, if my verdict on 'p' is , then 'q' is also I The fact that the preceding is not too pages were written on the assumption that 'q' is Fs rather than harmful however. The relevant property of the 'F ' falsity of 'q' was that it led ' falsity of 'q' has this to the ' ' falsity of 'p ~ q'. It is easy to see that the ' property, too. When a statement is false because of a presupposition failure, it does not matter whether the presupposition in question also suffers from a presupposition failure. So much for the ' falsity of 'q'. What about the and ' ' sup­ positions of 'p'? Let us start with falsity. We can suppose 'p' to be in two ways, viz. in the self-referential way that (178) invites us to ((183)),'and in the non-self-referential way ((184)) that allows us the hypothesis that (178) is in fact (183) ρ (184) ρ

q r

PROPOSITIONAL OPERATORS

174

As to the non-self-referential supposition, it has no discriminative value. It only produces a trivial truth-value condition. Take (184). Via the truth-valueconditional identity between 'p' and ' p ~ q ' (184) leads to (185), which is per­ fectly acceptable. (185) (p ~ q) If we take the 'p leads to (186).

r q' supposition, however, the result is less trivial. (183)

(186) (p ~ q)

q

(186) is a contradiction, for it requires 'q' to be relative to itself ('q' is to be both a true presupposition for 'p' and a false one for 'p~q'), which is impossi­ ble. So (186) is somehow false, and its falsity derives from that of the premise (183). If (183) is false, then the relation between 'p' and 'q' cannot be one of falsity. At first sight, there are four possibilities: (187) (188) (189) (190)

ρ ρ ρ ρ

! ~ ◊

q q q q

The first three have already been dealt with: the analysis of (187) and (188) led us to the conclusion that (178) is relative to 'r', while (189) has been shown to be compatible with this conclusion. As to the fourth possibility, (190), we find ourselves dealing with the supposition that 'p' i s ( N o w , if (190) is Τ , then (191) should be Ts., too. (191) (p ~ q)

q

But (191) is a contradiction: 'q' cannot be of itself. Hence, (191) is some­ how false, and so is (190). Therefore, the relation between 'p' and 'q' is not one of |' indeterminacy. Neither is it one of truth, 'F s ' falsity, 'U s ' indeter­ minacy , or falsity, of course, as I argued above. What was also argued for above is that the reason why ' p ! . q ' , p ~ q ' , and 'p ◊ q' are false is that they are all externally false with respect to V'. I believe that the falsity of 'p q' and of 'ρ q' can be similarly accounted for. My claim — which properly belongs in a theorv of external truth-values, left undeveloped in this book—is that when 'p' isj relative to 'r' because of the falsity of '¿7', it is immaterial whether the truth-value of 'p' relative to 'q' is internal or external. In other words, when (184) is T s , then (192), (193), (194), (195), and (196) are all T s , too. (184) ρ

)r

TRUTH, FALSITY, AND POSSIBILITY

175

(192) (Ρ ! (193) (Ρ~ (194) (Ρ ◊ (195) (196) In all of these cases, 'ρ' suffers from a presupposition failure; in (195) 'p' suf­ fers from a double presupposition failure, and in (196) 'p' suffers from a pre-' supposition failure and a presupposition indeterminacy. In trying to do away with paradoxes, one always runs the risk of creating new ones. This is the last issue that I will take up in connection with the Liar Paradox. If the Liar statement is/ , what then is the status of the statement in (197)? (197) Statement (197) is As a symbolic representation of (197) I will use (198): (198) ρ

q

Of course, the 'p' of (198) is 'p q' itself. If the 'p q' of (197) has only one truth-value, just like the simple Liar statement in (178), then I can determine it by assuming 'p' to be true — '!p' will have the same truth-value conditions as 'p q'. Suppose, then, that 'p' is T . Symbolically: (199)

p\q

Given that 'p' equals (200) (p

'p

q','p

q'

should be Τs , too.

q)!q

But this conclusion, less redundantly formulated as (198), leads to a con­ tradiction , for I took 'p' to be Ts of 'q', and 'p' cannot be simultaneously T and relative to 'q'. So (200) is false somehow,On all prior occasions, the falsity connected with such a contradiction was '( falsity. So why shouldn't it be one this time? (197) furthermore lacks an Independent 'q' just as much as (178) does, and if this translates into an( ) 'q' and, therefore, into an 'p' in the case of (178), it may reasonably be supposed to do the same for (197). To settle the argument, I would need a truth-table for 'p q'. Unfortu­ nately, owing to the circumstance that the study of external truth-values is set apart for future study, I do not have this yet. But perhaps (201) is a part of it.

PROPOSITIONAL OPERATORS

176 (201)

Ρ

...

...

τs

...

...

Fs

... ...

(201) shows that if 'ρ' is_Ts, then 'p q' can be If this is plausible, so is the claim that (197) is (199) corresponds to the 'if 'p' isΤ'sbit of (201), and q' can be the judgment that (200) is false corresponds to the 'then 'p part. Conclusion: (197) is just as as is (178); as in the case of (178), the falsity is relative to some independent V . " (202) (p _ q)

r

One could check this hypothesis on the suppositions that 'p' is F , U . and I will give a nutshell presentation. With the 'F ' and 'U ' suppositions we geTvacuous truth-value conditions. If 'p' is F ((203)), then it should be F that'ρ'is ((204)). (203) 'p ~ q (204) (ρ q) ~ q This is correct, but vacuous. Similarly, if 'p' is U ((205)), it is U that 'p' is ((206)). (205) ρ ◊ q (206) (ρ q) ◊ q is,

Suppose now that'p'is ((208)). (207) ρ q (208)(ρq)

|((207)), in which case it should be

that'p'

q

If it is that 'ρ' isl , then it is neither Τ , not F , nor U that 'p' is But . So the conclusion is somehow the supposition was that it is Ts that 'p' is false, the premise is arguably somehow false, too, and the falsity of the latter is arguably the V-relative variety: (209) (p

q)

r

Suppose, finally, that 'p' i s ( ( 2 1 0 ) ) , in which case it should be that'p'is| ((211)). (210) p (211) (p

q q)

q

But (211 ) is a contradiction and it is somehow false. Hence the premise is argu-

MODALITY

177

ably somehow false and this 'somehow false' is arguably t h e f a l s i t y , in which case 'p' is arguably relative to 'r'. To repeat the general conclusion: both the simple and the sophisticated Liar statements are . They differ in one detail: (178) has vacuous 'U ' conditions, while ( 1 9 ) h a s vacuous 'U ' and 'F s ' conditions. Let us briefly return to the Truth-Teller and Doubter Paradoxes. (177) Statement (177) is true. (179) Statement (179) is undetermined ('U s ' sense). I maintain that (177) is and that (179) is In essence, the arguments go as follows. Suppose that (177) is Ts. Then it should be Τ that (177) is Τ , which is correct. So (177) has a 'Ts' condition, but a vacuous one. The vacuousness is due to the fact that (177) will never be Τ , or F , nor U , which means that its presupposition 'q' is not true. For the Liar statements, the untruth of 'q' was an outright falsity, a presupposition failure, and the supposition that a Liar statement is Τ led to a contradiction, making this supposition demonstrably false. For the Truth-Teller statement, however, the untruth of 'q' is an inde­ terminacy, and the supposition that the Truth-Teller statement is Τ does not lead to a contradiction, but to vacuousness. For (179), however, we get a con­ tradiction. If (179) is Τ , then it should be Τ that (179) is U , but this gives a contradiction: (179) cannot be both U and Τ of itself. Hence it is arguably false that (179) is Τ and this 'false' is arguably an Other paradoxes are : (212) Statement (212) is U* s . (213) Statement (213) is U*s (214) Statement (214) is U**s. (215) Statement (215) is , All of these can be called 'Doubter Paradoxes'; all except (212) can be called 'Liar Paradoxes'. 76 Their analysis should not present any basic problems. 4.

Modality

For many logicians, possibility is not something that is primarily under­ stood in terms of truth and falsity. Rather, they conceive of possibility as hav­ ing to do with necessity and impossibility. The truth-possibility-falsity dimen­ sion, studied in the preceding section, will be called 'non-modal. The other dimension, that of necessity-possibility-impossibility is ''modal'.77 In many ways, the analysis of modality is analogous to that of truth, possi-

PROPOSITIONAL OPERATORS

178

bility, and falsity. In both types of analysis, we are confronted with a small set of pseudo-monadic, presuppositional, bound or unbound operators, some of which are possibility operators and all of which have to be understood, at least partially, in terms of conditionality. I have already introduced two modal operators, viz. '→' and 'p → q' was to mean 'p is a sufficient condition for q' and 'q is a necessary condition for p ' . The star on the arrow in indicates that the condition in question is a are conditional possibly necessary but at least sufficient one. Both '→' and operators; they are not presuppositional. Conditional modality will be re­ served for the next section. At present, I will focus on presuppositional mod­ ality. 4.1. Necessity, contingency, and impossibility The first modal operator to be considered is presuppositional necessity ( ' □ ' ) . Though necessity is not the same as necessary truth, the two phrases will be used interchangeably: after all, '□ p ' and '□ ! p ' have identical truth-value conditions. In 'D p ' , ' □ ' is used pseudo-monadically. Claiming that an operator is pseudo-monadic indicates that it is really n-adic. At first sight, η seems to be 2: nothing is necessary that isn't necessary for something. There is no such thing as absolute necessity. A conflict, for example, can be necessary; but it is only necessary in virtue of a certain, historical development. Simi­ larly, it is necessary that every human being has both a mother and a father; but this is a necessary consequence of our biological constitution, since human beings are not equipped for parthenogeny. So all '□ p ' claims would seem to abbreviate 'p □ q' claims; as a presupposition, 'q' can be left unexpressed. With the help of the conditional operator *→, I could thus define ' □ p ' and 'p □ q" as follows: (216) (q

)Λq

Notice that I have used'*→rather than'→' : the 'q' that is sufficient for 'p' may be necessary, too. The conflict that proves necessary because of a certain, his­ torical development may not result at all without the development in ques­ tion, in which case the latter is not only sufficient but also necessary. (216) is only a first attempt. To improve it, we start out from (a) the trivial claim that '(q p) Λ q' contains two implicit truth operators, and (b) the nontrivial claim that the second relata of these operators should be made explicit: (217)

!(q

p)Λ!q

MODALITY

179

The reason why we should bother about these truth operators is that there are at least two interesting ways to define their second relata, and that one of the two defines truth rather than necessity. The two possibilities are 'q' and 'r': either 'q p ' and 'q' are true of '¿7' itself, or else there is yet a third relatum, V , that they are both true of. If we choose 'q', we end up defining truth. Con­ sider (218): (218) ((q

p)!q)Λ(q!q)

Expanding the first conjunct gives us: (219) ((qiq)

(p ! q)) Λ (q !q)

As a definition of necessary truth, (219) is wrong. (219) says that 'q' is a possi­ bly necessary and at least sufficient condition for 'p' to be true of 'q' which is not a necessary feature of necessary truth. Suppose that 'p' says that A is emprisoned in Belgium, and that 'q' is an SOA about a court decision in Ger­ many. If the emprisonment of A proves necessary on account of the court de­ cision, there still is no sense in which the assertion that A is emprisoned in Bel­ gium is true of the German court decision SOA. Of course, 'p' may be true of 'q' Imagine 'p' as the emprisonment of A, and 'q' as the emprisonment of A and B. Even though (219) does not define necessary truth, it is not worthless: (219) happens to be logically equivalent with (154), which fact makes it a def­ inition of truth. (154) (q

(p!q))Λq

Suppose now we choose 'r'(220) ((q

p)!r)Λ(q!r)

If (220) is correct, then necessity or necessary truth is fundamentally triadic ' and were after all rather than dyadic. This finding is not too bizarre: ' triadic, too. The triadic view is not altogether unattractive either: necessary truth is necessarily 'truth of, just as all truth is 'truth of, but, by contrast to truth, necessary truth also concerns necessity; necessity, in its turn, is essen­ tially 'necessity for'. So when 'p' is necessarily true, it is true of 'r' that 'p' is necessary for 'q'. Both 'q' and V are presuppositions. Henceforth, when I use 'D' dyadically or rather, pseudo-dyadically, only the outermost presupposi­ tion 'r' will be mentioned. (221) ρ = pr

=

((q

p) !r) Λ (q ! r)

Notice that, given that obeys a Modus Ponens rule, '((¿7 p) ! r) Λ (q ! r)' implies 'ρ ! r'. This is a welcome consequence: all necessary truth is truth, but

PROPOSITIONAL OPERATORS

180

not all truth is necessary. Necessary truth stands to truth in the same way as necessary indetermi­ nacy (' ') and necessary falsity (' '), both of which could be called 'impos­ sibility', stand to indeterminacy and falsity. (222) (223)

p=p ρ = ρ

r = ((q←~p)!r)Λ(q!r) r = ((q →◊ P) ! r) Λ(q!r)

A graphic representation of the relation between '!', ' ◊ ' , and ' ~ ' , on the one hand, and 'D', '◊ ', and '  ', on the other, is Figure 29.

That ' ~ p ' implies ' p ' , but not vice versa is symbolized by the fact that the p ' stretch is totally contained in the ' ~ p ' stretch. Figure 29 clearly shows that ' „ p ' , ' p ' , and ' p' do not take up the same stretches of meaning as do ' ~ p " ' ◊ p ' , and '!p'. 'p' can be U**s, but neither necessarily true, necessarily indeterminate nor necessarily false. In that case, we say that 'p' is contingent. Just like indeterminacy, contingency is a side of possibility: while indeterminacy represents non-modal, truth-value possibil­ ity, contingency is modal possibility. Contingency is basically the possibility expressed by present-day English 'can', whereas indeterminacy is the possi­ bility of present-day English 'may' (see Van der Auwera n.d.e). Contingency will be represented by a dotted diamond (' ).

Setting off ' p ' against the top part of the scale in Figure 30, one sees how con­ tingency comes in each of the three stretches, so that we have contingent truth, contingent indeterminacy, as well as contingent falsity. Contingency-possibility is scalar just like indeterminacy-possibility. Fig­ ure 31 represents upperbound ( *') and lowerbound (' * ') contingency:

MODALITY

181

Figure 31 Upperbound contingency or rather, the monadic version of it, is the possibil­ ity that modal logicians usually talk about. 78 In V.5.2,1 will document the im­ portance of upperbound and lowerbound contingency. Double-bound con­ tingencies also exist, but they seem to be of little interest. On the basis of the above conditional analyses, the componential analyses of pseudo-monadic '', and will come out as follows :

Ρ

p

◊P

~ P

τs

US

FS

FS

Us

FS

US

FS

Us

FS

US

Us

Us FS

FS

Table 13 There are two valuations that are worth a brief comment, viz. those of the middle slots of the ' p ' and ' p ' columns. To say that if 'p' is U , ' p ' and p ' are F , is not self-evident. Let me illustrate the problem with the '  p ' case. If V is Us , then it is Us that 'p' is T and it is also U that 'p' is F . If 'p' is, say, T , it seems safe to say that it is U that 'p' is necessarily T . So, when it is U that 'p' is T , then it is Us that it is U s that 'p' is necessarily T s . This conclu­ sion confronts us with an iterated possibility operator. I haven't taken a stand yet on the interpretation of such a construction and will, in fact, leave this for future research. Suppose, however, that the 'U s ' possibility of a 'U s ' possibil­ ity reduces to a 'Us ' possibility, which is not implausible. In that case, the pre­ ceding argument has established that if 'p' is U s , 'D p ' is U s , too.

PROPOSITIONAL OPERATORS

182

p

Ρ

Us

τs Us

Us Fs

Fs

Table 14 This is not implausible. If a similar argument is made for the relation between ' ~ p ' and ' p', we get the scale of Figure 32.

ρ

ρ

ρ

ρ

Dp

ρ

Up

Figure 32 However attractive this may seem, it leaves one matter unresolved: we can no p ' implies ' ~ p' When 'p' is longer say that '  p ' implies 'p' nor that ' necessarily true, for example, 'p' needn't be Τ ; 'p' could also be U . Whatever answers this and other unsolved questions may get, they should not invalidate the main thesis that necessity, impossibility, and con­ tingency operators are essentially triadic. This thesis is irreconcilable with present, orthodox modal logic, where necessity, impossibility, and con­ tingency are conceived of as monadic. Occasionally, representatives of modal orthodoxy are aware of the dyadicness of modality. This awareness is often implicit, as when they use the concept of necessary conditionality or a possible worlds concept of accessibility (i.e. a relative possibility according to which possible worlds can be possible with respect to each other). Sometimes, the explicit recognition that modality can be dyadic results in a brief mentioning (see Dewey 1925: 65; Lewis and Langford 1959: 160; Bradley and Swartz 1979: 331-332; Ellis 1979: 32). Logicians rarely go any further (see Reichen­ bach 1947: 392-398; Hamlyn 1961; 1967; Sudberry 1980). It is very rare that they try to fully integrate dyadic modality in their logic (see von Wright 1957c [1953]; Juhos 1954; Smiley 1963; Hilpinen 1969; Kamlah and Lorenzen 1973: 183-184, 225-297; Bryant 1980).

MODALITY

183

4.2. Iterated modality In the preceding subsection, I have drawn attention to the problem of how to interpret an iterated indeterminacy operator. The analogous problem in modal logic is: How do we interpret expressions such as '    p ' and ' < p'? Is 'p' necessarily necessary when 'p' is necessary? Is 'p' necessary when 'p' is necessarily necessary? Is 'p' necessary when it is necessary that it is contingent that 'p' is necessary? Modal logicians often find these problems enigmatic. Iterated modalities, it is claimed (cp. von Wright 1957b: 77; Goble 1966: 197; Snyder 1971: 86), are foreign to our logical intuitions, in part be­ cause we hardly ever have a use for them. I admit that iterated modalities con­ stitute a problem and that we don't need them that often; I don't agree that they are all that enigmatic. I will briefly illustrate this claim with a discussion of the necessity of necessity, more particularly of the so-called 'Weak Reduction Principle', represented by the conjunction of (224) and (225). (224) p p (225) p·  ρ Remember, first, that I accept (226) but not (227): all necessary truth is truth, but not all truth is necessary. (226) Up ρ (227) ρ Up The sufficiency of (226) is once again the upperbound one: it is possible that the truth of 'p' can only be a necessary truth, in which case the necessary truth of 'p' is necessary and sufficient for the truth of 'p'. Given the hopefully uncontroversial position on (226) and (227), I do not see how there could be any doubt about (224) and (225): the former is true and the latter is false. At most, one could entertain some doubt about one peculiar instance of (225). If we translate (225) into a pseudo-dyadic format, there are five cases to be distinguished: (a) the (outermost) presupposition of the ' D p ' of the antecedent is different from that of the '  p ' of the consequent and that of 'D D p ' ((228)) ; (b) the presupposition of the antecedent '  p ' is identical to that of the consequent '  p ' , but not to that of '   p ' ((229)); (c) the presup­ position of the antecedent 'p ' is identical to that of ' ρ', but not to that of the consequent '  p ' ((230)) ; (d) the consequent presuppositions are identical ((231)); and (e) all the presuppositions are identical ((232)). (228) (pr) (229) (pr)

(ps)t (pr)s

PROPOSITIONAL OPERATORS

184

(230) (ρ S) (ρ  r)  S (231) (ρ  r) (ρ  s)  r (232) (pr) (ρ r) r The one expression that is not straightforwardly false is (232), since it seems to exhibit some kind of self-referential necessity. However, if we render it in a triadic fashion, all uncertainty disappears: (233) (((q

p)!r)Λ(q!r))

(s

(((q

p) !r) Λ (q !r)) Λ (s!r))

The antecedent of (233) locates the necessity of the necessary truth of 'p' rela­ tive to a presupposed 'r' in a necessary conditionality of 'p' for a presupposed 'q' 'q' itself is not necessary. This is different in the consequent: here 'q' is necessary for a presupposed 's'. So (233) is false. 4.3. Fatalistic necessity One of Lukasiewicz' early systems (Lukasiewicz 1930) has the unusual feature that every proposition implies its own necessity. Lukasiewicz later abandoned this principle; furthermore, it is completely foreign to classical modal logics. Yet the early Lukasiewicz was not alone in thinking that there is a sense in which a proposition implies its own necessity. Possibly, the idea al­ ready occurs in Aristotle's De Interpretatione (19a: 23-24), but there is some debate about the exact interpretation of this passage (see von Wright 1957c: 121-122; Ackrill 1963: 137-142; Rescher 1969; Frede 1972; Williams 1980). The passage, in its Scholastic formulation, runs as follows: "unumquodque, quando est, oportet esse". The idea also surfaces in what D. Lewis (1973: 8) calls "necessity in respect of all facts" or "fatalistic necessity". Lewis considers this to be a "degenerate" necessity, which would nicely account for the little attention it has gotten. In the brief discussion that follows, I will show that RPL accomodates fatalistic necessity in a natural and harmless way. Consider (221) again: (221) p = pr

= ((q-*>p) ! r) Λ (q ! r)

When 'ρ' is necessarily true, 'p' has two presuppositions. There is some 'q' for which 'p' is necessary, and there is some 'r' which both 'q' and the necessity of 'p' for 'q' are true of. There is nothing in this account to prevent 'q' and 'r' from being identical. Whatever fills the 'q' slot must be true of 'r' and must imply 'p' relative to 'r'. 'r' itself fulfills both these conditions: (234) ((r

p)!r)Λ(r!r)

MODALITY

185

So, (234) defines a subtype of necessity. Let me represent this by _ . (235)

p=p

r=((r

)!r)Λ(r!r)

But there is more. As I have already argued in V.4.1, (234), or its notational variant (236), defines truth. (236)

(r

(!r))Λr

So we have found a necessity that is and is implied by truth. In other words, necessity is fatalistic necessity, 'p' is fatalistically necessary relative to a pre­ supposed 'r' if that which guarantees the truth of 'p' relative to V is V' itself. We can define fatalistic necessity in a different way. There is nothing in (221) that prevents 'q' and 'p' from being identical. The 'q' slot filler must be at least sufficient for 'p'; 'p' itself is both necessary and sufficient for 'p'. So 'p' can fill the 'q' slot. (237) ((p

)! r )Λ(!)

(237) says that 'p' is necessarily true of V for no other reason than that 'p' is true of V , which is precisely what fatalistic necessity is all about. Finally, in line with the above arguments, we can talk about fatalistic necessity in yet a third way. 'p' is fatalistically necessary when 'p', 'q', and 'r' are all identical. (238) ((p

p)!)Λ(!)

4.4. Th necessity of possible worlds semantics While I accept possible worlds, I do not think that the current possible worlds definitions of necessity (in (239)) and of possibility (in (240)) are par­ ticularly revealing. (239) 'p' is necessary iff 'p' is true in all possible worlds (240) 'p' is possible iff 'p' is true in some possible worlds In what follows, I will have a closer look at the possible worlds necessity. (239) is an attempt to define necessary truth in terms of truth as such. This definition hinges on a universal quantification over possible worlds. Such a quantification is not as foreign to my own analysis as it might seem. When 'p' is Τ , 'ρ' is Τs of 'r'. 'r' stands for a number of entities: the particular SOA of which 'p' is Τ , an F-SOA of which 'p' is Τ , the possible world that contains this F-SOA and of which 'p ' is Τs , and, finally, the universe, the set of all possi­ ble worlds. So we have a universal quantification, too. We also have a re-

186

PROPOSITIONAL OPERATORS

stricted universal quantification over possible worlds, however, and this is the one that will be used in my argument. When 'p' is true, it is not true of one pos­ sible world only; 'p' is, trivially so, true of all the possible worlds of which 'p' is true. The contingent truth that I have written this very sentence on a Wednes­ day evening, for example, is not only true of an F-SOA, the universe, or of the one possible and actual world in which I have indeed written this sentence on a Wednesday evening; it is true of all the possible worlds in which I would have written this sentence on a Wednesday evening. Notice that the universality of the quantification is restricted: in the case at hand, the truth of 'p' does not quantify over all possible worlds, but only over all possible worlds of which 'p' is true. (241) summarizes this claim in a format that resembles (239): (241) 'p' is true iff 'p' is true of all possible worlds of which 'p' is true (241) is, of course, circular and trivial. The restricted universal quantification of (241) characterizes all truth; it also characterizes necessary truth. (242) 'p' is necessarily true iff 'p' is necessarily true of all possible worlds of which 'p' is necessarily true As the necessary truth of 'p' relative to the presupposed V is the same as the truth of both 'q p ' and 'q' relative to the presupposed V, (242) can be re­ phrased as follows: (243) 'p' is necessarily true iff 'p' is necessarily true of all possible worlds of which 'q p ' and 'q' are true When 'p' is necessarily true of something, then 'p' is also true of it; this is a gen­ eral characteristic of the relation between truth and necessary truth. In the case under consideration, however, the converse also holds. When 'p' is true of all possible worlds of which both 'q p ' and 'q' are true, then 'p' is neces­ sarily true. So (243) is equivalent with (244): (244) 'p' is necessarily true iff 'p' is true of all possible worlds of which both 'q p ' and 'q' are true (244) has brought us close to the canonical possible worlds definition of neces­ sity. (239) and (244) are equivalent except for universal quantification: in (244), it is restricted, while it seems to be unrestricted in (239). But this dis­ tinction is only an apparent one. What (239) does not show is that the possible worlds semanticist does impose a restriction on the universal quantification. The possible worlds theorist distinguishes between various types of necessity,

MODALITY

187

each type being associated with a restriction. For the subtype of logical neces­ sity, for example, only logically possible worlds are considered. In the case of physical necessity, the possible worlds under consideration are the physically possible ones. Thus, despite its 'neutral' formulation, the universal quantifi­ cation over possible worlds in the definition of necessity in (239) involves a re­ striction, too. It remains to be shown that it is the same type of restriction as that of (244). Let us have a look at a particular subtype of necessity, viz. logical neces­ sity. Its possible worlds definition is given in (245). (245) 'p' is logically necesary iff 'p' is true in all logically possible worlds The particular restriction here is logical. A logically possible world is a possi­ ble world in which the laws of logic hold. These laws constitute a small set of logically necessary truths, from which all the other logically necessary truths have to follow. If 'p' is a logically necessary truth, then the logically possible worlds obey the laws of logic and the latter imply 'p'. I can thus render (245) by (246). (246) 'p' is logically necessary iff 'p' is true in all possible worlds in which the laws of logic hold and in which these imply 'p' It should be clear by now that this restriction on universal quantification is of the ((q p) ! r) Λ (q ! r)' type. If I now abstract from the logicality of the necessity of (246), I can rewrite it as (244), which in turn gets us back to (243) and (242). (242) 'p' is necessarily true iff 'p' is necessarily true of all possible worlds of which 'p' is necessarily true The important thing about (242) is not just that it is trivial, but that it has got nothing to do with the necessity of necessary truth; the characteristic it de­ scribes depends only on the fact that necessary truth is a type of truth. All truth involves a restricted universal quantification over possible worlds. I conclude that the attempt to define necessity by (239) has misfired. For one thing, its formulation wrongly suggest that we are dealing with unrestricted universal quantification. For another, if one makes the restrictions on universal quan­ tification explicit, one sees that (239) inadvertently capitalizes on the truth of necessary truth, rather than on its necessity. Throughout this whole process of trivializing (239), I have — somewhat hypocritically — tried to fit (239) into my own framework, thus neglecting the basic intuition that (239) was designed to capture. This intuitive content is the

PROPOSITIONAL OPERATORS

188

following: when 'p' is necessary, then 'ρ' is true, whatever else is true or false — not quite 'whatever' of course: the universal quantification is restricted. The intuition underlying (239) is correct, but incomplete. It is true that neces­ sary truth is relatively independent of other truths. It is equally true, however, that there are truths on which necessary truth is dependent. Here I come back to my main thesis: all necessity is relative. More particularly, the necessity operator is triadic. In the intuition underlying the possible worlds definition, the necessity operator is misconstrued as monadic. 4.5. Generic modality In ordinary language, modality is usually expressed by modal verbs (e.g. 'must'), adverbs (e.g. 'possibly'), adjectives (e.g. 'necessary'), and nouns (e.g. 'necessity'). In view of the discussion of the next section, I want to draw attention to a type of modality that is conveyed by a particular use of deter­ miners and/or tenses, rather than by any expressly modal signals. Consider (247): (247) A whale lives in the sea. In most contexts, the point of (247) is not to introduce a particular whale and to say that it lives in the sea. In its preferred interpretation, (247) says that it is a necessary characteristic of the typical whale that it lives in the sea. The use of the definite article in (247) is often called 'generic'. I will appropriate this term to denote the modality that is part of the preferred interpretation of (247). I do not know whether (247) is ambiguous between the generic, and the non-generic or 'particular' readings, both of which are literal, or whether they are both non-literal, the literal meaning being a more abstract one. I do know that the choice between the two interpretations is often determined by con­ text. There are some cases, however, where the choice is independent of con­ text. It seems to me that (248), for example, is always generic, and that (249) is always particular. (248) Kangaroos have no tails. (249) There is a whale living in the sea now. In such cases, genericity and particularity seem to go with the literal mean­ ings.

IMPLICATION

5.

189

Implication "Even the crows on the roof tops are cawing about the question which condi­ tionals are true." (attributed by Sextus Empiricus, the third century sceptic, to his (near-)contemporary Callimachus, an Alexandrine poet; quoted by Mates 1961: 42-43)

It is surprising to see how few logicians have made a connection between the modal logical necessity operator and the necessity of a necessary condi­ tion. It is equally astonishing that logicians have made so little of the relation between the notions of necessary and sufficient conditionality and the study of conditional operators. 79 A partial explanation, I might venture, is that the theory of sufficient and necessary conditionality is underdeveloped and under­ appreciated. In the preceding section, the modal operators were claimed to represent conditionality, in particular, presuppositional pseudo-monadic conditional­ ity. The present section will claim that the conditional operator 'if ... then' is essentially modal. So both sections deal with conditionality and with mod­ ality. The distinction is that I was earlier concerned with the conditionality/ modality that typically allows a pseudo-monadic and bipresuppositional ex­ pression, and that the conditionality/modality that is at issue now is typically expressed by a pseudo-dyadic and monopresuppositional operator, viz. by 'if ... then'. Note that the claim that 'if ... then' is a modal operator implies that RPL is an essentially modal logic. In RPL, modality is not a dimension that is merely added to a non-modal core. The very core is modal. This is not to deny that one can abstract from modality or that the abstraction might be interest­ ing. I do hold, however, that this abstraction goes hand in hand with a loss of descriptive adequacy. Up to now, the terms 'implication' and 'conditional' have been used somewhat indiscriminately. Henceforth, the arrows and their interpretations will be called 'conditional/implicative operators' or 'implications'. Thus both the arrow of (250) and the 'if ... then' of (251) will count as implications. (250) ρ q (251) If it rains, I will take my umbrella. A wff such as (251), which is composed of two wffs and an implication, will be called a 'conditional'. (251) and all other 'if... then' assertions will be termed 'conditionals', too.

PROPOSITIONAL OPERATORS

190

The following discussion splits up into two subsections. In the first, I will defend the claim that all uses of 'if p, then q' literally mean that 'p' is at least sufficient for 'q' This hypothesis may seem simple and plausible, but the number of objections is enormous. Hence, most of my energy will go to the discussion of these objections. I will also analyze the relation between my 'at least sufficiency implication' and implications proposed in the literature. In the second subsection, I will try to account for what will be called 'generic' and 'particular', 'indicative' and 'subjunctive', 'problematical' and 'counterfac­ tual' conditionals. Here the proposal is complex and the number of objections is small. Hence the emphasis is on the presentation of the hypothesis rather than on any objections. I will impose three general restrictions on my exposé. Firstly, I will disre­ gard a conditional's time dimension. Secondly, I will concentrate on the rela­ tion between the antecedent and the consequent, and on the status of the ante­ cedent , but not on that of the consequent. Thirdly and most importantly, I will not discuss the achievements of the seemingly growing number of inves­ tigators that try to account for 'if... then' in terms of justification or assertability conditions, often formalizing their results in a probability calculus (see Jef­ frey 1964; E.W. Adams 1965,1966,1975,1983; Ellis 1973; Stalnaker 1970; D. Lewis 1976; Cooper 1978: 158-211). There are two possible motivations for such a strategy. Either one maintains that it is senseless to provide 'if... then' with truth-value conditions, as the notion of a truth-value would have no clear sense when applied to conditionals ( see e.g. E.W. Adams 1965:169-170). Or one holds that 'if... then' simply has the truth-value conditions of material im­ plication (see Grice 1975, n.d.). From both positions, it follows that 'if ... then' does not have any truth-value conditions of its own, and both positions have led people to postulate conditions other than truth-value conditions, such as the aforementioned justification or assertability conditions. I feel that this strategy is misguided, and in the following pages, I will defend a truthvalue-conditional approach. This does not mean that I would exclude consid­ erations of justifiability or probability as irrelevant. Lowerbound indetermi­ nacy, for example, which is at least close to (im)probability, will be seen to play an important role. 5.1. Sufficiency 5.1.1. The connection thesis The claim that 'if... then' always means that 'p' is at least sufficient for 'q'

IMPLICATION

191

is not essentially new. But it has been and still is remarkably unpopular. Many logicians denied that there is any connection between 'p' and 'q' other than the sober relation of material implication. The latter would represent what is common to or relevant in all 'if ... then' uses. Thus, most logicians concen­ trated on material implication rather than on 'if ... then' itself, and were not motivated to seriously entertain the thesis that 'p' is at least sufficient for 'q'. Partly, this was because what they needed the thesis for, i.e. 'if ... then', had moved outside the scope of their attention. Partly also because the notion of sufficient conditionality was not really thought of as worthy of study. It is true that there have always been logicians that were not won over by material im­ plication (e.g. MacColl 1906; Nelson 1930; Lewis and Langford 1959), but they could not stop the success of the Russellian truth-functionalist program (cp. Rescher 1974: 85-96). It is also true that people's views on the relation be­ tween 'if ... then' and material implication have become increasingly more sophisticated. The catalyst triggering this development was the problem of counterfactuals. Two factors were involved here: First of all, most logicians, including authorities such as Quine (1951: 16-17; 1965: 21-22) and Goodman (1965: 4), were convinced that a counterfactual implication could not be a material implication. If it could, all counterfactual conditionals would be true, for the mere falsity of the antecedent is enough to make a material conditional true. Second, the problem of counterfactuals could not be dismissed as mere hairsplitting. On the contrary, it was felt to be intimately connected with our understanding of laws, dispositions, the problem of induction, and the theory of truth. 80 Both factors were instrumental in bringing 'if... then' back to the forefront of logical speculation. An interesting characteristic of most (all?) re­ cent 'if ... then' theories, however, is that they still assume the relevance of material implication. D. Lewis (1973), for example, considers a counterfac­ tual implication to be a 'variably strict' implication, i.e. something like a strict implication which, in its turn, is the necessity of a material implication. So material implication has by no means lost its value, even if it has become an in­ strument, rather than an object of investigation. In this changing logical landscape, there run at least two streams of thought in which the sufficiency thesis surfaces. First of all, in the non-techni­ cal passages surrounding their formal, explicit accounts, logicians and lin­ guists occasionally state that there is at least some connection between 'if ... then' and sufficient conditionality. Thus Suppes (1957:8) calls 'p is a sufficient condition for q' an idiom that has "approximately the same meaning as 'if... then'". Glethmann (1979: 120) introduces a conditional operator that can be

192

PROPOSITIONAL OPERATORS

rendered by both 'if p, then q' and 'q is a necessary condition for/?', but he leaves it vague what the exact relation between these two phrases is. Kambartel (1971: 764), writing an encyclopedic entry on 'condition', deals with both the 'if p, then q' and 'p is sufficient for q' expressions, without specifying their connection, however. In his very informal, though thoroughly interesting essay on argumentation, Flew (1975:38) explicitly states "For to say If ρ then q just is to say that ρ is some kind of sufficient condition of q. " A number of logi­ cians connect sufficiency with the vague and general notion of implication (see Menger 1939: 631; Danto 1968: 51) or with the more specific notion of strict implication (see V.5.1.3.2), both of which are in turn related to 'if ... then'. The linguist Ducrot (1971) relates sufficiency to material implication, which would grosso modo correspond to 'if... then'. That there is at least some con­ nection between 'if ... then' and sufficiency is also implicit in the decision to call implications 'necessitations' (see van Fraassen 1968; Snyder 1971: 214; Boër and Lycan 1976: 6; Pollock 1976b: 27, 33-38). The other contexts in which the sufficiency thesis crops up are cases of explicit, but casual mentioning by authors who go on to study something else. Thus Roëlofs (1930) endorses a sufficiency thesis, but he is not really in­ terested in 'if... then' as such, but only in 'unless'. Pap (1958:331) approvingly mentions a sufficiency thesis in an analysis of C.W. Morris's views on analycity. Boudon (1974: 24) mentions the thesis, not because he is interested in 'if ... then' as such, but because he is working out a methodology for sociology. A telling final example is Lauerbach (1979: 205-206). 'Officially', she does not subscribe to any sufficiency thesis. Yet, in a passage where she is no longer concerned with the literal meaning of 'if ... then' but rather with conversa­ tional implicatures, she inadvertently commits herself to the sufficiency thesis anyway — the passage in question may be the only one in the whole book in which she uses the term 'sufficient condition'. The sufficiency thesis that I propose has two special features. First, the sufficiency is not the unbound variety, but the upperbound one. Second, the sufficiency of 'p' versus 'q' is relative to a presupposed 'r'. That the sufficiency must be upperbound is easy to see. Compare the following conditionals: (252) If the drink is too strong, it lacks sugar. (253) If the drink lacks sugar, it is too strong. (252) and (253) are perfectly compatible. If it is true at all that 'p' in 'if/?, then q' is somehow sufficient for 'q', then the above compatibility proves that the sufficiency must be upperbound. Indeed, if both (252) and (253) are true, then

193

IMPLICATION

'/?' in both (252) and (253) is in fact ns for 'q\ As to the relativization to a pre­ supposed 'r', it makes explicit that 'q' need not be true of 'p'. (254) (p

q)!r

The argument has been given above, in the analysis of pseudo-monadic neces­ sity (V.4.1). The truth-table for pseudo-dyadic 'p q' is very simple.81

P

τs

τ s

Us Fs

Us

Us Fs Us Us

Us Us

Fs

F S

Us Us

Table 15 No combination of truth-values of 'p' and 'q' is sufficient for the truth of 'p q'. Only two combinations are sufficient for the falsity of 'p q': when 'p' is T , 'q' must be T , too; so when 'p' is Ts and 'q' is not Ts , 'ρ q' will be F . In all other cases we get 'U '. 5.1.2. Objections A radical objection to any theory positing a connection between the 'p' and the 'q' of 'if p, then q' would be to say that "the notion of connection or de­ pendence ... is too vague to be a formal concept of logic" (Suppes 1957:8; . Bigelow 1976: 218). But this objection does not hold water against the suffi­ ciency thesis, as advocated above. No doubt the general notion of connection is vague, but no logician can seriously protest against the concept of sufficient conditionality, since it is one of their instruments (cp. IV.3), also in the study of' if ...then'. "... the task is to discover the necessary and sufficient conditions under which counterfactual coupling of antecedent and consequent is warranted." (Goodman 1965: 36; my emphasis) " The sufficient and necessary condition of the truth of 'If he felt embarassed, he showed no signs of it...'". (Strawson 1952: 89; my emphasis)

If both Goodman and Strawson use the concept of sufficient conditionality to analyze implications, we could go ahead and claim that an 'if... then' relation

PROPOSITIONAL OPERATORS

194

is a sufficient conditionality, without risking to be told that this claim is hopelessly vague. A less radical, but very common objection goes along the following lines. Conditionals are found having apparently totally unrelated antecedents and consequents. When such a consequent is felt to be obviously false, then the whole conditional is understood as a rhetorical denial of the antecedent. The following example is due to Mayo (1957: 292):82 (255) If he's a logician, then I'm a Chinaman. (255) is a way of saying that the man one is talking about is not a logician. Hence, so the objection goes, there is no connection between antecedent and consequent. I think that there are two mistakes in this reasoning. First of all, from the point of view of propositional logic there is no reason why the consequent should be false. The unanalyzed 'p' and 'q' are arbitrary; their specific con­ tents do not matter. So, when in a case such as (255), we restrict our attention to the falsity of the consequent, then we are no longer doing propositional logic. Second, I admit that the explanation of (255)'s functioning as an emphat­ ic denial of the antecedent depends on the fact that its consequent is normally taken to be false. But it also depends on the existence of a sufficiency relation between antecedent and consequent. The rhetorical effect only comes off when the falsity of the consequent leads the interpreter to infer that the ante­ cedent is no less false, the reason being that the antecedent is sufficient for the consequent, or in other words, that the consequent is necessary for the ante­ cedent. Thus the antecedent is understood to be false because one of its neces­ sary conditions is false. A similar explanation must be given for what Sørensen (1978) has called 'asseverative' 'if: (256) If I've said it once, I've said it a hundred times. (257) She's over forty, if she's a day. In their appropriate contexts, the antecedents of (256) and (257) are obviously true. On the strength of the antecedent's sufficiency for the consequent, they convey that their consequents are also true. The next example is due to Ellis (1978:109): (258) If the weather is fine today, then I had bacon and eggs for break­ fast yesterday. Ellis's verdict is this:

IMPLICATION

195

"since conditionals with epistemically and theoretically unrelated anteced­ ents and consequents are rarely asserted or denied, there is no established practice of accepting or rejecting them". (1978: 109)

To which I say: If Ellis had stuck to propositional logic, he might have come to the conclusion that an 'if ρ, then q' means that 'p' is sufficient for 'q', independent of what 'p' and 'q' are. Now just why in (258) the antecedent is sufficient for the consequent is indeed a little hard to imagine. The reasons for this are not lin­ guistic, however; rather, they have to do with our ideas of what is a normal course of events and what is not. Imagine a lunatic who forgets what he has for breakfast and who is convinced that each breakfast determines the next day's weather. Such a person would only have to look at the weather to find out about yesterday's breakfast, and might indeed have a use for a conditional such as (258). A final (and much discussed) example of the same vintage is (259). It goes back to E.W. Adams (1970: 90). (259) If Oswald did not kill Kennedy, then someone else did. According to Ellis (1978: 124; 1979: 68), there is no connection between Os­ wald's not killing Kennedy and someone else's killing Kennedy. Again I must protest. There are special reasons why the antecedent, 'not-p', is sufficient for the consequent, 'q', having to do with what is known from context: viz., that either 'p' or 'q' is true. Given the truth of this disjunction, the falsity of one dis­ junct is sufficient for the truth of the other. Thus, what I am saying is that the fact that Oswald did not kill Kennedy is indeed sufficient for the fact that someone else did. A different type of objection to the connection thesis is due to Stalnaker (1975: 167-168). Stalnaker rightly claims that conditionals are judged true when their consequents are taken to be true independent of whether the ante­ cedents are true. (260) If the Chinese enter the Vietnam conflict, the United States will use nuclear weapons. One may have beUeved that the U.S. would use nuclear weapons no matter what happened, in particular whether or not the Chinese entered the Vietnam conflict. For Stalnaker, this militates against the idea that there must be a con­ nection between antecedent and consequent. I disagree. Even in the case de­ scribed by Stalnaker, a Chinese intervention is still a sufficient condition for a U.S. nuclear involvement. Of course, an abstention on the part of the Chinese is no less of a sufficient condition, but that does not diminish the sufficiency of

196

PROPOSITIONAL OPERATORS

the intervention. Nevertheless, Stalnaker's example, even though it fails to provide counterevidence to the sufficiency analysis, is instructive. When 'p' is sufficient for 'q' yet the truth-value of 'q' is independent of that of 'q' suffi­ ciency demands a special treatment. We already have the necessary machin­ ery: in Stalnaker's example, 'p' does not only imply 'q'; because of the con­ stancy of the implication, 'p' presupposes 'q'. A similar explanation must be given to conditionals such as (261), made famous by Austin (1956). (261) If you are thirsty, there is beer in the fridge. I grant Austin (1956), as well as Ducrot (1972: 178), and Mackie (1973a: 9495), that there is more to be said about such uses of 'if... then' than what is of­ fered in my sufficiency-and-presupposition analysis. But I would deny that examples such as the above constitute counterevidence. There are many variants on the Stalnaker-Austin objections. One that deserves brief mention is illustrated in an example due to Pollock (1976b: 2728), and supposed to support the claim that 'if' can have the force of 'even if'. Consider (262), said about a match that has been soaked in water: (262) If this match were struck, it couldn't light. Similar examples are due to Mackie (1973a: 72): (263) I wouldn't marry him if he were the last man on earth. (264) He couldn't stop making money if he tried. And, as Ducrot (1972: 172-174) has remarked, questions are particularly prone to generate the 'even if' reading: (265) Will John leave if Peter comes? = Will John leave because of Peter's coming? (='if') or = Will John leave despite Peter's coming? (='even if') The problem posed by the 'even if' readings is this: does adding 'even' make the antecedent any less sufficient for the consequent? No. Striking the match that has been soaked in water is certainly and trivially sufficient for it not to light. Of course, not striking the soggy match is no less sufficient. Finally, the type of objection which has been the most influential of all. Take a conditional such as (266): (266) If a match is struck, it will light. A critic might say that it is obviously false to claim that the mere striking of a

IMPLICATION

197

match is sufficient for its lighting. There are many other conditions. The match must be struck in the right way, for example; the tip of the match must have the right chemical composition; there must be enough oxygen in the air; the match must be dry; etc. Let me call this set of conditions 'C'. Then only the conjunction of 'p' and 'C' is is sufficient for 'p': (267) (Λ)

q

One may further want to argue that there is yet another condition: viz. that there be a law 'L' according to which a match will light if we are dealing with a proper match that is properly struck in the proper circumstances, and which furthermore specifies what 'proper' means. Then: (268) (p Λ  Λ L)

q

Under both analyses (267) and (268), 'p', taken by itself, is no longer a suffi­ cient condition. In one form or another, this point of view underlies most post­ war logico-philosophical work on conditionals, both in the so-called 'metalin­ guistic'84 and in the 'possible worlds' 85 approaches. However widespread this view, I still believe it to be misguided. I do not deny that it takes more than merely striking a match for it to light. The problem is not that I am too squeamish to burden my account with such factors as the presence of oxygen, the match's dryness, its chemical composi­ tion, etc. My disagreement is due to my conviction that the factors making up the set of conditions 'C' (with or without the law 'L') should not be lodged in the antecedent. A positive justification for this hypothesis is that, according to the theory presented in this book, there is another, perfectly natural place for such factors. Recall that whenever 'p q' is true, it is true of some V: (254) (p

q)!r

One of the entities that can occupy the 'r' position is a possible world. If this happens to be the actual world, then it will contain just those types of matches, match striking techniques, and match striking circumstances that 'C' and 'L' refer to. Thus I contend that the proper location for 'C' (and 'L') is the relatum 'r'. If I use V for the 'C and L' of (268), I can rewrite (268) as (269): (269) (Λr)

q

Despite some superficial similarities, the difference between (254) and (269) is important: only if one subscribes to a theory that embodies (254), can one maintain the connection thesis.

198

PROPOSITIONAL OPERATORS

A further indication for preferring (254) to (269) is that whatever intu­ itive appeal the (269) analysis type has, is also captured by the (254) analysis. Thus I would want to say, on any further development of RPL, that when 'p q' is true of 'r', '((p Λ r) q)' must be true of 'r', too. (270) ((Λr)

q) !r

Thus (254) is sufficient for (270). The converse does not hold, however. If this is correct, then the account defended here allows one to derive a result that can be argued to render the intuition underlying the rival account. I also contend that (269) accounts are misguided. One of the problems of such accounts is the nature of 'r'. Within a possible worlds account, the de­ scription of  concerns the nature of certain possible worlds. Suppose that (271) (due to D. Lewis 1973) is uttered about the actual world; suppose fur­ thermore that it is counterfactual (cp. V.5.2). (271) If kangaroos had no tails, they would topple over. The possible worlds that possible worlds semanticists would be interested in are those in which kangaroos have no tails; however, their interest wouldn't really concern all of such worlds. '"If kangaroos had no tails, they would topple over' is true (or false, as the case may be) at our world, quite without regard to those possible worlds where kangaroos walk around on crutches, and stay upright that way. Those worlds are too far away from ours. What is meant by the counterfactual is that, things being pretty much as it actually is, the kangaroos' inability to use crutches being pretty much as it is actually is, and so on — if kangaroos had no tails they would topple over." (D. Lewis 1973: 8-9)

This citation helps us understand why it has become a key issue to describe just what closeness, or similarity, or minimality of change really amounts to (see Stalnaker 1975 [1968]; D. Lewis 1973; Nute 1975b; Tichy 1976; Pollock 1976a, 1976b; Jackson 1977: 16-18). Yet, this kind of investigation misleadingly suggests that a counterfactual is true of the actual world, supposing that this is the possible world that one is talking about, because of some possible worlds that are almost, but not quite like the actual one. In my view, such counterfac­ tual is true of the actual world because of the actual world. When it is true of our actual world that kangaroos would topple over if they had no tails, then it is precisely our world that is characterized by (a) the fact that kangaroos do have tails; and (b) the fact that it is sufficient for a kangaroo to topple over for it to have no tail. I do not deny that if kangaroos had no tails, our world would have other counterfactual properties, such as the circumstance that kan-

IMPLICATION

199

garoos would leave different traces, for example. But this has little to do with the meaning of the counterfactual in question. Neither do I deny that there are possible worlds in which kangaroos have no tails. But no matter how many there are, no matter how close some may be to the actual world, it is nothing short of the actual world that is needed for it to be true of the actual world that kangaroos would topple over if they had no tails. This idea seems to me to be so hard to get around that even possible worlds semanticists apparently feel obliged to accommodate it. Consider D. Lewis — see also Stalnaker (1975: 178-179) and Ishiguro (1979: 363): "On my theory also, most counterfactuals express contingent propositions about the world. It may seem that they are about other worlds than ours; so they are, but they are about our actual world as well. The truth of a counterfactual at our world depends on the character of the closest antecedentworlds to ours. Which worlds those are depends on which world is ours." (D. Lewis 1973: 69)

So D. Lewis would agree that counterfactuals—or at least most counterfactu­ als — are about the actual world. What I do not understand is that this relation has to be mediated by other possible worlds. Observe that this criticism is primarily directed at the 'maximal' notion of possible worlds (see II.2.3). I have less qualms about an approach in which 'possible worlds' is synonymous with 'SOAs', and that thus allows one to say that counterfactuals are about the SOAs of just one possible world. It is in­ teresting that some authors who seem to subscribe to the maximal notion sometimes slip into SOA talk. In the opening lines of this book, before he tightens up his ideas and turns to modal logic, D. Lewis (1973:1) speaks about possible states of affairs rather than about possible worlds: "If kangaroos had no tails, they would topple over' seems to me to mean something like this: in any possible state of affairs in which kangaroos have no tails, and which resembles our actual state of affairs as much as kangaroos having no tails permits it to, the kangaroos topple over."

This may, of course, be an insignificant slip. In the absence of any overt state­ ments, Lewis's view of the relation between SOAs and possible worlds must remain an open question (cp. Stalnaker 1975: 178-179; McLean 1976: 32). A final remark on metalinguistic and possible worlds accounts: The big question confronting the student of conditionals, i.e. the description of 'r', has been claimed to have a very simple answer, in case the antecedent is judged to be impossible. Take example (272), due to D. Lewis (1973: 24-26): (272) If there were a largest prime p,p! + 2 would be a prime.

PROPOSITIONAL OPERATORS

200

For Lewis such conditionals are vacuously true. Rescher, however, maintains that such utterances "cannot rationally be made" (Rescher 1973b: 266). My comment on these apparently contradictory views can be brief. As long as the logic defining the meaning of 'if... then' is a propositional one, I am not too in­ terested in the impossibility of antecedents such as that of (272). 5.1.3. Other implications In the preceding pages, I have proffered the proposal that the 'if... then' implication is a sufficiency relation. The value of this proposal could obviously be judged better, if compared to some of the other proposals that have seen the light. Though the number of implications that have been proposed in the literature is large, the following discussion will be limited to material, strict, and D. Lewis's (1973) variably strict implication. One very general re­ striction of the discussion is that I will abstract from the fact that the implica­ tions mentioned above are usually given a two-valued analysis, while my suffi­ ciency implication is a three-valued operator. 5.1.3.1. Material implication I will not belabor the obvious point that a sufficiency implication is differ­ ent from a material implication ('⊃'). For a three-valued 'p ⊃ q' to be true of 'r', it would seem to me to be necessary and sufficient that either 'p Λ q', '◊p q' is true ofr. Now, when'p q' is true ofr, it is also the case that either is true of r. How­ ever, these are only necessary conditions for 'p q' to be true of r, even though, in certain peculiar cases, they may be sufficient as well. (273) « p

q)!r)

(274) ⊃(((p⊃q)!r) 5.1.3.2. Strict implication

((p⊃q)!r) ((p

q) ! r))

The claim that ' ( p ⊃q ) ! r' is necessary for '(p q) ! r' might lead one to think that a sufficiency implication is really nothing else than the necessity of a material implication. (275) ((p

q)!r) = ((p⊃,q) r)

This would be an interesting result, for we could then profit from the already existing literature on the necessity of material implication. Construed monadically, this necessity is nothing else than C.I. Lewis's strict implication. Some­ thing along the lines of (275) has in fact been entertained by von Wright (1974: 5-7).86

IMPLICATION

201

Nevertheless, (275) is false. ' ( p ⊃ q )  r ' says that there is some's' that is true of r and from which it follows that '(p⊃ q , ) ' is also true of r. (276) ((p ⊃q) r) =

((s

(p⊃q))!r)Λ(s!r))

The 's' in question may be 'p q' — see (273) — but it need not. So a suffi­ ciency implication implies a 'strict' implication, but not conversely. (277) ((p

q)!r)

((⊃

q)r)

(278) ~(((p ⊃ q)r) ((p q)!r)) The essential difference between sufficiency and 'strict' implication, one might say, is the locus of the modality. For 'strict' implication, the modality sits between 'p ⊃ q' and V . With sufficiency implication, however, it sits be­ tween'p' and'q,'. 5.1.3.3. Variably strict implication The preceding considerations have established that a sufficiency implica­ tion can be regarded as a subtype of 'strict implication'. This brings me to D. Lewis's (1973) variably strict implication ('→'), which can be regarded as a subtype of strict implication, too. My discusion of 'p → q' can be short, since I have already criticized the possible worlds semantics that goes with it. In what follows, I will merely discuss the reason for Lewis's dissatisfaction with strict implication and for constructing a new, variably strict implication. I will argue that his reason is uncompelling. Lewis (1973: 10) wants us to consider sequences of counterfactuals such as: (279) If the USA threw its weapons into the sea tomorrow, there would be war; but if the USA and the other nuclear powers all threw their weapons into the sea tomorrow there would be peace; but if they did sö without sufficient precautions against polluting the world's fisheries there would be war; but if, after doing so, they immediately offered generous reparations for the pollution there would be peace; ... Suppose that we represent the implications of (279) by '%'. Then some of the logical structure of (279) can be exhibited as follows: (280) ρ % q (Λr)%~q (ρ Λ r Λ s) % q (p Λ r s Λ t) % ~ q

202

PROPOSITIONAL OPERATORS

The problem we are confronted with is that each of these conditionals seems to contradict the immediately preceding one. Take the second conditional, for example. On any reasonable account of implication, 'p Λ r' will be taken to imply 'p'. Given the first conditional, one would expect 'p Λ r' to imply 'q' Yet the point of the second conditional is that it implies '~q'.'pΛr' cannot both imply 'q' and ' ~ ' . S o w e get a contradiction, yet perhaps only an appar­ ent one, for (279) seems to be a perfectly reasonable piece of discourse. According to Lewis, it is the counterfactual conditional operator that is to be blamed for this 'paradox'. This is a mistake. For one thing, a text such as (281) illustrates the very same problem, although it is expressed with indica­ tive conditionals. (281) If the USA throws its weapons into the sea tomorrow, there will be war; but if the USA and the other nuclear powers all throw their weapons into the sea tomorrow there will be peace; but... For another, I think that the paradoxical effect does not depend on conditionaUty at all. The case at hand simply illustrates the distinction between Τ ', Τ ', and Τ '. Take the first two conditionals. It is clear that the antecedent of s, ns

the second conditional can be characterized as sufficient for the antecedent of the first conditional. Thus, 'p Λ r' can be characterized as 's(p)'. Since, fur­ thermore, both antecedents can be taken in a T s , n s ' , Τ s , s ' , o r ' T ' s sense, the meaning of the first conditional can be represented as 'ns(p)', 's(p)', or 's* (p)'. That of the second antecedent, however, can only be represented as 's(p)': whatever is ns,s, ors* for a sufficient condition is itself a sufficient con­ dition. Thus, if the ambiguities of the consequent are left out of account, the sequence of conditionals can be taken in three different ways: (282) ns(p)%q s(p) % ~ q (283) s(p)%q s(p) % ~ q (284)

s*(p)%q s(p) % ~ q

Only in the case of (283) does the sequence of conditionals result in a possible contradiction; other readings are non-contradictory. This 'solution' is based on a general thesis on the subcategorization of truth. I see no reason not to adopt it and to try, instead, to solve the 'paradox' by constructing a special implication.87 Variably strict implication is essen­ tially such an implication.

IMPLICATION

203

5.2. Possibility I claim that English conditionals not only mean that 'p' is sufficient for 'q', but also that 'p' is possible. This claim raises another question: If 'if p, then q' means that 'p' is possible, which possibility is it then? We have indeed distin­ guished rather many possibility types, both modal and non-modal. But such variety of possibility types is not a priori unwelcome; after all, English does have a variety of conditionals. (285) If John comes, Mary will be happy. (286) If John came, Mary would be happy. (285) is an example of an indicative conditional, while (286) illustrates a sub­ junctive conditional. 88 Subjunctive conditionals, so it seems, come in two var­ ieties. Roughly, (286) may be understood as meaning that John is not coming or that he is not likely to come. The first reading will be called 'counterfactual', and the second 'problematical'. Both of these distinctions, which have not been duly appreciated by logicians and philosophers, 89 are central in what fol­ lows. To begin to unravel these strands of meaning, I propose to consider the phenomenon of genericity again. It will be remembered from V.4.5 that genericity was loosely characterized as a type of modality that is not expressed by any modal verb, adverb, adjective, or noun, but that is a function of context and generic uses of determiners and tenses. On the criterion of genericity, conditionals split up into three groups: (a)

conditionals that cannot be generic; (287) If John were here now, things would look quite different.

(b)

conditionals that are always generic; (288) If kangaroos have no tail, they topple over.

(c)

conditionals that may or may not be generic. (289) If those people have no ID cards, they are in big trouble. (i)

the conditional is particular when it can be para­ phrased as 'If the people standing over there have no ID cards on them now, then they are in big trouble.' (ii) the conditional is generic when it can be paraphrased as 'If that kind of people have no ID cards, then they are always in big trouble.'

The relevance of the genericity-particularity dimension is that it partially de-

204

PROPOSITIONAL OPERATORS

termines whether the antecedent possibility is modal or not. In what follows, I will restrict myself to cases in which conditionals are always generic or always particular, i.e. to cases in which genericity or particularity seem to belong to the literal meaning. 5.2.1. Particular conditionals The antecedent possibility of a particular conditional is always an indetermi­ nacy. Let me argue this for indicatives first. (290) If John is there now, I can go and ask him. As a first approximation, one can say that (290) means, among other things, that it is possible that John is there, in the sense that it may be the case that John is there and that it may also be the case that John is not there. If this is felt to be a reasonable paraphrase, then it is clear that the possibility of 'p' is an in­ determinacy. We can be more specific, however. The antecedent indetermi­ nacy of an indicative conditional is upperbound ('◊*')· An upperbound inde­ terminacy of 'p' relative to a 'q', it will be remembered, does not only allow that 'p' may be true of V , as is the case for all indeterminacy types; it further­ more allows that 'p' is true of V . This (290), for example, does not simply mean that it is possible that John is there. It means that it is at least possible that John is there. Consequently, (290) is incompatible with John's not being there. Compare the following sequences: (291) -- John is there now. — Well, if John is there now, I can go and ask him. (292) ~--John may be there now. -- Well, if John is there now, I can go and ask him. (293) -- John is not there now. ?-- Well, if John is there now, I can go and ask him. I assume that the 'well' of the second speaker shows that he or she accepts — or acts as if (see III.2.1.3) — the truth of what the first speaker says. If this is correct, then the appropriateness of the second speaker's conditional in (291) and (292), compared with its inappropriateness in (293), demonstrates that the antecedent indeterminacy is upperbound. This is not to say that the latter second speaker may not be understood, despite the bad grammar of (293). He or she should have used subjunctives. (294) » John is not there. - Well, if John were there, I could go and ask him.

IMPLICATION

205

Under this account, the particular indicative implication, symbolized as ', can be defined as follows: (295) It is tempting to hypothesize that the antecedent of a subjunctive particu­ lar conditional can be characterized in terms of lowerbound indeterminacy. The temptation of this proposal lies in its symmetry. However, it is only fair to point out that its development will bring in a sizable measure of asymmetry, too. We have seen in V.3.1 that, under the unmarked orientation, '◊* p' means 'at least possible', and '◊* ρ' 'at most possible'.

Figure 29 Whether 'p' is at least possible ('U* ') or at most possible ('U *s '), in both cases 'p' is possible. Semi-formally: (296) at least possible (297) at most possible

possible possible

In this respect, 'at least possible' is not different from any other 'at least' meaning. Consider the 'at least two' on a finite l-to-3 scale:

Figure 30 Clearly, there must be two instances of something whenever there are at least two. (298) at least two

two

The explanation is simple: 'two' literally means 'at least two', just as 'possible' literally means 'at least possible'. So 'at least two' and 'at least possible' must

206

PROPOSITIONAL OPERATORS

imply 'two' and 'possible'. The fact that 'at most possible' also implies 'possi­ ble' is not, however, paralleled by a similar implication from 'at most two' to 'two'. When there are at most two instances of something, it would be wrong to say that there must be two. (299) ~ (at most two

two)

The discrepancy between 'at most possible' and 'at most two' could be explained and formalized in a scalarity framework, too; however, that would lead us too far afield. Let it suffice here to have shown that not every 'at most something' can be called this 'something', whereas every 'at least something' is this 'something', and for a very general reason. One 'at most something' that can be called this 'something' is 'at most possible', but the very fact that it cannot be justified on the same general grounds as 'at least possible' makes 'at most possible' into a less clear and less transparent case of 'possible' than 'at least possible'. The claim presented above can be buttressed with some independent ar­ guments. First, while upperbound indeterminacy can only be considered to be an indeterminacy, lowerbound indeterminacy can be looked upon as a falsity (see V.3.1). The obvious conclusion is, again, that lowerbound indeterminacy is not as clear-cut a case of indeterminacy as upperbound indeterminacy. Sec­ ond, there seem to be mixed intuitions about the question whether the narrow falsity of 'p' is sufficient for 'p' to be at most indeterminate. In one sense, it is: when 'p' is at most indeterminate, it is either indeterminate or false. In another sense, it is not: when 'p' is false, there is no way that 'p' can still be in­ determinate, not even at most indeterminate. There are no such apparently contradictory intuitions about upperbound indeterminacy. However strange a mixture of symmetry and asymmetry the relation be­ tween lowerbound and upperbound indeterminacy may be, lowerbound inde­ terminacy is precisely what is needed for dealing with subjunctive particular conditionals. Hence I define a particular subjunctive implication (' ) as follows: (300) (300) is a definition of the literal meaning of a subjunctive particular con­ ditional. It also generates the distinction between problematical and counterfactual, which are non-literal meanings. The literal meaning of 'p ◊*r' f leaves it vague whether 'p' is U or F of r. Hence the literal meaning of '(p q) ! r)', which contains 'p ◊* r', is also vague. When its 'p ◊ * r ' is taken to be true, because 'p ~ r' is true, we get the counterfactual; when the truth of 'p ◊ * r ' is

IMPLICATION

207

understood to be due to the truth of 'p ◊ r', we get the problematical. Notice that a counterfactual is by no means a conjunction of an implica­ tion and a negation of its antecedent. A counterfactual is a conjunction of an implication and a possibility of its antecedent, more particularly, a lowerbound indeterminacy that is instantiated by narrow falsity. This is quite essen­ tial: what a counterfactual conveys is something false, represented as possible without being any less false for that matter. Lowerbound indeterminacy is the appropriate tool to render this. Similarly, a problematical particular conditional is not just the conjunc­ tion of an implication and the possibility of its antecedent. It is the conjunction of an implication and the lowerbound indeterminacy of an antecedent that is instantiated by unbound indeterminacy. Thus the problematical is close to an indicative. The latter can involve unbound antecedent indeterminacy, too. The difference is, however, that the indicative has an upperbound indetermi­ nacy. Both when we say (290) and we say (301) we allow that it is just possible ('U s ') that John is there. (290) If John is there now, I can go and ask him. (301) If John were there now, I could go and ask him. While in (290), this unbound indeterminacy is allowed because of its suffi­ ciency for an upperbound indeterminacy, in (301) it is due to its sufficiency for a lowerbound indeterminacy. The other difference between particular indica­ tives and particular problematical is, of course, that the antecedent indeter­ minacy of the former, but not of the latter, can be instantiated by the truth of the antecedent. In the same way as lowerbound indeterminacy is vague be­ tween narrow falsity and unbound indeterminacy, upperbound indetermi­ nacy is vague between truth and unbound indeterminacy. Interestingly enough, however, while many investigators have been aware of the vagueness of subjunctives, the corresponding vagueness of indicatives has not got much attention at all (see Lauerbach 1979: 183-186; Van der Auwera n.d.a). This discrepancy is not surprising. First of all, I have argued above that lowerbound and upperbound indeterminacy are not as symmetrical as they seem to be: compared to upperbound indeterminacy, lowerbound indetermi­ nacy is not very clear or homogeneous. The contrast between the disjuncts of lowerbound indeterminacy, between narrow falsity and unbound indetermi­ nacy, is much more striking than that between the disjuncts of upperbound in­ determinacy. Secondly, the point of the distinction between the two non-lit­ eral meanings of particular indicatives would be to separate the case where 'p'

208

PROPOSITIONAL OPERATORS

is true of r from that where 'p' is just (unboundly) indeterminate of r. In a lan­ guage such as English, however, there is little need for such a distinction, for there is a host of expressions that have '(p q)!r' and 'p ! r' as their literal meaning. (302) John is there and therefore I can go and ask him. Since John is there, I can go and ask him. I can go and ask John, because he is there. I can go and ask John for he is there. John is there. So I can go and ask him. John is there. Hence I can go and ask him. This is not to say that speakers will never use 'if... then' to convey that the an­ tecedent is true. In example (291), the second speaker may be intending the 'if as a near-synonym of 'since'. (291) - John is there now. - Well, if John is there now, I can go and ask him. In that case, the truth of the antecedent is conveyed as a non-literal meaning through the mediation of a literal meaning of upperbound indeterminacy. By contrast, in (302), the truth of the 'antecedent' comes off as a literal meaning, not mediated by any indeterminacy. Of course, the operators in (302) have a lot in common with 'if ... then' .90 There may also be languages in which 'if... then' and one or more of the operators of (302) translate into the same word. The Papuan language Hua could be such a language (see Haiman 1978: 581583; cp. also Inoue 1983). 5.2.2. Generic conditionals Particular conditionals have been analyzed in terms of an antecedent in­ determinacy. For generic conditionals, the situation is more complicated. Consider the following conditional: (288) If kangaroos have no tail, they topple over. (288) has two types of generic readings. Below are two rough paraphrases: (303) I do not know what typical kangaroos are like, in particular, I do not know whether they have a tail or not, but I do know that if they have no tail, they topple over. (304) Sometimes kangaroos have no tail. Well then, whenever kan­ garoos have no tail, they topple over.

IMPLICATION

209

In the first reading, the antecedent possibility is non-modal (indeterminacy); in the second, it is modal (contingency). The implication of the first reading will be symbolized as ' and that of the second reading as . I will deal with implications first. The antecedent of (288) is (305): (305) Kangaroos have no tail. (305) says that the typical or generic kangaroo has no tail, or in other words, that it is an essential or necessary characteristic of the typical kangaroo that it lacks a tail. To render the necessity, I will represent (305) as ' □ p ' , and this is also the way I will represent the antecedent of (288) in its (303) reading — though not in its (304) reading. The consequent of (288), in its (303) reading, is no less generic: (306) Kangaroos topple over. So I will analyze it as 'q'. Given these analyses, and given the contention that a conditional has an antecedent indeterminacy, the indicative implication is defined as follows: (307) Applied to (288), (307) says that the typical kangaroo's necessary lack of tail is at least sufficient, if not necessary, for its necessarily toppling over, and that it is indeterminate—in the 'at least' sense—whether the lack of a tail is a neces­ sary feature of the typical kangaroo. The subjunctive ' implication, illus­ trated in (308), is the same as the indicative one, except that the indeterminacy is lowerbound. (308) If kangaroos had no tail, they would topple over. roughly paraphrased as 'It is at most indeterminate, if not down­ right false, that typical kangaroos have no tail, but the typical kangaroo's lack of tail would be sufficient for its toppling over. (309) As the paraphrase of (308) indicates, subjunctive conditionals can have problematical as well as counterfactual readings, just like particular subjunc­ tive conditionals. So much for v conditionals. conditionals differ from them both in their sufficiency implication and their antecedent possibility. (310) repeats the sufficiency implication of a conditional:

210

PROPOSITIONAL OPERATORS

(310) A somewhat more explicit formulation is (311): (311) Notice that both the antecedent and the consequent are necessary relative to r; the implication, however, is just true of r. In a conditional, it is the other way around: only the implication is necessary relative to r, whereas the antecedent and consequent are merely true of r. (312) Or, in a simpler format: (313) To see this, consider (288) again: (288) If kangaroos have no tail, they topple over. In the reading that I am focusing on now, (288) says that it is a necessary fea­ ture of the typical kangaroo that a lack of a tail is sufficient, if not necessary, for toppling over. Of course, (288) says more; in particular, it characterizes the antecedent with an upperbound contingency: the lack of a tail is at least a contingent feature, if not a necessary one, of the typical kangaroo. So I can symbolize the antecedent of an indicative conditional as: (314) ρ

*r

An interesting notational variant of (314) is (315): (315) (p!r)

*r

(315) stipulates that it is an upperbound contingent characteristic of the typi­ cal kangaroo that it is true of the typical kangaroo that it has no tail. The value of this formula is that it contrasts, in an illuminating way, with a formula that captures the antecedent possibility of the indicative conditional, as shown in (316): (316) (p r ) ◊ * r In (316), the non-modal possibility operator has scope over the modal operator of necessity. In (315), however, the corresponding modal possibility operator has scope over the corresponding non-modal operator of truth. The full definition of an indicative implication is given in (317) : (317)

IMPLICATION

It differs from the subjunctive on the contingency:

211

' implication only by the type of boundness

(318) If we agree to stretch the meanings of the terms somewhat, then subjunctive conditionals can be said to have both counterfactual and problematical readings. A counterfactual , conditional does not imply the falsity of the antecedent, but its impossibility. Similarly, its problematical counterpart im­ plies the contingency rather than the indeterminacy of the antecedent. Our findings about generic conditionals can be summarized in the follow­ ing way: (a) (b)

(c) (d) (e)

The implication of a generic conditional is a combination of a necessity ('□') and a normal sufficiency implication ('(p q) ! r'). There are two subtypes: if the necessity sits between 'p q' and 'r', we get a ' ' conditional; if the necessity operates on both 'p' and 'q', we get a ' ' conditional. In ' ' conditionals, indicatives and subjunctives are distin­ guished in terms of the non-modal possibility of 'r'. In →conditionals, indicatives and subjunctives are distin­ guished in terms of the modal possibility of 'p ! r', For both types of generic conditionals — as well as for particular conditionals — the distinction between indicatives and subjunc­ tives (and their subtypes) is based on the boundness of the possi­ bility: upperbound possibility defines indicatives, and lowerbound possibility subjunctives.

The distinction between and conditionals seems to be situated on the level of literal meaning. At least, I do not see any attractive way to derive one as a non-literal meaning from the other, or to derive both as non-literal meanings from yet a third meaning. 5.2.3. Objections As pointed out already, there has been relatively little research on what con­ stitutes the difference between indicatives and subjunctives, still less on the distinction between problematicals and counterfactuals, and perhaps least on the one between particular and (the two kinds of) generic conditionals. There certainly has not been any proposal that capitalizes on the possibility of the an­ tecedent the way I have done it.91 It is interesting to speculate on why this is so. In part, I believe, it is due to the fact that in English, and probably many Ian-

212

PROPOSITIONAL OPERATORS

guages of the Standard Average European variety, the antecedent possibility is not normally signaled by any of the more usual, overt possibility markers such as 'possible', 'possibly', 'perhaps', 'can', 'may', or 'might'. If some prom­ inent linguists or logicians had been native speakers of Thai, for example, they might have paid more attention to antecedent possibility. Indeed, if one speaks Thai, it is hard not to be struck by the connection between possibility and antecedents: the thaà part of the verbal thaà dzja, meaning something like 'it is possible that', stands for 'if. In any case, as the perspective advocated here is rather new, the litera­ ture does not contain too many objections. In What follows, I will restrict my­ self to a minimal discussion of the status of the antecedent of a counterf actual and of the prospects of a quantificational analysis of generics. According to my account, counterf actuals imply the falsity—or impossi­ bility — of their antecedents. This does not mean, of course, that subjunctives as such imply an antecedent falsity. They only imply the lowerbound possibil­ ity of the antecedents. Problematical subjunctives do not imply any anteced­ ent falsity, either. Still, the relation between a counterfactual conditional and the falsity of its antecedent is one of implication. There is an alternative hypothesis. For many, the relation in question is not an implicative one, but something weaker. Those people tend to resort to notions such as presupposition or implicature (see Ayers 1965:352-355; E. W. Adams 1970, 1975: 103; Karttunen 1971; Ducrot 1972: 185-189; D. Lewis 1973: 3; J.S. Edwards 1974:90;Bennet 1974:387; Kempson 1975:219; Wilson 1975:121-122; Karttunen and Peters 1977:363-366; Lauerbach 1979:203-212; W. Davis 1979: 545-546). However, instead of a complete theory of presup­ position or implicature, all we get is some evidence supposed to prop up this position. The following is what D. Lewis (1973: 27) has to offer (see also Lauerbach 1979: 206-207): (319) -- If Casper had come, it would have been a good party. --That's true; for he did, and it was a good party. You didn't see him because you spent the whole time in the kitchen, missing all the fun. With some reservations, Lewis maintains that the acceptability of the second speaker's answer shows that the supposed counterfactual — 'supposed', be­ cause Lewis has no eye for the subjunctive meaning as such, nor for the prob­ lematical — of the first speaker can be true while its antecedent is true. Hence a counterfactual cannot imply that its antecedent is false. If Lewis's assess-

POSTLIMINARIES

213

ment of the conversation in (319) is correct, he also falsifies the thesis that sub­ junctives as such imply the lowerbound possibility of their antecedents. But I think Lewis is wrong. I do not deny that the second speaker's answer is under­ standable and to the point, but I do believe that it is somewhat misleading, or at least elliptical. In my view, the second speaker means something along the following lines: (320) It is true that Caspar's arrival was sufficient f or a good party. In other words, 'that' would only refer to a part of the conditional. Were it to refer to the whole conditional, then the second speaker would be inconsistent even when the subjunctive was not meant as a counterfactual. If this analysis is correct, then Lewis's dialogue does not offer any good reason why a counterfactuality or lowerbound possibility cannot be implied. The second issue concerns quantification. One may reject my propositional analysis of generic conditionals and prefer to analyze (288) along the lines of predicate logic, like in (321). (288) If kangaroos have no tail, they topple over. (321) For any kangaroo, if it has no tail, it topples over. My answer is in three parts. First, I do not deny that a quantificational analysis of (288) is feasible. But second, I am not sure that it is necessary. Quine's 'Maxim of Shallow Analysis' (Quine 1960:160) tells us not to introduce more logical structure than is necessary: perhaps a propositional analysis contains enough structure. Third, it is not clear to me that (321) is a good paraphrase of (288) (cp. Carlson 1979: 67-68). Perhaps, (288) only refers to typical kan­ garoos and is not falsified by the existence of a kangaroo with built-in crutches that does not topple over if it has no tail. (321), however, may well refer to all kangaroos, whether typical or not, and whether having built-in crutches or not. 6. Postliminaries To stop here is to leave much undone. The preceding analyses of some as­ pects of the meaning of some propositional operators of English are only pre­ paratory to a new logic, and I have had many occasions to show that the prep­ aration is both incomplete and tentative. And yet, if the unorthodox mold in which I have cast these preliminary investigations is both plausible and prom­ ising, then my call for a new logic is no longer a philosopher's slogan only. I can see at least four high-priority tasks for future research. The first is

214

PROPOSITIONAL OPERATORS

that of testing the hypotheses against a wider range of languages (see Van der Auwera (ed.) 1983). The second is that of filling in the gaps of the preceding analysis. For example, I haven't analyzed the consequents of my implications yet. I also do not know whether my implications allow the 'paradoxes of impli­ cation', or why they do or don't. Neither do I know whether my implications are transitive, whether they allow contraposition, whether they can be de­ fined in terms of disjunction and negation, etc. Another high-priority task is that of extending the repertoire of RPL operators. The first operator that should be examined is the disjunction (see Van der Auwera, n.d.b). Then there are implications other than 'if... then', such as 'only if... then' (see Van der Auwera n.d.c), 'even if... then', 'unless', 'not unless', and 'whether'. Of great interest are also such implication-like operators as 'hence' (see Van der Auwera 1979c, 1979e, 1980b), 'therefore', 'because', and even 'but' (see Van der Auwera 1979d: 116-118). Perhaps the description of these three tasks as well as the general trend of this chapter has made the reader forget that RPL is not only a linguistic theory. To the extent that RPL is about language, it should also be about the mind and about reality as a whole. Thus, the reflectionist orientation, espe­ cially its mentalist dimension, is another feature that should attract future re­ search. If the linguistic analysis does not allow a theory about the propositional logical validity of inferences, then either the reflection thesis is mistak­ en or the linguistic analysis is. Thus the linguistic analysis must at the earliest be tested against our intuitions about argumentative validity. I admit that many of the arguments of this book may be divorced from réflectionism. One might accept most of the theses on what it is to mean some­ thing, for example, or on the relevance of scalarity theory for our understand­ ing of conditionals, without accepting the reflectionism appropriate to these theses. In this way, some of the ideas defended here might be found fruitful despite their Speculative Grammarian presentation. This is not to say that the reflectionism is only a veneer. On the contrary, if one wants to get down to the basics of what logic is all about, to the fundamentals of speech act theory, or to the division of labor between semantics and pragmatics, for example, I do not see how one can do without the reflection thesis as an overall principle. Many of the fundamental ideas of this book are both ancient and simple. Yet most of them have not been given proper attention. The problem is not, for example, that we did not know that language somehow reflects the mind and reality, that nothing can be true without being true of something, or that nothing can be necessary without being necessary of something for some-

POSTLIMINARIES

215

thing. The mere acceptance of such ideas is a relatively trivial matter. It be­ comes much less trivial if one tries to base an entire theory of meaning on the reflection idea, if one gives truth a dyadic truth-table, or if one embarks on triadic modal logics.

NOTES 1. The part of the dissertation that is left out here is a Speculative Grammarian analysis of subjecttopic phenomena. It has appeared separately (Van der Auwera 1981a). 2. Yet, in practice and in some of his later work (e.g. Quine 1970; Quine and Ullian 1970), Quine's conservatism on logic is possibly due to a conviction that logic is self-evident. Consider the following: "If sheer logic is not conclusive, what is?" (Quine 1970: 81) If this is not an appeal to self-evidence, what is? For a discussion of the discrepancy in Quine, see S. Haack (1974: 15ff.), R. Haack (1978), and Gochet (1978:156-162, 205-206). 3. For some related speculations on how scientific communication is impossible unless scientists al­ ready understand a natural language, see Kamlah and Lorenzen (1973: 15-25). 4. If one is familiar with the realism-conceptualism-nominalism triad, one will expect the term 'conceptualism'. I will set the latter aside as a name for a particular subtype of mentalism. 5. To fully appreciate the vagueness of the word 'concept', one could read Mundle's "The use of 'concept' in linguistic philosophy" (1970: 91-109). 6. The passage from Austin demonstrates the impurity of Ordinary Language Philosophy. As for Ideal Language Philosophy, it seems obvious that one cannot construct an ideal language without relying on an ordinary one and on the theory of reality it encapsulates. 7. The term 'instrumentalism' is more often used for a conception of science according to which the question of what it is that science is all about matters (much) less than what it is good for or the mere fact that it 'works'. As there is no inconsistency in imagining science as something true and as some­ thing that 'works', I do not follow this usage. 8. Lest it be thought that I am wasting my time on an objection that is so silly that nobody in his or her right mind would support it, here is just one passage which embraces the central idea: "Even when it is true that Toby sighed there is some difficulty in finding an object other than itself for the statement to be related to. What is the fact which the proposi­ tion that Toby sighed, if true, fits? The fact, surely, that Toby sighed. The trouble here is that it fits too well. The, fitting relation is interesting only if it is irreflexive. In­ formation is not often to be gained from ascertaining that a structure is mappable on to itself.... certainly the fact that Toby sighed looks uncannily like a projection on to reality of the proposition that Toby sighed." (Williams 1976: 75-76) 9. It has been disregarded, though. Popper's 'logic' of knowledge, untainted by human subjectiv­ ity, is an example. See Popper (1968) and S. Haack (1979b).

218

NOTES

10. This attitude of intended naïveté and non-commitment on the deeper questions will play an im­ portant role in this study. I will call it 'minimal ontology' (see II.2.2, below). 11. Van der Auwera ( 1980c) contains a deeper discussion of this issue and develops a theory of fic­ tion. 12. For an ontology in which SO As are states, see von Wright (1974: 13-16). Yet it must be men­ tioned that von Wright's states are somewhat different from mine. For me the staying on of a state is just a state. For von Wright (1974:14) it may "by logical courtesy" be regarded as an event. 13. The phrasing with it is true that and it is not true that is purposely long-winded. It allows me to re­ main uncommitted on whether the 'logic' of SOAs is bivalent, as C.I. Lewis would claim, or manyvalued, as I will claim in IV.4.3. 14. This cannot be said about everything else that has been called 'ontologicai priority'. Mundle (1970: 147) is basically correct, I believe, when he argues that Strawson's (1959) identifiability criterion has no ontologicai implications. Whitehead's (1919) observability or Carnap's (1966) epistemological criteria do not fare any better. See S. Haack (1976b; 1979a) for a recent discussion. 15. A telling sign of an intellectual climate is the type of textbook it allows. Thus it may be pointed out that 1979 saw the appearance of what may be thefirstintroductory textbook on logic—and not just modal logic — that is founded on the possible worlds idea, viz. Bradley and Swartz (1979). 16. Whether or not Stalnaker (1976b) would be a realist, Stalnaker (1979) seems to have settled for mentalism. 17. Possibly C.I. Lewis (1946) is a realist too. Remember that his SO As seem to be ontological en­ tities that are knowable as well as discussable. His possible worlds might have to be understood in a similar fashion. Consider: "Anything which could appropriately be called a world, must be such that one or the other of every pair of contradictory propositions would apply to or be true of it; and such that all the propositions thus holding of it will be mutually consistent.... Such a possible world is thinkable, in whatever sense the actual world or whole of reality is thinkable." (C.I. Lewis 1946: 56) If C.I. Lewis also believes that the possible worlds are ontological in whatever sense the actual world is, then he is a realist. 18. The realist is presented as one who believes in a "Platonic realm where possible worlds are graven on crystalline tablets or neatly stored away on museum shelves" (Rescher 1975: 3) and in "different planets populated by strange beings andflorawhich we could somehow examine if only we had the right equipment" (Merrill 1978: 320). 19. Bradley and Swartz (1979) profess to be realists. Yet, their realism only makes them conceive possible worlds as abstract entities like numbers. But, again, what are numbers? And whereas on page 66 fn. 2, they claim to prefer Platonic realism to conceptualism, on page 5 they want to locate possible worlds, "as it were, in conceptual space". 20. I am perhaps not alone in advocating a notion of reality that is even 'larger' than a possible world. Nute's (1980:28) 'hypothetical situations' are supposed to correspond to 'possible worlds', and, as hypothetical situations make up his 'actual world', the latter might be the same as my 'universe'.

NOTES

219

21. This contrast, which is in its essential thrust quite classical, is not rendered useless by the fact that one can say — as, typically, pragmatists would have it — that a belief can cause an effort to make the OOM conform to the M or, informally, that a belief can guide action. This only happens, though, when a desire is in play. Similarly, it is correct to say that a desire can result from the fact that the M reflects a part of the OOM, but this only amounts to the contention that a belief can lead to a desire. 22. The following idea seems to be reminiscent of a view about propositions expounded by Husserl around the turn of the century (see Willard 1972). 23. The latter universal could be considered to be an SOA, too. More on the connection between universals and SOAs in IV.2. 24. For some further ideas on the different meanings of the term 'reflection', see Schaff (1973:126128). 25. This part of the account of intentionality is an expansion on Allwood (1976:13-16). Itisobvious that I do not use the term 'intentionality' as phenomenologists (see Aquila 1977, for further refer­ ences) and recently also Searle (1979a, b, c) have done. What they have in mind is the property of mental phenomena of being directed at something. To use the terminology developed here, it is the fact that mental states and objects involve conceptualizations. For some ideas on the relation be­ tween the two intentionality concepts, see Searle (1979a: 89-90; 1979c). 26. This is a point of much debate. Aune (1977:63) and Allwood (1976:12; 1978:9) would seem to share the view outlined here. For some discussion, see also Hamlyn (1971). 27. For clear statements on this matter, see e.g. Allwood (1976:6,13-16; 1978) and Van Dijk (1977: 173; 1978: 33-34). A recent and original defense is Searle (1979c). For a discussion of a sociologist's understanding of action, see Rubinstein (1977). While most attention is paid to intentions, a recent discussion of the role of consciousness is found in Donaldson (1976: especially 76-102). 28. A third type of approach, completely foreign to my framework, is that of 'Behaviorism' or 'Observationism', according to which actions are not determined by a mental substratum or by a sur­ rounding social context, but only by the observable material movements. An interesting attack on this doctrine is Daveney (1974). A recent, personal overview of the different theories of action can be found in the first chapter of L. Davis (1979). 29. The parallel is only partial. On the one hand, Parret (1979a) proposes a 'psycho-pragmatics', a pragmatics that is based on underlying mental states. On the other hand, Parret (n.d.b) accuses Searle of psychologism, a taint Parret wants to be free from. 30. The readings in question are by no means obligatory. One can imagine that (2) is uttered about a bus in which the weight of the passengers on the platform can trigger off three rings as a sign to the driver that the bus is full. Or suppose that (2) is said by an instructor who is demonstrating the effect of pushing a certain button. Both contexts lack the individual who means or should mean that the bus is full. Similarly, there are situations in which somebody might or might be assumed to mean measles by means of spots. Imagine a doctor who has invented a shorthand in which a certain configuration of spots stands for measles. 31. Notice that both (10) and (11) can reflect an indeterminacy belief. Yet they are not synony­ mous. The indeterminacy of (10) is somewhat different from that of (11). I will give a more precise account of this distinction when I come to scalarity theory (V.3.1).

220

NOTES

32. The exact number of basic speech acts is not too important, however. One could argue for three, bearing in mind that this is as far as one can get when one only invokes the categories of be­ lieving and desiring. One could defend the number two, if one has a reason for emphasizing the dis­ tinction between the reflection of a belief (assertions) and that of a desire (interrogatives and opta­ tive-imperatives). One might also feel that there are four basic speech acts. This would emphasize the distinction between optatives and imperatives. 33. Few have yet advocated the need for a sociology of logic(ians), but Willard (1979:161) is one of them. 34. For a most forceful description of the conservative ingredient in logic, it pays to return to Schil­ ler and to quote him in full: "As an institution Formal Logic gives instruction to a large percentage of the ablest minds, and employment to a large number of able men, all of whom are profession­ ally averse from a radical reform of their subject, all of whom have their logic lec­ tures written out, many of whom have committed themselves in print, while not a few, and among these precisely most of the senior 'authorities' have undergone that hardening of the mental fibre and loss of elasticity which age and dogmatic habits tend to bring about. How then is it psychologically possible that logicians will adopt, consider, or even understand far-reaching novelties of thought?" (Schiller 1912: 385) 35. The present indictments against 'the logicians' are generic; my claims about the species of logi­ cians are not falsified by the existence of certain of its members that have real empirical concerns. It is interesting to see, however, how these empirically minded members can have a hard time escap­ ing from the canonical preoccupation with formal matters. If anybody may be credited for his sin­ cere interest in an empirical matter such as ordinary language, then certainly Strawson may. Con­ sider now his ambiguous position in the Introduction to logical theory (1952). The logician is com­ pared to a geographer "who is passionately addicted to geometry, and insists on using in his draw­ ings only geometrical figures for which rules of construction can be given; and on using as few of such rules as he can" (1952:58). Strawson admits that the map never fits, but he still calls it a 'map'. For a critique of this comparison from the side of the formally preoccupied, see Quine (1966:148151). 36. The term 'realism', when applied to logic, can carry two other meanings. First, it may be a synonym for 'absolutism' (see IV.1.2). Second, as there is a realist position on the nature of truth, the logical theory based on this position may, by extension, be called a 'realist' one, too (see Platts 1979). 37. Mundle (1970:183) has noticed that this very sentence is omitted from the later editions. In the 1948 edition (page 204), Russell claims that the truths of logic are true independently of the exis­ tence of the universe. Before the 1918 realism, there was a Platonic realism of a world that is "un­ changeable, rigid, exact, delightful to the mathematician, the logician, the builder of metaphysical systems, and all who love perfection more than life" (Russell 1912: 156). 38. It is quite common to speak about 'conventionalism' (e.g. Berger 1977: 41), but the latter is more often used for the view that "all (duly suitable) systems are on the same level, and the choice between them is a matter of essentially arbitrary convention" (Rescher 1977: 237). 39. The term 'instrumentalism' has also been used for the idea that a logic can neither be correct

NOTES

221

nor incorrect, but only more or less fruitful or convenient (see Rescher 1977: Chapter 13-14; S. Haack (1978: 221 ff). See also note 7. A possible synonym is 'operationalism'. 40. It may be objected that the last few years have brought about a significant change in logicians' attitudes towards natural language. I will discuss this point in the next section. 41. This citation gives the impression that the normative aspects are much more important than the descriptive ones. In the same book, however, Rescher (1977: 261) sees fit to write: "Thus while the systematization at issue may refine the presystematic practice in matters of occasional detail, it cannot readjust this to the point of abandonment." (my emphasis) See also Nute (1980: 4). 42. The following argument can also be found in Sober (1978: 177-179), who takes it back all the way to Kant. For a related argument, see also Ellis (1979: V, 44). 43. The analogy is not new. From Antiquity through the Middle Ages, speech and reasoning, on the one hand, and grammar and logic as the articulations of the principles of speech and reasoning, on the other, were held to be analogous. What was absent or underemphasized, was the idea that these principles are descriptive of an empirical matter, viz. a competence. 44. A similar mixture of descriptivism and anti-descriptivism can be found in Glethmann's dialogical logic. Compare the Zinov'ev citation with Glethmann: "When one keeps in mind that... dialogical logic wants to regulate the ordinary lan­ guage usage of certain connectives like 'and' and that it cannot be based on any ordi­ nary language intuitive meaning 48 ... 48. And yet the enterprise should have an ordinary language adequacy". (Glethmann 1979: 55-56; my translation). 45. S. Haack's decision to opt for a mentalism, albeit of the prescriptivist type, is preceded by a critique of Frege (S. Haack 1978:239-242). She has also competently answered Popper's celebrated "Epistemology without a knowing subject" (1968) with her own "Epistemology with a knowing subject" (1979b). Other considerations on Popper's anti-mentalism are offered by Krige (1978) and Ball (1981). Sober (1978:165-174) has evaluated Frege's anti-mentalism andits ramifications. Meiland (1976) and Nunn (1979) have reassessed Husserl (see also Willard 1972). For a re-evaluation of Mill's mentalism, see McRae (1973: xxxix-xlviii). For a comparison with behaviorism, see Block (1981). 46. For an example and further references, see Braine (1978). A symptom of the change in the in­ tellectual climate is the reaction to Braine's article by the logician Grandy, who writes that "the re­ cent interest in natural reasoning is welcomed by logicians" (1979:152). I believe that Grandy is ac­ tually mistaken and that the majority of logicians couldn't care less; still, the appearance of this kind of statement is interesting. 47. Fallacies may become habitual, too. To clarify the restriction idea, here is the sophisticated 'sociological' restriction of Blanche's 'logique reflexive': "Logique reflexive is the study of natural logic (logique opératoire) to the extent that the latter is judged valid by those that are considered the most competent in the mat­ ter, those whose logical acumen and rectitude are best known, in short it is the study of natural logic at its highest stage of development." (Blanche 1967:118; my transla­ tion)

NOTES

222

48. See also Lukasiewicz (1970c: 247-248 [1937]. In all fairness of Lukasiewicz, it must be pointed out that he later changed his mind (see Lukasiewicz 1970d: 333 [1952]). 49. The fact that the terms 'depraved semantics' and 'patter' are blatantly disrespectful suggests that they are formulated from a formalist perspective. Even so, Plantinga is only interested in 'de­ praved' semantics, while Haack urges the view that the latter is absolutely essential. 50. Of course, the phrase 'a true desire' can be interpreted as 'a real or sincere desire'. This sense of truth is not my concern. For a discussion of the Tarskian notion of satisfaction, see IV.4.6. 51. Compare: "One is used to considering the concept of condition as an unproblematic and stable tool without making its exact meaning, i.e. its systematic value, explicit." (Puntel 1978: 67; my translation) "It is significant that in most theories of meaning 'condition' means no more than something like 'specification' ('Bestimmung')" (Puntel 1978: 207; my translation) 52. A case apart is the 19th-century philosopher and logician Sir William Hamilton. He was in­ terested in conditionality for a totally different reason. According to Hamilton, everything we think about is conditioned. All contents of thought must be seen as relative to something else. The unconditioned is simply inconceivable. "To think is to condition; and conditional limitation is the fundamental law of the possibility of thought." (quoted from Geduldig 1976: 23) Unfortunately, Hamilton's interesting position in the theory of knowledge seems to have had no ef­ fect on his logic; neither was he interested in any theory of conditions. Another isolated figure is the German physiologist Max Verworn. Verworn (1912) proposed that science should be a search for, and an analysis of conditions rather than causes and called this view 'Konditionismus'. One of the kernel theses of his 'conditionism' comes close to Hamilton: "Nothing is isolated or absolute. Everything, i.e. all events and states are con­ ditioned by other events or states. (The thesis that all that is or happens is con­ ditioned.) (Verworn 1912: 45; my translation) Verworn differs from Hamilton in that he (1912: 17) connects his thesis with logic, observing the close connection between the notion of condition and the conditional sentence. Unfortunately, Verworn is not a logician, and so he does not expand on this observation. 53. The quotation marks around 'obtain' show that I am aware of using ontological vocabulary. The entities that were said to Obtain' (see the introduction to IV.3) were particular SOAs. In fact, I have not defined any predicate characterizing what happens to propositions when particular SOAs obtain, beliefs and assertions are true, and desires are satisfied. In view of the linguistic turn the study will take, this deficiency will not be remedied. 54. The discussion of conditionahty also assumes a prior grasp of notions of identity and differ­ ence. Remember (from IV.3.1.1) how some χ is se for some z iff x and z are identical except for the fact that χ contains more entities than z. For some remarks on the relation between conditionahty and identity, see Van der Auwera (1980c: 159-168). 55. On the pivotal role of truth in classical logic, see Frege: "The word 'true' indicates the aim of logic as does 'beautiful' that of aesthetics or 'good' that of ethics." (Frege 1967:17)

NOTES

223

It is also common to consider logic as the science of certain types of truth, the so-called 'truths of reason' (e.g. Chisholm, 1966: 70), or of the 'preservation of truth' (e.g. Hacking 1979). 56. Notice that I am not saying that such claims are trivial. For a good defense of non-triviality, see Platts (1979: 12-13, 71-72, 225-226). 57. It is not impossible that the presence of a chair and a table in my dining room on April 30th, 1980 is in fact sufficient for there to be a chair in my kitchen the day afterwards. Perhaps I just happen to move chairs back and forth between kitchen and dining room, leaving them in either place for one day at a time. The only sufficiency that I need for the definition of truth, however, is the one that is due to a structural contrast between propositions. 58. This contrasts with the common practice (e.g. Davidson 1969) of relativizing the assertion to the particular SOA in which it is asserted (speaker, place and time of utterance). 59. Notice how mentalist and nominalist truth are defined in terms of ontological truth. Admit­ tedly, mentalists and nominalists may ban the notion of ontological truth altogether. Kamlah and Lorenzen (1973: 121-124,143-145), for example, define truth as what is agreed upon by a group of investigators acting in specific ways. For a discussion of such 'intersubjective' truth theories, see Puntel (1978: 142-171) (see also IV.4.4, below). 60. An interesting illustration of such a mix-up is found in Peirce's conception of truth (cp. S. Haack 1976a: 329; 1976c: especially 243-244). 61. Sometimes the Correspondence Theory is explained in a way that makes it almost inseparable from my dyadicness thesis. Consider Davidson (1979: 748): "A true statement is a statement that is true to the facts. This remark seems to em­ body the same sort of obvious and essential wisdom about truth as the following about motherhood: a mother is a person who is the mother of someone." That Davidson is not a supporter cf the 'truth of thesis is due to the fact that he does not take the above description of the Correspondence Theory seriously, as he discards facts. Another interest­ ing claim once made in the debate on the Correspondence Theory comes from F.H. Bradley (1911: 316): "Truth to be true must be true of something, and this something itself is not truth. This obvious view I endorse." Judging from this passage, Bradley would have supported the 'truth-of thesis. In fact, however, most of Bradley's energy is spent on the debate between Correspondence and Coherence Theories, a debate in which he defends the theory that is furthest from my 'truth'-from-'truth of thesis. A genuine combination of this thesis and of the Correspondence Theory, however, is Bayliss's 'Exemplificational Theory of Truth' (1948), allowing for the claim that "it is not the case that first-order propositions ... are true simply, true at all times, at all places, and under all circumstances. Rather they are true of limited states of af­ fairs." (Bayliss 1948: 472) 62. Compare R.M. Adams (1947: 231): "Indeed, I do not think there have been many philosophers who have thought that the notion of truth must be based on a prior notion of truth in a possible world." I do not think that it is significant that Adams speaks about 'truth in' rather than 'truth of'. Mates (1968: 508-509) and Bar-Hillel (1973: 307), however, have suggested a distinction.

224.

NOTES

63. Cp. also Bayliss (1948: 471-472) and Unger (1975: 272-313). Maybe this 'maximality' idea also underlies Frege's view that all true sentences have identical reference, viz. 'the True' (see Frege 1892). 64. The present defense of three-valuedness is different from the one in Van der Auwera (1980c: 280-281). I earlier tried to justify three-valuedness as a consequence of the fact that assertions or be­ liefs are evaluated in terms of a double ontological relatum, viz. the conjunction of the universe and the F-SOA. 65. I do not think that there is as sharp a distinction between a theory about the nature of truth and one about the criteria for truth as commonly held (cp. Rescher 1973b; Bunge 1974: 93-97; Dima 1977; Puntel 1978: 184-187,200-204). 66. I am using the term 'holism' in a less than strict sense. I do not wish to imply that the set of all be­ liefs has a reality independent of the sum of its parts. 67. A very interesting definition of satisfiability is McCawley's (1981: 70): "A proposition which is true in at least one state of affairs is said to be SATISFIABLE." The interesting feature of this definition is that it mentions a notion of 'truth of/in'. But the point is left in midair. McCawley (1981) nowhere explicitly espouses a dyadic view of truth, nor do we find any explicit argument against the priority of satisfaction or any explicit statement on the relation be­ tween Tarskian satisfaction and satisfiability (it is only the book's index which indirectly shows that the satisfaction of satisfiability and Tarskian satisfaction are the same sort of thing). It is further­ more unclear whether McCawley's notion of 'state of affairs' has any value in the explanation of truth and satisfiability, since it is itself defined in terms of truth-values: "A 'state of affairs' in this case is taken to be a set of truth values for the atomic prop­ ositions of the system, that is, a 'state of affairs' amounts to a line of a truth table." (McCawley 1981: 74) 68. In earlier work on what is here called 'RPL' I worked on the assumption that it was truth-func­ tional (see Van der Auwera 1978c: 107-134; 1979b, 1979c, 1979d, 1979e, 1980b). 69. There are two problems with this definition. First, it is blatantly circular. If a non-circular defin­ ition is wanted, I would claim that there is a disjunction that allows me to state that the possibility that ρ means that it is either true that ρ or it is false that p. This claim will not be substantiated here, however, for the disjunction will not be given any systematic analysis (see Van der Auwera 1978c: 127-128, n.d.b). Second, there are other possibility types than the one described by saying that a possibility is a possibility for both truth and falsity. I will come to them in a little while. 70. For an excellent survey of 'Redundancy Theories', see Franzen (1978,1979). My present com­ mitment to the Redundancy Theory contrasts with the position taken in Van der Auwera (1980c: 316-318). 71. The term misleadingly suggests that there exists something like a canonical scalarity theory. In fact, there are only a number of more or less compatible proposals (see Horn 1972; Fauconnier 1975a, 1975b; Ducrot 1978, 1980). Some interesting contributions come from the study of degree particles in German (e.g. Altmann 1976; König 1979,1981), Dutch (e.g. Vandeweghe 1979,1981, 1983), and English (e.g. Van der Auwera n.d.b).

NOTES

225

72. Suppose, however, that we live in a community that measures the outside temperature with a three-point scale, going from 1 (cold) to 3 (warm). Suppose, moreover, that there are two people engaged in a conversation and that it is relatively cold. Both interlocutors are aware of this and when they start discussing the weather, one of them says that the temperature is at least 2. What he means, is that the temperature is at least 2, if not 1,i.e. 2 or 1. 73. The terminology was first introduced for a different type of possibility, viz. the one that has to be defined in terms of necessity and impossibility and which will be dealt with in V.4 (see Hintikka 1960; Karttunen 1972: 5-6; Horn 1972: 113-118; 1973). 74. This is why I accepted Table 4 in Van der Auwera (1980c: 315-323). 75. I am assuming that the falsity is internal. However, I will argue below that the claim holds good even if the falsity is external. 76. (213) has gotten a lot of attention recently and is also called the 'Strenghtened Liar Paradox'. The term is due to van Fraassen (1968), but the problem had already been articulated by Mackie and Smart (1953, 1954). See Van der Auwera (n.d.e) for some discussion. 77. Thus I use the term 'modal' less liberally than is commonly done. For some investigators, all possibility talk is modality talk. In the present framework, there are both modal and non-modal possibilities. 78. This is not to say that unbound contingency has gotten no attention at all. Aristotle was in­ terested in both, but maybe only because he mixed them up (cp. Lukasiewicz 1957: 134-135,154155;Hintikka 1960; Horn 1972:113-116). Some signs of a modern interest in unbound contingency can be found in Reichenbach (1947: 128, 392), Carnap (1956: 175), Montgomery and Routley (1966), Stahl (1977), and in Bradley and Swartz (1979: 14). 79. A good illustration is Sosa's collection of papers, Causation and conditionals (1975). The no­ tions of sufficient and necessary conditionality play an important role in most of the causation pa­ pers, but not in the ones on conditionals. 80. The opening lines of the paper (Goodman, 1965: 3) that was most responsible for the quicken­ ing of philosophical interest in counterfactuals leave no doubt about this: "The analysis of counterfactuals is no fussy little grammatical exercise. Indeed, if we lack the means for interpreting counterf actual conditionals, we can hardly claim to have any adequate philosophy of science." 81. It is remarkable that Table 15 is not paralleled by any of the more common three-valued impli­ cation tables (cp. S. Haack 1974: 168-172). 82. Examples such as (255) are often claimed to support the thesis that 'if ... then' is essentially a material implication. This claim is as false as the current objection. 83. Austin (1952; 1956) has unearthed another interesting usage of 'if ... then': (a) I can if I choose. But (a) is even less of a threat to the sufficiency thesis since it simply states that the speaker's want­ ing to do something is already sufficient for him or her to be able to do it. (I am by no means the first

NOTES

226

to think that cases such as (a) pose much less of problem for conditional theories than has been claimed; compare Mackie 1973a: 96.) 84. This is the work done and inspired by Chisholm (1946; 1955) and Goodman (1947). The term 'metalinguistic' is due to D. Lewis (1973) and Mackie (1973a), but is really a misnomer, for the metalinguistic character of these theories is not essential (see Bennett 1974: 386; Fine 1975: 451). Bennett (1974) and Barker (1979) have suggested the term 'consequence theory'. Pollock (1976b: 4) speaks about the 'linguistic approach', McLean (1976:47) about the 'system of statements view', and Slote (1978: 3) about the 'cotenability treament'. 85. This approach started with Stalnaker (1975 [1968]) and its most impressive result so far is D. Lewis (1973). See also Sobel (1970: 429-442), Apostel (1974), Nute (1975a; 1975b; 1980), Pollock (1976a; 1976b), McLean (1976), Mondadori and Morton (1976), Bigelow (1976), and W. Davis (1979). 86. It is implicit in Bradley and Swartz (1979), too. Bradley and Swartz follow the majority of 20thcentury logicians in using the concept of sufficient conditionality without studying it (see IV.3). Here is an extract from the prose introduction to their concept of implication, which later turns out to be a strict implication: "For implication is the relation which holds between an ordered pair of propositions when the first cannot be true without the second also being true, i. e. when the truth of the first is a sufficient condition of the truth of the second. " (Bradley and Swartz 1979: 31; my emphasis) It is also interesting to see what happens in Strawson's Introduction to logical theory (1952). At the very end of his introduction, in which he discusses something that is very close or even identical to strict implication and which he calls 'entailment', Strawson writes the following: "Finally, two very useful additions to the logician's vocabulary are the phrases 'necessary condition' and 'sufficient condition'. When one statement entails another, the truth of the first is a sufficient condition of the truth of the second, and the truth of the second a necessary condition of the truth of the first." (1952: 25) Unfortunately, Strawson does not cash in on this idea. 'Sufficient' and 'sufficient condition' do not even make it to his index. 87. I also see no reason to accept Braine's view of this question. Braine (1979:41-42) thinks that the 'paradox' is due to a speaker's sloppiness. 'If the USA threw its weapons into the sea tomorrow' would be a typical example of unguarded language behavior: the speaker would really mean some­ thing more specific. This account might easily lead to the conclusion that speakers never mean what they say, which is not the case. 88. This terminology, though quite standard in the logico-philosophical literature, is not al­ together felicitous. For one thing, in legal language, a present subjunctive form can have the mean­ ing of the so-called indicative conditional. (b)

If any person be found guilty, he shall have the right of appeal. (due to Quirk, Greenbaum, Leech and Svartvik 1972: 748)

For another thing, except for 'were', English does not have any real past subjunctive form any­ more. So, strictly speaking, the 'came' of (286) is indicative.

NOTES

227

89. As far as the underestimation of the distinction between indicatives and subjunctives goes, see e.g. Lloyd (1952: 114), Ayers (1965), von Kutschera (1974), Stalnaker (1975: 166; 1976a [1975]). McLean (1976: 24), Ellis (1978: 188-124; 1979: 61-68), and Lowe (1979). The distinction between counterfactuals and problematicals has not been found worthy of serious study either, yet many investigators are aware of the distinction (see Anderson 1951; Schneider 1953: 623-624; Chisholm 1955: 105; von Wright 1957a: 134; Rescher 1964: 1; 1973b: 265, 273; Ayers 1965; E.W. Adams 1970; Sobel 1970: 430; Bacon 1971: 64; D. Lewis 1973: 4; Mackie 1973a: 63-119; von Kutschera 1974: 258; Fine 1975: 453; Stalnaker 1976a: 186-187; Cooper 1978: 164; and W. Davis 1979: 545-546). 90. Goodman (1965: 4) has called 'since' a 'factual conditional'. See also Ryle (1950) and Van der Auwera (1979c, 1979d, 1979e, 1980b). 91. The closest we get is Schachter (1971:105) (see also Karttunen and Peters 1977:367 ; 1979:8-9) : "a speaker can use a simple conditional only when he does not know the antecedent to be false. A speaker can use a subjunctive only when he does not know the ante­ cedent to be true."

REFERENCES Ackrill, J.L. (ed.) 1963 Aristotle's 'Categories' and 'De Interpretatione. Oxford: Oxford University Press. Adams, E.W. 1965 "The logic of conditionals". Inquiry 8.166-197. 1966

"Probability and the logic of conditionals". In J. Hintikka and P. Suppes (eds.), As­ pects of inductive logic. Amsterdam: North-Holland, 265-316.

1970

"Subjunctive and indicative conditionals". Foundations of Language 6.89-94.

1975

The logic of conditionals: An application of probability to deductive logic. Dordrecht: Reidel.

1983

"Probabilistic enthymemes". Journal of Pragmatics 7. 283-295.

Adams, R.M. 1974 Theories of actuality. Nous 8.203.231. Allwood, J. 1972 Negation and the strength of presuppositions or There is more to speaking than words. Göteborg: University of Göteborg. (Reprinted in O. Dahl (ed.) (1977), Logic,prag­ matics and grammar. Göteborg: University of Göteborg, 11-52.) 1976

Linguistic communication as action and cooperation: A study in pragmatics. Göteborg: University of Göteborg.

1978

On the analysis of communicative action. Göteborg: University of Göteborg.

Altmann, H. 1976 Die Gradpartikeln im Deutschen: Untersuchungen zu ihrer Syntax, Semantik und Pragmatik. Tübingen: Niemeyer. Anderson, A.R. 1951 "A note on counterfactuals". Analysis 12.35-38. Anderson, A.R. and N.D. Belnap Jr. 1975 Entailment: The logic of relevance and necessity. Princeton, N.J. : Princeton University Press. Apostel, L. 1974 Matière et forme I: Introduction à une epistemologie réaliste. Gent: Communication and Cognition.

230

REFERENCES

Aquila, R.E. 1977 Intentionality: A study of mental acts. University Park, Pa.: The Pennsylvania State University Press. Ash worth, E J . 1978 The tradition of medieval logic and speculative grammar from Anselm to the end of the seventeenth century: A bibliography from 1836 onwards. Toronto: Pontifical Institute of Medieval Studies. Aune, . 1977

Reason and action. Dordrecht: Reidel.

Austin, J.L. 1952 "What sort of 'if is the 'if of 'I can if I choose'?". Analysis 12.125-126. 1956

"Ifs and cans". Proceedings of the British Academy 42.109-132. (Reprinted in J.L. Austin (1961), 153-180, and in J.L. Austin (1970a), 205-232.)

1961

Philosophical papers. Oxford: Clarendon Press.

1970a

Philosophical papers, second edition. Oxford: Clarendon Press.

1970b

"Truth". In J.L. Austin (1970a), 117-128. (First published in Proceedings of the Aris­ totelian Society, Supplementary volume 24.111-128 [1950]. Also reprinted in J.L. Austin (1961), 85-101.)

1970c

"A plea for excuses". In J.L. Austin (1970a), 175-204. (First published in Proceedings of the Aristotelian Society 42.1-30 [1956]. Also reprinted in J.L. Austin (1961), 123152.)

1975

How to do things with words. The William James Lectures delivered at Harvard Univer­ sity in 1955, second edition. Oxford: Oxford University Press. [1962]

Ayer, A.J. 1956

The problem of knowledge. London: MacMillan, and New York: St Martin's Press.

1963 a

The concept of a person and other essays. London: Macmillan.

1963b

"Philosophy and language". In A.J. Ayer (1963a), 1-35.

1963c

"Truth". In A.J. Ayer (1963a), 162-187.

Ayers, M.R. 1965 "Counterfactuals and subjunctive conditionals". Mind 74.347-364. Bacon, J. 1971 "The subjunctive conditional as relevant implication". Philosophia 1.61-80. Bar-Hillel, Y. 1973 "Primary truth bearers". Dialectica 27.303-312. Ball, T. 1981

"Popper's psychologism". Philosophy of the Social Sciences 11.65-68.

REFERENCES

231

Barker, J.A. 1979 "Indicative conditionals". Studies in Language 3.141-152. Bayliss, C.A. 1948 "Facts, propositions, exemplifications, and truth". Mind 58.459-479. Bennett, J. 1974 "Counterfactuals and possible worlds". Canadian Journal of Philosophy 4.381-402. 1976

Linguistic behaviour. Cambridge: Cambridge University Press.

Benveniste, E. 1966 "Catégories de pensée et catégories de langue". In E. Benveniste, Problèmes de lin­ guistique générale. Paris: Gallimard, 63-74. Berger, F.R. 1977 Studying deductive logic. Englewood Cliffs, N.J.: Prentice Hall. Berlin, . and P. Kay 1969 Basic color terms: Their universality and evolution. Berkeley : University of California Press. Bigelow, J.C. 1976 "If-then meets the possible worlds". Philosophia 6.215-235. Blanche, R. 1967 Raison et discourse: Défense de la logique réflexive. Paris: Vrin. Blanshard,B. 1939 The nature of thought. London: George Allen and Unwin. Block, N. 1981

"Psychologism and behaviourism", The Psychological Review 90.5-43.

Blumberg, Α.Ε. 1967 "Logic, Modern". In P. Edwards (ed.), V.12-34. Boër, S.E. and W.G. Lycan 1976 "The myth of semantic presupposition". Ohio State University Working Papers in Lin­ guistics 21.1-90. Boudon, R. 1974 The logic of sociological explanation. Harmondsworth: Penguin. Bradley, F.H. 1911 "On some aspects of truth". Mind20.305-341. (Reprinted in F.H. Bradley (1914), Es­ says on truth and reality. Oxford: Clarendon Press, 310-352.) Bradley, R. and N. Swartz 1979 Possible worlds: An introduction to logic and its philosophy. Oxford: Basil Blackwell. Braine,M.D.S. 1978 "On the relation between the natural logic of reasoning and standard logic". Psychological Review 85.1-21. 1979

"On some claims about if-then". Linguistics and Philosophy 3.35-47.

232

REFERENCES

Broad, C D . 1930 "The principles of demonstrative induction (I)". Mind 39.302-317. Brody,B.A. 1967 "Logical terms, Glossary of'. In P. Edwards (ed.), V. 57-77. Bryant, J. 1980

"The logic of relative modality and the paradoxes of deontic logic". Notre Dame Jour­ nal of Formal Logic 21.78-88.

Bunge, M. 1974 Treatise of basic philosophy 2: Semantics II — Interpretation and truth. Dordrecht: Reidel. Pursill-Hall, G.L. 1971 Speculative grammars of the Middle Ages: The doctrine of the Partes Orationis of the Modistae. The Hague: Mouton. Carlson, G.N. 1979 "Generics and atemporal When". Linguistics and Philosophy 3.49-98. Carnap, R. 1956 Meaning and necessity: A study in semantics and modal logic. Chicago: The University of Chicago Press. 1966

Der logische Aufbau der Welt. Hamburg: Felix Meiner.

Castañeda, Η.-Ν. 1975 Thinking and doing: The philosophical foundations of institutions. Dordrecht: Reidel. Chisholm,R. 1946 "The contrary-to-fact conditional". Mind 55.289-307. (Reprinted in H. Feigl and W. Sellars (eds.) (1969), 482-497.) 1955

"Law statements and counterfactual inference". Analysis 15.97-105. (Reprinted in E. Sosa (ed.) (1975), 147-155.)

1966

Theory of knowledge. Englewood Cliffs, N.J. : Prentice-Hall.

Cohen, L.J. 1978 "The coherence theory of truth". Philosophical Studies 34.351-360. Cohen, M.R. 1944 A preface to logic. New York: Henry Holt. Cohen, M.R. and E. Nagel 1934 An introduction to logic and scientific method. New York: Harcourt, Brace. Cooper, W.S. 1978 Foundations of logico-linguistics: A unified theory of information, language, and logic. Dordrecht: Reidel.

REFERENCES

233

Cornforth, M. 1954 Dialectical materialism: An introductory course — Volume three: The theory of know­ ledge. London: Lawrence and Wishart. Covington, M.A. 1982 Syntactic theory in the high Middle Ages: Modistic models of sentence structure. Doctoral dissertation, Yale University. Danto, A.C. 1968 Analytical philosophy of knowledge. Cambridge: Cambridge University Press. Daveney, .. 1974 "Intentional behaviour". Journal for the Theory of Social Behaviour 4.111-129. Davidson, D. 1967 "Truth and meaning". Synthese 17.304-323. 1969

"True to the facts". The Journal of Philosophy 66.748-764.

Davis, J.W., D.J. Hockney, and W.K. Wilson (eds.) 1969 Philosophical logic. Dordrecht: Reidel. Davis, L.H. 1979 Theory of action. Englewood Cliffs, N.J. : Prentice-Hall. Davis, W.A. 1979 "Indicative and subjunctive conditionals". The Philosophical Review 88.544-564. De Pater, A. 1979 "Problemen rond een definitie van logika". Tijdschrift voor Filosofie 41.636-699. Dewey, J. 1925 Experience and nature. Chicago: Open Court. Dima, T. 1977

"The relation between correspondence and coherence in the problem of truth". Revue Roumaine de Sciences Sociales: Philosophie et Logique 21.71-76.

Donaldson, T.J. 1976 Towards a theory of action. Doctoral dissertation, University of Kansas. Ducrot, . 1971 "L'expression, en français, de la notion de condition suffisante". Langue française 12.60-67. 1972

Dire et ne pas dire: Principes de sémantique linguistique. Paris: Hermann.

1978

"Echelles argumentatives, échelles implicatives, et lois de discours". Semantikos 2.4367.

1980

Les échelles argumentatives. Paris: Minuit.

234

REFERENCES

Edwards, P. (ed.) 1967 The encycopedia of philosophy. New York: Macmillan and The Free Press, and London: Collier-MacMillan. Ellis, B. 1973

"The logic of subjective probability". British Journal for the Philosophy of Science 24.125-152.

1976

"Epistemic foundations of logic". Journal of Philosophical Logic 5.187-204.

1978

"A unified theory of conditionals: Journal of Philosophical Logic 7.107-124.

1979

Rational belief systems. Oxford: Basil Blackwell.

Fauconnier, G. 1975a "Pragmatic scales and logical structure". Linguistic Inquiry 6.353-375. 1975b

"Polarity and the scale principle". Papers from the Eleventh Regional Meeting of the Chicago Linguistic Society. Chicago: Linguistic Society, 188-199.

Feigl, H. and W. Sellars (eds.) 1949 Readings in philosophical analysis. New York: Appleton-Century-Crofts. Fine,K. 1975 Flew, A. 1975

"Critical notice on Counter f actuals by D. Lewis". Mind 83.451-458. Thinking about thinking (or, Do I sincerely want to be right?). Glasgow : Fontana/Col­ lins.

Franzen, W. 1978 "Zur Redundanztheorie der Wahrheit: Ein historischer und systematischer Überblick I". Conceptus 12.54-69. 1979 Frede, D. 1972

"Zur Redundanztheorie der Wahrheit: Ein historischer und systematischer Überblick II". Conceptus 13.47-62. "Omne quod est quando est necesse est esse". Archiv für Geschichte der Philosophie 54.153-167.

Freeman, D.H. 1967 Logic: The art of reasoning. New York: David McKay. Frege,G. 1892

1967

"Über Sinn und Bedeutung". Zeitschrift für Philosophie und philosophische Kritik N.F. 100.35-50. (Translated and reprinted in The Philosophical Review 57.209-230 (1948), and in H. Feigl and W. Sellars (eds.) (1949), 85-102.) "The thought: A logical inquiry". In P.F. Strawson (ed.), 17-38. (Translated and re­ printed version of "Der Gedanke: Eine logische Untersuchung". Beiträge zur

235

REFERENCES

Philosophie des deutschen Idealismus 1.58-77 [1918]. Also translated and reprinted in Mind 65.289-311 [19561.) French, P.A., .. Wehling, and H.K. Wertstein (eds.) 1979 Midwest studies in philosophy 4: Studies in metaphysics. Minneapolis: University of Minnesota Press. Gazdar, G. 1977 Implicature, presupposition and logical form. Bloomington, Ind. : Indiana University Linguistics Club. 1979

Pragmatics, implicature, presupposition, and logical form. New York: Academic Press.

Geduldig, G. 1976 Die Philosophie des Bedingten: Transzendental-philosophische Überlegungen zur Philosophie Sir William Hamiltons (1788-1856). Bonn: Bouvier Verlag Herbert Grundmann. Glethmann, C F . 1979 Protologik: Untersuchungen zur formalen Frankfurt am Main: Suhrkamp.

Logik

von

Begründungsdiskursen.

Goble,L.F. 1966 "The iteration of deontic modalities". Logique et Analyse 9.197-209. Gochet,P. 1978 Quine en perspective: Essai de philosophie comparée. Paris: Flammarion. Goodman, N. 1965 "The problem of counterfactual conditionals". In N. Goodman, Fact, fiction, and forecast. Indianapolis: Bobbs Merrill, 3-27. (Revised version of "The problem of counterfactual conditionals". The Journal of Philosophy 44.113-128 [1947]). Grandy, R.E. 1979 "Inference and if-then". Psychological Review 86.152-153. Grice, H.P. 1957 "Meaning". The Philosophical Review 66.377-388. (Reprinted in P.F. Strawson (ed.) (1967),49-58.) 1968

"Utterer's meaning, sentence meaning, and word-meaning". Foundations of Lan­ guage 4.225-242. (Reprinted in J.S. Searle (ed.) (1971), The philosophy of language. Oxford: Oxford University Press, 54-70.)

1969

"Utterer's meaning and intentions". The Philosophical Review 78.147-177.

1975

"Logic and conversation". In P. Cole and J.L. Morgan (eds.), Syntax and semantics 3: Speech acts. New York: Academic Press, 41-58.

n.d.

"Logic and Conversation". Unpublished lecture notes.

REFERENCES

236

Haack, R.J. 1978 "Quine's theory of logic". Erkenntnis 13.231-259. Haack, S. 1974

Deviant logic: Some philosophical issues. Cambridge: Cambridge University Press.

1976a

'"Is it true what they say about Tarski?'". Philosophy 51.323-336.

1976b 1976c

"Some preliminaries to ontology". Journal of Philosophical Logic 5.457-474. "The pragmatist theory of truth". British Journal for the Philosophy of Science 27.231249.

1977

"Lewis' ontologicai slum". The Review of Metaphysics 30.415-429.

1978

Philosophy of logics. Cambridge: Cambridge University Press.

1979a

"Descriptive and revisionary metaphysics". Philosophical Studies 35.361-371.

1979b

"Epistemology with a knowing subject". The Review of Metaphysics 33.309-333.

Hacking, I. 1979 "What is logic?". The Journal of Philosophy 76 "85-319. Haiman, J. 1978 "Conditionals are topics". Language 54.564-589. Hamlyn, D.W. 1961

"On necessary truth". Mind 70.514-525.

1967

"Contingent and necessary statements". In P. Edwards (ed.), II.198-205.

1971

"Unconscious intentions". Philosophy 46.12-22.

Hare, R.M. 1952 The language of morals. Oxford: Clarendon Press. 1970 "Meaning and speech acts". The Philosophical Review 79.3-24. (Reprinted in R.M. Hare (1972), Practical inferences and other essays. London: Macmillan, 74-93.) Harré, R. 1972

The philosophies of science: An introductory survey. London: Oxford University Press.

Hasenjaeger, G. 1962 Einführung in die Grundbegriffe und Probleme der modernen Logik. Freiburg: Karl Alber. Hazen, A.P. 1977 The foundations of modal logic. Doctoral dissertation, University of Pittsburgh. Henle,M. 1962

"On the relation between logic and thinking". Psychological Review 69.366-378.

REFERENCES

237

Herzberger, H.G. 1970 "Truth and modality in semantically closed languages". In R.L. Martin (ed.), The paradox of the liar. New Haven: Yale University Press. 25-46. Hilpinen, R. 1969 "An analysis of relativised modalities". In J.W. Davis, D.J. Hockney, and W.K. Wil­ son (eds.), 181-193. Hintikka, J. 1960 "Aristotle's different possibilities". Inquiry 3.18-28. 1971

"Semantics for propositional attitudes". In L. Linskey (ed.), Reference and modality. Oxford: Oxford University Press, 145-167. (First published in J.W. Davis, D.J. Hockney, and W.K. Wilson (eds.) (1969), 21-45.)

Horn, L.R. 1972 On the semantic properties of logical operators in English. Doctoral dissertation, University of California at Los Angeles. (Also published by Indiana University Lin­ guistics Club, Bloomington, Ind., 1976) 1973 Inoue, K. 1983

"Greek Grice". In Papers from the Ninth Regional Meeting of the Chicago Linguistic Society. Chicago: Linguistic Society, 205-214. "An analysis of a cleft conditional in Japanese : Where grammar meets rhetoric". Jour­ nal of Pragmatics 7.251-262.

Ishiguro, H. 1979 "Contingent truths and possible worlds", In P.A. French, .. Wehling, and H.K. Wertstein (eds.), 357-367. Jackson, F. 1977 "A causal theory of counterf actuals". Australasian Journal of Philosophy 55.3-21. James, W. 1890 The principles of psychology 1. New York: Henry Holt, and London: MacMillan. Jeffrey, R.C. 1964 "If. The Journal of Philosophy 61.702-703. Joachim, H.H. 1939 The nature of truth. London: Oxford University Press. Juhos, B. 1954 1967

"Ein-und zweistellige Modalitäten". Methodos 6.69-83. "Die 'intensionale' Wahrheit und die zwei Arten des Aussagengebrauchs". Kant-Stu­ dien 58.173-186.

Kambartel, F. 1971 "Bedingung". In J. Ritter (ed.), Historisches Wörterbuch der Philosophie 1. Basel: Schwabe, 762-765.

REFERENCES

238

Kamlah, W. and P. Lorenzen 1973 Logische Propädeutik: Vorschule des vernünftigen Redens. Mannheim: B.I.-Wis­ senschaftsverlag. Karttunen, L. 1971 "Counterfactual conditionals". Linguistic Inquiry 2.566-569. 1972

"Possible and must". In J.P. Kimball (ed.), Syntax and semantics 1. New York: Semi­ nar Press, 1-20.

Karttunen, L. and S. Peters 1977 "Requiem for presupposition". In Proceedings from the Third Annual Meeting of the Berkeley Linguistics Society. Berkeley: Linguistics Society, 360-371. 1979

"Conventional implicatures". In C.-K. Oh and D.A. Dinneen (eds.), 1-56.

Kempson, R.M. 1975 Presupposition and the delimitation of semantics. Cambridge: Cambridge University Press. Krige, J. 1978

"A critique of Popper's conception of the relationship between logic, psychology, and a critical epistemology". Inquiry 21.313-335.

Kripke, S.A. 1972 "Naming and necessity". In D. Davidson and G. Harman (eds. ), Semantics of natural language. Dordrecht: Reidel, 253-355. 1975 ''Outline of a theory of truth". The Journal of Philosophy 72.690-716. Kroy, M. 1976

Mentalism and modal logic: A study in the relations between logical and metaphysical systems. Wiesbaden: Athenaion.

Kuhn,T.S. 1962 The structure of scientific revolutions. Chicago: The University of Chicago Press. König, E. 1979 1981

"A semantic analysis of German 'Erst'". In R. Bäurle, U. Egli, and A. von Stechow (eds.), Semantics from different points of view. Berlin: Springer Verlag, 148-160. "The meaning of scalar particles in German". In H.-J. EikmeyerandH. Reiser(eds.), Words, worlds, and contexts: New approaches in word semantics. Berlin: Walter de Gruyter, 107-132.

Lauerbach, G. 1979 Form and Funktion englisher Konditionalsätze mit ' if : Eine konversationslogische und sprechakttheoretische Analyse. Tübingen: Niemeyer. Lewis, C.I. 1912 "Implication and the algebra of logic". Mind 21.522-531. 1946

An analysis of knowledge and valuation. LaSalle, 111.: Open Court.

REFERENCES

239

Lewis, C I . and C H . Langford 1959 Symbolic logic. New York: Dover Publications. Lewis, D. 1973 1976 Lipps, T. 1880

Counterfactuals. Oxford: Basil Blackwell. "Probabilities of conditionals and conditional probabilities". The Philosophical Re­ view 85.297-315. "Die Aufgabe der Erkenntnistheorie und die Wundt'sche Logik". Philosophische Monatshefte 16.529-539.

Lloyd, A.C. 1952 "Mr. Anderson on subjunctive and counterfactual conditionals". Analysis 12.113115. Lorenz, W. and G. Wotjak 1977 Zum Verhältnis von Abbild und Bedeutung: Überlegungen im Grenzfeld zwischen Er­ kenntnistheorie und Semantik. Berlin: Akademie-Verlag. Lowe, E.J. 1979 "Indicative and counterfactual conditionals". Analysis 39.139-141. Lyons, J. 1977

Semantics. Cambridge: Cambridge University Press.

Lukasiewicz, J. 1930 "Philosophische Bemerkungen zu mehrwertigen Systemen des Aussagenkalküls". Comptes rendus de la Société des Sciences et des Lettres de Varsovie cl. iii, 23.51-77. (Translated and reprinted in J. Lukasiewicz (1970a), 153-178.) 1957

Aristotle's syllogistic: From the standpoint of modern formal logic. Oxford: Clarendon Press.

1970a

Selected works. Amsterdam: North-Holland, and Warszawa: PWN-Polish Scientific Publishers.

1970b

"Logistic and philosophy". In J. Lukasiewicz (1970a), 115-131. (Translated and re­ printed version of "Logistyka a filozofia". Przeglad Filozoficny 39.115-131 [1936].)

1970c

"In defence of logistic". In J. Lukasiewicz (1970a), 236-249. (Translated and revised version of "W obronie logistyki". Studia Gnesnensia 15.22 [1937].)

1970d

"On the intuitionistic theory of deduction". In J. Lukasiewicz (1970a), 325-340. (First published in Indagationes Mathematicae. Koninklijke Nederlandse Academie der Wetenschappen. Proceedings Series A.3. 202-212 [1952].)

MacColl,H. 1906 Symbolic logic and its applications. London: Longman's-Green. Mackie, J.L. 1965 "Causes and conditions". American Philosophical Quarterly 2.245-264. (Partially re­ printed in E. Sosa (ed.) (1975), 15-38.)

240

REFERENCES

1973a

Truth, probability and paradox: Studies in philosoph:cal logic. Oxford: Clarendon Press.

1973b

"Simple truth". In J.L. Mackie (1973a), 17-63. (Revised version of "Simple truth". The Philosophical Quarterly 20.321-333 [1970].)

1979

"Mind, brain, and causation". In P.A. French, .. Wehling, and H.K. Wertstein (eds.), 19-29.

Mackie, J.L. and J.J.C. Smart 1953

"A variant of the 'heterological' paradox'. Analysis 13.61-66.

1954

"A variant of the 'heterological' paradox: A further note". Analysis 14.146-149.

Marc-Wogau, K. 1962 "On historical explanation". Theoria 28.213-233. Massey, G.J. 1970 Understanding symbolic logic. New York: Harper and Row. Mates, B. 1961

Stoic logic. Berkeley: University of California Press.

1968

"Leibniz on possible worlds". In B. van Rootselaar and J.F. Staal (eds.), 507-529.

1972

Elementary logic. Oxford: Oxford University Press.

Mayo, B. 1957 "Conditional statements". The Philosophical Review 66.291-303. McCawley, J.D. 1981 Everything that linguists have always wanted to know about logic — but were ashamed to ask. Oxford: Basil Blackwell. McLean, C.J. 1976 Understanding counterf'actuals. Doctoral dissertation, Brown University. McRae, R.F. 1973 "Introduction". In J.M. Robson (ed. ), Collected works ofJohn Stuart Mill 7. London: Routledge and Kegan Paul, and Toronto: University of Toronto Press, xxixlviii. Meiland, J.W. 1976 "Psychologism in logic: Husserl's critique". Inquiry 19.325-339. Menger, . 1939 "On necessary and on sufficient conditions in elementary mathematics". School, Sci­ ence and Mathematics 631-642. 1979

"A counterpart of Occam's razor". In K. Menger, Selected papers in logic and founda­ tions, didactics, economics. Dordrecht: Reidel, 105-135.

Merrill, G.H. 1978 "Formalization, possible worlds, and the foundations of modal logic". Erkenntnis 12. 305-327.

REFERENCES

241

Michael, F. and E. Michael 1979 "Peirce on the nature of logic". Notre Dame Journal of Formal Logic 20.84-88. Mondadori, F. and A. Morton 1976 "Modal realism: The poisoned pawn". The Philosophical Review 85.3-20. Montgomery, H.A. andF.R. Routley 1966 "Contingency and contingency bases for normal modal logics". Logique et Analyse 9.318-328. Mundle,C.W.K. 1970 A critique of linguistic philosophy. Oxford : Clarendon Press. Nagel, E. 1949

Nauta, D. 1974

"Logic without ontology". In H. Feigl and W. Sellars(eds.), 191-210. (First published in Y.H. Krikorian (ed.) (1944), Naturalism and the human spirit. New York: Colum­ bia University Press, 210-241.)

Logica en model. Amsterdam: Wetenschappelijke Uitgeverij.

Nelson, E.J. 1930 "Intensional relations". Mind 39.440-453. Nerlich, G. 1979 "Time and the direction of conditionship". Australasian Journal of Philosophy 57.314. Neurath, O. 1931 "Soziologie im Physikalismus". Erkenntnis 2.393-431. Nunn, R.T. 1979 "Psychologism, functionalism, and the modal status of logical laws: A reply to J.W. Meiland's objections to psychologism". Inquiry 22.343-349. Nute, D. 1975a

"Counterfactuals". Notre Dame Journal of Formal Logic 16.476-482.

1975b

"Counterfactuals and the similarity of worlds". The Journal of Philosophy 72.773-778.

1980

Topics in conditional logic. Dordrecht: Reidel.

Oh, C.-K. and D.A. Dinneen (eds.) 1979 Syntax and semantics 11: Presupposition. New York: Academic Press. Pap, A. 1958 Semantics and necessary truth: An inquiry into the foundations of analytical philosophy. New Haven: Yale University Press. Parret, H. 1979a "Ce qu'il faut croire et désirer, pour poser une question". Langue française 42.85-93. 1979b

Filosofie en taalwetenschap. Assen: Van Gorcum.

242

REFERENCES

n. d. a

Langage et pensée: La question du parallélisme logico-grammatical. To appear.

n.d.b

"A note on representationalism". In B. Gelder and P. van Geert (eds.), Knowledge and representation. London: Routledge and Kegan Paul. To appear.

Peirce, C S . 1974 Collected papers 1: Principles of philosophy. Cambridge, Mass. : The Belknap Press of Harvard University Press. Petrovie, G. 1967 Marx in the mid-twentieth century. Garden City, N. Y. : Doubleday. Plantinga, A. 1974 The nature of necessity. Oxford: Clarendon Press. 1977

"Actualism and possible worlds". In D. Holdcroft (ed.), Papers on logic and language. Warwick: University of Warwick, 135-155.

Platts, M. de Bretton 1979 Ways of meaning: An introduction to the philosophy of language. London: Routledge and Kegan Paul. Poland, W. 1896 The truth of thought or material logic: A short treatise on the initial philosophy, the groundwork necessary for the consistent pursuit of knowledge. New York: Silver, Burdett. Pollock, J.L. 1974 Knowledge and justification. Princeton: Princeton University Press. 1976a

"The 'Possible Worlds' analysis of counterfactuals". Philosophical Studies 29.469476.

1976b

Subjunctive reasoning. Dordrecht: Reidel.

1982

Language and thought. Princeton, N.J. : Princeton University Press.

Popper, K.R. 1968 "Epistemology without a knowing subject". In B. van Rootselaar and J.F. Staal (eds.), 333-373. (Reprinted in K.R. Popper (1972), Objective knowledge: An evolu­ tionary approach. Oxford: Clarendon Press, 106-152.) Prior, A.N. 1962 "Possible worlds". The Philosophical Quarterly 12.36-43. Puntel,L.B. 1978 Wahrheitstheorien in der neueren Philosophie: Eine kritisch-systematische Darstel­ lung. Darmstadt: Wissenschaftliche Buchgesellschaft. Quine, W.V.O. 1950 Methods of logic. New York: Henry Holt. 1951

Mathematical logic, second edition. Cambridge, Mass.: Harvard University Press. (First edition published by Norton, New York, 1940.)

REFERENCES

243

I960

Word and object. Cambridge, Mass. : The M.I.T. Press.

1961a

From a logical point of view, second edition. New York- Harper and Row. (First edi­ tion published by the Harvard University Press, Cambridge, Mass., 1953.)

1961b

"On what there is". In W.V.O. Quine (1961a), 1-19. (Revised version of "On what there is". The Review of Metaphysics 2.21-38 [1948].)

1961c

"Two dogmas of empiricism". In W.V.O. Quine (1961a), 20-46. (Revised version of "Two dogmas of empiricism". The Philosophical Review 60.20-43 [1951].)

1961d

"Notes on the theory of reference". In W.V.O. Quine (1961a), 130-138.

1965

Elementary logic, second edition. New York:  and Row. (First edition pub­ lished by Ginn, Boston, 1941.)

1966

"Mr. Strawson on logical theory". In W.V.O. Quine, The ways of paradox and other essays. New York: Random House, 135-155. (First published in Mind 62.433-451 [1953].)

1970

Philosophy of logic. Englewood Cliffs, N.J. : Prentice-Hall.

Quine, W.V.O. and J.S. Ullian 1970 The web of belief. New York: Random House. Quirk, R., S. Greenbaum, G. Leech, and J. Svartvik 1972 A grammar of contemporary English. London: Longman. Ramsey, F. P. 1978 "Facts and propositions". In F.P. Ramsey, Foundations, essays in philosophy, logic, mathematics and economics. London: Routledge and Kegan Paul, 40-57. (First pub­ lished in Proceedings of the Aristotelian Society, Supplementary volume 7.153-170 [1927].) Reichenbach,H. 1947 Elements of symbolic logic. New York: MacMillan. Reis, M. 1977

Präsuppositionen und Syntax. Tübingen: Niemeyer.

Rescher, N. 1964 Hypothetical reasoning. Amsterdam: North-Holland. 1969

"Truth and necessity in temporal perspective". In N. Rescher, Essays in philosophical analysis. Pittsburgh: University of Pittsburgh Press, 271-302.

1973a

Conceptual idealism. Oxford: Basil Blackwell.

1973b

The coherence theory of truth. Oxford: Clarendon Press.

1974

Studies in modality. Oxford: Basil Blackwell.

1975

A theory of possibility: A constructivistic and conceptualistic account of possible indi­ viduals and possible worlds. Oxford, Basil Blackwell.

244

REFERENCES

1977

Methodological pragmatism: A systems-theoretic approach to the theory of know­ ledge. Oxford: Basil Blackwell.

Resnik, M.D. 1979 "Frege as idealist and then realist". Inquiry 22.350-357. Richards, T. 1975 "The worlds of David Lewis". Australasian Journal of Philosophy 53.105-118. Roelofs,H.D. 1930 "Since Qua Non Conditions". Mind 39.194-201. Rollin, B.E. 1976 Natural and conventional meaning: An examination of the distinction. The Hague: Mouton. Rorty, R. 1979

Philosophy and the mirror of nature. Princeton, N.J. : Princeton University Press.

Rubinstein, D. 1977 "The concept of action in the social sciences". Journal for the Theory of Social Be­ haviour 7. 209-236. Russell, . 1912 The problems of philosophy. London: Williams and Norgate, and New York: Henry Holt. (Revised edition published by London University Press, London, 1959.) 1919 Ryle, G. 1949 1950

Introduction to mathematical philosophy. London: George Allen and Unwin. (Revised edition published by George Allen and Unwin, London, 1948.) The concept of mind. London: Hutchinson's University Library. "'If, 'So', and 'Because'". In M. Black (ed.), Philosophical analysis: A collection of essays. Ithaca, N.Y.: Cornell University Press, 323-340.

Sanford,D.H. 1976 "The direction of causation and the direction of conditionship". The Journal of Philosophy 73.193-207. Schachter, J .  1971 Presupposition and counterfactual conditional sentences. Doctoral dissertation, Uni­ versity of California at Los Angeles. Schaff, A. 1973 Language and cognition. New York: McGraw-Hill. (Translation of A. Schaff (1964), Jezyk a Poznanie. Warszawa: Panstwowe Wydawnictwo Paukowe.) Schiffer, S.R. 1972 Meaning. Oxford: Clarendon Press. Schiller, F.C.S. 1912 Formal logic: A scientific and social problem. London: Macmillan.

REFERENCES

245

Schneider, E.F. 1953 "Recent discussion of subjunctive conditionals". The Review of Metaphysics 6.623649. Scriven, M. 1964 Review of E. Nagel, The structure of science. The Review of Metaphysics 17.403-424. Searle, J.R. 1969 Speech acts: An essay in the philosophy of language. Cambridge: Cambridge Univer­ sity Press. 1975

"A taxonomy of illocutionary acts". In K. Gunderson (ed.), Language, mind and knowledge. Minneapolis: University of Minnesota Press, 344-369.

1976

"A classification of illocutionary acts". Language in Society 5.1-23.

1979a

"What is an intentional state?". Mind 88.74-92.

1979b

"Intentionality and the use of language". In A. Margalit (ed. ), Meaning and use. Dor­ drecht: Reidel, 181-197.

1979c

"The intentionality of intention and action". Inquiry 22.253-280.

Seddon, J.S. 1972 "Logicalpossibility". Mind 81.481-494. Seilars, W. 1962 "Truth and 'Correspondence'". The Journal of Philosophy 59.29-56. (Revision in W. Sellars (1963), Science, perception and reality. London: Routledge and Kegan Paul, and New York: The Humanities Press, 197-224. Sharvy, R. 1979 "Transitivity and conditionals". Logique et Analyse 87.347.351. Sinowjew, A.A. 1970 Über mehrwertige Logik: Ein Abriss. Braunschweig: Friedr. Vieweg und Son, and Basel: C.F. Winter'sehe Verlagshandlung. Skyrms,B. 1966 Choice and chance: An introduction to inductive logic. Belmont, Calif. : Dickenson. Slote, A. 1978

"Time in counterfactuals". The Philosophical Review 87.3-27.

Smiley, T. 1960

"Sense without denotation". Analysis 20.125-135.

1963

"Relative necessity". The Journal of Philosophical Logic 28.113-134.

Snyder, D.P. 1971 Modal logic and its applications. New York: Van Nostrand Reinhold. Sobel, J.H. 1970 "Utilitarianisms: Simple and general". Inquiry 13.394-449.

246

REFERENCES

Sober, E. 1978

"Psychologism". Journal for the Theory of Social Behaviour. 8.165-191.

Sommers, F. 1969 "On concepts of truth in natural languages". The Review of Metaphysics 23.259-286. Sosa, E. 1975

"Introduction". In E. Sosa (ed.), 1-4.

Sosa, E. (ed.) 1975 Causation and conditionals. Oxford: Oxford University Press. Stahl, G. 1977

"Indications formelles sur les syllogismes avec 'contingent'". Logique et Analyse 20.199-220.

Stalnaker, R.C. 1970 "Probability and conditionals". Philosophy of Science 37.64-80. 1975

"A theory of conditionals". In E. Sosa (ed.), 165-179. (Revised version of "A theory of conditionals". In N. Rescher (ed.) (1968), Studies in logical theory. Oxford: Basil Blackwell, 98-112.)

1976a

"Indicative conditionals". In A. Kasher (ed.), Language in focus: Foundations, methods, and systems - Essays in memory of Y. Bar-Hillel. Dordrecht: Reidel, 179196. (First published in Philosophia 5.269-286, [1975].)

1976b

"Possible worlds". Nous 10.65-75. (Reprinted in T. Honderlich and M. Burnyeat (eds.) (1979), Philosophy as it is. Harmondsworth: Penguin, 454-465.)

1979

"Anti-essentialism". In P.A. French, .. Wehling, and H.K. Wertstein (eds.), 343355.

Strawson, P.F. 1950

"On referring". Mind 69.320-344.

1952

Introduction to logical theory. London: Methuen.

1959

Individuals: An essay in descriptive metaphysics. London: Methuen.

Strawson, P.F. (ed.) 1967 Philosophical logic. Oxford: Oxford University Press. Sudberry, A. 1980 "The necessity of not doing otherwise". Australasian Journal of Philosophy 58.280283. Suppes, P. 1957 Introduction to logic. Princeton, N.J. : D. Van Nostrand Company. Sørensen, . 1973 "Asseverative If and its congeners". English Studies 59.248-254.

REFERENCES

247

Tarski, A. 1936 "Der Wahrheitsbegriff in den formalisierten Sprachen". Studia Philosophica 1.261405. (Translated and reprinted in A. Tarski (1956), Logic, semantics, metamathematics. Oxford: Clarendon Press, 152-278.) 1944

"The semantic concept of truth and the foundations of semantics". Phenomenological and Philosophical Research 4.341-376. (Reprinted in H. Feigl and W. Sellars (eds.) (1949), 52-84.)

1969

"Truth and proof". Scientific American 220.63-70, 75-77.

Taylor, R. 1966 Action and purpose. Englewood Cliffs, N.J. : Prentice-Hall. Tichy, P. 1976

"A counterexample to the Stalnaker-Lewis analysis of counterfactuals". Philosophi­ cal Studies 29.27'1-273.

Tranøy, K.E. 1970 Vilkarslogikk. Bergen: Universitetsforlaget. Tugendhat, E. 1976 Vorlesungen zur Einführung in die sprachanalytische Philosophie. Frankfurt am Main: Suhrkamp. Unger, P. 1975

Ignorance: A case for scepticism. Oxford: Clarendon Press.

Urmson, J.D. 1967 Philosophical analysis: Its development between the two world wars. London: Oxford University Press. Van der Auwera, J. 1978a Indirect speech acts revisited. Antwerp: University of Antwerp. (Also published by the Indiana University Linguistics Club, Bloomington, Ind., 1980.) 1978b

"Bestaan verstaan". De Nieuwe Taalgids 71.351-361.

1978c

Inleiding tot de linguistische pragmatiek. Leuven : Acco.

1979a

"Pragmatic presupposition : Shared beliefs in a theory of irrefutable meaning". In C.K. Oh and D.A. Dinneen (eds.), 249-264.

1979b

"On the truth-values of empirical sentential logic". In T. Pettersson (ed.), Papers from the Fifth Scandinavian Conference of Linguistics 2. Stockholm: Almquist & Wiksell, 167-178.

1979c

"'Dus'". In S. De Vriendt and  Peeters (eds.), Linguistics in Belgium 2. Brussels: Didier, 111-124.

1979d

"Conditions for empirical logics". In S. De Vriendt, M. Dominicy and  Peeters (eds.), Linguistics in Belgium 3. Brussels: Didier, 107-119.

1979e

"'Hence'". In J.-O. Östman (ed.) Reports on text linguistics: Semantics and cohesion. Åbo: Research Institute of the Åbo Akademi Foundation, 59-76.

248

REFERENCES

1980a

"On the meanings of basic speech acts". Journal of Pragmatics 4.253-264.

1980b

"'Hence'". York Papers in Linguistics 8.7-21.

1980c

Regaining speculative grammar. Speech acts, logic, and focus. Doctoral dissertation, University of Antwerp.

1981a

What do we talk about when we talk? Speculative grammar and the semantics and pragmatics of focus. Amsterdam: John Benjamins.

1981b

"Tagalog 'ang' : An exercise in universal grammar". In S. Daalder and M. Gerritsen (eds.), Linguistics in the Netherlands 1981. Amsterdam: North-Holland, 127-139.

1981c

"INUS conditions". Logique et Analyse 24.259-264.

1983

"Comrie on subjects". In W.U.S. van Lessen Kloeke and H. Bennis (eds.), Linguis­ tics in the Netherlands 1983. Dordrecht: Foris, 191-199.

n.d.a

"Lauerbach on the ambiguity of conditionals". To appear in Studia Filologiczne.

n.d.b

"'Or': A reconnaissance". To appear in M. Dominicy (ed.), Linguistics in Belgium 6. Brussels: Didier-Hattier.

n.d.c

'"Only if". To appear in M. Dominicy and S.P. Verluyten (eds.), Linguistics in Bel­ gium 7 Brussels: Didier-Hattier.

n.d.d

"Doubter paradoxes". Unpublished paper.

n.d.e

"Can, may, and their possibilities". Unpublished paper.

Van der Auwera, J. (ed.) 1983 Theme issue on Conditionals, Journal of Pragmatics 1.243-323. Vandeweghe, W. 1979 "Perspectivity operators in Dutch: al, nog, nogn ". In W. Vandeweghe and M. Vandevelde (eds.), Bedeutung, Sprechakte und Texte. Akten des 13. Linguistischen Kol­ loquiums, Gent 1978. Band2. Tübingen: Niemeyer, 111-122. 1981

"Al/nog/meer en perspektiviteitswisseling". In L. Goossens (ed.), Bijdragen over semantiek van het 33ste Vlaams filologencongres. Antwerp: University of Antwerp, 135-152.

1983

De partikels van de al/nog/pas- groep in het Nederlands: Een semantische en prag­ matische studie. Doctoral dissertation, State University of Ghent.

Van Dijk, T.A. 1977 Text and context: Explorations in the semantics and pragmatics of discourse. London : Longman. 1978

Taal en handelen: Een interdisciplinaire inleiding in de pragmatiek. Muiderberg: Coutinho.

van Fraassen, B.C. 1968 "Presupposition, implication, and self-reference". Journal of Philosophy 65.136-152.

REFERENCES

249

Van Rootselaar, . and J.F. Staal (eds.) 1968 Logic: Methodology and philosophy of science 3. Amsterdam: North-Holland. Verwora, M. 1912 Kausale und konditionale Weltanschauung. Jena: Verlag von Gustav Fischer. von Kutschera, F. 1974 "Indicative conditionals". Theoretical Linguistics 1.257-269. von Wright, G.H. 1941

The logical problem of induction. Helsingfors.

1942

"Några anmärkningar om nödvändiga och tillräckliga betingelser". Ajatus 2.220-239.

1951

Treatise on induction and probability. London: Routledge and Kegan Paul.

1957a 1957b

Logical studies. London: Routledge and Kegan Paul. "Interpretations of modal logic". In G.H. von Wright (1957a), 75-88. (Revised ver­ sion of "Interpretations of modal logic". Mind 61.165-177, [1952].)

1957c

"A new system of modal logic". In G.H. von Wright (1957a), 89-126. (Revised version of "A new system of modal logic". In Actes du Xlième Congrès International de Philosophie 5. Amsterdam: North-Holland, and Louvain: Nauwelaerts, 59-63, [1953].)

1959

On the logic of negation. (= Commentationes Physico-Mathematicae, 22.)

1970

"Deontic logic and the theory of conditions". In R. Hilpinen (ed.), Deontic logic: In­ troductory and systematic readings. Dordrecht: Reidel, 159-177. (Revised version of "Deontic logic and the theory of conditions". Crítica 2.3-25, [1968].)

1971

Explanation and understanding. Ithaca, N. Y. : Cornell University Press.

1974

Causality and determinism. New York: Columbia University Press.

1975

"On the logic and epistemology of the causal relation". In E. Sosa (ed.), 95-113. (First published in P. Suppes et al. (eds.) (1973), Logic, methodology and the philosophy of science 4. Amsterdam: North-Holland, 293-312.).

Warnock, G.J. 1958 English philosophy since 1900. London: Oxford University Press. Wertheimer, R. 1 968 "Conditions". The Journal of Philosophy 65.355-364. Whitehead, A.N. 1919 The concept of nature. Cambridge: Cambridge University Press. Whorf, B.J. 1956 "Languages and logic". In B.L. Whorf, Language, thought, and reality. Cambridge, Mass. : The M.I.T. Press, 233-245. (First published in Technology Review 43,250-252, 266, 268, 272 [1941].)

250

REFERENCES

Willard,5 D. 1972 "The paradox of logical psychologism: Husserl's way out". American Philosophical Quarterly 9.94-100. 1979

"Husserl's critique of extensionalist logic: 'A logic that does not understand itself". Idealistic Studies 9.143-164.

Williams, C.J.F. 1976

What is truth? Cambridge: Cambridge University Press.

1980

"What is, necessarily is, when it is". Analysis 49.127-131.

Wilson, D. 1975 Presuppositions and non-truth-conditional semantics. London: Academic Press. Wisdom, J.O. 1964 "Some overlooked aspects of Popper's contributions to philosophy, logic, and scien­ tific method". In M. Bunge (ed.), The critical approach to science and philosophy: In honor of Karl. R. Popper. London: The Free Press of Glencoe, Collier-Macmillan, 116-124. Wittgenstein, L. 1922 Tractatus logico-philosophicus. London: Kegan Paul, Trench, Trubner. Wunderlich, D. 1976 Studien zur Sprechakttheorie. Frankfurt am Main: Suhrkamp. Zinov'ev see Sinowjew

INDEX Absolutism, 75,220 Accessibility, 102 AckriU,J.L., 184 Action, 3, 31, 33, 36-39, 42-45, 49, 57 Actuality, 24-26, 87-88, 99-100, 161, 171 Adams, E.W., 190, 195, 212, 227 Adams, R.M., 223 Allwood, J., 2,37,41,54,164,219 Altmann, H., 224 Ambiguity, 69, 130, 188 'and', 64, 69, 77, 80. see also Conjunction Anderson, A.R., 129, 227 Antecedent, 194-213 Anti-descriptivism, 69-71, 221 Anti-psychologism, 10, 41, 65, 70 Apostel, L., 23,226 Aquila, R.E., 219 Aristotle, 1, 14, 62, 157, 184, 225 Ashworth, E.J., 1 Assertability condition, 190 Assertion, 4, 6, 19, 45-55, 80, 82, 85, 8788, 102-213, 220, 223 'at least', 109-110, 137, 156, 205-206 'at most', 138,205-206 Aune, ., 21,219 Austin, J.L., 13,54,101,118,196,217,225 Ayer, A.J., 10, 16, 89, 100-101 Ayers,M.R., 212,227 Bacon, J., 227 Ball, T., 221 Bar-Hillel,Y., 223 Barker, J.Α., 226 Basic condition, 91-92 Basic speech act, 4-5, 41, 50, 53-54, 220 Bayliss, C A . , 223-224 Behavior, 36-37, 44 Behaviorism, 219, 221 Belief, 3, 10-11, 27-33, 36, 46-57, 84, 8788,103-126, 161,218,220 Belnap,N.D., 129

Bennett, J., 41,48-49,89,212,226 Benveniste, E., 14 Berger, F.R., 220 Berlin, ., 17 Bigelow, J.C., 193,226 Bilateral, 138,141 Bipresuppositional, 169, 189 Bivalence. See Two-valuedness Blanche, R., 65,68,221 Blanshard,B., 119 Block, N., 221 Blumberg, Α.Ε., 126 Boër, S.E., 192 Boudon, R., 192 Bradley, F.H., 101,119,223 Bradley, R., 24, 182, 218, 225-226 Braine, M.D.S., 132, 221, 226 Broad, C D . , 89 Broad falsity, 142-154 Brody, B.A., 126 Bryant, J., 182 Bunge, M., 224 Bursill-Hall, G.L., 1 Carlson, G.N., 213 Carnap, R., 218,225 Case, 56 Castañeda, Η.-Ν., 7 Cause, 28,35,89-90 Chisholm, R., 223,226-227 Choice negation, 157 Chomsky, Ν., 6,70,73 Classical Propositional Logic (CPL), 7981, 87, 111-113, 131 Cohen, L.J., 119 Cohen, M., 62,65,68,129 Coherence Theory, 4, 101, 118-120, 124, 223 Color terms, 17 Competence, 70-71, 74 Completeness, 20, 26, 91, 97-98, 106

252

INDEX

Componential analysis, 130-177, 181 Concept, 10-12, 15, 21, 24, 28-31, 57-58, 217 Conceptualism, 9, 12-13, 15, 24, 66, 217218 Conceptualization, 28-35,46-47,58,78-79, 81-85, 103, 219 Condition, 4, 15, 87, 100, 222. See also Assertability condition; Basic condition; Necessary condition; Necessary and suffi­ cient condition; Sufficient condition Conditional, 4, 6, 159-160, 178, 189-213, 227. See also 'if ... then'; Implication Conditional analysis, 130-132 Conditionism, 222 Conjunction, 85, 111-113, 132-133, 162. See also 'and' Consciousness, 3, 27, 31-38, 44, 49, 56,5960, 219 Consequent, 194-213 Consistency, 118-119, 122 Context, 37, 109, 114, 188, 203 Contingency, 4,129,180-182,209-211,225 Conventionalism, 220 Conversational implicature, 5, 7,110,156, 192, 212 Cooper, W.S., 190,227 Cornforth, M., 5,76 Correspondence Theory, 4-5, 101, 114, 118-121, 124, 223 Counterfactual, 190-191, 198-199, 201213, 225-227 Covington, M.A., 1 Danto, A.C., 127,192 Daveney, .., 217 Davidson, D., 223 Davis, L., 219 Davis, W., 212,226-227 De Pater, Α., 72-76 Descriptive mentalism, 65-67, 72-74 Desire, 3, 10, 18, 27-31, 33-36, 52-57, 83, 85, 87-88, 102-103, 161, 220, 222 Dewey, J., 182 Dima, T., 224 Disjunction, 111-113, 137, 195, 214, 224 Doing, 36-38,43 Donaldson, T.J., 219 Double-bound, 141-156, 181 Doubter Paradox, 171, 177

Ducrot, O., 192, 196, 212, 224 Dyadicness, 4,114,129,132,158-167,182, 215, 223-224 Edwards, P., 212 Ellis, ., 61,66,182,190,194-195,221,227 Empirical, 1-2, 9, 70-71 Empirical interpretation, 75, 80-82 Entailment, 226 Epistemology, 46, 218, 221 Essentialism, 95 'even if', 196,214 Event, 3, 18, 20-22, 28-29, 31, 33, 38, 42 Exclusion negation, 157 Expansion, 92, 97, 116 Extension, 5-6 External, 168-175, 225 Fallibilism, 73,75 Falsity, 4, 28, 99, 115-116, 123, 129, 131, 133-177, 225, 227 Fatalistic necessity, 184-185 Fauconnier, G., 224 Fine, ., 226-227 Rew, Α., 90,100,192 Focus, 59-60, 108, 112, 123 Formal interpretation, 80-81 Formalism, 64-65, 67, 81, 222 Franzen, W., 224 Frede, D., 184 Freeman, D.H., 65 Frege, G., 65, 73, 114, 221-222, 224 Function, 91 Gazdar, G., 164 Geduldig, G., 222 Generic, 6, 129, 188, 190, 203-213 Genetic reflection, 31, 59-60 Glethmann, C F . , 191, 221 Goble, L.F.„ 183 Gochet,P., 124,217 Goodman, N., 191-193, 225-227 Grandy, R.E., 221 Greenbaum, S., 226 Grice, 6, 41-43, 48-49, 110, 156, 190 Haack, R., 75,217 Haack, S., 21, 24, 65-66, 70, 75, 79, 124, 217-218, 221-223, 225 Hacking, I., 223 Haiman, J., 208 Hamilton, W., 222 Hamlyn, D.W., 182,219

INDEX

Hare, R.M., 46,54 Harre, R., 1,65-66,74 Hasenjaeger, G., 76 Hazen, A.P., 24 Hegel, G.W.F., 119 Henle, M., 70 Herzberger, H.G., 157 Hilpinen, R., 182 Hintikka, J., 23,26,225 Holism, 121-124,224 Horn,L.R., 110,224-225 Husserl, E.G.A., 73-74, 219, 221 Hypervalue, 154-155 Idealism, 9 'if ... then', 3, 6, 77, 90, 129-130, 189-213, 225. See also Conditional; Implication Imperative, 4, 6, 50-55, 161, 218 Implication, 3,26,32,56,85,121,164-165, 189-214, 225-226. See also Conditional; 'if ... then'; Material implication; Strict im­ plication; Sufficient condition; Variably strict implication Impossibiüty, 4, 129, 133, 177-182, 211, 225 Impossibility condition, 98-99, 116 Indeterminacy, 4,50-51,115-116,123,129, 133-177, 180, 204-211, 219 Indicative, 190, 202-211, 226-227 Induction, 89, 191 Inoue, K., 208 Instantiation, 92, 97, 116 Instrumentalism, 14-15, 24, 38, 65-67, 69, 74, 217, 220-221 Intended meaning, 42-43, 49, 57, 59 Intension, 5-6 Intention, 3,18,27-28,33-38,42-44,48-49, 56, 219 Interactive device (ID), 27, 31-35, 37 Internal, 168-169, 171-172, 175, 225 Interrogative, 4, 6, 50-55, 103, 220 Intuition, 7 Ishiguro, H., 23,199 Iterated modality, 181, 183-184 Jackson, F., 198 James, W., 59 Janus scale, 140-141 Jeffrey, R.C., 190 Joachim, H.H., 119 Juhos, ., 127,182 Kambartel, F., 192

253 Kamlah, W., 182,217,223 Kant, I., 221 Karttunen, L., 164, 212, 225, 227 Kay, P., 17 Kempson, R., 164,212 Krige, J., 221 Kripke, S.A., 7, 23-24, 156-157 Kroy, M., 23 Kuhn,T.S., 1 König, E., 224 Langford, C.H. 182, 191 Lauerbach, G., 192, 207, 212 Leech, G., 226 Leibniz, G.W., 23, 114 Lewis, C L , 18-19, 26, 114, 182, 191, 200, 218 Lewis, D., 23, 184, 190-191, 198-202, 212213, 226-227 Liar Paradox, 4,171-177. See also Strength­ ened Liar Paradox Lie, 46-47 Linguistic meaning, 47-50, 105 Lipps, T., 65 Literal meaning, 110, 130, 155-156, 166167, 169, 188, 204-208, 211 Lloyd, A.C., 227 Logical atomism, 5, 6, 13, 118 Lorenz, W., 5 Lorenzen, P., 182, 217, 223 Lowe, E.J., 227 Lowerbound, 140-211 Lycan, W.G., 192 Lyons, J., 46,54 Lukasiewicz, J., 75-76, 184, 222, 225 MacColl, H., 191 Mackie, J.L., 16, 24, 89, 94, 101,114-115, 126, 171, 196, 225-227 Many-subvaluedness, 4-5, 100, 117, 218 Marc-Wogau, K., 89 Massey, G.J., 126 Material implication, 6, 71, 190-192, 200, 225 Materialism, 5, 9, 118 Mates, ., 23,63,114,189,223 Mathematics, 24, 62-63, 68 Maximality, 26, 199, 224 Mayo, ., 194 McCawley, J.D., 62, 132, 157, 224 McLean,  J., 199,226-227

254

INDEX

McRae, R.F., 221 Meiland, J.W., 221 Menger, ., 192 Mentalism, 6, 10-12, 20-21, 23-25, 63, 6574,76,78-79, 81-85,105,117,214,217-218, 221,223 Mental state, 4, 28-36, 55-60, 83-85, 219 Merrill, G.H., 24,218 Metalanguage, 90, 133 Metalinguistic theory, 197, 199, 226 Metaphor, 47, 59 Methodology, 1-3, 89 Michael, F. and E., 66 Mill, J.S., 221 Minimal ontology, 3, 9, 20-22, 24, 26, 2930, 85-86, 218 Modality, 26, 129, 177-189, 203, 225 Modal logic, 89-90, 189, 215, 218 Monadicness, 4,144,158,161,163,181-182 Mondadori, F., 226 Monopresuppositional, 169, 189 Montgomery, H.A. 225 Mood, 54 Morris,  W . , 192 Morton, Α., 226 Mundle, C.W.K., 11, 217-218, 220 n-adic, 132-133, 167, 178 Nagel, E., 62,65-66,69-70 Narrow falsity, 142-154 Natural meaning, 42-43 Nauta, D., 67 Necessary condition, 4, 88-99, 129, 159160, 163, 178-189, 225 Necessary and sufficient condition, 4, 8889, 91-92, 97-99, 101, 105-106, 112, 115, 130-131, 159-160, 178, 193 Necessity, 3-4, 7, 15, 129, 133, 177-188, 200-201,209-211,214,225 Nelson, E.J., 191 Nerlich, G., 94 Neurath, O., 120 Nominalism, 9-12, 14-15, 20-21, 24-25, 63, 65-68, 71-73, 76, 78-79, 81-85, 105, 130, 217, 223 Non-natural meaning, 42-43 Non-world, 22,24,29,31,84 Nunn, R.T., 221 Nute, D., 23, 198, 218, 221, 226 Object, 15, 18, 20-22, 27-29, 31-32

Object language, 90, 133 Object of consciousness, 31-33, 35, 59 Occam, W. of, 144 Ontological meaning, 45-46, 105 Ontological priority, 17-18, 22, 218 Ontological truth, 104, 120-121, 223 Ontology, 2-4, 6-7, 9, 14-26, 63, 66-67, 78 Operationalism, 221 Optative, 4, 6, 50-54, 82, 161, 220 Pap, Α., 192 Paradigm, 1,61-62 Parret, H., 1, 17,41,54,219 Particular (vs. generic), 6, 188, 190, 203211 Particular (vs. universal), 30, 83-85, 104 Peirce, C S . , 66,74,223 Performance, 70-71 Performative, 54, 74 Peters, S., 164,212,227 Petrovic, G., 118 Philosophy of action, 3, 36-39, 49 Philosophy of logic, 61-76 Philosophy of mind, 3-4, 9-14, 27-36, 41, 63, 66-67, 78 Phrastic, 46, 51, 58, 77-79, 81-85, 87, 102103, 110 Plantinga, Α., 24, 26, 79, 114, 222 Platts, M., 101, 104, 113, 126, 220, 223 Pluralism, 73, 75 Poland, W., 118 Pollock, J.L. 47, 61, 192, 196, 198, 226 Popper, K.R., 73,217,221 Positivism, 6, 21 Possibility, 7, 26, 115, 129, 203-213, 224225. See also Contingency; Indeterminacy Possible world, 3, 15, 22-26, 78, 84, 107, 114,121-122,126,129,159,167,173,182, 185-188, 197-199, 201, 218, 223 Pragmatic presupposition, 57, 164 Pragmatics, 4, 15, 41, 45, 55-60, 77-78, 8283, 85, 87-88, 117, 130, 214 Pragmatism, 2, 120 Prescriptive mentalism, 65-67, 69, 74, 221 Presupposition, 4, 129, 133, 157-170, 178185, 192-193, 196, 212. See also Pragmatic presupposition; Semantic presupposition Presupposition failure, 157, 168-177 Presupposition indeterminacy, 175, 177 Primitive, 3, 7, 12, 28-29, 89, 99, 101, 111

INDEX

Prior, A.N., 26 Probability, 190 Problematical, 190, 203-212, 227 Promise, 45 Proposition, 19, 46, 77-79, 81-86, 90-91, 102-103, 106, 134-135, 219, 222 Pseudo-dyadicness, 133,169,179,189,193 Pseudo-monadicness, 4,114,133,157,169, 171, 178, 189, 193 Psychological meaning, 46-47, 49-50, 105 Psychologism, 6, 65, 219 Psychology, 59, 70, 110 Puntel, L.B., 101, 118-120, 124, 222-224 Quantification, 185-188,212-213 Quine, W.V.O., 2,7,65-66,113,117,124, 191, 213, 217, 220 Quirk, R., 226 Ramsey, F.P., 101 Realism, 9-15, 20-21, 23-26, 63, 65-68, 7174, 76, 78-79, 81-85, 104, 217-218, 220 Redundancy Theory, 133-136, 224 Reflection, 1, 4-5, 9, 12-18, 24-25, 28-35, 46, 49-50, 55, 57, 59-60, 74, 76, 118, 130, 214-215 Reflectionist Propositional Logic, 78-215 Reflectionist Sentential Logic, 77-78 Refutability, 44-49, 53, 105 Reichenbach, Η., 182, 225 Reis, M., 164 Rescher, N., 24,70,119,184,191,200,218, 220-221, 224, 227 Resnik, M.D., 65 Richards, T., 23 Roëlofs, H.D., 192 Rollin, B.E., 42 Rorty, R., 5 Routley, F.R., 225 Rubinstein, D., 37,219 Russell, ., 65,191,220 Ryle, G., 10-11,73,227 Sanford, D.H., 94 Satisfaction, 87-88,100,115,124-127,161, 222, 224 Scalarity, 129,133,137,154,159-160,205206, 219, 224 Scepticism, 7, 16, 104 Schachter, J.C., 227 Schaff, Α., 5,219 Schiffer, J.R., 48

255 Schiller, F.C.S., 62,220 Schneider, E.F., 227 Scriven, M., 89 Searle, J.R., 28, 36, 41, 49, 54, 89, 219 Self-evidence, 1-2, 6-7, 217 Self-reference, 68, 173-174, 184 Sellars, W., 118 Semantic presupposition, 56 Semantics, 4, 15, 41, 45, 55-60, 77-78, 8283, 85, 130, 214 Sextus Empiricus, 189 Sharvy, R., 94 Simplicity, 2, 85-86, 101 Skyrms, ., 89 Slote, Α., 226 Smart, J.J.C., 225 Smiley, T., 156,182 Snyder, D.P., 183,192 Sobel, J.H. 226-227 Sober, E., 221 Sociology, 37, 192, 219, 221 Sommers, F., 127 Sosa, E., 225 Speaking-as-if, 47-59, 108, 110 Speculative Grammar, 1, 28, 41, 61, 87, 214, 217 Speech act, 3-4, 36, 41-57, 77, 84, 214. See also Basic speech act Stahl, G., 225 Stalnaker,R.C, 23,190,195-196,198-199, 218, 226-227 State, 18, 20-22, 28-29, 31, 33, 218 State of affairs (SOA), 3,15,18-22,26,2835, 46, 78-199, 218-224 Storing device (SD), 27, 31-35 Strawson, P.F., 14, 86, 164, 193, 218, 220, 226 Strengthened Liar Paradox, 225 Strict implication, 71, 191-192, 200-201, 226 Strong descriptivism, 72-74, 76 Subject, 59-60,217 Subjunctive, 190, 203-213, 226-227 Subvalue, 100, 105, 116, 134-135, 146-147 Sudberry, Α., 182 Sufficient condition, 4, 88-99, 102-103, 105106,110,112,115,129,159-160,163, 178, 189-202, 223, 225-226 Supervalue, 117, 140-142 Suppes, P., 191, 193

256

INDEX

Svartvik, J., 226 Swartz, Ν., 24, 182, 218, 225-226 Sorensen, ., 194 Tarski, A., 124-127, 222, 224 Taylor, R., 89 Thinker-talker, 16, 120-121 Three-valuedness, 4-5, 100, 104, 115-117, 133-157, 200, 224-225 Tichy, P., 198 Topic, 59-60,217 Tranoy, K.E., 89 Triadicness, 129, 169, 179, 182, 215 Trivalence. See Three-valuedness Truth, 4,15,28,46,61,80,87,99-127,129, 133-227 Truth condition, 87-88, 100, 131-177 Truth-functional, 5, 131-132, 161, 224 Truth-Teller Paradox, 171, 177 Truth-value, 61,87,100,115-117,120-124, 130-177, 190, 224 Truth-value condition, 131-177, 190 Truth-value paradox, 133, 169-177 Tugendhat, E., 54, 100, 127 Two-supervaluedness, 4-5, 118, 150-151 Two-valuedness, 117, 133, 142, 156, 218 Ullian, J.S., 217 Unbound, 142-165, 178, 192 Undeterminedness. See Indeterminacy Unger, P., 11, 104, 118,224 Unilateral, 139 Univalence, 142

Universal (philosophical sense), 15,30,8385, 104, 219 Universal (other senses), 5, 38, 75, 130 Universe, 26, 107-108, 114-116, 121-122, 126, 159, 167, 173, 185-186, 218, 224 Upperbound, 140-211 Urmson, J.D., 5 Vagueness, 69-70, 130, 193-194, 206-207 Van der Auwera, J., 48,55,57,60,91,156, 171, 180, 207, 214, 217-218, 222, 224-225, 227 Vandeweghe, W., 224 Van Dijk, Τ.Α., 219 van Fraassen, ., 192, 225 Variably strict implication, 191, 200-202 Verworn, M., 222 von Kutschera, K., 227 von Wright, G.H., 87-90, 157, 182-184, 200, 218, 227 Warnock, F., 12 Weak descriptivism, 69, 71-72, 81 Wertheimer, R., 94 Whitehead, A.N., 218 Whorf, B.J., 5 Willard, D., 63,221 Williams, C.J.F., 101, 184, 217 Wilson, D., 164,212 Wisdom, J.O., 63 Wittgenstein, L., 6, 73, 118 Wotjak, G., 5 Wunderlich, D., 54 Zinov'ev, A.A., 66, 71, 221