Meaning, Quantification, Necessity: Themes in Philosophical Logic 0710007590, 9780710007599

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International Library of Philosophy

Editor:

Ted Honderich

A Catalogue o f books already published i n the International Library of Philosophy will be found at the end o f this volume

Meaning, Quantification, Necessity

Themes in philosophical logic Martin Davies

ROUTLEDGE & KEGAN PAUL London, Boston and Henley

CONTENTS

Preface

IX

Part One: Meaning and T r u t h I

Meaning 1

3 3

Theories of meaning

2 Propositional attitudes and actual languages 3 Meaning, convention, and mood II

III

Truth

27

1

Truth conditions

27

2

The marks of truth

33

3

Meaning and truth conditions

37

4

Truth conditions

44

and semantic theories

Structure 1

Structural

52 constraints

52

2 Finiteness and semantic primitives 3 Truth theories and structure 4 Structure and surface syntax IV

7 18

Understanding

57 62 64 73

1 Full understanding of a language 2 Implicit knowledge and linguistics

vii

73 81

Contents Part Two: Quantification and Reference V

VI

VII

Names 1 Names and semantic theories 2 Genuine singular reference 3 Description theories of names 4 Reference and predicates

89 89 94 103 108

Quantifiers 1 Truth and satisfaction 2 Binary quantification 3 Predicate quantification 4 Substitutional quantification

114 114 123 136 142

Descriptions 1 Descriptions and quantifiers 2 Speaker's reference 3 Underspecification and anaphora

149 149 152 160

4 Pronouns 5 Pronouns

and anaphora and speaker's reference

166 176

Part Three: Necessity and Actuality VIII

Necessity

187

1 Necessity and sentences 2 Possible worlds 3 Modality and tense 4 IX

Necessity,

quantification,

187 193 201 and existence

Actuality 1 Actuality 2 Actuality, 3 Actuality 4 Actuality

209 220

and modal logic fixed actuality, and necessity and the contingent a priori and the necessary a posteriori

220 224 230 238

Appendices

243

Bibliography

269

Index

279

viii

PREFACE

I n a certain sense of the word 'introductory', this is an introductory book on philosophical logic. It is not introductory in the (positive) sense that i t would be readily intelligible to someone who had no prior acquaintance w i t h philosophical logic. On the contrary, I have assumed some familiarity w i t h philosophical logic and w i t h elementary formal logic (including, for example, the notions o f theory, rule o f inference, rule o f proof, function, interpretation, and isomorphism). I t is, rather, introductory i n the (negative) sense that nobody who has engaged upon serious research in philosophical logic will find much, or perhaps anything, that is new here. For this is not a work o f originality, but o f synthesis. I have aimed to bring together ideas i n such a way as to provide a final year undergraduate, or a first year graduate student, w i t h the sort o f background which w i l l enable him or her to proceed w i t h serious research. The philosophical logician, or philosopher o f language, raises, and attempts to answer, questions at two different levels. A t the lower level the questions concern the linguistic or semantic function o f particular words, or kinds o f words, in natural or formal languages. The philosophical logician seeks to articulate the contributions made to the meanings o f whole sentences by, for example, names, predicates, quantifier expressions, definite descriptions, pronouns, demonstratives, and adverbs. To this extent he shares a project w i t h other theorists, principally w i t h linguists. A t the higher level the questions concern the theoretical concepts which are crucially employed at the lower level; for example, the concepts of meaning, t r u t h , and semantic structure.

I'rejace

These questions are characteristically philosophical, and by raising them the philosophical logician parts company w i t h some other theorists and, in particular, w i t h the linguist. His answers to questions at the higlier level guide and i n f o r m , and are i n turn informed by, his answers to questions at the lower level. I t has seemed to me natural to begin w i t h questions at the higher level and, amongst such questions, to begin w i t h the concept o f meaning and to proceed thence to the concept o f t r u t h . I t may seem that i n this last matter I am simply reversing an order o f priorities which has been constitutive o f what might be called 'Davidson's programme', and preferring an order o f priorities constitutive o f what miglit be called 'Grice's programme'. But i n fact I do not beheve that there is, or needs to be, any such opposition between these two programmes. In any case, we cannot hope to elucidate the concept o f linguistic meaning w i t h o u t having recourse to some fundamental facts about language use, facts about the propositional attitudes o f language users. A n d once the concept o f meaning is thus elucidated (whatever the details), the concept o f t r u t h can be elucidated i n one more step. For i f a sentence s means that p , then x is true i f and only i f p. A t the lower level the philosophical logician shares a project w i t h the linguist. But even here the philosopher may take steps where the linguist has no desire to foUow. For example, names, being unstructured expressions, are formally rather simple. A name only has to be assigned a bearer. Yet names give rise to deep philosophical questions clustering around so-called description theories o f names, questions which serve as a reminder o f the connection between linguistic meaning and propositional attitudes. For example, again, certain features o f quantifier expressions in natural languages may suggest philosophical questions about, say, the essential features o f quantification. In order to answer those questions, the philosophical logician might consider quantifier expressions o f a kind w h i c h do not occur in natural languages and which, to that extent, have no call upon the attentions o f the linguist.

rrcjacc

philosopher w i t h the resources to dissolve a philosophical puzzle. Such, indeed, seems to be the case w i t h two dimensional modal logic and the puzzle o f truths which are contingent yet knowable a priori. The differences between the philosophical logician's project and the linguist's project should not be underestimated. But they leave a considerable area o f common interest. This common interest has not, perhaps, been quite as fruitful as miglit have been hoped ten or fifteen years ago. (Work on Montague grammar constitutes a single, but sizeable, exception.) One might conjecture that this lack o f fruit is not unrelated to attacks made by many philosophers upon what they regard as the psychological pretensions o f linguistics. Such attacks seem t o me mistaken, and I should have liked to have written a book about philosophical logic for linguists as well as philosophers. Unfortunately, my lack o f the requisite expertise in linguistics has prevented this. But I hope that this book w i l l , at least, not be counter-productive. When 1 arrived in Oxford in 1973, interest in philosophical logic was approaching its peak. The doctoral thesis which is a rather distant ancestor o f this book was written over the next three years, and owed a very great deal to the prior and continuing work o f Gareth Evans, John McDowell, and Christopher Peacocke. This book has accumulated further debts to those three, and to others. I am grateful to Mark Platts for the suggestion that the thesis might be turned into a book, and to Anita Avramides, Jennifer Hornsby, John McDowell, Christopher Peacocke, Mark Sainsbury, David Wiggins, and Stephen Williams for reading greater or smaller portions o f the manuscript and suggesting many improvements. Geoffrey PuUum and Deirdre Wilson gave me helpful advice on linguistics. U o y d Humberstone kindly allowed me to use the main ideas o f a paper which we wrote j o i n t l y . I have made more detailed acknowledgments in the nptes at the end o f each chapter, but i t is not always easy to trace the ancestry o f one's thoughts. So it is virtually certain that at some points I have used other people's ideas in a way that is not acknowledged here, or in the text or the notes. I apologize in advance for any such oversiglits.

There is another way in which the interests o f the philosophical logician and tlie linguist may fail to coincide. A formal system which is set up to reproduce certain features of natural languages may invite a generalization which does not itself answer to any feature o f natural languages. Such a generalization need be o f no concern to the linguist, and on many occasions i t w i l l be o f no proper concern to the philosopher either. But sometimes such a generalization may arm the

I gladly acknowledge a great debt to the Fellows o f Magdalen College for electing me to a Fellowship by Examination and thus providing me w i t h the opportunity to write the book, and to the members o f the Department o f Philosophy at Monash University for inviting me to visit there for the first half o f 1979.

x

xi

During the time that I have been at Magdalen my approach to

Preface philosopliical logic has been influenced by many conversations w i t h Peter Strawson. He has taught me much, and has been an unfailing source o f encouragement and good advice. Some months after this book was delivered to the publisher, Gareth Evans died (at the age o f 34). I n writing this book I have been greatly indebted to h i m , so perhaps i t may be allowed t o stand as a partial testimony to his interest i n , and influence u p o n , graduate students and others over the past decade.

xii

PART ONE

MEANING AND TRUTH

I MEANING

1

THEORIES OF M E A N I N G

The phrase 'theory of meaning' occupies a central place in philosophical logic. Yet that phrase is ambiguous. We need to distinguish: (1)

a (perhaps formalized) theory which, for some particular language L, yields a meaning specification for each well-formed sentence o f Z,; that is, a theory which yields a theorem o f the form s means (in L) that p

(2)

for each sentence s L; a (discursive) theory which illuminates the concept o f meaning; that is, a philosophical account which analyses meaning in terms o f other concepts, or at least reveals the location of the concept o f meaning w i t h respect to other concepts.

Concerning theories o f meaning in the first sense (theories, o f meaning), there are five brief preliminary points to be made. Someone might be concerned that, i f a theory, o f meaning for English is a theory which yields such theorems as 'Everest is a mountain' means (in English) that Everest is a mountain then a theory, o f meaning is something with an air of triviality about i t . The first three points are intended to ease tiiat worry, although the third also has a stipulative component. 3

Meaning

caning and Truth (1)

A theoryi o f meaning is a tlieory about a particular language, the object language (OL), and i t is itself cast in a particular language, the metalanguage {ML). But what the theorems o f the theory state in thcyWL about particular OL sentences could as readily be stated in any o f a host o f languages. What a Frenchman knows when he knows what the English sentence 'Everest is a m o u n t a i n ' means is just what an Englishman knows when he knows what that sentence means, although what a Frenchman would write down as part o f a theoryi o f meaning for English would be a French sentence mentioning that English sentence and so would be different from what an Englishman would write down as part of a theory, o f meaning for English.

(2)

A t h e o r y i o f meaning for one language cast in a second language is very different from a theory of translation for the first language into the second, even i f the language in which the theory o f translation is cast is itself the second language. We must contrast: (i)

'Kungen vet att Stockholm ar en stor stad' means (in Swedish) that the King knows that Stockholm is a large city;

(ii) 'Kungen vet att Stockholm ar en stor stad' means ( i n Swedish) what 'The K i n g knows that Stockholm is a large c i t y ' means (in English). In (i) a certain English sentence is used i n specifying the meaning o f a Swedish sentence. In (ii) that same English sentence is mentioned as a sentence which means the same as the Swedish sentence. What obscures the difference is that, since the translation theory is cast i n English as well as being a theory o f translation into English, anyone who can read the theory probably knows what the mentioned EngUsh sentence means, and so can come to k n o w what the Swedish sentence means. But the difference remains. What is stated by (i) is something knowledge o f which itself suffices (e.g. in a Frenchman) for knowing what the Swedish sentence means. What is stated by (ii) is something knowledge o f which does not itself so suffice (e.g. in a Frenchman). (On this point, see Lewis, 1972, pp. 16970, and Evans and McDowell, 1976, p p . v i i - x i . ) (3)

The meaning specifications provided by a t h e o r y i o f meaning for a language might or might not provide conceptual analyses o f the meanings o f sentences o f that language. A theoryi o f 4

meaning for Swedish in Enghsh miglit specify the meanings o f Swedish sentences containing the present tensed verb 'vet' either by using the simple verb 'knows' or by using the phrase 'has a justified true belief. Using the phrase to provide a conceptual analysis provides greater philosophical illumination, but that illumination is a contribution to epistemology rather than to philosophical logic. A meaning specification may be conceptually unilluminating, in this sense, w i t h o u t being trivial or empty. What is stated by a meaning specification which does not provide conceptual analysis, for a Swedish sentence containing 'vet', is sometliing that most people do not know. It is not built into the notion o f a theoryi o f meaning, as that notion is used here, that the theorems o f such a theory should provide conceptual analyses. (We allow, in the terminology o f D u m m e t t , 1975, that a theoryi o f meaning may be modest rather than full-blooded) The fourth and fifth points are o f an almost wholly stipulative character. The fourth is related to the topic of Chapter I I I . The full significance o f the f i f t h will be seen in Chapter V I I I . (4)

A theoryi o f meaning for a particular language L might have for each sentence o f L an axiom specifying that sentence's meaning. I f L had infinitely many sentences then the theory would have infinitely many proper axioms (that is, infinitely many axioms other than those o f the background logic o f the theory). This would prevent a theorist from listing all the proper axioms, but i t need not prevent h i m from specifying them. There might be an effectively recognizable feature such that the proper axioms are all and only the sentences o f the ML which have that feature. In that case the proper axioms could be specified by a proper axiom schema. As we shall see ". (in Section I I I . l ) there is a project which a theoryi o f meaning . will not serve well i f i t simply has an axiom for each sentence ; o f the OL. But it is not built into the notion o f a theoryi o f meaning, as such, that i t should have only finitely many proper axioms.

(5)

A t h e o r y i o f meaning for a particular language seems to state contingent facts about that language. It seems to be a merely contingent truth that 'Det regnar' means (in Swedish) that i t is raining. Here we face a choice. We could regard a language as 5

Meaning

Meaning and Truth a changeable and indeed changing thing. In that case Swedish is a language which has the contingent property that in i t , at present, 'Det regnar' means that it is raining. But let us instead regard a language as an unchanging and, indeed, unchangeable thing. I t is a consequence of this stipulation that the language which is i n fact at present spoken i n Sweden has the noncontingent property that in i t 'Det regnar' means that i t is raining. A language in which those words did not mean that i t is raining w o u l d be a different language. But we still have room for a contingent fact. I t is a contingent fact that the people o f Sweden speak a language i n which 'Det regnar' means that i t is raining. A quite different language could, i f things had gone differently, have been spoken in that country. Ignoring for the moment b o t h context dependence and ambiguity we could regard a language as an order pair < S^, JO where 5** is a set o f sentences and ^ is a set o f meaning specifications, one for each sentence in Sf. I f < JC> = L and s is a sentence o f y for which Jif specifies. s means that p then s is a sentence o f L and s means ( i n L) that p (cf. Lewis, 1975, p. 3). With the notion o f a theory, o f meaning thus clarified we must face a very natural question. How could any contribution be made to philosophical logic by attending to theories, o f meaning for particular languages? For i f one seeks to construct theories which provide conceptual analyses then one may contribute to philosophy but not specifically to philosophical logic, while i f one seeks to construct theories which do not provide conceptual analyses then one may contribute, at best, to international relations or tourism. One answer to this question is that a contribution can be made to philosophical logic by stating, quite generally, under what conditions a correct theory, o f meaning for a language L is an adequate theory for the language of a given population G; that is, by stating under what conditions the language L is the actual language o f G. (Let us ignore populations w i t h bilingual members.) To state these conditions would be to provide a t h e o r y 2 o f meaning, that is, a philosophical elucidation o f the concept o f meaning.

6

2

PROPOSITIONAL A T T I T U D E S A N D A C T U A L LANGUAGES

The thought that elucidation o f the concept o f linguistic meaning' (meaning in a language) must proceed via an account o f what i t is for members o f a population to speak that language is a compelling one. It does not require us to deny that there are languages which no one speaks. It just requires us to deny that the significance o f the claim that a certain sentence s means that p in a language L can be appreciated independently o f any consideration o f what i t would be to speak/,. I f members of a population G share a language L in which x means that p then those members can use utterances o f x to express their behef that p. This claim is very rough, but refining i t promises to yield us an account, employing the concepts o f the propositional attitudes (behef, desire, intention, and so on), o f what i t is for L to be the actual language o f G. That account will constitute a condition o f adequacy upon any theory which purports to be a theory, o f meaning for the language o f G. Let us call any such condhion of adequacy a prop-j ositional attitude constraint {PAC). [ To see more clearly why there will be some such PAC which a theory must meet w i t h respect to a population, i f that theory is to be an adequate theory, o f meaning for the language of that population (equivalently: i f the language for which that theory is a correct theory, o f meaning is to be the actual language of that population) imagine that a language L = is spoken in a population G. Then the meaning specifications i n J( cz.Xi contribute towards our interpretation o f the utterances, b y members o f G, o f (indicative) sentences in 9" and o f sentences (in other moods) closely related to sentences in Sf; that is, towards our redescription of those utterances as linguistic acts of certain kinds (assertions, commands, questions, and so on) and w i t h certain contents (an assertion that Everest is a mountain, a command that the criminal be found, a question whether it is raining). But the meaning specifications in ^ can make only a partial contribution towards our interpretation o f the utterances o f members o f G, because the meaning specifications do not by themselves license the redescription o f utterances as linguistic acts o f certain kinds. Rather, given an utterance ( o f an indicative sentence x or a closely related sentence in another mood) which is already redescribed(at least provisionally) as a linguistic act of a certain k i n d , a meaning specification {s means that p) licenses the further redescripfion o f the utterance as a linguistic act with a certain content (an assertion that p, a command that p, a question 7

Meaning and Truth

Meaning

whether p). What is needed, in addition to the meaning specifications, is wliat Jolm McDowell (1976, p. 44) has called a theory of force. (A rather different use o f that phrase is made i n D u m m e t t , 1973, p. 416.)

as intentional action must render that behaviour intelligible in the light o f the agent's propositional attitudes. This brief sketch o f an argument to show that there w i l l be some PAC itself suggests a constraint; a constraint which has been stated very clearly by John McDowell (1976, pp. 4 4 - 5 ) :

A theory of force does two things. First, it licenses redescription o f utterances, performed by members of G, as linguistic acts o f various kinds. Second, it specifies for each utterance type a sentence in 6^. The meaning specification for this sentence provides the content o f linguistic acts performed in utterances of that type. We can suppose that the theory of force does this second thing by having as a component an ordered pair where t/ is a collection o f utterance types a n d / i s a function on U such that for each utterance type u, f(u) = , where x is a sentence in y and w is a mood. We can suppose that the theory o f force does the first thing, at least in part, by taking the mood o f an utterance type as a prima facie indicator o f the kind o f linguistic act performed, that is, o f force. But we must have i t clearly in mind that mood and force may come apart in t w o ways. On the one hand, an utterance i n , say, the imperative mood may be advanced w i t h o u t imperatival (or any other) force so that the utterance is not a command (or any kind o f linguistic act at all). On the other hand, an utterance i n , say, the indicative mood may be advanced w i t h imperatival force so that the utterance is a command. Let us, for the moment, leave i t vague just how (in view o f the potential gap between mood and force) the assignment of force is completed. (What seems to be needed, in a full account, is a substantive principle o f classification of linguistic acts into kinds; we shall return to this point shortly.)

PAC 1

Acceptabihty, in a bipartite theory o f the sort constituted by combining a [theory, o f meaning] w i t h a theory o f force, would require that the descriptions of [linguistic] acts which it yields should fit coherently into a wider context, in which the speakers' behaviour in general, including their linguistic behaviour, under those descriptions, and their non-hnguistic behaviour, under suitable descriptions, can be made sufficiently intelligible in the light o f propositional attitudes (centrally, beliefs and desires) whose ascription to them is sufficiently intelligible in the light o f their behaviour, again, and o f the facts which impinge on them.

the utterance is redescribed as an assertion that the door is shut. To spell this out generally, but in detail, would be to contribute to a philosophical account o f meaning (a t h e o r y 2 o f meaning), for i t would be to locate the concept o f meaning (in a language) w i t h respect to the concepts o f assertion, command, question, and so on. A further contribution w o u l d be made by stating (again, generally but in detail) under what conditions licensed redescriptions are correct. The inevitabihty o f some PAC follows from the fact that any redescription o f behaviour

No one could object to what this constraint says, but one might doubt whether i t says quite enougli. For there are two apparent gaps i n the account which would be provided by PAC 1 of what i t is for a theory to be an adequate theory, of meaning for the language o f a populaUon. The first apparent gap is this. The constraint PAC 1 does not itself tell us what propositional attitudes can be attributed to a member o f a population on the basis o f an utterance described as a linguistic act o f a certain kind and w i t h a certain content. One might, for example, think intuitively that assertion is an expression o f behef. But PAC 1 does not itself tell us whether, and i f so under what conditions, an utterance described as an assertion that p can be made intelligible in the light o f the absence, in the speaker, o f a belief that p. Nor does PAC 1 itself tell us whether an utterance described as an assertion that p can invariably be made intelligible in the light o f the presence, in the speaker, of a beUef that p \, for example, i t can be made intelligible in the light o f the presence, in the speaker, o f an intention that no one should know whether he, the speaker, believes that p. What is needed in this case is a fuller specification of the propositional attitudes (beliefs, desires, intentions, and so on) which need to be present i f a speaker is to assert that p. What is needed more generally is a fuller specification o f the (conceptual) connections between propositional attitudes and kinds o f linguistic acts.

8

9

A theory, o f meaning and a theory o f force j o i n t l y license the redescription o f utterances as linguistic acts of certain kinds and w i t h certain contents. I f an utterance o f type u is certified as being advanced w i t h assertoric force and i f f(u) = , then via the meaning specification 'The door is shut' means that the door is shut

Meaning and Truth The need for such a fuUer specification is increased by the fact that mood is, at best, a prima facie indicator o f force. We left i t vague (four paragraphs back) just how the assignment of force is completed. One appealing picture is this. The theory o f force assigns to each utterance type an indicative sentence and a mood, and mood is taken as a prima facie indicator of force. So the theory o f force licenses provisional redescription o f utterances as linguistic acts o f certain kinds. The redescriptions licensed by the bipartite theory (the theoryi o f meaning and the theory o f force together) are then checked against PAC 1, and the assignment o f force is completed by such revisions of the provisional redescriptions as may be required as a consequence o f infringement o f PAC 1. This picture is appealing, but w i t h o u t a fuller specification of the connections between propositional attitudes and kinds o f linguistic acts we cannot tell whether a provisional redescription does infringe PAC 1, and we cannot tell what revision would be required. On the other hand, i f we had such a fuller specification (which would not be specific to any particular language or population) then we could allow that, for any given language and population, a theory of force need have just t w o components: an ordered pair , where/assigns to each utterance type in U an indicative sentence and a mood, and a (prima facie indication) function from moods to forces (that is, from moods to kinds o f linguistic act). •^The second apparent gap is this. There is nothing in PAC 1 about the conventional nature o f language use. So suppose that L =

where . ^ c o n t a i n s just one sentence 'Grrr' and Ji^ specifies that 'Grrr' means that the speaker is angry. Suppose that members of a population G occasionally come out w i t h utterances o f ' G r r r ' to 'get across' the message that they are angry, but that on each occasion o f use they rely upon the audience's recognition that 'Grrr' is hke the sound made by an angry dog. Then it would be odd to say t h a t L is the actual language o f C since, intuitively, members o f G are not using a language at all; the expression 'Grrr' has no linguistic (roughly: conventional) meaning in that population. But it is difficult to see why PAC I would not be met, w i t h respect to the population G, by a t h e o r y i o f meaning for L w i t h just one axiom 'Grrr' means (in L) that the speaker is angry together w i t h some theory o f force. (This example is borrowed from Schiffer, 1972, pp. 119-20.) 10

Meaning A proponent o f PAC 1 might reply that this second gap shows, at most, that PAC 1 provides a necessary but not a sufficient condition o f adequacy upon theoriesi o f meaning. But for two reasons we should not rest w i t h that reply. One reason is that unless we at least indicate how to advance from PAC 1 towards a necessary and sufficient condition of adequacy we can hardly claim to have elucidated the concept o f linguistic meaning. The other reason is that there is no filling the first gap w i t h o u t filling this second gap too because, for at least some kinds o f linguistic act (including assertion), performing an act o f that ? kind by an utterance of a certain type involves trading upon the fact that that utterance type has a certain linguistic (roughly: conventional), meaning i n the population. ' What all this suggests is that PAC 1 needs, ideally, to be augmented by a PAC which provides a necessary and sufficient condition of adequacy; that is, a necessary and sufficient condition for a language to be the actual language o f a population. This would fill the second gap, and could be appealed to in the substantive principle of classification o f linguistic acts into kinds which would fill the first gap. The natural place to look for richer accounts of the actual language relation, and o f kinds o f linguistic acts, i n terms o f propositional attitudes, is in Grice's programme. For two concepts employed there promise the kind of elucidation which we seek, namely the concepts o f utterer's occasion-meaning {s-meaning) and o f convention. (For a list of books and papers in Grice's progranmie, see the notes to this chapter.) Very roughly, a speaker S s-means that p by his utterance (token) X directed at audience A, just in case (1)

S intends that x wiU produce in A an (activated) behef that/?;

(2)

for some feature F oix,S intends t h a t ^ l should recognize 5"s primary intention (the intention in (1)) in part by recognizing x to have feature F;

(3)

S intends thaty4's recognition o f 5"s primary intention should be part o f .4's reason for believing that p ; S does not intend t h a t / I should be deceived about S's intentions.

(4)

Condition (4) includes: (4a) S does not intend that A should think that S lacks the intention in (2); 11

Meaning and Truth

Meaning

(4b) S does not intend that A should think that S lacks the intention in (3); (4c) S does not intend that A should think that S does intend that A should think that ;S' lacks the intention in (2); (4d)

(5) (6) (7) (8)

X y X y

does does does does

not not not not

disbelieve disbelieve disbelieve disbelieve

(4); (3); (6); (5);

A n d perhaps an even weaker notion defined by replacing (3) and (4) by S-meaning something need not rely upon any linguistic (roughly: conventional) significance o f the utterance type. I n the example above, members of G s-mean by their utterances of 'Grrr' that they are angry. The feature F (in condition (2)) i n this case would be: resembling the sound o f an angry dog. Similarly, we could define s-commanding directed a t ^ . We replace (1) by (l')

that p by an utterance x

S intends t h a t x w i l l produce i n ^ the response t h a t ^ brings it about t h a t p ;

and make a corresponding change i n (3). And we can define s-asking whether p . Equally roughly, a convention i n a population G is a regularity R such that i t is common knowledge i n G that (1) (2) (3) (4) (5)

everyone in G conforms toR\ everyone in G believes that everyone else in G conforms to R, everyone in G has a reason to conform ioR, furnished by the belief in (2); there is a general preference in G for general conformity to rather than slightly less than general conformity; there is an alternative regularity R' which would have served G reasonably well.

(This definition is taken directly from Lewis, 1975, pp. 5-6.) The notion o f common knowledge used i n this definition is itself defined as follows. It is common knowledge between x and y that p just i n case (1) (2) (3) (4)

X knows J'knows x knows y knows

that p ; that p ; that knows t h a t p ; that x knows that p; 12

(3') X does not disbelieve (2); (4') y does not disbelieve (1); might suffice (ibid. p. 6). We do not have to concern ourselves w i t h the details o f these definitions to see how they might be used to provide a further i M C . Thus consider the following. PAC 2 A correct theoryi o f meaning for/, = < y J(>\% adequate as a theoryi o f meaning for the language of population G [equivalently: L is the actual language o f G] just i n case there is an ordered pair < U,f> such that for every sentence X i n Sf, i f s means (in V) that p then (i) there is an utterance type M in (/ such that / ( M ) = and there is a convention in G to s-mean that p by audience-directed utterances of type M ; [and (h) i f there are utterance types ul and u? such that/(u.O = and f(u?) = then there are conventions in G to s-command that p by audience-directed utterances of type u! and to s-ask whether p by audience-directed utterances of type u?]. Implicit in PAC 2 is an assumption that, in any theory o f force, the {prima facie indication) function from moods to kinds o f linguistic act will associate s-meaning w i t h the indicative mood, s-connnandingi w i t h the imperative mood, and s-asking w i t i i the interrogative mood.: According to PAC 2 (and upon that assumption) what i t is for a! language L to be the actual language o f a population G is for there to be, for each sentence x o f that language, conventions in G to use utterances o f x, and of closely related sentences in other moods, to perform linguistic acts o f kinds determined by the moods o f the utterance types and w i t h contents .determined by the meaning (in V) ofx. Although we have a definition o f s-meaning, and (in PAC 13

2) a

Meaning and Truth

Meaning

provisional account o f the actual language relation between languages and populations, we do not yet have an account o f assertion. A n assertion that p is, roughly, an act o f s-meaning that/?, i n which the speaker trades upon the fact that the sentence which he uses means that p in the language o f the population. I f s means that p in the language o f the population then there is a regularity o f use o f utterances o f s to s-mean that p (clause (1) o f the definition o f convention), members o f the population beheve that there is such a regularity (clause (2)), and this beUef provides members w i t h a reason to continue to use X to s-mean that p (clause (3)). That suggests the following definition o f assertion. A speaker S asserts that p in his utterance (token) X o f type u directed at audience A just i n case S s-means that p by X and the feature F in clause (2) o f the definition o f s-meaning is:

certain kinds and w i t h certain contents, and these regularities are conventions. I f the regularities are conventions then the s-meanings are acts of assertion, the s-commandings are connnands, and the s-askings are questions. The redescriptions might fail on this first assessment; there might be no appropriate regularities, or there might be regularities which are not conventions. Whether they pass or fail on this first assessment, the redescriptions must also be assessed according to PAC I. For the redescriptions yield, via the definitions o f kinds of linguistic acts, attributions o f propositional attitudes to speakers, and one must judge wlietlier tiicsc attributions make sense o f the total pattern o f behaviour (linguistic and non-linguistic) of the speakers. I f the redescriptions fail on either assessment then one miglit try out other theories o f force. I f that does not help then one must conclude that L is not the actual language o f G. Perhaps some language other than L is the actual language of G. Or perhaps no language is the actual language o f G. (As the example of 'Grrr' indicates, this may be the case even though there are in G regularities o f use o f utterances o f various types to s-mean, s-command and s-ask various things.) Our intuitive grasp upon what it is for a population to use a language will furnish plenty o f counterexamples to PAC 2 as it stands. But there would be httle point in considering even modest refinements i f there were good arguments against the whole project o f augmenting PAC 7 by a PAC o f a broadly Gricean kind. Some writers do indeed take themselves to have such arguments quite apart from any detailed counterexamples. One objection begins from the indisputable point that i f Z, is a language w i t h infinitely many sentences then for any population G there w i l l be infinitely many sentences o f Z which are never used in G. Mark Platts (1979, pp. 89-90) put the objection this way:

being an utterance o f a type such that there is, in the population, a regularity o f use o f utterances o f that type to s-mean that p (cf. Schiffer, 1972, pp. 122-8). Such a definition w o u l d play a part in filling the first gap left by PAC I, for it yields a fuher specificafion o f the propositional attitudes which need to be present i f a speaker is to assert that p. A n d , just as we could define assertion in terms o f smeaning, so we could define command in terms o f s-commanding and question in terms of s-asking.

All this suggests a picture of the way in which one might set out to answer tlie question wiiether a certain language Z is the actual language o f a population G. I f L is to be the actual language o f G then there must be a theory of force which inter alia relates the utterance types used in G to the (indicative) sentences i n L (that is, to the members of y if L = < y J(>). So one might t r y out a provisional hypothesis about an ordered pair and a provisional hypothesis that the indicative mood is a prima facie indication o f s-meaning, the imperative mood is a prima facie indication o f s-commanding, and the interrogative mood is a prima facie indicafion of s-asking. The theory o f force w i t h these two components, and the meaning specifications for L (that is, the members o f J(), j o i n t l y license the redescription o f utterances made by members o f G as linguistic acts o f certain kinds (at this stage, s-meanings, s-commandings, s-askings) and w i t h certain contents. One would assess these redescriptions i n two ways. I f L is the actual language o f G then, according to PAC 2, there are regularities o f use of utterances o f certain types to perform linguistic acts o f 14

The majority o f . . . sentences . . . will never be uttered. They will not therefore be uttered w i t h any i n t e n t i o n s . . . . The obvious move . . . is to hold the mcanhigs o f such sentences to be definable in terms o f hypothetical intentions. . . . But now Grice faces a dilemma: either there is some constraint upon these hypothetical intentions . . . or there is not. I f there is none, the meanings o f unuttered sentences will be left completely indeterminate. . . . There must therefore be some constraint. Generally the constraint upon the hypothetical intentions with which a sentence can be uttered. .. is precisely the meaning of the sentence.. . . the

15

Meaning and Truth attempt to define the meanings o f unuttered sentences i n terms o f hypothetical intentions . . . is hopeless: for it presupposes a prior notion o f sentence-meaning. ( M y itahcs) This objection will be revealed as groundless by the considerations o f Section I V . 1, but we can already see in outline how a reply would go. The problem (briefly) is that we may want to say that x means that p in the language o f G even though no utterances o f a type suitably related to x are ever performed in G; we may want to say that L is the actual language o f G even though some sentences o f L are never used in G. The solution (briefly) is that we shall only want to say the first thing i f x is constructed out o f building blocks which occur in sentences which are used in G, and, what is more, whose occurrence there plays a role (to be specified in Section I V . 1) i n the use o f those sentences in G; and we shall only want to say the second thing i f L is the smallest language which contains all the sentences which can be constructed out o f the building blocks which occur i n , and whose occurrence plays a role in the use of, the sentences which members o f G do use. What constrains the intentions w i t h which members o f G would utter an indicative sentence x (or a closely related sentence in another mood) is not the meaning, in some prior sense, o f x but rather the intentions w i t h which members o f G do utter sentences from whose building blocks x is constructed. (On this problem and solution, see Loar, 1976, pp. 158-60.)

Meaning A second objection to the project o f augmenting ZMC 7 by a Gricean PAC is that PAC 2, and the accompanying definitions o f s-meaning and assertion in terms o f propositional attitudes, encourage the implausible view that one can first determine what a man's propositional attitudes are (merely by attending to his non-linguistic behaviour) and then, via the Gricean definitions o f s-meaning, assertion, and so on, proceed to describe the man as performing linguistic acts o f specific kinds and w i t h specific contents. A n extreme version o f this view is that one can observe a single utterance x and, on the basis o f the non-linguistic behaviour surrounding x and independently o f anything one may k n o w about other utterances, attribute to the utterer sufficiently fine-grained propositional attitudes to permit the redescription o f A: as a linguistic act of a determinate kind and w i t h a determinate and fine-grained content. The implausibility o f this view attaches primarily to the idea that a man's non-linguistic behaviour may put us into a position to assign specific contents to his utterances. For we narrow down the content o f the linguistic act performed in a certain utterance, by looking at the circumstances in which the speaker produces other utterances o f the same type and o f syntactically related types. ( I n practice, we assume that the contents o f linguistic acts are systematically related to the syntacfic form o f the sentence used.) The extreme version o f the view is more implausible stiO, because attribution o f propositional attitudes on the basis o f a limited range of behaviour is answerable to other behaviour o f the same agent.

Acceptance o f a solution along these (briefly indicated) Hues may be encouraged once we notice that the same problem would arise i f one settled for PAC I alone, as Platts thinks we should. Suppose that we have a correct t h e o r y i o f meaning forZ,, and a theory o f force. Are these theories j o i n t l y acceptable for a population G even i f L contains sentences never used in G? The answer furnished by PAC 1 alone is, presumably, that the theories are j o i n t l y acceptable i f the redescriptions which they would license would fit into a wider context in which speakers' behaviour could be made intelligible in the liglit o f propositional attitudes. But whether such redescriptions would so f i t depends upon what Unguistic acts members o f G would perform using those sentences, and that, according to the original objection, is constrained by the meaning o f those sentences i n a prior sense. But what could the prior sense be? The only candidate is the meaning o f the sentences in L. But that can constrain hnguistic acts performed by members o f G only i f Z, is their actual language. A n d whether Z, is their actual language is precisely the original problem.

But although the view is implausible, and although its implausibihty may constitute an objection to certain projects within Grice's programme, we are not committed to the view by accepting ZMC 2 and the definitions o f assertion and s-meaning. Consider first the extreme version of the view. To state in psychological vocabulary a necessary and sufficient condition for an utterance to be an act o f s-meaning that p is not at all to suggest that it can be determined just by looking at that utterance and the immediately surrounding behaviour whether that condition obtains. What has been argued by Jonathan Bermett (1976, pp. 147-8) is that a short stretch o f behaviour may provide overwhelming evidence that a certain man's utterance is an act o f smeaning something, and may provide a reason to ascribe a determinate content to the act. His very plausible example is o f a languageless creature s-meaning that his audience risks being hit on the head by a coconut. But i t is doubtful whether, i f we really restrict ourselves to

16

17

Meaning and Truth the immediately surrounding behaviour, we can be justified in ascribing precisely that content as against, for example, that the audience risks being hit on the top by a heavy, edible object, or even just a pain producing object. We need other behaviour to convince us that the speaker has (and here employs) the concepts o f a head and o f a coconut. A n d this further need should not be obscured by the fact that i t may be very likely indeed that such further behaviour would be forthcoming. As for the view in its less extreme version, it is no part of PAC 2 to deny that, i n practice, the way to proceed w i t h interpretation o f a man's utterances is to t r y out a scheme o f redescription o f those utterances as linguistic acts, and see how the resulting propositional attitude attributions contribute to the project o f rendering the man intelligible, and then to revise those redescriptions in respect o f the k i n d o f linguistic act and o f the content. N o r is it part o f PAC 2 to hold that this is merely the best policy i n practice. I t is consistent w i t h PAC 2 to hold that this practical poUey sustained by a deep conceptual t r u t h about propositional attitude attribution. (See e.g. Davidson, 1974, especially pp. 311-12.)

3

M E A N I N G , C O N V E N T I O N , A N D MOOD

Our intuitive grasp o f what i t is for a language t o be the actual language of a population reveals that the condition imposed by PAC 2 is too severe to be a necessary condition for the obtaining o f the actual language relation. For, according to PAC 2 , i f a language in which a sentence s means that p is to be the actual language of G, then there must be, in G, a regularity of use o f utterances o f s to s-mean that p. But in familiar cases o f language use there are too many linguistic acts which are not acts o f s-meaning, too m a n y examination answers, confessions, reminders, and utterances directed at counter-suggestible audiences (Grice, 1969, pp. 166-8), too m a n y stories, rote repetitions, illustrations, suppositions, parodies, charades, chants, and conspicuously unmeant compliments (Davidson, 1 9 7 9 , ' p H ) . I t is simply not plausible to maintain that there is a regularity o f use o f indicative sentences to perform acts o f s-meaning.

Meaning L is the actual language o f G just in case there is an ordered pair

[and there is a (prima facie indication) funcfion from moods (assigned to members o f t/ by /) to kinds o f linguistic act] such that, for every sentence sinL (that is, in y if L = < y,J(>), if s means (in V) that p then. . . . But we cannot complete the definition shnply by putting together, i n the most obvious way, the concepts o f s-meanmg and of convention (as in PAC 2). We need a new completion o f the definition o f the actual language relation, and w i t h i t a new definition of assertion as a special kind o f s-meaning. To the extent that the condition imposed by PAC 2 is too severe, we need to make use, in a new definition, of a concept weaker than that o f s-meaning (and concepts weaker than those of s-commanding and s-asking), or a concept weaker than that of convention, or both. Grice's programme provides at least two examples of concepts weaker than that o f s-meaning. Let us consider those first. A speaker S s-means* that p by his utterance (token) x directed at audience A, just in case (1*) S intends thutx w i l l produce in A an (activated) belief that S believes t h a t p ; (2*) for some feature Fofx,S intends that A should recognize S's primary intention in part by recognizing ;c to have feature F; (3*) S intends t h a t ^ ' s recognition o f iS's primary intention should be part o f ^ ' s reason for believing that S believes that p; (4*) S does not intend that A should be deceived about S's intentions. (We are not strictly jusfified in saying that s-meaning* is a weaker concept than s-meaning, since we have not shown that all cases o f smeaning are also cases o f s-meaning*. Nor is i t obvious that it can be shown.)

We can leave the definitions o f s-meaning and o f convention intact, and we can leave the general form o f the definition o f the actual language relation intact. The definition w i l l begin

The concept o f s-meaning* is usually brouglit in to meet the fact that examination answers, confessions, reminders, and utterances directed at counter-suggestible audiences are not cases o f s-meaning (see e.g. Grice, 1969, p. 171). I t is not ahogether clear that all o f these (that all confessions, for example) are cases o f s-meaning*. A n d it is not altogether clear that it would not be preferable to notice the element o f ritual in at least some o f these cases and to describe them as ("derivative) cases in which there is a pretence o f s-meaning. But, in

18

19

Meaning and Truth

Meaning

any case, there are stiJl too many hnguistic acts which are not acts o f s-meaning and not acts o f s-meaning* either. Even i f we a l t e r / M C 2 by replacing 's-mean' with 's-mcan*', the condition which is imposed upon the use o f indicative sentences is still too severe to be a necessary condition for the obtaining o f the actual language relation. S-meaning and s-meaning* are b o t h instances o f a more general notion. I n each case there is a propositional attitude \IJ such that a speaker's primary intention is that the audience should i// that p. So let us define the quite general notion o f weak-s-meaning (ws-meaning). A speaker S ws-means that p by his utterance (token) x directed at audience A, just in case there is some propositional attitude ip such that

ws-commanding. Then, armed with those three concepts, and with the original concept o f convention, we can give a new definition o f the actual language relation.

(wl) (w2) (w3)

5 intends t h a t x w i l l produce inA a [p t h a t p ; as ( 2 * ) ; S intends t h a t ^ ' s recognition o f 5"s primary intention

(w4)

as ( 4 * ) .

siiould be part ofA's

reason for i//-ing t h a t p ;

(For some values of'i//' the w o r d 'reason' i n (w3) may be inappropriate, and may have to be replaced. I n general, one might read 'basis'.) We need to define appropriate generalizations o f the concepts o f s-commanding and s-asking, too. A definition o f ws-commanding might begin as follows. A speaker S ws-commands that p by his utterance (token) X directed at audience A, just in case there is some propositional attitude \p such that (wl')

S intends that x w i l l produce i n ^ a i// to bring it about that p;

Given that beginning, we could easily fill in the other clauses ( w 2 ' ) (w4'). But s-commanding, as it was defined earlier, is not obviously an instance o f this general notion. I n order to make i t so, we need to replace the clause (l')

S intends that x w i l l produce in A the response that A brings it about t h a t p ;

with (l")

S intends that x wiU produce i n A an intention to bring i t about that p ;

So let us suppose that this alteration is made, and that the concept o f ws-asking is defined analogously to the concepts o f ws-meaning and 20

PAC3

L is the actual language o f G just in case there is an ordered pair such that for every sentence s in L, i f s means (in L) that p then (i) there is an utterance type u in U such t h a t / ( M ) = and there is a convention in G to ws-mean t h a t p by audience-directed utterances o f u; [and (ii) i f there are utterance types u! and u? such that /(«.') = and f{u?) = then there are conventions in G to ws-command that p by audience-directed utterances o f type u! and to ws-ask whether p by audience-directed utterances of type u?].

Along w i t h this new definition o f the actual language relation we have a new definition o f asserfion. A speaker S asserts that p in his utterance (token) X o f type u dhected at audience A just in case S s-means that p by x and the feature Fin clause (2) o f the definition o f s-meaning is: being an utterance o f a type such that there is, in the population, a regularity o f use o f utterances o f that type to ws-mean that p. A n d just as we define assertion as a kind o f s-meaning, so we can define saying that p as ws-meaning that p in which F is that same feature. The concept o f saying is very much more general than the concept o f assertion, and i t is a concept which, intuitively, we need. For many linguistic acts which are performed using indicative utterance types, and which involve trading upon the fact that an utterance type has a certain linguistic meaning i n the population, are nevertheless not assertions. Thus, for example, an utterance o f the sentence 'The door is shut', performed w i t h the overt intenfion o f g e t t m g ^ to believe that S desires that A bring i t about that the door is shut, would count as a saying that the door is shut but not as an assertion that the door is shut. A n d the same can be said o f ironic statements, and o f many jokes (Peacocke, 1976, p. 184): I f i n response to a remark that one's tape recorder is malfunctioning, another replies 'Nixon w i l l be pleased to help you w i t h any difficulties y o u have w i t h the "Erase" b u t t o n ' as a joke, he does strictly and hterally say that N i x o n w i l l be pleased to . .. etc. But he does not assert that N i x o n w i l l be pleased . . . etc. 21

Meaning

Meaning and Truth To the extent that it avoids tlie problem that there are too many linguistic acts which are not acts of s-meaning (or of s-meaning*), PAC 3 is an improvement over PAC 2. Indeed, PAC 3 avoids that problem to such an extent that it allows, at least as a theoretical possibility, that a population could have a language L as their actual language even though members of the population never used sentences of L in acts of s-meaning (or of s-meaning*) at all. This theoretical possibility might be important i f we were to cease ignoring populations with bilingual members. For a population might use two languages, one of which was reserved for use in stories, rote repetitions, illustrations, suppositions, parodies, charades, chants, and conspicuously unmeant compliments. And we should want to allow (in a fully general account) that eacli of the two languages was an actual language of tliat population. There is, however, a problem with PAC 3, for it allows that an utterance type may be classified as indicative even though there is no use of utterances of that type to perform acts of s-meaning (or of s-meaning*), and that is not obviously consistent with the intuition that the use of utterances of indicative types to perform acts of smeaning (or perhaps, of s-meaning*) is, in a certain sense, the norm. (Similarly, the use of utterances of imperative and interrogative types to perform acts of s-commanding and s-asking, respectively, is the norm. To be the normal use. in this sense, is not to be the usual or statisticallv- most frequent use (cf. Dandson. 1979. p. 11).) We have akeady seen how an utterance of The door is shut' might be an act of ws-meaning (a saying that the door is shut) which is also classifiable as an act of ws-commanding. It is a theoretical possibiHty that, in a certain population, all acts of ws-meaning should be acts of ws-commanding. So suppose, for a moment, that in a certain population this is so, and that for each sentence s ofL there are two utterance types Ui and which can be used interchangeably. For all that PAC 3 says, one of «, and is indicative and the other is imperative. For all that PAC 3 says, different moods are used quite indifferently. And this goes against our intuition. We can approach the same point from a slightly different direction. It is miphcit in PAC 3 that, in any theory of force, the (prima facie indication) function from moods to kinds of linguistic act will associate ws-meaning with the indicative mood, ws-commanding with the unperative mood, and ws-asking with the interrogative mood. It seems to be a matter of practical necessity that, in any population, the syntactic form of a man's utterance should constitute, for an audience, 22

prima facie evidence as to what more specific kind of linguistic act is being performed. What is implicit in PAC 3 is, that if, in a certain population, the indicative mood constitutes, for an audience, prima facie evidence that an act of s-meaning is being performed, then that is a quite superficial feature of the linguistic behaviour of that population. And this is counter-intuitive, since it is some such facts as that the indicative mood constitutes, for an audience, prima facie evidence that an act of s-meaning is being performed that provide the conceptual anchoring of the various moods. If a mood is to be the indicative mood then it should be the case either (i) that, in the population, that mood constitutes, for an audience, prima facie evidence that an act of s-meaning is being performed, or else (ii) that, for some relatively specific kind of linguistic act which is more naturally regarded as derivative from s-meaning than from scommanding or s-asking (such as s-meaning*), that mood constitutes, for an audience, prima facie evidence that an act of that kind is being performed. In a similar way we could spell out what it is for a mood to be the imperative mood, or the interrogative mood. Let us say that ^ is a good mood function just in case ^ is a function 1 from moods to pairs andg (m) = < / : , , ATj> tlien (a) tliere is a convention in G to Ki tfiat p by audience-directed utterances of M; and (b) an audience-directed utterance of u constitutes, for the audience, prima facie evidence that an act of A^2-ing is being performed. In most cases tliere will be some mood m such that for every sentence s in Z, there is an utterance type u for which f{u) = ; namely, the indicative mood. Such a mood might be said to be comprehensive. It is not required by PAC 4 that any mood be comprehensive. The definitions of assertion and of saying can remain as they were after PAC 3 save that we shall now require that the utterance be in the indicative mood. This has the (intuitively pleasing) consequence that assertion is the norm for saying (see again Peacocke, 1976, p. 184). Doubtless there are objections which could be raised agaimi PAC 4. Doubtless further refinements are needed. (For example, something needs to be said about the way in which audience-directed utterances in certain moods constitute prima facie evidence that linguistic acts of certain kinds are being performed.) But let us conclude this section by doing two things. Let us, first, recall the two apparent gaps in the account provided by PAC 1 and, second, note briefly some other ways in which one might provide a definition of the actual language relation. The two apparent gaps were these. The constraint PAC 1 does not itself tell us what propositional attitudes can be attributed to a member of a population on the basis of an utterance described as a linguistic act of a certain kind and with a certain content. And there is nothing in PAC 1 about the conventional nature of language use. The definitions of s-meaning, assertion, saying, and the rest go some way towards filling the first gap (see also Schiffer, 1972, Chapter IV). The definition of the actual language relation fills the second gap. And in fillhig those gaps we have introduced just one complication into the picture. Because linguistic acts of a certain kind may constitute the normal use of an utterance type without constituting a regular use, we have had to allow that a mood is associated with two kinds of linguistic act, one less specific and one more specific. Here, finally, are three other ways in which one miglit provide a definition of the actual language relation. 24

Meaning (1) The definitions PAC 2, PAC 3 and PAC 4 all involve the idea of conventions to perform linguistic acts of various kinds, where the kinds of linguistic act are defined in terms of intentions about intenUons. According to the definition of convention, language users have knowledge about intentions about intentions, of a quite complicated sort. So one might try to provide a definition of the actual language relation which does not involve the attribution of quite such complicated knowledge to ordinary language users. One might, in particular, require only that there be a convention to use utterances of a certain type with the intention, for some propositional attitude i//, to produce in the audience a i// with a certain content (and to do this without any intention to deceive the audience about one's intentions). It is plausible that one could argue that i f a speaker were to make an utterance with such an intention, and if the presence of the convention constituted part of his reason for using an utterance of that type, then the speaker would perform an act of ws-meaning (cf. Lewis, 1969, pp. 152-9). (2) Although there is no regularity of use of utterances of 'The door is shut' to s-mean that the door is shut, an utterance of that sentence does count, for an audience, as prima facie evidence (i) that the speaker s-mcans tiiat the door is shut, and (ii) that the speaker believes that the door is shut. One might provide a definition of the actual language relation which requires not common knowledge about intentions about intentions, but instead, common knowledge that audiences take utterances as prima facie evidence about speakers' beliefs. (For this kind of definition, see Peacocke, 1976.) (3) The condition imposed hy PAC 2 was too severe. We need to make use, in any new definition, of a concept weaker than that of s-meaning, or a concept weaker than that of convention (or both). In PAC4 we used the concept of convention and a concept weaker than that of s-mcaning (namely, ws-mcaning). One might provide a definition of the actual language relation by using a concept weaker than that of convention. In particular, one might borrow from Grice the concept of having a certain procedure in one's repertoire, and require only that members of a population have the use of certain utterances to s-mean certain things in their repertoire (see Grice, 1968 and Schiffer, 1972, pp. 132-6). 25

Meaning and Truth

II

NOTES In this chapter I am indebted to conversations with Anita Avramides, Simon Blackburn (particularly in the final paragraph at (1)), Christopher Peacocke (particularly concerning the theory of force), and Peter Strawson. At many points I have followed Peacocke, (1976); my definition of weak-s-meaning, for example, is based upon Peacocke's definition of saying (p. 1 86). Some fundamental books and papers in Grice's programme are these: Grice (1957), (1968), and (1969); Strawson (1964a) and (1970a); Schiffer (1972); Lewis (1969) and (1975). Bennett's paper (1973) and subsequent book (1976), and Searle (1969), have also been influential. For a discussion of Strawson (1970a) see McDowell (1980) and Strawson (1980). For a discussion of Lewis (1969) and (1975) and, in particular, an objection to clause (5) in the definition of convention, see Burge (1975). For the purposes of exposition I have ignored the fact that in many Hnguistic acts the expression used is, strictly speaking, not grammatical. Thus, when I say, for example, that the actual language of a population contains the sentences which members of the population use, I do not wish to be taken to be denying that specification of the class of (grammatical) sentences which members of the population use already requires syntactic theorizing.

TRUTH

1

TRUTH CONDITIONS

If the philosophical account of meaning which was barely outlined in Chapter I were made fully general and fully detailed then it would constitute a map of a certain region of conceptual space, namely a central tract within the broader area which is the territory of philosophical logic. It is certain that the concept of truth lies in that region, and yet its location would not be revealed by the map, for the account in Chapter I did not appeal to that concept. This omission holds the promise of elucidation. If we can say where truth is related with respect to meaning then the account of meaning will furnish an account of truth. And it is not difficult to state the location of truth. For any language L = < S^, Ji> the extension of the predicate 'is true (in Z,)' is a subset of 9' determined by the rule {T) From: s means (in L ) that/? infer: s is true (in L) iff p (where ' i f f abbreviates 'if and only i f ) . The converse of (J) is not an acceptable rule. This is particularly clear (a) i f ' i f f is read as the material biconditional. From s means (in L) that snow is white we infer by (7) X is true (in L) iff snow is white. Using the undoubted truth

26

27

Meaning and Truth Snow is white i f f the earth moves we can proceed thence to s is true (in L) i f f the earth moves. And from that the converse of (7) would yield a falsehood. The converse of (7) is no more acceptable (b) i f ' i f f is read as a strict or modal biconditional, expressmg broadly logical equivalence (see Plantinga, 1979, p. 2). For by (7) and the truth

Concernmg theories, cf truth, we can make five preliminary points corresponding to those we made concerning theories, of meaning at the beginning of Chapter I . (1) A theory, of truth is a theory about a particular object language (OL), cast in a particular metalanguage (ML). But what the theorems of the theory state in that ML could be stated in other languages. (2) There is a world of difference between (i) 'Snon ar vit' is true (in Swedish) iff snow is white

Snow is white i f f (snow is white and 12^ = 144) we obtain

and (ii) 'Snon ar vit' is true (in Swediili) iff 'Snow is white' is true (in English).

s is true (in L) i f f (snow is white and 12^ = 144) from which the converse of (T) would yield a falsehood. (It might be thought that on this second reading of ' i f f i is true (in L) i f f snow is white is itself false, since s could have meant that snow is black, foi example. But recall that a language in which x means that snow is black is a different language from L in which s means that snow is white (cf. Wallace, 1972,p.242 and 1975a, p. 57; Baldwin, 1975, p. 84; Peacocke, 1978,p.477).) Corresponding to these two readings of ' i f f there are two notions of a truth condition: (i)-c.material truth condition, and (ii) a strict truth condition. The unacccptabiUty of the converse of (T) on either reading of ' i f f shows that for the corresponding notions of truth condition it is not a sufficient condition for s to mean (in L) that p, that a truth (in L) condition for s is that p. For these two notions of truth condition it is false that 'to give truth conditions is a way of giving the meaning of the sentence' (Davidson, 1967, p. 7; for a retraction see Davidson, 1973a, p.325; see also Section II.3). Adding rule (7^ to a theory, of meaning for a particular language is one way of providing a theory, of truth for that language. In general a theory, of truth is a (perhaps formalized) theory which, for some particular language L , yields a truth condition specificaticn (material or strict) for each well-formed sentence of L ; that is, a theory which yields at least one theorem of the form s is true (in L) iff p

It would not be correct to mark the contrast by saying that what is stated by (i) is something knowledge of which itself suffices (e.g. in a Frenchman) for knowing what the Swedish sentence means. For it clearly does not so suffice. But what is stated by (i) is something knowledge of which does itself suffice (e.g. in a Frenchman) for knowing that the Swedish sentence does not mean, for example, that snow is black. What is stated by (ii) is something knowledge of which does not itself suffice for even that. (See again, Evans and McDowell, 1976, pp. vii-xi.) (3) It is not built into the notion of a theory, of truth, as that notion is used here, that the truth condition specifications which it yields as theorems should provide conceptual analyses. (4) It is not built into the notion of a theory, of truth, as such, that it ^ o u l d have only finitely many proper axioms. (5) BecauJwhat a certain sentence means in a language Z, is a non-contingent property of / we can assign to sentences strict truth (in L) conditions. But not just any material truth condition specification can be elevated to a strict truth condition specification. If, for example, a sentence x means (in L) that snow is white then (reading ' i f f as the material biconditional) we have both s is true (in L) i f f snow is white and s is true (in L) iff the earth moves

for each sentence s of i . 28

29

as correct (material) truth condition specifications. But, i f ' i f f is mstead read as a strict or modal biconditional, only the first of these is a correct (strict) truth condition specification. A theoryi of truth for a particular language is no more a theory^ of truth (a discursive theory which illuminates the concept of truth) than a theoryi of meaning is a theory2 of meaning. But just as we can ificias lUMjBing spesciSczQaBs yielded by a tbeoiyi of msaning axs correct for the language o f a given population, so we can provide a theory2 of truth by stating, in general, under what conditions the (material) truth condition specifications yielded by a theoryj of truth correctly fix the extension of the truth predicate for the language of a given population. And we have the two raw materials with which to state this. For it is obviously a necessary and sufficient condition for a theory, o f truth 6 to be correct for the language o f a given population G that there be a language L such that L is the actual language of G and 0 is a correct theory, of truth for L. We have (in Chapter I) a (provisional) account of what it is for L to be the actual language of G. And we know what is a sufficient condition for 6 to be correct for Z,(= < £ ^ , ^ > ) , namely that d should have for each sentence s in just one theorem o f the form s is true (in L) iff p and that this should be the result of applying rule (7^ to the meaning specification ui ^ for s. So it is a necessary and sufficient condition for the correctness of 9 that 9 should determine the same extension for the truth (in L) predicate as a theory meeting the sufficient condition; that is, that for each s in 5''the theorems of 9 which are of the form s is true (in L) iff p should be materially equivalent to the sentence of that form which would be a theorem of a theory meeting the sufficient condition. (Similarly, we can state a necessary and sufficient condition for the correctness of a theory which delivers strict truth condition specifications.) Adding rule ( I ) to a theory, of meaning for a language is by no means the only way, or even the most familiar way, of providing a theory, of truth. Let us fix upon a very simple propositional calculus language/,, with just three atomic sentences x,, S2 and X3, where 30

s, means (in Z,,) that snow is white 52 means (in Z,,) that the earth moves 53 means (in Z,,) that grass is blue and with the connectives ' & ' , 'v' and ' ~ ' with their usual meanings. (To avoid any questions about temporal relativity, read 'snow is white' as 'snow is always white', and so on.) Here is the famUiar way to provide a theory, of truth for a language like Z-i. First, to list, for the atomic sentences, the truth (in Z , ) condition spedfications which would be obtained via rule (7): (Tla) (Tib) (Tic)

Si is true (in Z,,) S: is true (in S3 is true (in Z,,)

snow is white the cartli moves grass is blue.

Here '• . This ordered pair would not exist i f ni were not to exist. (Cf. Donnellan, 1974, p. 225.) Given that representation it follows that all singular beliefs concerning « i to the effect that it is Q i liave (he same content. And i f all such behefs have the same content then one ought to be able to substitute co-referring names within hyjierintensional operators (such as 'John believes that') soba vcrilalc. So it may seem that the GSR theorist can make nothing o f (he idea that someone might beheve WviiQinx but not believe that (2]/(2 even thouglwi, = ; ( 2 -

I f the i n t u i t i o n that there can be no illusion o f understanding and no illusion o f belief is to count against the GSR theorist, then the i n t u i t i o n must be supported by an argument. Yet i t is exceedingly difficult to see how such an argument can be given w i t h o u t simply begging the question against the GSR tiieorist and insisting from the outset that (almost) all beliefs are general behefs. A n d the i n t u i t i o n w i l l perhaps seem even less secure i f we consider an analogy between illusion and pretence. Suppose that a group o f people decide to pretend that there is an object w i t h which they have frequent perceptual contact (perhaps, that there is a man frequently to be seen about the village w h o has mysterious powers). They pretend to name the object and pretend to make assertions about i t and t o express beliefs and other propositional attitudes concerning i t . (Perhaps they introduce the name

This supposed difficulty (as presented) depends upon assimilating genuine singular reference to something rather different which might be called direct reference. According to a direct reference theorist meaning cuts no finer than reference in the case o f names; (roughly) the meaning is the object referred to. But the GSR (licorist's opponent may well respond that although genuine singular reference can be distinguished from direct reference, the GSR theorist occupies an unstable middle position between the direct reference theorist on one side and the opponent on the other. For, he may say, i f two coreferring names are to have different meanings then those meanings must be descriptive. A behef about the object which is assigned to both names as their reference must be a behef about the object thought o f as, say, the F. But then the (allegedly singular) belief concerning x

98

99 • '

'1:,

.1

./w.^

Quantification

and

Reference

(thought o f as tlie F), to the effect that i t is thus and so, is nothing other than the belief that the F is thus and so (that is, the behef that whichever object is uniquely F is thus and so). A n d that is a purely general behef. The opponent's response will be seen at its best i f we focus upon a certain familiar example. 'Hesperus' and 'Phosphorus' might be held by a GSR theorist to be two names w i t h the same reference, namely the planet Venus, b u t w i t h different meanings. The opponent's response, applied to this example, is that once one moves away from the (direct reference theorist's) view that the sentence 'Hesperus is not Phosphorus' has the same meaning as (and so expresses the same belief as) the sentence 'Hesperus is not Hesperus', one must introduce some descriptive meaning for the two names, and say that 'Hesperus' has as a component o f its meaning the meaning o f a description 'the IT and that 'Phosphorus' has as a component o f its meaning the meaning o f a description 'the P\, the opponent may conclude, once one has introduced those descriptive components one w i l l have to admit that the behef expressed by 'Hesperus is not Phosphorus' is precisely the (purely general) behef that the H is not the P (that is, the belief that whatever is uniquely H is not also uniquely P). Simon Blackburn (1979, pp. 3 0 - 1 ) has put the opponent's view very clearly. We all k n o w , in these stories, what is going on. The Babylonians v/ere deceived by the separate appearances o f H e s p e r u s . . . . A l l we have to do to k n o w what is going on is to incorporate this i n t o our ascription o f behef: the Babylonians beheved that the tiling (appearhig in way 1) was not identical w i t h the tiling (appearing in way 2 ) . But although the opponent's view can be stated quite persuasively, there are clearly two points at which his response to the GSR theorist would need to be filled out. One is the claim that some descriptive component must be introduced into the meanings o f proper names. The other is the clahn that i f the meaning o f a name has a descriptive component then beliefs expressed by sentences contaming the name are purely general. Neither o f these steps is at all obvious.

Names contents). I t is intuitively sufficient for two behefs concerning the same object (to the effect that i t is thus and so) to have different contents that having those beliefs should involve thinking about the same object in two different ways. ( I n this connection, Frege, 1892, spoke o f differing modes of presentation o f the same object.) A n d it is intuitively sufficient for two beUefs concerning the same object (to the effect that i t is thus and so) to involve thinking about the object in two different ways that those behefs should be systematically sensitive to two different kinds o f evidence (involving that same object). So suppose that the two names 'Hesperus' and 'Phosphorus' are associated w i t h two different ways o f thinking about the planet Venus (or, perhaps better, w i t h two mutually exclusive ranges o f ways o f thinking about the planet Venus). Suppose (what is intuitively sufficient for this) that mastery o f the two names 'Hesperus' and 'Phosphorus' involves two quite different dispositions to form beliefs; a disposidon to form behefs (which one expresses using 'Hesperus') on the basis o f evidence which, as the theorist might put i t , involves the planet Venus as seen in the evening, and a disposition to form beliefs (which one expresses using 'Phosphorus') on the basis o f evidence which, as the theorist might put i t , involves the planet Venus as seen i n the morning. Despite the theorist's description o f these dispositions, there is no evident reason why having such dispositions should involve having, or bringing to bear, the concepts o f evening and morning. So there is no immediate move from the idea that 'Hesperus' and 'Phosphorus' might differ in meaning in this way, to the idea that the meaning o f 'Hesperus', for example, should have as a component the meaning o f 'the heavenly body which appears in the evening'. In fact there is no reason w h y , in order to have a disposition o f the kind we are considering, one must antecedently have in mind a description and judge the relevance o f evidence involving an object according as that object fits or fails to fit that description (see McDowell, 1977, pp. 176-8 and Evans, forthcoming a).

I f two co-referring names are to differ in meaning then certainly sentences which differ only i n which o f the t w o names is used must have different meanings, and so via the actual language relation must be used to express different behefs (that is, beliefs w i t h different

Nevertheless, the opponent might be able to fill the first gap in his response. For i f someone has a disposition to form 'Hesperus' expressed behefs on the basis o f evidence involving Venus as seen in the evening, then ( i t is plausible to hold) that person has aU the conceptual apparatus he needs for the introduction o f a predicate ' / T which applies to any object according as that object appears in the way in which Venus appears on the occasions which are evidentially relevant to 'Hesperus' expressed behefs. So there is a description ' t h e / / ' which, altiiougli it is

100

101

Quantification

and

Reference

not antecedently available, is such that tliinking about Venus i n the 'Hesperus' way is (plausibly) thinking about Venus as the H. We shall call ' H ' a WT predicate. Let us simply grant that, at least i n the case o f this familiar example, the opponent has filled the first gap in his response to the G'.S7^ theorist. Then, to fiU the second gap, he must show that believing concerning Hesperus (that is, concerning Venus), as the H, that i t is thus and so is just beheving that the H is thus and so. Scliiffer (1978, p. 184) claims that, in a case in which the behever beheves that there is a unique H, tliis second gap can be fihed: [S] upposc that Ralph knows that there is just one / / , and beheves Venus to be thus and so under the description 'FT. This behef . . . reduces to his behef that the H is thus and so. f'l have altered Schiffer's example.) This is no argument. But perhaps the opponent may advance an argument as follows. To explain how the belief that Hesperus is Phosphorus can be different from the behef that Hesperus is Hesperus one must reveal the information value o f the first as different from that o f the second. I f this difference is a product o f the difference between the meanings o f the descriptions 'the / / ' and 'the P' then surely the content o f the first behef is just that the / / is the P (that is, that a single object is both uniquely / / and uniquely P). To this argument the GSR theorist may reply that i n general the best way to specify the content o f a behef which a man expresses i n his use o f a certain sentence is to use a sentence which has the same meaning as that man's sentence; to say, 'He believes that . . .' where what fills the gap is a sentence o f the reporter's language w i t h the same meaning as the used sentence o f the behever's language, hideed, this is the only way except in those cases where the beUever is thinking about an object in some relatively specific way and uses, i n the expression of his behef, a proper name which is associated w i t h a less specific way, or a wider range o f ways, o f thinking about that object. In such a case i t might be possible to use an expression (another proper name or perhaps a demonstrative) associated w i t h the more specific way o f thinking about the object, i n order to specify more finely the content o f the man's behef. I n either case (unless the question is to be begged against the GSR theorist) faithful specifications o f singular behefs expressed using proper names will themselves employ proper names or other genuine singular referring expressions. A n d this should 102

Names not create a puzzle unless one is absolutely in the grip o f the ordered pair conception o f the content o f singular behefs. Once one is free from the grip o f that conception (as the GSR theorist is free from i t ) the notion o f a way o f thinking about an object will account for the possibihty that someone may beheve that Hesperus is thus and so w i t h o u t beheving that Phosphorus is thus and so.

3

DESCRIPTION THEORIES OF NAMES

The GSR theorist's opponent is a description theorist. In fact, two kinds o f descnption theorist can be distinguished; the first makes a clear semantic proposal while the second does not. According to a description theorist o f the first kind (such as the opponent described in Section V . 2 ) each proper name has the same meaning as some definite description. This is a clear semantic proposal: for any population which has as its actual language a language containing a name of a certain object there is a description which that object uniquely fits, such that the meaning o f the name in that population is just the meaning o f that description. A description theorist o f this first kind must avoid two putative objections. The first is that the description tiieorist pays too little respect to the unreflective nature o f mastery o f a name. The description which is offered as giving the meaning o f a name must not be such as t o involve the attribution to members o f the population o f a degree o f conceptual sophistication which is cleady not required for mastery of the name. Thus, in the 'Hesperus' case, it would be an error to offer the description 'the heavenly body which appears in the evening'. But at least in tliis case, the description theorist can avoid this first putative objection by offering a conceptually more modest description, perhaps indeed the description 'the ' / / ' (making use o f a predicate furnished by a way o f thinking, or range o f ways of thinking, about the object named, that is, a WT predicate). The second putative objection is thai the description theorist pays too little respect to the tc-salicnce of the _y object which is assigned to a name as its reference. For almost any description 'the F' which the description theorist offers as giving the meaning o f a name c, the sentence '0{c is not F ) ' is cleady true, while '^0(tlie F is n o t / 0 ' 'las a false reading. This objection can be overcome. The technical detaUs must wait until Part Three (see, in particular. Section I X . 3 ) , but i t suffices for now to imagine that a particular kind 103

Quantification

and

Reference

o f definite description beginning witfi 'the*' is tailored to have the property that the t r u t h , even w i t h respect to counterfactual situations, o f 'the* F is thus and so' turns upon how things are w i t h the object which is actually uniquely F. This has the consequence that i f c is a name o f an object which is (actuaUy) uniquely F, then ^0 (c is thus and so)^ has the same t r u t h value as ^0 (the* F is thus and so)^ and (c is thus and so)' has the same t r u t l i value as ' • (the* F is thus and s o ) ' . Tims, in the case o f 'Hesperus' both putative objections can be avoided by offering the description 'the* / / ' as giving the meaning o f the name. The description theorist's semantic proposal is, nevertheless, not credible. For each name he must provide (even i n cases i n which members o f the population are none too reflective about their own sensitivity to evidence) a description 'the F ' which plausibly gives the meaning o f the name in the shared language o f the population (so that, at least, the named object is uniquely F ) , and such that members o f the population beheve that there is a unique F (because i f a member o f the population did not beheve that there is a unique F then he w o u l d not beheve that the (unique) F is thus and so). He then faces a dilemma. Either he looks to a WT predicate, or else he does not. I f he does look to a WT predicate then he faces the difficulty that, to the extent that mastery o f a name requires thinking about the named object i n a particular way, that way may be highly unspecific. Consequently, i f ' F ' is introduced as a WT predicate then it is not generally the case that the named object is uniquely F , and i t is not generaUy the case that members o f the population beheve that there is a unique F . (Concentration upon 'Hesperus' and 'Phosphorus' may obscure this very obvious point. That is w h y those names provide the description theorist's most favoured case.) I f on the other hand he looks to some predicate other tiian a WT predicate then he faces an equaUy serious difficulty. For i f c is a name and ' F ' is not a WT predicate then, in general, the belief which is expressed by 'c i s F ' is a belief which could have been incorrect even though some object was uniquely F . The description theorist is unable to say i n what that incorrectness would have consisted.

Names proposal in that most favoured case; his argument had a serious gap.) So the description theorist might launch a counterattack by claiming that the first horn is itself disastrous for the GSR theorist. For suppose that 'Bert' and 'Harry' are two names o f the same man, each associated w i t h the same highly unspecific way, or wide range o f ways, o f thinking about that man. Then one could believe that Bert is thus and so and fail to believe that Harry is thus and so, by failing to realize that Bert and Harry arc the same man. A n d it seems tiiat the GSR theorist is unable to offer any account o f the content o f the two behefs which explains how someone can have one belief w i t h o u t the other ( c f Kripke, 1979 and Schiffer, 1978, p. 184). This is indeed a puzzle, but not a puzzle which is particulariy relevant to the GSR theorist. 'Bert' and 'Harry' are synonymous names: ex hypothesi they have the same meaning. A man may master each o f these names (know the meaning o f each name) and yet sincerely assent to 'Bert is rich' but sincerely dissent from 'Harry is rich' (not know that they mean the same). This phenomenon, although puzzling, has nothing especially to do w i t h names. I n general it is possible to know the meaning o f each o f two synonymous expressions without knowing that they mean the same. One way o f drawing attention to this phenomenon is to point to the apparent failure o f substitutivity o f synonyms salva veritate w i t h i n such operators as 'John believes that' ( c f Burge, 1978). Some account must be given o f this phenomenon as i t occurs in general, and whatever account is given can be applied to the case o f names. Thus, for example, one might adopt the position that strictly and literally synonyms can be substituted salva veritate in belief contexts, but that when someone reports a man's behef using that man's own language it is usually assumed (because i t is usuaUy correct to assume) that the man would, i f sincere, assent to the sentence used in the specification o f the content o f the belief On such an account the man who believes that Bert is rich believes that Harry is rich. He fails to assent to 'Harry is rich' because he fails to realize that the sentence expresses one o f his behefs. In any case, the counterattack by the description theorist o f the first kind fails, and his semantic proposal is not credible. (See Appendix 4.)

There is a feature o f this dilemma which may suggest a line o f counterattack for the description theorist. For the difficulty raised in the second h o r n o f the dilemma does not apply to WT predicates. Indeed, there are no very obvious difficulties for the description theorist i n his most favoured case, when he does look to WT predicates. (This is not to say that one must accept the description theorist's

A description theorist o f the second kind is not primarily concerned to make a semantic proposal. His theory is primarily a theory about thouglit, that is, about the propositional atdtudes o f individual speakers. His main claim is that there are (almost) no singular beliefs (again an exception may be made for singular beliefs concerning

104

105

Quantification and Reference

Names

oneself or one's present stage, and one's present experiences). I t may consistently (though perhaps misleadingly) be allowed by such a theorist that a man may be reported as beheving, for example, that Whitlam is modest, or even as beheving concerning Wliitlam that he is modest. Such a report wiU be correct just i n case the man has a general belief that the object (or perhaps, an object) which is . . . is modest, and this belief is related in a certain way to the man Wliitlam. The nature o f the required relation may be varied to yield various different description theories o f thought. One possibility is that the relation should be one o f f i t : the descriptive material (fiUing the gap marked by ' . . . ' ) should fit the man Wliitlam. Another possibility is that the relation should be a causal one (a generalization o f the information yielding relation involved in perception): the general belief should stand in a certam causal relation to the man Whitlam. Other possibilities lie between these t w o . In any case, the crucial feature o f a description theory o f thought is that, even i f i t allows a certain kind o f belief ascription which might be called singular belief ascription, such ascription is not ascription o f singular beliefs.

had just the propositional attitudes whicli we in fact have i f certain objects had not existed, a conclusion quite inconsistent w i t h a description theory o f thouglit. It is, o f course, open to a description theorist o f the second kind to offer a different account o f the actual language relation, no longer in terms o f propositional attitudes. But until such an account is forthcoming any description theorist who makes a semantic proposal such as that countenanced by Blackburn wiU seem to have 'ignored the connection between semantics and psychology' (Scliiffer, 1978, p. 175). I f the connection between semantics and psychology (between semantics and propositional attitudes) is respected, then serious difficulties arise for description theories o f thought. Whatever the details o f one's account o f this connection one must make room for tlie idea that in a sincere assertion a speaker expresses a behef, so that the assertion is true or false according as the expressed belief is correct or incorrect. Suppose that someone has had frequent perceptual contact w i t h Whitlam and has thereby built up a dossier, a mixture o f information and misinformation, which he labels w i t h the name 'Whitlam'. Suppose that the descriptive material in the dossier fits a certain Johnson far better than it fits Wliitlam. And suppose that our man sincerely conies out w i t h 'Whitlam is modest'. What has he asserted, and on what does the truth o f his assertion turn? I f the relation which is relevant to singular behef ascription is a relation o f fit then our man may be reported as believing that Johnson is modest and so, presumably, as asserthig that Johnson is modest. The truth o f the assertion depends upon whether Johnson is modest. I f on the other hand the relation is a causal one then our man may be reported as believing that Whitlam is modest and so, presumably, as asserting that Whitlam is modest. The truth o f the assertion depends upon whether Whitlam is modest. The first answer takes seriously (he fact that our man's belief is, according to tlie descnption (lieory, the purely general belief (lia( the object (or perhaps, an object) which is . . . is modest. And i t takes seriously the connection between correct belief and true assertion. But as an answer to the question about assertion the first answer is, as Evans says, 'outrageous'. For i t has the consequence that

A description theory o f thought is not primarily a semantic theory. Blackburn (1979, p. 31) suggests, for example, that semantic questions are questions about a technical notion o f behef expression which is quite unrelated to a theory o f thought: The semantic problem here is to decide whether we should attribute a meaning (or a truth-condition) to sentences in which the name is used. . . when there is nobody to serve as referent. Suppose that we remain faithful to the directly referential account. . . and grasp the nettle: sentences using such a name are given no truth-condition. [ I f speakers use such sentences] then they literally express no beliefs at all. . . . [Tjhis solves the semantic problem. . . b u t leaves the philosophy i n a very embryonic state. It is, however, a mistake to hold that a semantic theory and a theory o f thought are independent. For suppose that someone decides upon the solution t o the semantic problem about empty names which Blackburn countenances. I t foUows that certain sentences o f our language w o u l d not have meant what they in fact mean i f certain objects had not existed. (Indeed, under those circumstances no sentences w o y l d have meant what those sentences o f our language in fact mean.) A n d as we saw in Section V . 2 this leads, via any account o f the actual language relation i n a Gricean spirit, to the conclusion that we would not have 106

i f I was previously innocent o f knowledge or belief regarding Whitlam, and Johnson is wrongly introduced to me as Whitlam, then I must speak the truth in uttering 'Whitlam is here' since 107

Names

Quantification and Reference Joliiison satisfies tlie overwlielining majority o f descriptions I would

at least i n the (arguably central) case o f genuine singular reference to

associate w i t h the name and Johnson is here. (Evans, 1973,pp. 194-5;

medium-sized material objects (chairs, cats, or men). Names go together

1 have altered the example.)

w i t h predicates to form atomic (subject-predicate) sentences. So i t is

The second answer, on the other hand, is a plausible answer to the question about assertion. Suppose that Whitlam is not modest and that Johnson is modest. Then the assertion is false. But the second answer leaves the description theorist unable to give any account o f our man's error in behef which led to this sincere but false assertion. For his belief is the general beUef that the object (or perhaps, an object) which is . . . is modest, and that belief is correct. Conversely suppose tiiat Whillain is modest and thai Johnson is not modest. Then the assertion is true. B u t the behef that the object (or an object) which is . . . is modest is incorrect. I t is certainly the case that our man may beheve correctly that someone is modest; so i f he makes a sincere true assertion then he has at least one correct belief But t o the extent that this fact is allowed to comfort tlie description theorist in this case i t makes his difficulties in the former case more acute ( c f Blackb u r n , 1979, p. 35).

natural to ask whether the semantic function o f predicates is anything like genuine singular reference. To ask this question is not to ask whether predicates are names. It is a familiar point that i f predicates were treated as names then one would be left w i t h o u t an account o f the difference between a sentence and a list. A predicate is, rather, assigned a semantic property which precisely fits i t to go together with a name (or a pair o f names) to form a sentence with a meaning and with truth conditions. This latter fact may suggest an easy answer to the original question. For, it may be said, the assignment o f a semantic property to the predicate 'is modest' does not involve the assigmnent to that predicate o f an object to which i t might stand in a relation analogous to that o f genuhie singular reference, the predicate 'is modest' is merely true o f objects according as those objects are or are not modest. But one must not leap too hastily from the claim that predicates are not names to the claim that predicates

The description theorist may, finaUy, attempt to avoid the diffi-

are not assigned

objects. Certainly a predicate must be

assigned a semantic property o f a k i n d different from that assigned

culties arising from these t w o possible answers by incorporating the

to names. Certainly the assignment o f such a semantic property need

attractive features o f the second answer into the first. He may suggest

not involve the explicit correlation o f an expression and an object.

incorporating into the descriptive material which must f i t an object

But the assignment to a predicate o f a semantic property by which it

(according to the first answer) the predicate 'object which stands in

contributes to the truth conditions o f sentences in which i t occurs,

such and such an information yielding causal relation to my " W h i t l a m "

as for example

labeUed dossier', and he may suggest that fit in respect o f tins predicate {^l)VPil'

be allowed to outweigli lack o f fit in respect o f other predicates. But this is a deeply unattractive suggestion, for the conceptual sophisti-

(/?f/(7))]

can be reformulated as

cation which it requhes o f speakers (by requiring mastery o f the concept

is true

( V - y ) [ r p , 7 ' is true ^ > / ? e / ( 7 ) e

o f a certain, rather closely circumscribed, k i n d o f causal

{x.Qix)]

relation) is very great. What is more, i t is difficult to see how the

in which there is explicit correlation o f an expression and a set (waiving

description theorist can revise the suggestion ( t o avoid this objection)

any difficulties which may arise because o f the vagueness o f predicates),

w i t h o u t either reintroducing the problem that the descriptive material

or as

may fit the wrong object or else smugghng i n t o the descriptive material

( V 7 ) [ ' P i 7 ' is true

Ref{y)

exemphfies being Qi\

a predicate making use o f the notion o f a genuinely singular behef in which there is explicit correlation o f an expression and a property (or an attribute, or a universal). So the original, natural, question can 4

REFERENCE A N D PREDICATES

be asked agam. Is the relation o f a predicate to its correlated set (its extension) or to its correlated property anything like the relation o f

Names refer to objects. The semantic function o f names is that o f

genuine singular reference? Let us consider the set and the property

genuine singular reference, and we have some grasp upon that n o t i o n

i n turn.

108

109

Quantification and Reference

Names

The relation between the predicate 'is modest' and the set o f modest things (call this set 'AT) is strikingly unlike the relation o f genuine singular reference. First, the t r u t h w i t h respect to counterfactual situations o f sentences containhig 'is modest' does not turn upon iiow things are w i t h the set M. I f Whitlam is i n fact modest then Whitlam is a member oi M. But although Whitlam miglit not have been modest, so that the sentence 'Whitlam is modest' comes out false w i t h respect to some counterfactual situations, Whitlam could not have failed to be a member o f M. With respect to counterfactual situations i t is sets other than M which are relevant to the t r u t i i or falsity o f 'Whitlam is modest". What is more, i t is obviously not the case that i f two predicates are correlated w i t h the same set then one can be substituted for the other salva veritate w i t h i n intensional operators. In short, the set correlated w i t h a predicate is not tc-salient. Second, the semantic property assigned to the predicate 'is modest' is indifferent to the existence or non-existence o f the set M. Suppose (for the purpose o f the example) that N i x o n is i n fact modest. Then, since a set's existence depends upon the existence o f its members, i f Nixon had not existed then the set M would not have existed. But intuitively the predicate 'is modest' would have made just the contribution to the meanings o f sentences which i t i n fact makes had Nixon not existed. Corresponding to this i n t u i t i o n via the actual language relation is the striking implausibUity o f the claim that the belief that Whitlam is modest is a belief which i t would be knpossible to have i f N i x o n were not to exist. I n short, the set correlated w i t h a predicate is not e-salient.

introduction o f what is syntactically a name by the ruling 'Let us call whichever set has as members precisely the modest objects " M " ' is similar to the second kind o f introduction. One could adopt such a ruling without knowhig whicli set had precisely those members. What seems to correspond, in the case o f a set, to the perceptual contact which enables one to reidentify a material object is exhaustive knowledge o f the membership o f the set. Such knowledge would make a person sensitive to the difference between that set and others, and would enable a person to use a name whose relation to the set was that o f genuine singular reference. The fact that such knowledge is not required for mastery o f the predicate 'is modest' corresponds to the absence o f e-salience in respect of the relation between a predicate and its extension.

To assign a predicate a semantic property by whicli i t contributes to the meanings o f sentences in which it occurs is not to fit that predicate to play a role in the expression o f singular beliefs concerning a certain set. To sharpen tliis point a little we might reflect upon the introduction o f a name o f a set. I f a name o f a material object is to be introduced then the surest way is to introduce i t via the sort o f perceptual contact w i t h the object which w i l l enable a person using the name reliably to identify the object as the same again, that is, will make a person sensitive to the difference between that object and others. This introduction o f a name w i t h the semantic function o f genuine singular reference stands i n contrast to the introduction o f an expression which has the syntactic form o f a name by some such ruhng as 'Let us caU whichever object is uniquely F " J i m " ' . I n this latter case the introduction does not permit the expression o f beliefs any less general than those which could be expressed before the introduction. The 110

The relation between the predicate 'is modest' and the property o f being modest (modesty) is rather more like the relation o f genuine singular reference. First, the truth w i t h respect to counterfactual situations o f sentences containing 'is modest' turns upon how things are w i t h the property o f being modest. This is so whichever o f two possible decisions one takes as to how finely properties are to be discruninated. One possible decision treats 'property' as co-ordinate w i t h 'proposition', so that two predicates are correlated w i t h the same property just in case they are synonymous. The other possible decision treats differences o f meaning amongst broadly logically equivalent predicates as corresponding to different ways o f tliinking about the same property, so that two predicates are correlated w i t h the same property just in case they are broadly logicaUy equivalent. One's actual decision would be answerable to broader tiieoretical concerns (as perhaps the appeal to properties in scientific explanation). But in either case i f two predicates are correlated w i t h the same property then one can be substituted for the oi\\ex salva veritate w i t h i n intensional operators. In short, the property correlated w i t h a predicate is tc-salient. Second, the semantic property assigned to the predicate 'is modest' is not indifferent to the existence or non-existence o f the property o f being modest. I f there were no such thing as being modest then the predicate 'is modest' would not contribute to the meanings of sentences as i t in fact does. Correspondingly, the behef that Whitlam is modest is a belief which i t would be impossible to have i f there were no such thing as being modest. In short, the property correlated w i t h a predicate is e-salient. The

relation between the predicate 'is modest' and the property o f 111

Quantification

and

Reference

being modest is tlius analogous to the relation o f genuine singular reference whicli would hold between a name ('modesty') and that property. To express the point, one naturally reaches for Strawson's (1959, pp. 146-7) terminology. A name and a predicate may introduce the same object, namely the same property; the difference between the name and the predicate is not i n what is introduced but i n the style of introduction. One must acknowledge, however, that the presence o f e-salience in respect o f the relation between a predicate and a property is simply a product o f the fact that we have no grasp on the existence or nonexistence o f tlie property o f being modest, for example, independent of its being possible or impossible meaningfully to say o f things that they are (or are not) modest. (The thinness o f tliis requirement for existence raises a puzzle over what i t is that philosophers deny when they deny that properties exist.) What corresponds, i n the case o f the property o f being modest, to the sort o f perceptual contact w i t h a material object which makes a person sensitive to the difference between that object and others is just learning what i t is for things to be modest. I t is tliis which makes a person sensitive to the difference between that property and others. Thus, even whUe one draws an analogy ( i n the basic case o f subjectpredicate sentences) between the relation o f genuine singular reference to material objects on one hand, and the relation between a predicate and a property on the other, one cannot fail to be impressed by a disanalogy between material objects and the properties which they exemphfy. ( I t is presumably this disanalogy which prompts the claim that properties do not exist.)

Names A property collects objects into its extension, and one property is distinguished from another just by being a different way o f coUecting objects. I n the case o f sensitivity to the difference between being modest and other properties, there is nothing more to be grasped than the principle o f coUection (and distinction) by which modest objects are collected and unniodest objects excluded. In tiie case o f sensitivity to the difference between one material object and others there is something to be grasped prior to any principle o f collection of properties which a material object may (derivatively) furnish. One has to grasp the notion o f a certain kind o f (contingent) occupant o f space and time.

NOTES In this chapter I am particularly indebted to several conversations with Simon Blackburn and John McDowell. The account of genuine singular reference is essentially that of McDoweh (1977) and (1981). McDoweU (1978) is a reply to Field (1972). See also Davidson (1977b). More generally on the topics of this chapter, see Russell (1918, pp. 241-54), Searle (1958), Donnellan (1972), Kripke (1972), and Sainsbury (1979, pp. 57-94). On the subject-predicate distinction, see Strawson (1959, pp. 137-247), (1961), and (1970b). For what is, in effect, the use o f 'the*' see, for example, Plantinga (1978).

I t might be said: . . . we could view [material] particulars as principles o f distinction among concepts [properties]. I n relation to any given particular at any time, we could sort concepts i n t o those i t exemplified at that time and the rest. For an answer t o this i t is enough to revert to our question o f the form: what ultimately differentiates one particular from another, one general concept from another? Concepts are ultimately differentiated just as the principles o f distinction among particulars that they are. But particulars could not begin to serve as principles o f distinction among concepts unless we had some other way o f identifying and differentiating them. We . . . ultimately differentiate them . . . by their exclusive occupation o f a tract o f physical space-time. (Strawson, 1974a, p. 19.) 112

113

iJuufitiJiers

VI

(yv,)(FiVi

&R,

r,))

( V v , ) ( P i " ^ . & CRv2)Ri

(v^.vi))

(Vv,)(3.;2)(Pi>'i &«.(i'2,

QUANTIFIERS

vi)).

The fact that the connectives have this new role and yet are not ambiguous calls for a degree o f sophistication in a semantic theory and, in parficular, hi a theory of truth conditions. I f we arc to continue

to

regard

the connectives as fundamentally operators upon

sentences then a way has to be found o f deriving their contributions to the t r u t h conditions o f quantified sentences such as ( V v , ) ( / ' , v , ScRiim^,

Vi))

in which ' & ' joins ' F i V , ' and 'RiiiUj,

v^y (which are not sentences

and do not have truth condifions), from the familiar axioms which 1

speak only o f sentences and trutli (see Evans, 1977, p. 471).

TRUTH A N D SATISFACTION

A first thouglit might be this: The languages which we have considered have been syntactically very

'(

simple. I n each case i t has been possible t o give a formahy straight-

(in the domain o f quanfification) is such that i f a name (in />«)

forward theory o f t r u t h conditions and theory o f meaning. I t is time

of that object is substituted for V , ' in 'J\

to consider a quantificational language.

then the result is a sentence which is true (in L(,).

)(PiVi

&Ri

(ifi2, Vi))' is true (in L ^ ) i f f every object (1112, v,)'

Let L(, be a language whose atomic sentences are constructed from the one-place predicates ' P , ' , . . . , '/"lo', the two-place predicates

Here the truth conditions o f a (]uantified sentence are sjiecified in

. . . , '/?io', and the names ' w i . . . , ' w , o ' . Further, Lf, contains the

terms

t r u t h functional connectives ' & ' , ' v ' ,

connective ' & ' is certainly regarded as fundamentally an

a n d F i n a l l y , / . f i c o n t a i n s the

o f the t r u t h conditions o f subject-predicate sentences. The operator

two familiar quantifiers ' V and ' 3 ' together w i t h associated variables

upon sentences. But since

V , ' , V 2 ' , . . . . The syntactic rule which governs the quantifiers can be

not (we may suppose) o f all objects in the domain o f quantification,

stated as foUows. I f yl is a (possibly complex) sentence in which a name

contahis names o f only ten objects and

the trudi condition specificalion is incorrect. Objects whicli arc in (he

c occurs at least once and in which ' v , ' (the / t h variable) does not

domahi o f quantification but which have no name (in Lf,) vacuously

occur, tiien the result o f replacing c at some or all o f its occurrences

meet the condition following 'such that'. One way around (his dilTicuhy is (o iiUroduce, as a (cchnical auxili-

by ' v , ' and prefixing the resultant string w i t h ' ( Vi^,)' or ' ( 3 i ' , ) ' is occurs as a bound variable). In the

ary, an ex(ended language / / conlaining a name o f each object in the

complex sentences constructed hi accordance w i t h this rule the truth

domain o f quan(ifica(ion o f / . , , . Thus / / is (o be a language wi(h (wo

itself a sentence ( i n which

'c,'

have a new syntactic role, for they occur

important features. First, i(s (|uantilier-fiee part is an extension o f the

between (or m the case o f ' ~ ' i n front of) expressions which are not

quantifier-free part o f A,,, in the sense thai / / contains all the predi-

functional

connectives

themselves sentences. Thus, along w i t h P l W l & /?i ( W 2 , W 3 ) (Vw^PiV,

cates, names and connectives o f Lf, w i t h the same meanings. Second, L

contains a name o f each object in the intended doniam o f quantifi-

cation o f Z,6. The idea is then to specify the t r u t h condifions o f

&(3V2)/?l(W2,l'2)

quanfified sentences o f Lf, by appealing to / / . For example, TriLe,Xyi'i)PiP:)^ ( V x ) ( V Y S L * ) {RefiL*,

we have 114

y) = x'^Tr{L\. 115

Quaiiiification

and

Qiicjiilijicis

Rcjercncc

i'Tr ( / - 6 , . . . ) ' abbreviates ' . . . is true (in Z s ) ' - The quantifier '( Vx)' is a quantifier in tlie ML whose domain o f quantification is exactly that o f the OL quantifiers. The quantifier ' ( V 7 e L*)' ranges over names i n L * . I t is made explicit, here and henceforth, that the reference relation holds only relative to a language.) Since the predicate T j ' h a s the same meaning i n L * as inL^, and since biconditionals such as Tr(Le,'Pimr)^Qi>h

the quantifiers are being defined in terms o f their semantic properties in L * . A x i o m (Q2) simply records the other important feature o f L * . iQ3.1)

Ref{L\'m,')

and so on up to (Q4.1)

are assumed to be hiterpretational, we have ( V7 e L') [Tr (L\ 7')

same meanings in / / as in Lf,. Second, the semantic properties in Lf, o f

^ Q, (Ref(L\.

{Q5.1)

{Q3.10),

( Vy&L*)

and so on up to

and

(Vx)id.yeL^Ref(L\y)=x.

so

[Tr {L\ Q,

{Ref{L\y))\

{Q4.10),

(VT.SeZO [Tr{L\ (7,6)1 ) ^ 5x

A n d since L * contains a name o f each object we have

=

on up

iRef(L\y),Ref{L\8))] to

{Q3.10).

('(V7,6e//)'

abbreviates

'(YyeL*)

( V S e Z , * ) ' . ) These are simply the expected axioms for the subjectGiven these i t is not difficult t o derive

predicate part o f Z,6.

TriLe,Xyv,)P,vr) ( V x ) 5 , (x, n , ) .

Just as in the case o f QTO, variations on tiie theme set out here are possible. First, i t is possible (and in fact usual) to replace (S9) and (SIO) by the neater axioms ( Ys) ( V4>) [s satisfies ' ( V v , ) * v , ' ( Ys' i: s) (s' satisfies ''Pr-,' ) ]

{s*it))]

(The quantifier '( V f ) ' ranges over names and

variables.) The axioms {S4.1)-{S4.10)

" (Vx)Si

Given the premise (provided by a theory about sequences) tliat there is at least one sequence we have

Tr (Le,'(

( V s ) ( V f ) [s satisfies 'P,t^

,miy

from which, by the dcfinilioii o f trulli in terms o f satisfaction we have

Atomic predicates are governed by axioms which specify under what

{S3.1)

[x satisfies'( Vv,)Ri(vi

( Ys) ( V4>) [s satisfies ' ( Hi;,) ) ( V y ) [MCorr i'P, Y) ^ f( Vvi)') ((Woman who admires x ) : i ; ; j ' is A m e r i c a n ) ] . The surface sentence Some women who admire most philosophers are American is naturally interpreted as corresponding to a quite different sentence at the level o f input. The use o f the passive 'is admired b y ' is no help. Stress is certainly no help in w r i t t e n English. A n d 'most' does not have a special wide-scope form. I t is i n such cases that natural language users reach for 'such that' or a similar locution. For w i t h the aid o f such expressions impoverishment is overcome. We have Most philosophers are such that some women who admire them are American or O f most philosophers it's true that some women who admire them are American. Interesting questions naturally arise. Is there any semantically significant characterization o f the point at which 'such that' (or a similar locution) is needed in English? Is the point at which such a locution is needed uniform across different natural languages? But such questions w i l l go unanswered here. Let us t u r n from these differences between English and Z-7 and compare the four binary quantifiers which we have so far considered w i t h another, namely, 'more'. Consider the following sentences: Most philosophers are men There are more philosophers than men. 132

Quantijiers The expression 'there are more . . . than . . .' takes two predicates to make a sentence, and i t can be assigned a semantic property by an axiom o f the same form as that for 'MOST'. (V*, [ 7 > ( r ( M 0 R E v,) (v,-; '^v,)'*) ^ ( M O R E x ) (Sat (x, r * i ; , i ) ; S a t (x, '^vi''))] But there are striking differences between the syntactic behaviour o f 'there are more . . . than . . . ' and 'most'. I n English b o t h the places provided by 'there are more . . . than . . . ' must be occupied by comm o n nouns or phrases built from common nouns, whereas only the first place provided b y 'most' must be so occupied. A n d the 'there are' form o f the 'more' quantifier is reminiscent not so much o f the binary 'some' quantifier as o f the one-place quantifier 'there are some . . .'. What is more, in a satisfaction theory ' M O R E ' needs an axiom o f a slightly different form from that for 'MOST'. ( V x ) ( V * , ^ ) [x satisfies ^(MORE v,) ('I'v,-; ^vt)' (MORE s') (x' i X & s' satisfies ''i>Vi''; x' i x & x ' satisfies f ^ v / ^ ) ]

^

On the right hand side o f the biconditional the expression 'x' ^ x' must occur twice (see Humberstone, 1979, p. 176). These differences, though unimportant i n themselves, suggest that there may be a semantic difference between 'most' and 'more' which is w o r t h investigating. This suggestion is correct. To make the difference vivid we should consider first one-place quantifiers. With each oneplace quanfifier Q we can associate a function from pairs o f cardinahties to t r u t h values ( T and F ) such that i f a is the cardinality o f the set o f Fs and b is the cardinality o f the set o f non-Fs then r ( Q x ) f x i is true i f f / g () = T. Thus, for example, '(Yx)Fx' is true just in case b = 0, ' ( ^x)Fx' is true just in case a 0, and (at least in the case where the domain o f quantification is finite) '(most x)Fx' is true just in case a is greater than b. Let us call such funcfions fg 'M-funcfions' (cf. Mostowski, 1957). One way o f generalizing M-functions t o the case o f binary quanfification is to associate w i t h a binary quantifier Q a function fg from pairs o f pairs o f cardinalities to t r u t h values such that i f a is the cardinahty o f the set of Fs, b is the cardinaHty o f the set o f non-Fs, c is the cardinality o f the set o f Gs and d is the cardinality o f the set o f non-Gs, then 133

Quantification '{Qx) (For

(Fx; Gxy

and

Reference

is true i f f / g (,)

= T.

this generalization, see Altham and Tennant, 1975.) But i t is

clear that ' E V E R Y ' , 'SOME', 'MOST', and ' F E W are binary quantifiers w i t h which no such function can be associated. 'We cannot tell whether most Fs are Gs just by looking at how many Fs, non-Fs, Gs and non-Gs there are. We need to k n o w how the individuals involved are distributed across these sets' (Humberstone, 1979, p. 175). I t is equally clear that such a function can be associated w i t h ' M O R E ' , for '(MORE x) Gxy

(Fx;

is true just in case a is greater than c.

A different generalization is needed to cover the four binary quantifiers o f 7.7. With each such binary quantifier Q we can associate a function / g from pairs o f cardinahties to t r u t h values (indeed the same function as was associated w i t h the corresponding one-place quantifier) such that i f a is the cardinality o f the set o f Fs which are also Gs and b is the cardinality o f the set o f Fs which are non-Gs then '(Qx)

(Fx; Gxy

is true i f f / g ()

= T.

In the case o f these quantifiers the cardinality o f the set o f Fs is not directly relevant. The set o f Fs serves only to yield a restriction to a subset o f the set o f Gs and a subset o f the set o f non-Gs. I t is clear that ' M O R E ' is not a quantifier w i t h which such a function can be associated. I t is certainly possible to generalize the original notion o f an M function so as to cover the cases o f 'MOST' and o f ' M O R E ' , and indeed all quantifiers o f any number o f places (ibid.). But the difference between the t w o generalizations w h i c h we have just considered corresponds to a semantic difference between the binary quantifiers of LT, on one hand, and ' M O R E ' , on the other. The binary quantifiers of L ^ are restrictive binary quantifiers; in each case the first place is restrictive w i t h respect to the second place. The quantifier 'MORE' is a pure binary quantifier; neither place is restrictive w i t h respect to tlie other. Quantifier expressions i n English such as 'most philosophers', 'every man', and so on should be seen as semantically complex expressions which result when the first place o f a restrictive binary quantifier is occupied by a restricting common noun. They are restricted one-place quantifiers. I n the limiting case in which the common noun is ' t i l i n g ' the restriction is vacuous. But there is another k i n d o f one-place quantifier expression in English, namely 'there are some . . .', 'there are few . . .', and so on. I t would be a mistake to treat b o t h the 134

binary quantifier 'some' and the one-place quantifier 'there are some' as semantic primitives. Rather 'there are some' might be seen as resulting when the second place provided by the 'some' quantifier is occupied by a predicate ( w i t h the form o f a verb) which is as unspecific as the common noun 'thing', namely the predicate 'is' or 'exists'. (See Strawson, 1974a, pp. 114-15 for an interesting suggestion about the occurrence o f 'there' i n these one-place quantifier expressions.) The similarity between 'There are some Fs' and 'There are more Fs than Gs' suggests, perhaps, that the binary 'more' quantifier is itself not a semantic primitive, and that we might find a restrictive 'more' quantifier. A first thouglit would be that the semantically primitive quantifier is the three-place quantifier i n 'More Fs are Gs than are Hs'. O f the three places provided by this quantifier the first is restrictive w i t h respect to the second and third. But there is another three-place 'more' quantifier in 'More Fs than Gs are Hs\f the three places provided by this quantifier the first and second are both restrictive w i t h respect to the tliird. And there is a four-place 'more' quantifier in 'More Fs are Gs than Hs are A:S'. Of the four places provided by this quantifier the first and third are restrictive w i t h respect to the second and fourth respectively. Thus we can associate w i t h tills four-place quantifier a function / from pairs o f pairs o f cardinalities to t r u t h values, such that i f a is the cardinality o f the set o f Fs which are Gs, b is the cardinality o f the set o f Fs which are non-Gs, c is the cardinality o f the set o f Hs which are A's, and d is the cardinality o f the set o f / / s w h i c h are non-A's, then 'More Fs are Gs than Hs are A s ' is true i f f f(,) =T For f(,)= T just in case a is greater than c. The natural suggestion is then that at the level o f input to a semantic theory for English there should be a single four-place 'more' quantifier ' M O R E " ' . According to this suggestion, the surface sentence More men than women are philosophers w i l l be related, by a simple application o f a (perhaps complicated) deletion rule in the syntactic theory, to the sentence ( M O R E " x) (Man x,xisa philosopher)

philosopher; Woman

at the level o f input. The surface sentence 135

x.xisa

Quantification

and

Reference

More men are plumbers than philosophers w i l l be similarly related to the sentence (MORE'' x) (Man x, x is a plumber; Man x, x is a philosopher) at the level o f input. A n d the surface sentence There are more cats than dogs w i l l be related i n a slightly more complicated way to ( M O R E " x ) (Cat x, x exists; Dog x, x exists). It would remain to connect these uses o f 'more' w i t h those which seem to have nothing to do w i t h quantification, as i n John is more w i t t y than perceptive and, indeed, w i t h comparatives i n general.

3

PREDICATE Q U A N T I F I C A T I O N

I n the quantificational idioms w h i c h we have considered ( i n Sections V I . 1 and V I . 2 ) , two simple but notable features coincide. First, the bound variables o f quantification occupy positions which can be occupied by names, and the axioms stating the semantic properties o f the quantifiers speak o f sentences i n which names (perhaps i n an extended language) occupy the position which is occupied i n a quantified sentence by a bound variable. I n short, the quantification is quantification into name position. Second, the objects some o f which are named by names i n the original language, and all o f which are named by names in the extended language, have the property that the t r u t h o f quantified sentences turns upon the difference between one such object and t w o . Thus, for example, the sentence ' ( H x ) (Gx & Hxy differs from the sentence ' ( a x ) G x & ( a x ) 7 / x ' precisely i n that what is required for the t r u t h o f the former sentence is that a single object ( o f the kind named by occupants o f the position here occupied by ' x ' ) should be b o t h G and H. Similarly, the sentence

Quantifiers (SOME x ) ( F x ; G x ) & (SOME x ) ( F x ; / / x ) precisely in that what is required for the truth o f the former sentence is that a single F object should be both G and / / . In short, the quantification is quantification over those objects. (For this account o f quantification over objects o f a certain kind see Evans, 1975.) I t does not suffice for a batch o f sentences to involve quantification over objects o f a certain kind (in the sense just introduced) that the t r u t h of sentences in that batch requires the existence o f objects o f that k i n d . No doubt the truth o f 'It's raining' requires the existence o f raindrops, b u t a batch o f such feature placing sentences does not involve quantification over raindrops so long as mastery o f those sentences does not require sensitivity to the occurrence, co-occurrence and non-occurrence o f features within the boundaries o f single raindrops or t o relations between raindrops (see again Evans, 1975). I t is natural to ask whether these two features o f the quantificational idioms considered so far are really essential to the semantic nature o f quantification. One way to focus upon the question is to consider two apparent counterexamples to the claim that the features are essential, namely quantificafion into predicate position and subsfitufional quanfification into name posifion. Quantification into predicate position is an apparent counterexample to the general claim that the features are essential for the very straightforward reason that, since predicates are not names, i t is not quantificafion into name position. Substitutional quantification into name position is an apparent counterexample because i t is usually held not to be quantification over objects o f the k i n d named. For, first, a subsfitutionally quantified sentence may be true in virtue o f the t r u t h o f an unquantified sentence in which an empty name (an expression w i t h the syntacfic form o f a name but which is assigned no object as reference) occupies the name position. A n d , second, i t is possible to quanfify substitufionally into name posifions which do not admit substitution o f co-referring names salva veritate, thus producing quantified sentences whose truth turns not merely upon the difference between one object o f the kind named and t w o , but also, perhaps, upon the difference between one way o f thinking about an object and two. We shall reflect upon these two apparent counterexamples in this secfion and the next. The thesis that i t is an essential feature o f quantification that i t be quanfification i n t o name position has been maintained by Quine (1970, pp. 6 6 - 7 ) :

(SOMEx)(Fx;Gx&y/x) differs from the sentence 136

137

Quantification

and

Reference

Consider first some ordinary quantifications: '( 3 x ) {x walks)'

Quantifiers The task of someone who wants to reject the thesis that it is an

which are sensitive to the difference between co-extensive properties.

say that these entities are attributes. . . .

one set and two. There are no contexts in this very simple language

The logician who grasps this point, and still quantifies 'F\y

for the t r u t h o f quantified sentences o f Lg is the difference between

hence t o treat predicates as names o f entities o f some s o r t . . . .

name. The first thing to notice is that the difference which is crucial

is t o treat predicate positions suddenly as name positions, and

theory) w i t h o u t letting go o f the thought that a predicate is not a

instance. . . . To p u t the predicate letter ' F ' i n a quantifier, then,

position is to provide a semantic theory for l.f^ (in particular, a (rutii

position where a name could stand; a name of a walker, for

essential feature o f quantification tliat i t be quantification into name

. . . . Tiie open sentence after the quantifier shows ' x ' in a

Predicates have attributes as their 'intensions' or meanings.. .

What is more, there are no contexts in Lg which are sensitive to the

quantification in Ag is over (in the sense recently introduced) subsets

belong in predicate positions. They belong in name positions.

objects other than objects named in Lg are members o f them. So the

neither. Variables eligible for quantification therefore do not

difference between two sets which differ only in respect of which

and they have sets as their extensions; b u t they are names o f

o f the set o f named objects. The domain of quantification is some set

to an extended language L^g which contains, for each set in the domain

quite unclear is how i t is supposed t o follow that the position o f

surprising, then, that a t r u t h theory for/.g can be provided by appealing

cates are not names o f sets or of properties (attributes). But what is

o f such subsets (perhaps not the set of all such subsets). I t will not be

We are committed (by Section V.4) to agreeing w i t h Quine that predi-

abbreviate 'Z,*g'by '//'.

provided our only grasp upon the concept o f a name, and upon the

extension (that is, its extension in the set o f named objects). Let us

it w o u l d follow i f the accessibility of name position t o quantification

o f quantification, a one-place atomic predicate w i t h that set as its

predicates is not open to quantification (cf. Boolos, 1975). Perhaps

subject-predicate distinction. But there is much else that can be said about names and about the subject-predicate distinction, and indeed that has been said (see Strawson, 1974b, p. 68). To restrict the number o f complications arising, let us consider just quantification into the position of one-place predicates. The language L 4 contains ten one-place predicates and ten names. The language which we shall now consider is an extension o f L 4

containing the

connectives ' & ' , ' v ' , and ' ~ ' , and predicate quantifiers together w i t h associated variables ' F , ' , ' F j ' , . . . . The syntactic rule for the quantifiers is exactly analogous t o that for the quantifiers into name position (Section V I . 1). I f / I is a (possibly complex) sentence i n which a one-

The theory for Z,g is very similar to QTd. In order to simplify the presentation o f the axioms we introduce an abbreviation. Corr (//, (Tr (7 n 'is modest') X is modest)]. Since it is not assumed that the PRef axioms admit even substitution of synonymous names salva veritate, axioms of the same form as this one for 'is modest' can be used for expressions which have the syntactic form of atomic predicates but which create opaque contexts for names. The substitutional quantifier 'E', for example, is governed by an axiom in the statement of which objectual quantification over expressions is used in the ML:

Quantifiers quantification in the ML by a pair of axioms: ( V 7 ) (Ex) PRef (y, x) (Ax)(3y)PRefiy, x). From such axioms homophonic biconditionals are straightforwardly forthcoming. Let us then examine such a truth theory a little more closely first, in the case in which the base language contains empty names, and second, in the case in which the base language contains opaque contexts for names. Consider the sentence '(Evi) V i is modest'. Unless the syntactic form of this sentence is higlily misleading it lias as a semantic constituent the predicate 'is modest'. So the canonical derivation of a truth condition specifying biconditional sliould employ the axiom for that predicate. This fact serves to focus our attention upon that axiom, which appears to offer a uniform account of atomic sentences of two kinds: atomic sentences containing names and atomic sentences containing empty names. As semantic theorists with some grasp upon subject-predicate sentences containing (non-empty) names we may well doubt that any such uniform account is genuinely possible, and in particular we may doubt that there is any such notion as pseudoreference which includes the reference relation between names and objects as a special case. In short, so far from providing an answer to our question about quantification this case simply raises a host of problems of its own. To say this is not to deny that one might simply award the sentence 'Alpha is modest' truth conditions (and so a truth value) by fiat, nor that one might introduce a context C for predicates such that ^C(is modest)' is true just in case for some name 7, 70 'is modest' is true. Of course one can do those things. But this fact highlights the difference between what is not, and what is, here in question. It does not help towards an answer to our question that C can be introduced as an abbreviation of the context for some name 7,70 ' . . . ' is true.

And objectual quantification over expressions is related to substitutional

Let us henceforth leave empty names out of consideration. The case in which the base language contains opaque contexts for names includes two subcases corresponding to two kinds of opacity. On one hand, an expression with the syntactic form of an atomic predicate may take a name to yield a sentence in which that name occurs as a semantic constituent, creating a context whicli, thougli

144

145

(V$)

[Tr (f(Evi)Vii) « ( H 7 ) 7-/- ( r * 7 ^ ) ] .

Quantification and Reference opaque, does admit substitution of synonymous names salva veritate. Tills is the kind of opacity produced by hyperintensional operators. The syntactic form of the name is strictly irrelevant to the meaning of the resulting sentence; all that is relevant is the meaning of the name (as stated in an MRef axiom). It is because the presence, in the language, of hyperintensional sentence operators would block the construction of a truth theory meeting SC that we here imagine the same kind of opacity to be introduced by an expression with the syntactic form of an atomic predicate. (It is a further question whether any such expressions of natural language introduce this kind of opacity.) On the other hand, an expression with the syntactic form of an atomic predicate may take a name to yield a sentence in which that name does not occur as a semantic constituent (but is merely mentioned) creating a context which does not admit substitution of synonymous names (but only of equiform names) salva veritate. This is the kind of opacity produced by quotation. The meaning of the name is strictly irrelevant to the meaning of the resulting sentence; all that is relevant is the syntactic form of the name. (These two subcases are not exhaustive. The expression . . . is so-called because of his height takes a name to make a sentence in which the name occurs as a semantic constituent but also creates a context which does not admit substitution of synonymous names salva veritate^ It is a relatively straightforward matter to provide a truth theory (of the Kripkean form) for a substitutionally quantified language whose base language involves opacity of just the first kind. Thus suppose that Z,9 is a substitutionally quantified language whose base language contains the ten one-place predicates ' f i ' , . . . , ' / ' l o ' and ten names ' W i ' , . . . , V«io', together with ten quasi-predicates Xi, . .., X^o which introduce opacity of the first kind. Because of this opacity axioms for the names must specify more than simply a reference for each name. But because the opacity is of the first kind no new notion of pseudoreference is needed; the familiar MRef will serve. Thus for a name 'mi' we have MRefm,'mi\mi) for a predicate 'Pi' we have ( V ^ e L , ) (Ax) [MRef (L,, 7, x) ^ {Tr (L,, ^P,7^) « ^ix)] 146

Quantifiers and for a quasi-predicate 'Xj' we have ( V 7 e i , ) (Ax) [MRefiL,, 7, x) (7> (A,, 'X, 7') - ^ . x)]. Truth functional connectives are governed by axioms of the familiar form. For 'E' we have ( VGL,) [Trm, '(EvOd'Vii) ^ {-^-r^L,) Tr^, U\>-^^)]. There is a similar axiom for 'A', and we need ( V7G/,9 ) (Ex) MRefiLg, 7, x) and (Ax)C5yGL,)MRef(L,,y, x). The provision of such a truth theory does not reveal any particular quantificational idiom of natural language as substitutional quantification. It simply establishes the possibility of a quantificational idiom which has the syntactic form of quantification into name position, whose syntactic form is not misleading as to its semantic nature, and which is not quantification over objects of the kind named. And that possibility is enough to refute the thesis presently under consideration about the essential features of quantification. The quantification in Lg is not quanfification over objects of the kind named because fiie truth of '(Evj )A'i Vi', for example, does not turn upon there being a (named) object with a certain property (associated with 'Xi'). The difference which is crucial for the truth of quantified sentences of Lg is not that between one (named) object and two, nor that between one name and two (for there are no sentences whose truth is sensitive to the difference between one name and two with the same meaning). Rather, this quantification is quantificafion over meanings of names in Lg. If we were to accept that the meaning of a name is determined by an object referred to and a (relatively unspecific) way of thinking about that object, then we might say that the quantification is over ordered pairs of objects and ways of thinking, wiiere the domain of relevant pairs is restricted in some way to those associated with names in Lg. If the quasi-predicate 'X,' has the meaning of Harry believes t h a t . . . is modest then we might specify the meaning of '(Evi)A', v,' as that there is an object (named in/,9)anda way of thinking about that object (expressed by a name in Lg) such that Harry believes, concerning that object, 147

Quantification and Reference thought about in that way, that it is modest. (The restrictions are in parentheses since the restriction of the domain to the correct class of ordered pairs might be achieved in some way other than by explicit appeal to the notion of a name in .) We saw (in Section VI.3) that it is not an essential feature of quantification that it should be quantification into name position. We have now seen, by considering a substitufionally quantified language whose base language involves opacity of just the first kind (the kind that would by introduced by hyperintensional sentence operators), that it is not an essential feature of quantification into name position that it should be quantification over objects of the kind named. (For a substitutionally quantified language whose base language involves opacity of the second kind, that is, of the kind introduced by quotation, see Appendix 6.)

. '

NOTES The possibility of employing a theory in the style of QTB rather than a theory in the style of QSd was pointed out to me by Gareth Evans, and my reasons for preferring QTB over QSB are just those which he gave. See Evans (1977). He called theories of the first kind 'Fregean', on the basis of Dummett (1973, Chapter 2). Theories of the second kind he called, of course, 'Tarskian'. See Tarski (1956), and for a standard textbook treatment see eg. Mendelson (1964, Chapter 2). On binary quantification see also Wallace (1965). On substitutional ' quantification see also Dunn and Belnap (1968), Wallace (1971), Camp (1975), and WaUace (1975b).

148

1 i ,' ' 1

VII DESCRIPTIONS

1 DESCRIPTIONS AND QUANTIFIERS In English, and doubfiess in other natural languages, definite descriptions have (almost) the same privileges of occurrence as proper names. What is more, (singular) definite descriptions and proper names both introduce individual objects which a sentence may be said to be about (in a highly pretheoretic sense of 'about'). So, someone might suggest, definite descriptions and proper names are semantically akin; expressions of both kinds are singular terms. (See Appendix 7.) This suggestion is unconvincing. For two very clear reasons a semantic theorist should not rush to assign to definite descriptions the semantic property of genuine smgular reference to objects. The first reason is that it is not only definite descriptions which have (ahnost) the same privileges of occurrence as names. What holds for 'the elephant' holds equally for 'some elephant(s)', 'every elephant', 'most elephants', and 'few elephants'. Indeed, it is impossible not to be impressed by the similarity of syntactic function between 'the' and expressions which are clearly binary quantifiers. The second reason is that, in the pretheoretic sense of 'about', quantifier phrases also introduce objects which a sentence may be said to be about. The sentence 'All elephants are playful' is, in that sense, about all elephants. Nor would it be wise for someone to take a stand on the fact that a (singular) definite description introduces a single object. It is too easy to ignore the fact that there are plural definite descriptions for which this is not the case. The suggestion is unconvincing because it is based upon quite superficial similarities between definite descriptions and names. Given 149

Quantification and Reference

Descriptions

a firm grasp upon the semantic difference between names on the one hand, and quantifier phrases on the other, it is easy to see that, at least in some of their uses, definite descriptions belong semantically with quantifier phrases. Let us recall the two main features (or batches of features) of the reference relation between names and objects. The object which is assigned to a name as its reference is tc-salient and e-salient (Section V.2). And let us consider, as a typical example of a quantifier phrase, the expression 'all philosophers'. Suppose that X, . . ., Z are all the philosophers there are. Then the semantic property assigned to the phrase 'all philosophers' is indifferent to the existence or non-existence of X, Y, . . Z. The meanings of sentences containing that quantifier phrase are existence independent (rather than existence dependent) with respect to those objects. Similarly, the beUefs expressed by sentences containing that quantifier phrase are existence independent. They are not singular beliefs concerning X, Y, . . ., Z, since a man may well beheve that all philosophers are modest, say, even though he has been totally causally isolated from X, Y, . . Z. Those objects are not e-salient, and clearly no other objects are e-salient either. What is more, the truth of sentences containing 'all philosophers' does not depend (with respect to actual and counterfactual situations) upon how things are with X, Y, . . . , Z. Those objects do not 'enter the truth conditions' of sentences containing that phrase. The sentence 'All philosophers are modest' could be true, for example, even though none of X, Y, ..., Z was modest. Those objects are not tc-salient, and clearly no other objects are tcsalient either. Thus, in general, one cannot assign to a quantifier phrase objects which are tc-salient and e-salient. In this semantic respect quantifier phrases are sharply different from names. Let us distinguish one kind of use of definite descriptions. A speaker may come out with the sentence The tallest philosopher is over seven feet tall to make a sincere assertion even though there is no person concerning whom the speaker beUeves that he is the tallest philosopher. The speaker may simply believe, on purely general grounds, that there is some philosopher who is taller than the rest, and that whoever is tallest is over seven feet tall. The speaker might equally well have come out with the sentence The tallest philosopher, whoever that is, is over seven feet taU

to indicate his lack of singular beUefs. Let us call such uses 'whateverthat-is uses'. In at least these uses definite descriptions are semantically akin to quantifier phrases. Thus suppose that, in fact, X is the tallest philosopher. The sentence 'The tallest philosopher is over seven feet tall' would mean just what it in fact means even if X were not to exist. Similarly, the beUef that the tallest philosopher is over seven feet tall is a beUef which it would be possible to have even if X were not to exist. The object X is not e-salient, and clearly no other object is e-salient either. What is more, the truth of sentences containing 'the tallest philosopher' in whatever-that-is uses does not depend (with respect to actual and counterfactual situations) upon how things are with X. That object does not 'enter the truth conditions' of sentences containing that definite description in that kind of use. The sentence 'The tallest philosopher is over seven feet tall'could be true, for example, even though X was not over seven feet tall. The object X is not tcsalient, and clearly no other object is tc-salient either. In whatever-that-is uses, definite descriptions are semantically akin to quantifiers, and it is quite plausible that in such uses a definite description 'the F* is logically equivalent to the complex expression (ax) [Fx &.(Yy)iFy-^y = x)&...x] so that a sentence 'The Fis G' containing a definite description in such a use is equivalent to ( ax) [Fx & (Yy) (Fy^y=x)& Gx]. Let us call this equivalence the Russellian equivalence (cf. Russell, 1905, p. 44). One can consistently accept the Russellian equivalence but reject the suggestion that each surface sentence containing a definite description in a whatever-that-is use should be 'preprocessed' into a sentence, at the level of input to a semantic theory, which does not contain a definite description but is (according to the Russellian equivalence) logically equivalent to the surface sentence. And one should reject that further suggestion, for it clearly infringes SC. (Rejection of that suggestion is not ipso facto criticism of Russell, for it is arguable that Russell's proposal for eUminating definite descriptions answered to a project quite different from that of constructing structurally adequate semantic theories for natural languages. See Sainsbury, 1979, pp. 154-60.) It is a straightforward matter to add one more binary quantifier 'THE' to the language L-j, and to add one more axiom to the truth

150

151

Quantification and Reference

theory for that language. If, as we supposed (Section VI.2), the ML contains the binary quantifiers of the OL together with the one-place quantifiers ' V' and ' 3 ' then the Russellian equivalence, in the form (THE x) {Fx; Gx) ^ ( 3x) [Fx & ( Yy) {Fy-^y=x)& Gx] will be a theorem schema of the logic of the ML. The quantifier 'THE', like the quantifiers of Z-7, is a restrictive binary quantifier. For we can associate with 'THE' a function / from pairs of cardinalities to truth values such that if a is the cardinality of the set of Fs which are Gs and b is the cardinaUty of the set of Fs which are non-Gs then '(THE x) {Fx; Gx)' is true iff/() = T, namely the function / such that/() = T just in case a = 1 and b=0.

Descriptions

2 SPEAKER'S REFERENCE Sentences containing definite descriptions in their whatever-that-is uses can be represented with the help of the binary quantifier 'THE'. The question which confronts the semantic theorist is whether the semantic account which he offers for whatever-that-is uses also covers other uses of definite descriptions. For there are certairdy uses which are quite unlike whatever-that-is uses. Consider the following extended passage from Mitchell, An Introduction to Logic (1962, pp. 84-5): Defmite descriptions, occurring as the subjects of sentences, have at least two distinct functions, which may be illustrated by two sets of examples: 1. 'The Prime Minister presides at Cabinet meetings' 'The Sovereign of Great Britain is the head of the Commonwealth' 'The man who wrote this unsigned letter had a bad pen' 2. 'The Prime Minister has invited me to lunch' 'The Queen made a tour of the Commonwealth' 'The author of Waverley limped' It is not difficult to see that the grammatical subjects of the sentences quoted in List 1 are not used - as proper names, for example, are used-to refer uniquely. For 'The Prime Minister' and 'The Sovereign' we can substitute, without change of

meaning, 'Whoever is Prime Minister' and 'Whoever is Sovereign' . . . With the sentences in List 2 the case is different. The subjectphrases serve to identify individuals, and what is predicated in each case is predicated of the individuals so identified. On the one hand, a speaker may know or believe that there is a unique Prime Minister and know or beUeve that the office of Prime Minister involves presiding over Cabinet meetings, without knowing or believing concerning any particular object that it is Prime Minister or that it presides at Cabinet meetings. If such a speaker comes out with the first sentence on List 1 to make an assertion then he does not express a singular belief and his audience can know perfectly well what he has asserted without, for example, coming to believe concerning some particular object that it presides at Cabinet meetings or is believed by the speaker to preside at Cabinet meetings. This is a whatever-that-is use of the defmite description, and the sentence as used on such an occasion would be represented at the level of input to a semantic theory as containing the binary quantifier 'THE'. On the other hand, a speaker may know concerning a particular object that it is Prime Minister and may want to put his audience in a position to know concerning that object that it has invited the speaker to lunch. Such a speaker may come out with the first sentence on Ust 2 precisely in order to communicate, or 'get across', to his audience the information concerning that object that it has invited him to lunch. This is not a whatever-that-is use of the definite description. The question for the semantic theorist is whether the difference in uses corresponds to a semantic difference in the definite description as used on the two occasions, whether, that is, the defmite article 'the' is ambiguous. In order to characterize the second kind of use more precisely, let us introduce a notion closely related to that of s-meaning (cf. Section 1.2). A speaker S s-means concerning an object z that it is thus and so, by his utterance (token) x directed at audience A, just in case (1) S intends concerning z that x will produce in A an (activated) belief concerning it {z) that it is thus and so; (2) for some feature F oix,S intends that^ should recognize iS's primary intention in part by recognizing x to have feature F; in particular, for some feature G of x, 5 intends that^ should recognize concerning z that5"s primary intention concerns it in part by recognizing x to have feature G;

152

153

Quantijicatian

/

and

KeJ'erence

(3) S intends that A's recognition of 5's primary intention should be part of >l's reason for beUeving concerning z that it is thus and so; (4) S does not intend that A should be deceived about 5's intentions. What is characteristic of the second kind of use is that the speaker s-means concerning, for example, the object z which is in fact the Prime Minister that it has invited him to lunch. In this case the relevant feature (G) of the utterance might be that it contains a definite description such that it is common knowledge between speaker and audience that each believes the description to apply literally to the object z. But other cases are possible. It is certainly possible for a speaker to s-mean concerningz thatitis modest by an utterance of 'The tallest philosopher is modest' even though z is not, and is not believed by speaker and audience to be, the tallest philosopher. The relevant feature of the utterance might be, for example, that it contains a description which patently does not apply literally to z (an ironic or 'scare quoted' use of a description). Let us say that when a speaker s-means concerning z that it is thus and so there is speaker's reference to z. In his influential paper, 'Reference and definite descriptions' (1966), Donnellan offered labels for roughly these two kinds of use of definite descriptions. He called the whatever-that-is uses 'attributive' and the uses in which there is speaker's reference to a particular object 'referentiar (Donnellan, 1966, p. 285): A speaker who uses a definite description attributively in an assertion states something about whoever or whatever is the so-and-so. A speaker who uses a definite description referentially in an assertion, on the other hand, uses the descripdon to enable his audience to pick out whom or what he is talking about and states something about that person or thing. Having labelled two kinds of use, Donnellan went on to argue that a Russellian theory, even if appropriate for attributive uses, would not cover referential uses. (He seemed, in short, to be arguing for an ambiguity in 'the', although at one point he explicitly denied that definite descriptions are ambiguous; ibid. p. 297). Before we consider further the prospects for a Russellian theory, it is important to clarify what is, in fact, a very wide variety of uses of definite descriptions. For the variety may be obscured by the use of just two labels. The first thing to notice is that Donnellan's positive 154 7

I ^Ar..\:c..- !

I^cscripti(x)«p]

where '**' is the material biconditional i n the A/L and ' • ' is a modal operator in the ML expressing broadly logical necessity). For such a theory does not state enough about, say, the sentence S\o yield any consequences at all for the material or strict truth conditions o f f John believes that Si ^. But, as we shall now see in some detail, the intensional operators ' • ' and '0' can be treated as sentence operators in a theory which yields strict truth condition specifications (see also Peacocke, 1978, pp. 4 7 6 - 7 ) . Before we give the axioms o f a truth theory for L 1 0 we must specify the background logic o f the ML in which the theory is cast. In particular, we must specify the modal component o f that background logic. First, as a k i n d o f prehniinary, we have the axiom schema

relating the two modal operators. Then we have the following rule o f proof, called 'Necessitation' (Nee):

the last paragraph o f Appendix 6.) But the fact that the axiom for

important semantic differences.

proof at the end o f tliat section). Hyperintensional operators also resist treatment in a theory which yields strict truth condition specifications ( o f the form

is an intensional sentence

operator, unlike ' ~ ' which is extensional and unlike 'John beheves that' whicli is hyperintensional. These semantic differences become clear when we t r y t o construct theories o f t r u t h for languages containing the three operators. For a theory which yields only material t r u t l i condition specifications

(of

the f o r m

ha \-na (Here ' P is read as 'there is a p r o o f from the logic alone o f . . . ' . ) A n d we have the axiom schema • (a -> |3)

-*

•|3).

This schema and the rule Nec could, in the presence of the non-modal component o f the logic (classical propositional calculus, say), be replaced by the extended rule o f necessitation Qi

Tr(s)^p

(Da

"/I

• a,,..., •«„

l-n|3

where ' « • ' is the material biconditional i n the ML) does not state enough about, say, the sentence Si to yield any consequences at all for the material t r u t h conditions o f either 'Osi'' or "^John believes that Si ^. Intensional and hyperintensional operators thus resist treatment in a theory which yields only material t r u t h condition specifications (cf. Section I I . 5 , and in particular the discussion o f rules o f

(where ' P is read as 'yield by the logic alone'). I n either case the resulting system is the very weak modal logic K. The slightly stronger system T is the result o f adding to K the following axiom schema (the r axiom):

188

189

• a ^ a.

Necessity

and

Actuality

Necessity

Clearly, the axioms and rules o f the system T are faithful to the i n tended meanings o f ' • ' and '0'. The system S4 is the result o f adding t o r t h e following axiom schema (the^^^ axiom):

For we know from our consideration of the t r u t h theory Td for Li that from the unmodalized versions of (NTla)

nUa.

•a

Tr(L

Arguably, this too is faithful to the intended meaning o f

Finally,

10, f ~ X i ^ )

-B

So, given the extended rule o f necessitation, we can prove the strict t r u t h condition specification for f - x , !

(the Brouwerian

(NTla)

The system S5 can also be obtained by adding to T the following axiom schema (the S5 axiom): Oa ^

and (NT4).

from the modalized

axioms

The axioms for ' • ' and '0' have the same f o r m as

that f o r T h u s f o r ' • ' w e have

nOa.

a

we can prove,

~ ( s n o w is white).

the system S5 is the result o f adding t o S4 the following axiom schema axiom):

and (NT4)

by (non-modal) logic alone, the biconditional

(NT5)

n(Ya)[Tr(Lio,

But the use o{(NT5)

'Oa^)

^

aTr(Lio,o)\.

in the derivations o f strict t r u t h c o n d i t i o n specifi-

cations is slightly different from that o f (NT4).

DOa.

This schema seems to be no less faithful to the intended meaning o f '0' than the S4 axiom is to the intended meaning o f

(Cf. Hughes

and Cresswell, 1972, pp. 2 2 - 6 0 ) .

Thus consider the

sentence 'Dsi \t is not the case that from the unmodalized versions o f (NTla)

and (NT5)

we can prove the material t r u t h c o n d i t i o n specifi-

cation Tr(Lio,

We can now give the axioms o f a t r u t h theory for Ljo cast i n aMZ,

"^Dxi^)

• (snow is white).

whose background logic has as its modal component the system S5.

For, since ' • ' is intensional, a material t r u t h condition specification

The axioms for the atomic sentences

for x i (provided by the unmodahzed version o{ (NTla))

, ^ 2 . and X3 must, obviously,

specify the strict t r u t h conditions o f those sentences. So we have {NTla) for Si,

•

even a material truth condition specification for ^ D x i ^ we have to

[ r r ( L i o , X i ) ^ snow is white]

and similar axioms (NTlb)

and (NTlc)

for X2 and S3. ( I t is

w o r t h repeating here that there is no objection to be made against (NTla)

by claiming that Si

make use o f a strict t r u t h condition specification for x, (provided by the modalized axiom (NTla)).

Tr(Lio, for ' v ' and

(We

should not allow our use o f corner quotes i n abbreviating what would otherwise be w r i t t e n o u t using the concatenation functor ' n ' to obscure

Thus, in order to apply the extended rule o f necessitation and so to derive a strict truth condition specification for ' ^ • x i ' , we need the

the fact that the t r u t h o f these axioms depends upon the following property o f that functor. Whatever the value o f that functor applied

ditional

to a pair o f expressions i n fact is, i t is not possible that the value o f that functor applied to those expressions should have been anything other than what i t i n fact is. See Peacocke, 1978, note 8.) From these axioms we can prove, for example, [Tr(Lio,

1 ) -t^ ~ (snow is w h i t e ) ] . 190

yields (by

** • ( s n o w is white).

'Osi'')

modalized axiom (NT5)

•

• ( s n o w is white)

propositional calculus alone)

(Tr(Lio,o)&Tr(Lio,T))] and (NT4)

we have

and this, together w i t h the unmodalized version of (NT5),

a(Ya)(YT)[Tr(Lio,'o&T')^

for ' & ' , and similar axioms (NTS)

From (NTla)

• 7>(Z,io,Xi)

might have meant something different.

See Peacocke, 1978, pp. 477-8.) We have (NT2)

has no conse-

quences for the material t r u t h conditions o f r O x , ^. I n order t o derive

and the following doubly modalized bicon-

• • [rr(Lio,Xi)

snow is w h i t e ] .

This last foEows from (NTla) by the S4 axiom. The formal difference between the derivations o f strict t r u t h cond i t i o n specifications for f ~ x , ^ and for 'Osi^ semantic difference

between

corresponds to the deep

the extensional operator 191

'~'

and the

Certainly the sentence S j contributes to the intensional operator strict t r u t h conditions o f b o t h ^ and 'Hsi'' by its own strict t r u t h conditions; ' ~ ' and ' • ' are alike in not being hyperintensional. But the fact that Si contributes to the strict t r u t h conditions o f ^~Si ^ b y its own strict t r u t h conditions is related very simply (by the extended rule o f necessitation) to the fact that Si contributes to the material t r u t h conditions of ^~s,^ by its own material t r u t h conditions. I n contrast, the fact that Si contributes to the strict t r u t h conditions o f fOsi^ by its own strict t r u t h conditions is related rather differently (by the S4 axiom and the extended rule o f necessitation) to the fact that Xi contributes even to the material t r u t h conditions of 'Osi'' b y its own strict t r u t h conditions. Let us call this t r u t h theory 'NTd'. The derivations o f strict t r u t h condition specifications for i and 'Osi ^ are enough to indicate a canonical p r o o f procedure which yields, for each sentence o f Z,,o, a canonical theorem of the form niTriLio,s)^p]. We shall say that a theory o f strict t r u t h conditions for a language L, together w i t h a canonical proof procedure, is interpretational just i n case replacing a[Tr(L,...)^

]

by . . . means (in L) that in the canonical theorems yields correct meaning (in L) specifications. Then, given that Td is interpretational for Li, i t follows that NTd (together w i t h the indicated canonical p r o o f procedure) is interpretational for Lio. What is more,7V7'9 meets ^C. I n particular, the canonical derivation o f a strict t r u t h condition specification for a modal sentence ^Oa^ employs resources already sufficient for the canonical derivation o f a strict t r u t l i condition specification for the contained sentence a. This answers to the fact that someone who knows what a modal sentence ^ D a ' means is thereby i n a position to know what the contained sentence a means. We noticed at the beginning o f this section that i t is a feature o f modal sentences o f English that the sentence which is w i t h i n the scope o f a modal adverb or phrase is a semantic constituent o f the resulting modal sentence. So, to that extent a theory i n the style o f NTO would be appropriate for a 192

fragment o f English containing modal adverbs and phrases. A t r u t h theory in the style o f NTS would not be appropriate for a fragment o f English containing the modal adverb 'necessarily' i f the following claim about that adverb were strictly correct (Quine, 1960, p.196): 'necessarily' amounts to 'is analytic' plus an antecedent pair o f quotation marks. For example, the sentence (1) Necessarily 9 >

4

is explained thus (2) '9 > 4 ' is analytic. The primary reason is not that the use o f the predicate o f sentences 'is analytic' renders the necessity too narrow, and certainly narrower than broadly logical necessity. The inappropriateness which is our present concern would remain i f 'is analytic' were replaced by some other predicate o f sentences such as 'is a necessarily true sentence'. The crucial point is that i f the modal adverb really amounted to a predicate o f sentences plus an antecedent pair o f quotation marks then someone could know the meaning o f a modal sentence w i t h o u t being in a position to know the meaning o f the contained sentence, for the contained sentence would be mentioned but not used. So i f the claim i n the passage from Quine were strictly correct, i f modality were really metalinguistic, then a theory i n the style of NTd would infringe SC. Of course, no concession to the idea that modahty is metalinguistic is made by the presence i n a t r u t h theory of the biconditional W)^D7'Kiio,

(Ya)[Tr(Lio,

a)].

That biconditional no more shows that modal sentences are metalinguistic than the biconditional (Va)

[Tr{Lio,

'~a')

^ ~ TriL^o,

o)]

shows that negative sentences are metalinguistic.

2

POSSIBLE WORLDS

I t is common, natural, and heuristicaUy useful to say that a modal sentence ^Da'' is true just i n case a is true w i t h respect to every possible (actual or counterfactual) situation, or every possible state 193

/Vec-essity Necessity

and

Actuality

o f affairs, or every possible w o r l d , and similarly that ^a^ is true j u s t in case a is true w i t h respect to some possible situation, possible state o f affairs, or possible w o r l d . Yet i n the t r u t h theory NTd for the modal language Z-jo no explicit use is made o f the concept o f a possible world. We nmst examine that concept a little more closely, and enquire after its proper role i n semantic theorizing about modal sentences. Let us begin w i t h some reflections concerning the relation between model theory and t r u t h theory, for such reflections may seem to provide an argument i n favour o f the explicit employment o f the apparatus o f possible worlds i n a t r u t h theory for a modal language. The central concept o f model theory is truth-in-a-model or t r u t h upon-an-interpretation, and the business o f model theory is to characterize validity. A n argument from a„ to j3 is said to be valid just i n case /} is true i n every model i n which all o f a j , . . . , a„ are true. Derivatively, a sentence is said to be valid just i n case i t is true i n every model. Consider the quantificational language Z g . A model appropriate for Lf, comprises a set o f objects (the domain o f the model) together w i t h an appropriate assignment o f an extension for each atomic predicate and a reference for each name in Z g . Most standard treatments o f model theory for quantificational languages make use o f a modelrelative satisfaction relation between sequences o f members o f the domain and formulae o f tlie language. Truth-in-a-model is then defined in tenns o f satisfaction-in-a-model. A model theory for Zg w i l l deliver such theorems as ( V Z ) [ T r i i'Pimi') ^ Refj ( ' m , ) ( V Z ) [TrjCYVi)PiVr) (YxeDomain (Z)) (xsExtj ('Pi'))]

e Extj

('/>,')]

(where the quantifier '(YI)' ranges over models appropriate for Le, and the language parameter is suppressed). One needs two things i n order t o proceed from such a model theory to a t r u t h theory (in this case, perhaps, a satisfaction theory) for Z g . One is a specification o f an intended model or interpretation Z*, that is a specification o f an intended domain o f quantificafion, an intended extension for each atomic predicate and an intended reference for each name. The other is the biconditional (Ya)[Tr(a)

o

Trj*(cj)]

( t r u t h is just t r u t h upon the intended interpretation, or t r u t h i n the intended model). The model Z* is not merely a pure set theoretic 194

rthic to the model whose domain comprises structure which is isomorp language refer and over which they the objects to which speakers ^^^^^^ ^^.^^^^ _^ ^ quantify. Rather, y i t s e i r ^ ^ ^^^^^^^^ ^ ^ ^ ^ ^^^^^^ appropriate for Consider "O^J^^^J^^l, where W is a set, w* is a particular desigZ)o is a triple , w , ^ .^^^^igns to each ordered pair o f a member nated member ot W, anu ^^^^^ ^^^^^ ^^^^^.^^ ^ o f W and an atomic sentcnci- u lu 01 IV dim du o ^^g^ j^Qj y3i.y model to model) to a extended (in a way whici ^^^^ ^^^^^^^ ^ ^^^^^^ o f and function r which assigns t ^^^^ ^ ^ ^^^^ ^ ^^.^ any sentence o f Z.o a t r u ^^^^ ^^^^^^^ ^^^^ ^ ^ ^^^^ ^ ^^.^ true w i t h respect to ^ 0 " ^ ^ j^^^ members o f W are often to be true i n the model purposes o f model theory spoken o f as possib e wo ^^^^^^^^^^ ^^, ^^^^ j,^gy the metaphysicd nature ^j^g^jetj^ objects. The relation between can be assumed to be s.^^^^^^ ^^^^ ^^^^ model theory and t r u t n ^^^^ ^^^^^^ obtained from the model expect that a t r u t h lieory ^p^^jfj^^^j^^ intended set o f possible theory just indicated by i ^^.^^^^ .^^^j, ^ ^ ^ ^ . ^ j ^ ^ ^ ^ j ^ ^ ^ ^ worlds (not just set the ^^^^^^ ^^^^^^^ intended evaluintended designated ^ o r i v^^^^^^ ^^^^ ^^^^^ ^.^^ ^^^p^^^ p^^^.^^ ation function (assignmg ^ ^^^^ ^ ^^^^ ^ ^ worlds). Thus one may '^^^ ^ ^ ^ J , ^ , should make explicit use o j , f l , c t i o n s provide an argument i n favour To the extent that t n ^^^^^^ argument is unsuccessful. I t is o f a possible worlds truti ^^^^^^^ validity is to have any interest certainly correct that it l i ^^.^.^^ ^^^^ argument fiom a , , then i t must be a consequ ^ ^^^^ (simpliciter) then |3 is true, . . ., a„ to /3 that i a i , • and i t must be a conseq sentence is true I t is proper relation between v w i t h t r u t h i n an mtendeci

-^^^^ validity of a sentence that that ^^^^^^^ ^^^^ sufficient to estabhsh this t^uth that truth should be equated ^^^^^ ^^^^^^^

sufficient that t r u t h theory ^^^^^ ^^^^ ^^^^ o f Z , . This

and model theory should ^^^^^^^^ sufficient to establish the is sufficient, but i t is n o i ^^^^^^ ^^^^^ ^^^^^^ ^ . ^ p j ^ proper relation between ^^^^ ^^^^^.^^ ^^^^^ be some model appropria ^^^^ ^^^.^^^ ^^^^ ^^^^ and only the sentences o ^^^^ ^ ^ ^ ^ ^^^^^^^ p^^^.^^^^^^ in that model. I n the ca ^^^^^^ ^^^^^ p^^^ theoretic model it is sufficient that the ^^^^^^^ ^^-^^^ ^^^^ ^^^^ such that aU and only tlie 195

Necessity

and

Necessity

Actuality

true in that model. Acceptance o f the existence o f such a model does

( V w ) World (w)

not require any sympathy at all for the idea o f possible worlds. Still

( V w ) {{World

less does i t require explicit employment in a t r u t h theory for L ,0 o f the possible worlds apparatus. (Cf. Plantinga, 1 9 7 4 , pp. 1 2 6 - 8 , This account o f the relation between validity and t r u t h raises questions about the idea that model theory explains the validity o f arguments; cf. Evans, 1 9 7 6 . )

For all that has been said so far, i t is open to a semantic theorist to provide, for a modal language, either a possible worlds t r u t h theory or a t r u t h theory i n the style oiNTd.

In fact, however, there seem to

be reasons for preferring a theory i n the style o f NTO

(an operator

(w) V ~ x , ' ( w ) ) & X 2 ' ( w ) )

which do not correspond to any sentence o f L I Q . (Cf. Wallace, 1 9 7 2 , p. 2 4 3 . This objection also applies i f binary quantification is used.) The theorist who adopts this first strategy seems bound to hold t h a t i j o is an impoverished language, and this is inconsistent w i t l i already made for NTO

the claim

that i t both meets SC and delivers t r u t h con-

d i t i o n specifications for precisely the sentences o f I m . I t is possible to alter the first strategy so as t o meet this prima facie objecdon, for one can do away w i t h the predicate ' World' and assume that the domain o f quantification is aheady restricted to possible worlds. I n that case

theory). There are t w o ways i n w h i c h a semantic theorist might provide

the

a possible worlds t r u t h theory. On the one hand he miglit 'preprocess'

But once the first strategy is altered i n this way the best that can be

'preprocessed' form o f ^Usi^

would be simply r ( V w ) x i ' ( w ) i .

the sentences o f L j o , say, so that at the level o f input the sentence

said for i t is that the 'preprocessing' is quite trivial: one writes ' x i ' ( w ) '

T D x i ^ is represented as

instead o f ' x j ' and ' ( V w ) ' instead o f ' • ' . And the worst that can be

iyw){World{w)

said for i t is that i t seems to involve a denial that the expressions X j , x j ,

-> x i ' ( w ) )

and X3 o f

or perhaps as ( E V E R Y w) {World (w); x , '

The main difference between the theory which results upon the

(w)).

According to this first strategy the language at the level o f input w o u l d be a quantificational language w i t h a one-place atomic predicate

'World'

and a one-place atomic predicate (true o f possible worlds) corresponding to each atomic sentence o f Z-io- The quantificational language w o u l d contain no operators which are other than extensional, and the t r u t h theory would take the familiar shape o f theories o f material truth conditions for quanfificational languages. On the other hand, the semantic theorist might apply a t r u t h theory to Z-io directly, and make use o f the apparatus o f possible worlds only i n stating i n the ML

the t r u t h conditions o f OL

are really sentences (cf. Section V I I I . 3 ) . The first strategy

is not, then, particularly attractive.

sentences. I n particular, the t r u t h

predicate w o u l d be explicitly relativized to possible worlds, and the theory w o u l d deliver such theorems as the following: ( Vw) [ (w, X i ) - f * snow is white i n w ] ( V w ) ( V a ) [Tr{w, ^Ua^) ^ {Yw')Tr{w',a)].

second strategy and the operator theory NTd

is that the former is cast

i n a ML which contains no operators which are other than extensional while the latter is cast in a ML which itself contains intensional operators. I n the former case the background logic o f the ML is standard first-order

logic; i n the latter case the background logic o f the ML is

modal logic. A crucial feature o f the second strategy is that in the axioms for atomic sentences we find ML predicates o f one more place than miglit have been expected. In the expression 'snow is white in w ' we have not the one-place predicate "white' but a two-place predicate ' w h i t e ' ' true o f pairs of material objects and possible worlds. Similarly, i f one constructed a t r u t h theory for a modal language extending L^^, then one would on this second strategy have as a theorem (Vw)

[r/-(w,'p,w,')

^

c?i'(«.,w)].

On the right hand side o f this biconditional we have not the one-place

Against the first strategy there is a prima facie objection that i n such

predicate 'Qi'

a t r u t h theory the resources used i n the canonical derivations o f bicon-

similarity

between

ditionals for sentences at the level o f input w h i c h correspond t o sen-

one-place

predicates must not be allowed to obscure the fact that

tences o f Z,io are already sufficient for the derivation o f biconditionals

some account must be given o f the meanings o f ML

for sentences such as

taining the new expressions. The only available account seems to be 196

but a two-place predicate ' Q , " .

The typographical

the new two-place predicates and the famihar

197

sentences con-

Necessity

and

Actuality

along the following lines. I f 7 is a name o f an object x and 5 is a name o f a possible w o r l d w then ^Wnte'{-y,by is true just i n case x would be white i f w were to obtain ( r g i ' C T , ^ ) ^ is true just i n case would be g i i f w were to obtain). But tliis account at least suggests that it would be preferable to do w i t h o u t the new two-place predicates, and instead regard rwhite(7)i as a sentence and 4 n 5^ as an intensional sentence operator (equivalent to ^if 5 were to obtain then . . .^). And this last has the added advantage that i t avoids the denial (implicit i n the second strategy) that ML expressions such as 'snow is white' and ' Q i « r are really sentences. But, o f course, this advantageous alteration to the second strategy destroys the mam difference between the resulting theory and the operator theory NTd. For once that alteration is made the expression '(Vw) (. . . (in w ) ) ' is revealed as an intensional sentence operator. Thus a semantic theorist who b o t h cares about semantic structure and values such grasp as he may have upon the notion o f a sentence w i l l do well to adopt an operator theory i n the style of NTd. For a semantic theorist who adopts an operator theory there remains the question whether it is really even legitimate to speak o f possible worlds and to say that certain sentences are true w i t h respect t o certam possible worlds. On the one hand, David Lewis (1973, p p . 8 4 , 85) has written, '1 believe that there are possible worlds other than the one we happen to inhabit' and 'Our actual world is only one world among others'. On the other hand, many philosophers have rejected such realism about possible worlds. Colin McGinn (1981), for example, has urged, i n short, that 'there are no possible worlds in objective reaUty'. Possible worlds terminology is undoubtedly heuristicaUy useful. I f we are to continue to use i t , even i n informal exposition, then we must at least reflect briefly upon the nature o f our commitment to possible worlds. The continued use o f the heuristicaUy useful terminology is consistent w i t h two intuitively plausible claims. One is that possible worlds are abstract objects rather than, as on Lewis's view, objects o f the same k i n d as '1 and aU my surroundings'. The other is that the notion of a possible world is conceptuaUy posterior to the notions o f necessity and possibility expressed by ' • ' and ' 0 ' . (These two claims might be attributed to Stalnaker, 1976 and Kripke, 1972, respectively.) So let us briefly attempt to mark out a position embodying these two claims and intermediate between the position o f Lewis, on the one hand, and the position o f those for w h o m McGinn speaks, on the other. 198

JVecessity

Consider the foUowing celebrated passage from Lewis (1973, p. 84): I believe, and so do you, that things could have been different in countless ways. But what does this mean? Ordinary language permits the paraphrase: there are many ways things could have been besides the way they actuaUy are. On the face of it, this sentence is an existential quantification. It says that there exist many entities o f a certain description, to w i t 'ways things could have been'. I believe that things could have been different in countless ways; I beUeve permissible paraphrases of what I beUeve; taking the paraphrase at its face value, I therefore believe in the existence o f entities that might be called 'ways things could have been'. I prefer to call them 'possible worlds'. Clearly this passage does not provide any support for the idea that possible worlds are objects o f the same sort as ' I and aU my surroundings'. Rather, the passage supports the idea that possible worlds (ways things could have been) are akin to properties rather than to material objects. Stalnaker (1976, p. 68) has argued precisely this, against Lewis: 'The way things are is a property or state o f the world, not the world itself ... the way the world is could exist even i f a world that is that way did not.' It is not enough to say that a possible world is a way things could have been. No doubt things could have been different in such a way that Fraser would have been an opera singer. But there would be wide • agreement amongst those who make use o f the concept o f a possible world that one does not fully specify a possible world merely by saying that w i t h respect to i t , Fraser is an opera singer (Plantinga, 1974, pp. 4 4 - 5 ) : A possible world, then, is a possible state o f affairs - one that is possible i n the broadly logical sense. But not every possible state o f affairs is a possible world. To claim that honour, a state o f affairs must be maximal or complete.... [ A ] state o f affairs S is complete or maximal i f for every state o f affairs S', S includes S' or 5 precludes 5'. In fact, there are two slightly different ways in which the idea that a possible world is a maximal or complete state of affairs may be developed. On the one hand, we may consider states o f affairs which are maximal relative to a given language, where a state o f affairs is maximal relative to L just in case, w i t h respect to that state o f affairs, each 199

Necessity

and

Actuality

sentence o f L is determinately eitlier true or false. On the other hand, we may consider states o f affairs which are maximal relative to all possible languages, that is, which are such that, w i t h respect to that state o f affairs, every sentence of every language (including languages which no one uses or even could use) is determinately either true or false. The relation between the two concepts o f maximality is analogous to the relation between regions and points o f space. Fully determinate states are like points. States which are maximal relative to a language L are like regions whose points cannot be distinguished b y sentences o f L . Regions are divisible: a language can be extended so as to make finer discriminations. A n d points are the (perhaps idealized) limits o f this process o f division. There are doubts that can be raised about the coherence o f the notion o f a fully determinate counterfactual state o f affairs (see Appendix 9). I n any case, let us opt for regions rather than points. Then a possible w o r l d can be specified by a set o f sentences o f the language in question. Some philosophers might, indeed, prefer to identify possible worlds w i t h sets o f sentences (or w i t h sets o f propositions expressed by (context independent) sentences). But nothing actually requires this. I t is open to us to agree w i t h Lewis (1973, p. 85; and, in effect, w i t h Stalnaker, 1976, p. 70) that 'Possible worlds are what they are, and not some other thing'. To say that a possible w o r l d is a possible state o f affairs (actual or counterfactual situation) which is maximal relative to a certain language, and to say no more, may be to suggest that the concept o f a possible w o r l d can provide a reductive explanation o f the concepts o f broadly logical necessity and possibility. But, i n reality, the direction o f explanation is quite the reverse. The question which cries out for an answer is 'Which states o f affairs are possible?' A set o f sentences cannot be used to specify a possible w o r l d unless i t is genuinely possible that those sentences should all be true together (that is, unless the sentences are compossible). This requirement clearly rules out the occurrence in a single set of a sentence together w i t h its own negation, and i t rules out the occurrence o f such pairs as Someone is an oculist. No one is an eye doctor.

Necessity

that Whitlam should have been an alligator just in case 'Whitlam is an alligator' is true w i t h respect to some possible world (just i n case in some possible world Whitlam is an alligator). But this is a constraint upon the concept o f a possible world. (Someone who did not recognize i t as a constraint would not have grasped the concept o f a possible world.) I t is not an explanation (or even the beginning o f an explanation) o f the concept o f broadly logical possibility. The intermediate position which we have been attempting to mark out embodies the claim that the notion o f a possible world is conceptually posterior to the notion o f broadly logical possibility. But i t does not commit us to abstinence from modal theorizing (cf. Lewis, 1973, p. 85). Someone could adopt this intermediate position and go on to relate the question whether i t is possible that Whitlam should have been an alligator (and so, derivatively, the question whether there is a possible w o r l d in which Whitlam is an alligator) to more general philosophical questions about the relation between an object and its origin. He could proceed to draw an analogy between the causal continuity from origin to object and the causal continuity o f an object persisting through time. He could discover or invent ties between continuity, identity, and sortal predicates. Such a philosopher, whether his reasoning yielded essentiahst or anti-essentialist conclusions, would be engaged in modal theorizing. Nor does the intermediate position involve the claim that possible worlds exist only as a product o f our thought, that possible worlds are creatures o f our imagination (Lewis, 1973, p. 88), or that questions as to what possible worlds there are can be settled by stipulation (of. McGinn, 1981). Finally, we should clarify the use o f the expression 'the actual w o r l d ' . One amongst the possible worlds is actual, or obtains. This possible world is the actual world. I t is an abstract object just like all the other possible worlds. The actual world (in this sense) is not to be identified w i t h Lewis and all his surroundings. Its actuality consists i n the fact that just those sentences are true w i t h respect to it which are, i n fact, true.

3

M O D A L I T Y A N D TENSE

But questions remain. I t is not obvious, for example, whether the requirement rules out the occurrence o f the English sentence 'Whitlam is an alligator', for i t is not obvious whether i t is possible that Whitlam should have been an alligator. Certamly we can say that i t is possible

As the development o f the discipline o f tense logic parallel to that o f modal logic indicates, there are many formal similarities between temporal adverbs and modal adverbs. These formal similarities and the

200

201

jvecessiiy

una ^ciuuiiiy

underlying conceptual differences are w o r t h pursuing, and can profitably be pursued before we become involved w i t h quantified modal languages. I n order to uncover the conceptual differences we need to bring together some reflections concerning sentences, context dependence, and sentence operators. Let us begm by recalling Dummett's (1973, p. 195) remark about sentences (cf. Section V I . 1): '[Sjentencesare those linguistic expressions by means o f w h i c h i t is possible to do something, that is, to say something.' A n d let us add (cf. Section I I . 2 ) that when a speaker makes an utterance and thereby says something, or asserts something, his utterance is evaluable for T R U T H . ( T R U T H is the primary dimension o f assessment for utterances.) Typically the speaker expresses a belief about the way the world is; i f the w o r l d is, in fact, that way then his utterance is T R U E and his belief is correct. What is more, evaluafion o f an utterance for T R U T H is a once-for-all matter; T R U T H is not temporally relative. Concerning such evaluation Gareth Evans (forthcoming b. Section I ) wrote the following: One who utters the sentence-type ' I t is raining' rules out dry weather only at the tmie o f utterance; he does not rule out later dryness, and hence there can be no argument from the later state o f the weather to a reappraisal o f his utterance. Utterances have to be evaluated according to what they rule out, and so different utterances o f the same tensed sentence made at different times may have to be evaluated (once and for all) differently. (It does n o t , o f course, follow that the T R U T H o f an utterance is, i n general, anything other than a contingent matter.) Putting these points together we have the idea that an indicative sentence is an expression utterances o f which are evaluable for (non-relative) T R U T H . This idea about sentences does not have the consequence that every sentence can be assigned a condition for the application o f a nonrelative truth predicate. On the contrary, a sentence miglrt have semantic properties w h i c h yield a non-relative t r u t h condition only when a context o f utterance is fixed. Let us say that such a sentence is context dependent. While context dependence is absent the connection between the T R U T H o f utterances and the t r u t h o f sentences is very simple, for the t r u t h predicate applicable to sentences is just as non-relative as the T R U T H predicate applicable to utterances. Once context dependence enters, however, a semantic theorist may need to employ a contextrelative t r u t h predicate in his tlreory. I t is then a constraint upon the 202

concept o f context-relative t r u t l i o f s e n t e n c e s t h a t a n u t t e r a n c e of a sentence i n a context is T R U E just in case the sentence is true relative to that context. I n these reflections concerning sentences and context dependence we are simply following Frege (1918, p. 37): But are there not thouglits which are true today but false in she months time? The thought, for example, that the tree there is covered w i t h green leaves, will surely be false in six months time. No, for i t is not tlie same thouglit at all. The words 'this tree is covered w i t h green leaves' are not sufficient by themselves for the utterance, the time o f utterance is involved as well. Without the time-indication this gives we have no complete thought, i.e. no thought at all. Only a sentence supplemented by a timeindication and complete i n every respect expresses a thought. But this, i f i t is true, is tme not only today or tomorrow but timelessly. But we need, in addition, some reflections concerning sentence operators. So long as context dependence is absent we can say, simply enough, that a sentence operator O takes a sentence s to yield a sentence ^Os^ whose meaning depends systematically upon the meaning o f s. A n d , i f O is an extensional or intensional sentence operator, we can add that the strict condition for the (non-relative) truth of 'Os^ depends systematically upon that for the (non-relative) truth o f s. Once context dependence enters, however, we must be more careful. (In particular we must be more careful in our use of the expression 'meaning'.) For a context dependent sentence can be assigned two quite different kinds o f semantic property. I t can be assigned a semantic property just as i t stands, and i t can be assigned a semantic property relative to a given context. Kaplan (1977, Section V I ) has suggested some useful terminology to mark the distinction. A sentence has a character just as i t stands, and i t has a content relative to a given context. I t is the ciiaractcr which 'determines the content in varying contexts'; so the character might be thought of as a function from contexts to contents. Relative to a given context, i t is the content of a sentence which determines (in effect by rule (7) o f Section II.1) a non-relative truth condition. Thus Kaplan's notion of a content corresponds to Frege's notion o f a complete thouglit, and to the traditional notion o f a proposition. A n d the notion o f a character corresponds, perhaps, to the pretheoretic notion of the meaning of a context dependent sentence. 203

Necessity

and

Necessity

Actuality

Having thus distinguished the t w o Icinds o f semantic property which can be assigned to a context dependent sentence, we can continue our reflections concerning sentence operators. I n the case o f a context independent sentence we need consider only a content. (The character can be thought o f as a constant function taking all contexts to that same content.) So i f we have an account o f the application o f a sentence operator 0 to context independent sentences then we have an account o f the way i n w h i c h the meaning (content) o f ^Os^ depends systematically upon the meaning (content) o f x, and we can associate w i t h O a function fo from contents to contents. This account yields immediately and naturally an account o f the application o f O to context dependent sentences. The content o f ^Os^ relative to a given context is simply the value o f the function fo applied to the content o f s relative to that same context. Thus, for example, i f O is an extensional or intensional operator then the account o f the way i n w h i c h , i f 5 is context independent, the non-relative t r u t h condition o f ^Os^ depends systematically upon that o f x provides immediately an account o f the way in w h i c h , i f x is context dependent, the non-relative t r u t h condition o f ^Os^ i n a given context depends systematically upon that o f X i n that same context. Let us explicitly reserve the expression 'sentence operator' for an operator O w i t h the property that the content o f ^Os^ relative to a given context depends systematically upon the content o f x relative to that same context. I n contrast, a context shifting operator is an operator O w i t h the property that the content of 'Os^ relative to a given context depends systematically upon the content o f x relative to other contexts. I t is not easy to provide examples o f context shifting operators from natural languages, since i t is far from clear tliat such operators occur i n natural languages. But the following passage from David Lewis (1980, p. 84-5) provides a theoretically possible example:

I

can be assigned non-relative t r u t h conditions just as they stand. A n d i f we consider a context dependent sentence such as ' I am hungry now' then i t is very clear that the non-relative t r u t h condition o f • ( I am hungry now) i n a given context can be fully accounted for i n terms o f the semantic properties o f ' • ' and the non-relative t m t h condition o f ' I am hungry n o w ' i n that same context. The modal operators are sentence operators, as recently defined. Let us consider second a language w i t h significant use o f temporal adverbs, and let us focus upon the temporal adverbs which are formally analogous to ' • ' and ' 0 ' , namely, 'always' and 'somethnes'. In order to maintain a strict parallel w i t h the modal case one would need to h o l d that i n the temporally modified sentences Always (Whitlam is angry) Sometimes (Fraser is h o t ) the expressions 'Whitlam is angry' and 'Fraser is h o t ' themselves occur as sentences, and the expressions 'Always' and 'Sometimes' are sentence operators, as recently defined. I t is certainly the case that an utterance o f 'Whitlam is angry', for example, in a certain temporal context, that is, at a certain time, is T R U E just in case Whitlam is angry at that time. So the expression 'Whitlam is angry' is (at least when i t stands alone) a (context dependent) sentence. But i f one then represents Always (Wliitlam is angry)

To be sure, we could speak a language i n w h i c h 'As for y o u , I am hungry.' is true i f f ' I am hungry.' is true when the role o f speaker is shifted f r o m me to y o u - i n other words, i f f y o u are hungry. We could - b u t we d o n ' t .

as the result o f the application o f the operator 'Always' to that context dependent sentence then one must acknowledge that 'Always' is not a sentence operator, as recently defined, but a context shifting operator. (The t r u t h o f the temporally modified sentence, relative to a given context, depends upon the t r u t h o f the contained sentence relative t o (all) other contexts.) A n d to acknowledge that is to acknowledge a conceptual difference between the modal and the temporal cases. (The last two paragraphs state the main points o f Evans, forthcoming b. Section I I I . )

Armed now w i t h these reflections concerning sentences, context dependence, and sentence operators, we can compare languages containing modal and temporal adverbs. Let us consider first modal languages. There can be significant use o f modal adverbs w i t h o u t any involvement w i t h context dependence. The atomic sentences o f Z-io, for example.

Someone may try to restore an analogy by pointing out that just as 'Whitlam is angry'is a sentence which is true relative to various temporal contexts and 'Always (Whitlam is angry)' is a sentence which is true just i n case the contained sentence is true relative to every temporal context, so the atomic sentence Xi (of L i o ) , for example, is true relative

204

205

to v a r i o u s a c t u a l a n d c o u n t e r f a c t u a l situations a n d ^ Q s i ^ is a sentence

w h i c h is true just i n case Si is true relative to every actual and counterfactual situation. But pointing this out is not enough. For, according t o this first account o f the temporally modified sentences, 'always' is a context shifting operator. So, i n order to restore an analogy between the modal and the temporal cases, one w o u l d have to show that the relativity o f the t r u t h o f a sentence t o actual and counterfactual situations is a k i n d o f context dependence. But that relativity is not a k i n d o f context dependence; the sentences ( o f L I Q ) to which the modal operators are attached can be assigned contents just as they stand. Kaplan (1977) introduced the notion o f content as corresponding to the pretheoretic n o t i o n o f what is said. I f we were to regard the relativity of t r u t h to situations as a k i n d o f context dependence, then we should have to say (absurdly) that one carmot k n o w what has been said in an utterance o f unless one knows everything that is the case (that is, unless one knows w h i c h possible world is actual). A n d we should have to say that i f the w o r l d had been different i n any respect then something different w o u l d have been said (that is, the very same utterance w o u l d have expressed a different complete thought). There is thus no way to restore an analogy between the modal and the temporal cases i f temporal adverbs are treated as context shifting operators. I t is not obligatory that the temporal adverbs 'always' and 'sometimes' should be treated as context shifting operators. Nor is i t obviously desirable. For so treating those adverbs seems to make more difficult a semantic account o f sentences in w h i c h context dependent expressions like 'a moment ago' occur w i t h i n the scope o f those adverbs. Consider, for example, the sentence 'Sometime, everyone who coughed a moment ago w i l l sneeze'. I f 'sometime' is treated as a context shifting operator then that sentence is true relative to a given temporal context r just i n case, for some temporal context t' the sentence 'Everyone w h o coughed a moment ago sneezes' is true relative to t'. The expression 'a moment ago' is context dependent, so the t r u t h o f the latter sentence relative to the temporal context t' requires that everyone who coughed just before t' should sneeze at t'. But i t is neither necessary nor sufficient for the t r u t h o f the temporally modified sentence relative to the temporal context t, that there should be a time t' such that everyone who coughed just before t' sneezes at t'. What is necessary and sufficient for the t r u t h o f that sentence relative t o t is that there should be a time t' such that everyone who coughed just before t sneezes at t'. Treating those temporal adverbs as context shifting operators is a 206

consequence o f treating the expression 'Whitlam is angry' as a sentence even as i t occurs in 'Always (Whitlam is angry)'. A n alternative strategy is possible, and apparently preferable. One can hold tiiat an expression such as 'Whitlam is angry' is, strictly speaking, ambiguous. As i t stands alone, it is a context dependent sentence, but as i t occurs within the scope o f the temporal adverbs i t is not a sentence at all; rather, i t is similar to a predicate o f times. Let us consider, by way o f analogy, the following two examples. First, suppose that a language contains a range o f one-place atomic predicates 'Pi', . .., 'Pio', together w i t h the quantifiers ' V and ' H ' (and associated variables). A n d suppose that i t is a convention i n the use o f the language that an utterance o f an atomic predicate standing alone is T R U E just in case the predicate is true o f Tiny T i m . Thus a speaker who comes out w i t h 'Pi' says that Tiny Tim is Qi, while a speaker who comes out w i t h '(yvi)PiVi' says that everything is Qi. I n this case the expression 'Pi', as i t occurs in the surface language, is ambiguous as between a sentence and a predicate. A t the level o f input t o a semantic theory this ambiguity would be removed. The surface sentence 'Pi' w o u l d be represented as 'Pi (Tiny T i m ) ' . Second, suppose that the same predicates and quantifiers are used, but that there is a rather different convention governing the use o f atomic predicates standing alone. A n utterance o f an atomic predicate standing alone is T R U E just in case the predicate is true o f the person making the utterance. A speaker who comes out w i t h 'Pi' says that he himself is Qi, while a speaker who comes out w i t h ' ( V v j ) F i i ^ i ' says that everything is Qi. In this case also it would be natural to say that the expression 'Pi', as it occurs in the surface language, is ambiguous as between a (context dependent) sentence and a predicate. A t the level o f input to a semantic theory this ambiguity would be removed. The surface sentence 'Pi' would be represented as 'Pi ( I ) ' (where T is the first person singular pronoun, a context dependent genuine singular referring expression). I n a semantic theory the truth predicate and the reference functor would be relativized to contexts. This relativity would be idle i n the axioms for atomic predicates and for the quantifiers, b u t would be crucial in the derivation o f a truth condition specification for 'Pi(iy. We should expect some such theorem as the following: (yc)[Tr(c,'Pi(iy)CT2)^ requires that i n every possible world, i f all the objects named in Oi exist and are thus and so (as required for the t r u t h o f Oi) then all the objects named i n exist and are thus and so (as required for the t r u t h of 0 2 ) . I n particular, since ' F , o ' is (we suppose) an existence predicate, the sentence ' • ( P I Q W I - ^ / ^ I O ' « 2 ) ' is true just in case i n every possible world, i f exists then Uj exists.

can be heard (or even is naturally heard) as trivially true. I n that case.

This strong interpretation o f ' • ' has very clear merits. (As in the case o f the weak interpretation a certain amount o f care is needed i n constructing a t r u t h theory for a language containing such an operator;

216

217

Whitlam necessarily exists

^

Necessity

and

JWecessity

Actuality

see e,g. Peacocke, 1978.) I n fact, everything which can be expressed

sentence

usmg ' • ' under the weak interpretation can also be expressed using

'Whitlam is necessarUy human') the modal adverb operates only upon

operators, and that in these last two sentences (and in

' • ' under this strong interpretation. For example, what under the weak

a predicate ( i n the first, 'was born o f Judy Garland', and in the second,

interpretation is expressed by ' • / ' i W i ' is expressed under the strong

'gave b i r t h to l i z a MinneUi'). David Wiggins (1976) has urged just this.

interpretation by ' • ( / ' l o W i - > / ' I O T I ) ' (cf. Hazen, 1976, p . 3 3 ) . There

On his view modal adverbs can modify whole sentences, i n which case

are thus at least t w o views which a semantic theorist might take about

'necessarily' corresponds t o ' • ' under the strong interpretation. But

the use o f modal adverbs i n English. On the one hand, he might h o l d

they can also, w i t h o u t ambiguity, modify predicates, and a sentence

that the modal adverbs are ambiguous, and i n particular that 'necess-

made up of, say, a name and a necessitated predicate is true just in

arily' is ambiguous as between ' • ' under the weak interpretation (the

case in every possible w o r l d in which the named object exists i t has

preferred reading in claims about essential nature) and ' • ' under the

the property associated w i t h the predicate.

strong interpretation (the preferred reading i n modal claims about

Clearly there are a number o f things which a semantic theorist must

existence). On the other hand, he might h o l d that 'necessarily' is

do i f he is to make progress on this issue. He must obtain (presumably

univocal, and that speakers do not quite say what they mean (s-mean)

f r o m a linguist) data about the use o f modal adverbs i n natural languages.

when they make essentialist clakns. What a man w h o comes out w i t h

He must find a way to evaluate claims that the modal adverbs are

'Whitlam is necessarily h u m a n ' or 'Necessarily Whitlam is human'

ambiguous. A n d he must examine the semanfic nature o f the k i n d o f

strictly

and literally

univocally t o ' • '

says is false

(since

'necessarily'

corresponds

expression (modifying sentences or predicates) o f which, according to

under the strong interpretation). I n order t o say

Wiggins, modal adverbs are examples. I n particular, he must scrutinize

what he means ( w h i c h is more arguably true) the man should come

the claim that there is no ambiguity i n the use o f such expressions to

out w i t h 'Necessarily, i f Whitlam exists then he is human'.

modify b o t h sentences and predicates. EquaUy clearly, this is not the

I t is not clear that we can choose between these views given only

place to commence this massive task.

the facts which we have before us. But i n any case there is a (final) feature o f the use o f modal adverbs to w h i c h neither view answers particularly w e l l . Consider the two sentences Liza MinneUi was necessarily born o f Judy Garland Judy Garland necessarily gave b i r t h to Liza MinneUi. Many

speakers regard these sentences as requiring quite different

things for tlieir t r u t h , even though 'was born o f is just the converse o f 'gave b h t h t o ' . The first sentence is naturally heard as requiring for its t r u t h that in every possible w o r l d in which Liza Minnelli exists Judy Garland also exists and Liza Minnelli was born o f Judy Garland. The second sentence is naturally heard as requiring for its t r u t h that i n every possible w o r l d i n which Judy Garland exists Liza MinneUi exists and Judy Garland gave b i r t h t o Liza MinneUi. The first view, upon which 'necessarUy' i n sentences such as these corresponds t o ' • ' under the weak interpretation, clearly does not answer weU t o these facts about

NOTES In this chapter I am particularly indebted to Christopher Peacocke, Gareth Evans, and Stephen WiUiams. See Peacocke (1978), and for my earUer thoughts on this topic Davies (1978). Section V I I I . 3 relies very heavily upon an unpubhshed ancestor of Evans (forthcoming b), and upon numerous conversations w i t h Gareth Evans and Christopher Peacocke (to whom the points in the last two paragraphs of the section are attributable). Section V I I I . 4 owes a great deal to conversations w i t h Stephen Williams, to whom almost all the points i n the last five paragraphs of that section are attributable. The version of the Frege argument which is discussed in Section V I I I . 4 is not, perhaps, the most familiar version. See, for example, Davidson (1967, p. 3), Taylor (1976, pp. 266-74), and for Frege's version, 'On sense and reference' (1892, p. 64). On quantified modal logic i n general, see Kripke (1963).

language use. The second view can be made t o answer, b u t only by a relatively compUcated story about speakers failing t o say what they mean. What this suggests, perhaps, is that modal adverbs are not simply

218

219

I X

ACTUALITY

We n e e d to e x t e n d our m o d a l language b y the addition o f a n

operator

'A' corresponding to the adverb 'actually'. The main semantic feature o f such an operator is that for any sentence a, 'Ao^ is true w i t i i respect t o a given possible world just i n case a is true w i t h respect to the actual world (that is, just i n case a is actually true). Using this operator we can represent the Enghsh sentence ( w i t h a proviso t o be mentioned i n a moment) as follows. 0 ( V x ) (A (x is red) ->• x is shiny)

1

A C T U A L I T Y A N D M O D A L LOGIC

Consider the English sentence I t is possible that everything which is actually red should have been shiny. This sentence cannot, i t seems, be represented i n a quantified modal language such as Z, n . Certainly 0 ( V x ) (x is red -> x is shiny) w i l l not do. For that sentence is true just i n case there is a possible w o r l d in which everytliing which is red is also shiny, whereas the t r u t h o f the EngUsh sentence does not require that there be a possible world in w h i c h some thhigs are b o t h red and shiny. Equally certainly ( V x ) (x is red -> 0 ( x is shiny))

This sentence is true just in case there is some possible world w w i t h respect to which the sentence which follows ' 0 ' is true. That latter sentence is true w i t h respect to a world w just i n case, for each object X (in w), i f 7 is a name o f that object and 'A (y is red)' is true w i t h respect to w then ^y is shiny' is true w i t h respect to w. The sentence 'A (y is red)' is true w i t h respect to w just in case 'y is r e d ' is true w i t h respect to the actual world, that is, just i n case x is actually red, while ^7 is shmy' is true w i t h respect to w just in case x is shiny in w. Thus, the modal sentence is true just in case there is a possible world w such that every object (in w ) which is red in the actual world (is actually red) is shmy i n w. The proviso is this. Because the domain o f quantification varies from world to world, and i n particular because m some possible worlds objects which exist i n the actual world may fail to exist, the modal sentence containing 'A' is not quite equivalent to the Enghsh sentence w i t h which we began. For the sentence ( V x ) (A (x is red)

x is shiny)

may be true w i t h respect to a world in which some or all o f the objects which exist (and are red) in the actual world fail to exist. But intuitively what is requhed for tlie t r u t l i o f the English sentence is that there be a world m which all the objects which exist i n the actual world and are red m the actual world exist and are shiny. Evidently some alteration is needed in our account o f the conditions for the truth w i t h respect to possible worlds o f quantified sentences. But any alteration must leave i t the case that what is requhed for the t r u t h o f

w i l l not do. For that sentence is true just i n case, for each thing which is (actually) red, there is a possible world i n w h i c h that thing is shiny, whereas the t r u t h o f the English sentence requires that there be a possible w o r l d m w h i c h all the things which are actually red are shiny together. I t is not merely lack o f mgenuity which prevents us from fmdkig a way to represent the Enghsh sentence. I n order to avoid the inadequacy o f the second candidate i t is crucial that the universal quantifier occur w i t h i n the scope o f the modal operator ' 0 ' . But once the modal operator has wider scope than the quantifier a different inadequacy (that o f the first candidate) is inevitable.

for example, is just that there be a possible world w such that everything i n w which is not red in w is shiny i n w. It is quite difficult to see exactly what alteration is called for, and the difficulty is not reduced by considering (as ultimately one must) modal languages w i t h binary quantifiers instead o f ' V and ' H ' .

220

221

0 ( V x ) (~ (x is red) -> x is sliiny)

The

semantic

importance

tfie

of

'actually' operator

is, however,

largely independent o f these problems. Let us resort again to the pretence that the domain does not vary from w o r l d to w o r l d , and i n particular t l i a t everything which exists i n the actual w o r l d exists i n every possible w o r l d . Then, even given this pretence, the English sentence w i t h which we began cannot be represented i n a quantified modal language such as Z-n , for the inadequacies i n the two candidates which we considered had nothing to do w i t h the merely contingent existence o f red objects. But that English sentence can be represented w i t h the help o f and, given the pretence, no proviso is required. (The example employed i n these paragraphs, and much else i n this section, is borrowed from Crossley and Humberstone, 1977; see also Hazen, 1976, p p . 3 5 41.) Let us now consider some o f the more formal properties o f the 'actually' operator. Suppose that we wanted to give a t r u t h theory for a simple modal language ( w i t h o u t quantifiers) containing the operator 'A'. Then the theory w o u l d be cast i n a. ML the background logic o f w h i c h contained axioms for 'A'. Indeed, the modal component o f the background logic w o u l d be the system S5A which contains the axioms and rules o f S5 ( c f Section V I I I . 1) together w i t h the following four axiom schemata for 'A': (Al) (A2) (A3) (A4)

A(a^P)^(Aa^Afi) Aa —A-^a net ^ Aa Aa -> DAa.

The schema (A4) may seem a little surprising, b u t i t answers to the fact that since the t r u t h o f 'Aa^ w i t h respect to any possible w o r l d depends only upon the t r u t h o f a w i t h respect to the actual world, i f U a ' is true w i t h respect to any w o r l d then i t is true w i t h respect to every w o r l d . The other axiom schemata are clearly faithful to the intended meaning o f 'A\

•

(Va)

[TrCAo^)

Tr{a)\

( w i t h the language parameter suppressed), strict t r u t h condition specifying biconditionals for sentences contaming ' / I ' are forthcoming. On the side of model theory, also, the introduction of ' ^ ' is relatively straightforward. As before, a model is a triple where Wi% a set, w* is a particular designated member o f W, and K assigns to each ordered pair o f a member o f W and an atomic sentence a t r u t h value. The function V is extended to V*, and the clause for ' / I ' is, o f course, V*(w,

'Aa^)

= Tiff

V*(w*, a) = T.

A httle care is needed w i t h the notion o f validity, however. In the case o f a modal language w i t h o u t 'A' (such asZ-io), i f a sentence is true w i t h respect to the designated w o r l d ( w * ) in every model then the sentence is true w i t h respect to every w o r l d in every model. (Recall that for the purposes o f model theory the members o f W, the 'worlds', can be assumed to be set theoretic objects.) For suppose that Wj and are both members o f W and that a sentence a is true w i t h respect to Wj i n the model . Then a is also true w i t h respect t o i n the model , since the truth o f a sentence (not containing 'A') w i t h respect to a world, in a model, is independent o f which world is designated. B u t for sentences containing 'A' this is no longer the case. Suppose that F ( w i , a) = T and F ( w 2 , a) = F. Then U a ' is true w i t h respect to i n the model , but not true w i t h respect to Wi in the model . Thus, for such sentences we have to distinguish two notions o f validity. A sentence is generally valid just in case i t is true w i t h respect to every w o r l d i n every model. A sentence is real world valid just i n case it is true w i t h respect to the designated world in every model. The axioms o f the system S5A are geared to the notion of general validity. (They are complete in the sense that they yield as theorems all sentences which are generally valid.) A system geared to the notion o f real world validity would have as a theorem schema

As a consequence o f (A2) and (A3) we have the theorem schema Aa

• (a ^ |3) -> (^a ^ A0) and thence, via the S4 axiom and Nec (or via (Al),

(A4),

and Nec),

the schema • (a ^|3) -* n(Aa

Aj}).

This is enough t o ensure that i n a t r u t h theory containing the axiom 222

a

smce sentences o f that form, while clearly not generally valid, are certainly real w o r l d valid (and provide the best example o f the distinction). A n d i t w o u l d impose some restriction upon the rule Nec, for i t would not have as a theorem schema • (^a

*>a)

223

s i n c e s e n t e n c e s o f t h a t f o r m a r e n o t , i n g e n e r a l , even real world valid. This is not the place to argue the relative merits o f these two notions o f vahdity. It is enougli that they be distinguished.

2

A C T U A L I T Y , F I X E D A C T U A L I T Y , A N D NECESSITY

We noted (in Section I X . 1) that at first glance the axiom schema {A4) may seem surprising. Let us reflect upon i t further. The sentence ^2 means that the earth moves. I t expresses a t r u t h , but a t r u t h which can be k n o w n only a posteriori. One cannot k n o w a priori that the earth moves. Nor can one know a priori that actually the earth moves. So the sentence ^As2^ expresses a t r u t h , b u t a t r u t h which can be k n o w n only a posteriori (that is, an a posteriori truth). On the other hand, since 'Asi^ is true so also, (A4) assures us, is ^OAs2^. The sentence 'As2^ is necessarily true. Kripke (1972, pp. 260-3) has urged that philosophers should not confuse the distinction between the necessary and the contmgent w i t h that between the a priori and the a posteriori. I n ^As2^ we have a very clear example o f a sentence which expresses a necessary b u t a posteriori t r u t h . Rather similarly we have i n 'As2 ^ S2^ a very clear example o f a sentence w h i c h expresses a contingent but a priori t r u t h . One can know a priori that the earth actually moves i f f the earth moves. (Such knowledge is constitutive o f mastery o f the concept o f actuahty.) But the sentence ^As2 •^S2^ is not necessarily true. For suppose that i t were, that is, suppose that •'•(71x2 •^Xj)^ were true. Then ' n A s 2 -^Os2'' would be true also, and so (by (A4)) would 'As2 ^ 0 ^ 2 ^ • But 'As2^ is true while ^Os2' is false. There is more that can, and should, be said about these examples. Certainly ' is necessarily true m the sense o f 'necessarily' which is expressed by ' • ' . But, it is natural to say, i n some sense of'necessarily' (yet to be made precise) the sentence 'As2^ is not necessarily true. That sentence is true because ^2 is true w i t h respect to the actual w o r l d ; i t w o u l d have been false i f another possible w o r l d ( i n which the earth does not move) had been actual. The problem w i t h the modal languages which we have considered so far is that they make no provision for the idea that another possible w o r l d might have been actual. I n the model theory for S 5 A , for example, this is reflected i n the fact that in each model a single w o r l d is designated and for no sentence do we, i n evaluating its t r u t h or falsity in one model, consider variant models in w h i c h other worlds are designated. What is needed to overcome the 224

problei'i is not a replacement for for i t was precisely for its interaction w i t h ' • ' that 'A' was introduced. What is needed, rather, is a further operator (along w i t h ' • ' and 'A') which takes a sentence to make a sentence which is true w i t h respect to a possible world w just in case the contained sentence is true w i t h respect to w whichever world plays the role o f the actual w o r l d . Let us say that, i n that case, the contained sentence is fixedly true w i t h respect to w. Suppose now that ' J ^ ' is such an operator and consider the combination of operators '^A\, for any sentence a, ' .^Aa^ is true with respect to »V2 just in case for every world w, U a ' is true w i t h respect to W2 but w i t h w playing the role o f the actual w o r l d . This, in turn, is so just in case for every world w, a is true w i t h respect to w (with w also playing the role o f the actual world). Thus, for example, ' ^ A s 2 ^ is true (with respect 1° ^2 and w i t h Wi playing the role o f the actual world) just in case for every world w, S2 is true w i t h respect to w (with w also playing tiie role o f the actual world) that is, just i n case in every possible w o r l d the eartli moves. The sentence '^As2'' is equivalent to r n ^ ^ i . But consider, as a second example, tlie sentence '(^A) (As2y . Tliis is true ( w i t h respect to and w i t h Wj playing the role o f the actual world) just in case for every world w, ' A S 2 ' is true w i t h respect to w ( w i t h w also playing the role o f the actual world), that is, just in case in every possible world the earth moves. The sentence '(^A) (As2y is not equivalent to f Q / l x j ' . The former is false while the latter is true. The sentence ^^^2^ is necessarOy true (in the sense o f 'necessarUy' which is expressed by ' • ' ) but i t is not fixedly actuaUy true. There is, then, a sense of 'necessarily' i n which 'As2^ is not necessarUy true, namely the sense expressed by 'fixedly actuaUy'. The sentence 'As2 ^S2^ expresses a conthigeiit a priori t r u t h . Certainly that sentence is not necessarUy true i n the sense o f 'necessarUy' which is expressed by ' • ' . But, i t is natural to say, i n some sense o f 'necessarUy' the sentence ^As2 •^^2^ is necessarUy true. I t is, indeed, fbcedly actuaUy true. For the sentence '(^A) (As2 **S2V is true ( w i t h respect to ^2 and w i t h w , playing the role o f the actual world) just i n case for c'^ery world w, 'As2 **S2^ is true w i t h respect to w ( w i t h w also playing the role o f the actual w o r l d ) that is, just i n case i n every possible voM the earth moves i f f the earth moves. One (informal but suggestive) way o f statmg the mam semantic feature o f i s this. For any sentence a, ' ^Aa^ is true just in case every possible w o r l d has tlie property w h i c h the t r u t h o f a requires o f a w o r l d considered as actual. What the t r u t h o f ^ ^ 2 ' requires o f a

225

and A

Necessity

Actuality

ctviality

w o r l d considered as actual is just what the t r u t h o f ^2 requires o f a

quite w i t h o u t consequence. The sixth schema answers to the fact that and ' • ' are related to variations over exactly the same range o f

w o r l d (considered as actual), namely that i n that possible w o r l d the earth move. So '(^A)As2^

is not true. What the t r u t h o f 'Asi

possible worlds.

^

requires o f a w o r l d considered as actual is, clearly enough, nothing at ^S2y

all. So '(J^A)(As2

is true.

Second, as consequences o f the axioms and rules o f S5A^

we have

the theorem schemata

W i t h this m u c h b y way o f informal motivation for considering languages containing the 'fixedly' operator ' ^ ' alongside ' • ' and

J ^ D (a «|3)-> JJ^D ( D a « •/?) ^nia^P)-^ ^U{Aoi , that is, the t r u t h most closely related to the T R U T H o f utterances, the t r u t h at which sincere assertion aims, the t r u t h (one might say) which reahy matters. But we do not have i n the present (nor, i t seems, i n any other) example the combmation o f a priority and contingency i n that second sense (see Evans, 1979, p. 161). Let us now attempt to extend this strategy for dispelling the initial puzzlement which surrounds very simple examples o f the contingent a priori, so as to dispel such initial puzzlement as may surround examples o f the k i n d which Kripke gave. Here is an example o f that k i n d . Suppose that a group o f philosophers come to be impressed by the illumination provided by two dimensional modal logic, but lack any knowledge at aU as to the origins o f that discipline. Suppose that they nevertheless beheve that there is some member o f the past or present philosophical community who can reasonably be regarded as the inventor o f two dimensional modal logic. A n d suppose that they introduce the expression ( w i t h the syntactic form o f a name) 'Bruce F i x ' w i t h its reference fixed by the description 'the inventor o f t w o dimensional modal logic'. According to Kripke those philosophers are i n a position to know a priori that i f anyone uniquely invented two dimensional modal logic then Bruce Fix invented two dunensional modal logic. Yet the sentence (BF)

I f anyone uniquely invented two dimensional modal logic then Bruce Fix invented two dimensional modal logic

is only contingently true since the sentence which results from prefixmg (BF) w i t h ' • ' is false; i f Gough Whitlam had been a philosopher he might have invented two dunensional modal logic. (This example is simply a variant o f that discussed i n Evans, 1979, see p. 163 and pp. 1 7 0 - 1 . Cf. also Kripke, 1972, pp. 347-8, note 33.) 232

Actuality

To see how such initial puzzlement as surrounds this example may be dispelled, imagine for a moment that the philosophers had instead introduced the expression 'Bruce Fix'as an abbreviation for the definite description 'the actual inventor o f two dimensional modal logic'. One can certainly know a priori that i f anyone uniquely invented two dimensional modal logic then the actual inventor o f two dimensional modal logic invented i t . There is nothing more puzzhng about that piece o f a priori knowledge than there is about a priori knowledge that snow is actually white i f f snow is white. A n d the sentence {BF')

I f anyone uniquely invented two dimensional modal logic then the actual inventor o f two dimensional modal logic invented two dimensional modal logic

is contmgent i n the sense related to ' • ' . I f w , is the actual world then {BF') is true w i t h respect to w-i just in case i f anyone uniquely invented two dhnensional modal logic in then whoever invented i t in Wj invented i t i n w-i. Since in some possible worlds Whitlam or Tiny T i m invented two dimensional modal logic, the sentence which results from prefixing (BF') w i t h ' • ' is false. There is nothing more puzzling about that contingency than there is about the contingency (in the sense related to ' • ' ) o f 'Asi - ^ S i ' . And the persistent intuition that all a priori truths are, in some sense, necessary is answered to by the fact that {BF') is indeed true w i t h respect to every possible world considered as actual, so that the sentence which results from prefixing {BF') w i t h ' i ^ / l ' i s true. Had the philosophers introduced the expression 'Bruce F i x ' as an abbreviation o f the description 'the actual inventor o f t w o dimensional modal logic' then they would have provided themselves w i t h a clear, and not persistently puzzUng, example o f the contmgent a priori. The philosophers i n the example introduced the expression 'Bruce Fbc' w i t h its reference fixed by the description 'the inventor o f two dimensional modal logic'. A l l that is required in order that this and other Kripkean examples should not be persistentiy puzzUng is that Kripke's notion o f reference fixing should be interprctablc in such a way that fixing the reference o f an expression by a description has the same net effect (in point o f a priority and contingency) as introducing the expression as an abbreviation for the corresponding description begmning w i t h 'the a c t u a l . . .' instead o f ' t h e . . . ' . There are two features o f the description 'the actual inventor o f two dimensional modal logic' which are crucial in point o f a priority and 233

contingency. T h e first is that t h e man, F r a n l c V l a c h , to w h o m the description applies is tc-salient. The second is that that man is not e-salient. First, the concept o f tc-salience was introduced i n respect o f the objects referred to by gcnuhie singular referring expressions (cf. Section V.2). I f a name refers to a certain object then the t r u t h ( w i t h respect to actual and counterfactual situations) o f sentences containing the name depends upon how things are (in those situations) w i t h that object. A n d tc-sahence was explicitly related to the substitutabUity o f co-referrmg names salva veritate w i t h i n the scope o f the modal operators ' • ' and ' 0 ' . We did not, at that stage, consider such operators as M ' and But we can now say, w i t h a Uttle more precision, that an object is tc-salient for sentences containing a certain expression just i n case the t r u t h o f those sentences w i t h respect to possible worlds (the actual w o r l d bemg held constant) depends upon how things are w i t h that object i n those possible worlds. I t is a consequence o f this definition that the man Frank Vlach is tc-salient for sentences containing the expression 'the actual inventor o f t w o dimensional modal logic' and for sentences containing the genuhie singular referring expression 'Frank Vlach'. Thus any sentence • (the actual inventor o f t w o dimensional modal logic is thus and so) has the same t r u t i i value as • (Frank Vlach is thus and so) and any sentence 0 ( t h e actual inventor o f two dimensional modal logic is thus and so) has the same t r u t l i value as 0 (Frank Vlach is thus and so). (Thus the special k i n d of definite description beginning w i t h ' t i i e * ' , mentioned i n Section V.3, is equivalent to a definite description beginning w i t h 'the actual'.) It is the tc-salience o f the object to which an 'actualized' description applies that is crucial in point o f contingency (in the sense related to ' • ' ) . The sentence {BF') is contingent (in that sense) for the same reason that the sentence I f anyone uniquely invented t w o dhnensional modal logic then Frank Vlach invented two dimensional modal logic 234

is c o n t i n g e n t ( i n t h a t s e n s e ) . ( S e e E v a n s , 1 9 7 9 , p p .

184-5.)

Second, the concept o f e-salience was also introduced in respect o f the objects referred to by genuine singular referring expressions. I f a name refers to a certain object llicn tlic bcHcfs expressed by sentences containing the name are not indifferent to the existence or non-existence o f that object. (They are existence dependent.) And e-salience was explicitly related to the obtaining o f appropriate (information yielding) causal relations between the (medium-sized material) object referred to and the person who has the behefs. I f the man Frank Vlach were e-salient for sentences containing the expression 'the actual inventor o f two dimensional modal logic' then i t would not be possible for the philosophers i n the example (who do not stand i n an appropriate causal relation to that man) to know a priori, or even to beheve, that i f anyone uniquely invented two dimensional modal logic then the actual inventor of two dimensional modal logic invented two dimensional modal logic. I f the man Frank Vlach were e-salient then tlie philosophers in the example could know (perhaps a priori) that tiie sentence {BF') expresses a t r u t h , but they could not know (a priori or any other way) the truth which i t expresses (cf. Donnellan, 1977, p. 18 and Evans, 1979, p. 172). But tiiat man is not e-salient. Notiiing more in tlie way o f causal mteraction is requhed for knowledge (or beheQ that the actual inventor o f two dunensional modal logic is thus and so than is required for knowledge (or beUef) that the inventor o f two dunensional modal logic is thus and so. A l l that is required in addition is knowledge (available a priori) o f what the actuality o f the actual world consists i n . (See Evans, 1979, p. 178.) The Kripkean examples o f the contingent a priori wiU not be persistently puzzUng provided that the notion o f reference fixing used in those examples is interpretable in such a way tiiat i f the reference o f an expression is fixed by description tlien the object to whicli the description applies is tc-salient but not e-salient for sentences containing that expression. That the object is tc-saUcnt is quite explicit in Kripke's account. Where we have said that an object is tc-saliciil for sentences containing an expression, Kripke would say Uiat the expression rigidly designates the object. After giving his example of the contingent a priori he said the following (Kripke, 1972, pp. 274-5): [Tjhere is an intuitive difference between the phrase 'one meter' and the phrase 'the length o f S at '• The first phrase is meant to designate rigidly a certain length i n aU possible worlds, which in 235

t h e a c t u a l w o r l d h a p p e n s t o b e t h e l e n g t h o f t h e s t i c k S a.t to.

i n t e r p r e t a t i o n , it is t e m p t i n g t o d r a w a n a n a l o g y b e t w e e n the s e n t e n c e s

On the other hand 'the length o f 5 at f o ' does not designate anything rigidly.

in Kripkean examples and the context dependent sentence ' I am here', and to point to the contrast between knowing a priori that relative to any context o f utterance, that sentence expresses a t r u t h , and (what is impossible) knowing a priori where one is (see e.g. Blackburn, 1981, Section 3.3.3, and D u m m e t t , 1973, p. 122). But this first alternative interpretation o f the n o t i o n o f reference fixing, even i f i t were the only interpretation possible, w o u l d leave many examples o f contmgent a priori truths (those i n which there is expUcit use of 'actually') quite untouched. A n d , as we have seen, i t is not the only interpretation possible. There is, mdeed, a contrast between knowing a priori that the sentence {BF), for example, expresses a t r u t h and knowing a p n b n the t r u t h which i t expresses. But the second kind o f a priori knowledge is far f r o m impossible.

That the object is not e-saUent seems, at least, to be implicit i n Kripke's account. He offered as an example the expression 'Jack the Ripper' (ibid. p. 291): Another case . . . might be when the police i n London use the name 'Jack' or 'Jack the Ripper' to refer t o the man, whoever he is, w h o committed all these murders, or most o f them. Then they are giving the reference o f the name by a description. A n d he drew a contrast between the case o f an ordinary proper name and the case o f a name w i t h its reference fixed b y description. I n the former case 'it's i n virtue o f our connection w i t h other speakers i n the cormnunity, going back to the referent himself, that we refer to a certain m a n ' (ibid. p. 301). I n the latter case (ibid.): some man really gives a name by going into the privacy o f his room and saying that the referent is t o be the unique thing w i t h certain identifying properties. 'Jack the Ripper' was a possible example w h i c h I gave. The expression 'reference fixing' is, perhaps, potentially misleading since an expression w h i c h is introduced w i t h its reference fixed by description is not a genuine singular referring expression. But what is more i m p o r t a n t is that we have an interpretation o f the n o t i o n o f reference fixing such that introduction o f an expression w i t h its reference fixed by description gives rise to clear, but not persistently puzzling, cases o f the contmgent a priori. ( A n d this interpretation seems to be consistent w i t h Kripke's own use o f the notion.)

On the second alternative interpretation, a name w i t h its reference fixed by description is not a genuine singular referring expression but simply an abbreviation o f the reference fixing description, governed by a convention that sentences containing the name are always heard as though the description has wider scope than the modal operators ' • ' and ' 0 ' . I n that case the sentences i n the Kripkean examples express a priori truths but are not contingently true (in the sense related to ' • ' ) . For suppose that the expression 'Fred' is an abbreviation o f 'the F, governed by that convention. Then the sentence I f anything is uniquely F then Fred is F is, since i t does not contain ' • ' or ' 0 ' , an abbreviation o f I f anything is uniquely F then the

Fi%F

and so expresses an a priori truth. But that sentence is not merely contingently true; i t is necessarily true. The appearance o f contingency results f r o m the fact that the sentence

There are two .other possible interpretations o f the notion o f reference fixmg w h i c h deserve mention. On each o f these interpretations, the allegedly contingent a priori truths provided i n Kripkean examples are either not contingent or else not a priori. On the first alternative interpretafion a name w i t h its reference fixed b y description is a genuine singular referring expression. I n that case, the sentences in Kripkean examples are contingently true ( i n the sense related to ' • ' ) but the truths w h i c h are expressed b y those sentences are not a priori. A l l that can be k n o w n a priori is that those sentences express truths. (This is the interpretation offered i n Donnellan, 1977.) Given this

and so i t is not, properly speaking, the sentence on whose t r u t h or falsity the contmgency o f the original sentence turns (cf. Dummett, 1973, pp. 112-28).

236

237

• ( I f anything is uniquely F then Fred is F) is indeed false. But this sentence is a (rather misleading) abbreviation o f The F is an object x such that • ( i f anything is uniquely F then xisF)

In

order

to

deal w i t h

all the e x a m p l e s

of

the contingent a

priori

which we liave discussed, tliis alternative interpretation w o u l d need to be coupled w i t h the claim that 'actually' is itself simply a conventional indicator o f scope (rather like 'any' or 'a certain' (cf. Section VI.2) so that, for example, • (Snow is actually white i f f snow is white) is false only because i t is a (rather misleading) version o f Snow is white i f f • ( s n o w is white).

a n d a priority. W e c a n leave i t o p e n w h e t h e r s u c h descriptive n a m e s a s may occur in natural languages are best regarded as explicitly abbreviatory devices. The expression 'Bruce F i x ' is a descriptive name o f a man and 'Frank Vlach' is an ordinary proper name o f that same man. One can know only a posteriori that Bruce Fix is Frank Vlach. (And one can know only a posteriori that i f anyone uniquely invented two dimensional modal logic then Bruce Fix is Frank Vlach.) Yet the sentence

Bruce Fix is Frank Vlach

Sunilarly, according to that claim, the sentence which results from prefixing {BF') w i t h ' • ' i s false only because i t is a version of The inventor o f two dimensional modal logic is an object X such that • ( i f anyone uniquely invented two dhnensional modal logic then x invented two dhnensional modal logic). But the claim that 'actually' is simply a scope indicating device (so that everything which can be said using 'actually' can be said w i t h o u t i t provided that one is careful about scope distinctions) is incorrect. That was the point o f the original example I t is possible that everything which is actually red should have been shiny. A n d , even i f the claim were correct, i t w o u l d still be theoretically possible t o introduce an operator w i t h the semantic properties o f our 'y4' and so to provide a host o f examples o f the contingent a pn'ori. So this second alternative interpretation o f the n o t i o n o f reference fixing, even i f i t were the only interpretation possible, w o u l d leave many examples o f contmgent a priori truths quite untouched. A n d , as we have seen, i t is not the only mterpretation possible.

is ( w i t h a certain proviso) necessarily true in the sense of 'necessarily' expressed by ' • ' . (The proviso is that we ignore two problems which arise because men exist only contingently. One problem (related to the occurrence o f the ordinary proper name) is whether ' • ' is to be given a weak or a strong interpretation ( c f Section V I I I . 4 ) . The other problem (related to the occurrence, i n effect, o f a description containing 'actually') is how, exactly, quantifiers are to be interpreted when they occur w i t h m the scope of ' • ' or ' 0 ' and have ' / I ' occurring within then scope ( c f Section I X . l ) . ) Thus descriptive names provide clear examples o f identity statements which express necessary a posteriori truths. The identity statement is not, however, necessarily true in the sense o f 'necessarily' expressed by '^A\r the truth o f that sentence w i t h respect to a world w considered as actual requires that Frank Vlach invented two dimensional modal logic in w. If, in w. Tiny T i m invented t w o dimensional modal logic then the sentence Bruce Fix is Tiny T i m

Let us say that an expression which has the syntactic form o f a name and is mtroduced either w i t h its reference fixed by description or else as an abbreviation o f an 'actualized' description is a descriptive name. (This is the terminology o f Evans, 1979.) The two ways o f introducing a descriptive name have the same net effect i n point o f contingency

is true w i t h respect to w considered as actual, and an utterance in w o f that sentence would be a T R U E utterance (whUe an utterance in w o f 'Bruce Fix is Frank Vlach' would be a FALSE utterance). This provides a sharp contrast with identity statements in which two genuine singular referring expressions are used. Consider, for example, the two names ' w i ' and ' w i ' (in the language Ag) and suppose that 'Ri' is an identity predicate. Let us write 'mi = ^ 2 ' instead o f ' / ? i ( m i , m , ) ' . Then i f ' m , = ^ 2 ' is true i t is necessarily true in the sense o f 'necessarily' expressed by ' • ' and i n the sense expressed by 'S'A \t i t is necessarily true in the first sense is, of course, guaranteed by the tcsalience o f the objects ni and n-^. That i t is necessarily true i n the second sense is a consequence o f the fact that there is nothing i n the

238

239

4

A C T U A L I T Y A N D T H E NECESSARY A

POSTERIORI

semantic properties o f ' w j * , f o r e x a m p l e , t o a l l o w t h a t t h e r e f e r e n c e o f 'nil' could vary w i t h a variation i n which possible world is considered as actual. I f i n w o r l d w the object is not Qi but the object «3 is Qi, then the sentence ' P i ^ i ' is false w i t h respect to w considered as actual and an utterance in w of that sentence is a FALSE utterance. What is more, the belief expressed i n an utterance, i n that w o r l d , o f tliat sentence is a behef w h i c h i t w o u l d be impossible to have i f « [ were not to exist. I f an utterance i n w o f the sentence T i W i ' is T R U E i n some language, and expresses a belief which i t w o u l d be possible to have i f were not to exist but would be impossible to have were « 3 not to exist, then that language is a different language and i n i t the expression 'mi' has quite different semantic properties from those w h i c h i t has i n Z,^. The relation o f genuine smgular reference is not at all w o r l d relative. The relation between a descriptive name and its bearer is singly w o r l d relative: i t varies only w i t h w h i c h possible w o r l d plays the role o f the actual w o r l d . In general, the relation between a definite description and the object to w h i c h i t applies is doubly w o r l d relative. As such an example as the best friend o f everyone who actually came to the party shows, the relation varies b o t h w i t h w h i c h possible w o r l d plays the role o f the actual w o r l d and w i t h w h i c h possible w o r l d i t is w i t h respect t o w h i c h sentences are evaluated. True i d e n t i t y statements w h i c h contain a descriptive name and a genuine singular referring expression are necessarily true i n the sense o f 'necessarily' expressed by ' • ' b u t not i n the sense expressed by '^A', and they express a posteriori truths. True identity statements w h i c h contain two genuine singular referring expressions are necessarily true i n b o t h senses (and, indeed, in a t h h d sense o f 'necessarily' expressed by '^n'). But they may still express a posteriori truths i f the t w o names, for example, are not synonymous. Thus we cannot hope to establish that all and only sentences w h i c h are necessarily true in the sense o f 'necessarily' expressed by '^A' express A priori truths. The sentences which constitute exceptions to this neat equivalence have to be accounted for, and i n the case o f identity statements they can be accounted for i n terms o f the evident possibility that t w o genuine singular referring expressions might be conventionally associated w i t h quite different ways o f thinking about the same object (cf. Section V.3 and Appendix 4 ) . 240

M a n y p u t a t i v e e x a m p l e s o f t h e n e c e s s a r y a posteriori can, however, be illuminated by the distinction between two notions o f necessity. One example to which the distinction miglit be applied is that o f 'Hesperus' and 'Phosphorus'. These names provide the most favoured case for a description theorist of names just because i t is not wildly implausible that they are descriptive names w i t h their references fixed by descriptions which contain (conceptually modest) predicates furnished by our two ways o f thmking about the planet Venus (cf. Section V.3). Other examples concern expressions which seem to be names o f natural kinds. Kripke (1972, p. 323) discusses the case o f 'water' and ' H j O ' among others. Suppose that 'water' is a descriptive name o f a natural khid (in this case a chemical kind) w i t h its reference fixed by some such description as 'the k m d o f stuff which falls from the clouds as rain, flows in rivers, is colourless, odourless and tasteless (when pure), is drinkable.. . ' . A n d suppose that 'H2O' is an ordinary proper name o f that same chemical kind. Then the sentence 'Water is H2O' is necessarily true in the sense o f 'necessarily' expressed by ' • ' and expresses an a posteriori truth. But i t is not necessarily true in the sense expressed by ' J ^ 4 ' . A n utterance, in a possible world i n which chemically quite different stuff fell from the clouds as rain and so on, o f the sentence 'Water is H2O' would be a FALSE utterance. This brief account certainly seems to accord well w i t h i n t u i t i o n ; i t has the consequence, for example, that mastery o f the word 'water' does not requhe any knowledge o f chemistry. The main alternative account is one on which b o t h 'water' and 'H2O' are genuine singular referring expressions; on which, for example, an utterance o f 'Water is H2O' is T R U E whatever falls from the clouds, unless 'water' has a meaning different from that which it has in our language (cf. Putnam, 1973, pp. 700-4 and 1975, pp. 139-52). Which of the two accounts is uUimately preferable depends in part upon what is required for mastery o f a name o f something (a chemical kind) which is not a mediumsized material object, and so upon what is required i f a person is to have singular behefs concerning such a thing. But this is not the point at which to answer that (difficult) question nor, more generahy, to embark upon an investigation o f the semantic properties o f natural k i n d words. I t is enougli that we have seen how the ideas o f descriptive names and o f a distinction between two notions o f necessity (and o f contmgency) might have apphcation in that area.

yVGc'Cssitj'

unci

.^cjlt^ctlie_y'

NOTES L l o y d Humberstone introduced me to tlie logic of 'actually' i n 1974. Gareth Evans's elegant and convincing solution of the puzzle of the contingent a priori in 'Reference and contingency' (1979) persuaded me to return to the topic. For towards the end of his paper (p. 183) he points out (what is decisive against some purported solutions of the puzzle) that the 'actuaUy' operator generates examples of contingent a priori truths. WhUe 1 was visiting Monash University i n 1979, Lloyd Humberstone and I wrote 'Two notions of necessity' (1980), i n which Evans's solution is located against a background of modal logic with 'actuaUy' and 'fixedly'. The main points of this chapter are drawn immediately from that j o i n t paper. We also announced as forthcoming a more formal paper, 'The logic of " f i x e d l y " ' . This appears as Appendix 10.1 am grateful to L l o y d Humberstone for suggesting that I incorporate that material i n t o the present book. The tense logical analogue of 'actually' is, of course, 'now'; see Kamp (1971). M y claim that Frank Vlach can be regarded as the inventor of two dimensional modal logic is based upon testimony of David Lewis. Vlach was, in fact, working on tense logic. In his doctoral thesis (1973) he introduced an operator whose analogue i n modal logic ' t ' has the property that ^\a^ is true w i t h respect to world H'2 w i t h playing the role o f the actual world just i n case a is true with respect to u'2 w i t h H'2 also playing the role of the actual world. The modal prefix ' D f is equivalent to our '^A'; for the suggestion that ' D f is the a priori t r u t h operator see Stalnaker (1978, p. 320). For a fuUy general account of two dimensional modal logic see Segerberg (1973). See also Aqvist (1973), van Fraassen (1977) and Kaplan (1978). Interesting questions arise when two dimensional modal or tense logic is generalized to more than two dimensions (and ultimately to infinitely many dimensions). Such a generalization was outhned in Vlach's thesis. For a discussion see, for example, van Benthem (1977). On the contingent a priori see e.g. DonneUan (1977) and Schiffer (1977). For some more applications of 'actuaUy' and 'fixedly', see Davies and Humberstone (1980).

242

APPENDICES

APPENDIX 1

In the Preface to Truth and Other Enigmas (1978, p.xxiii), Dummett says: I am inclined at present to believe that it is not merely that a nonclassical theory of meaning will always admit a suitable notion of truth, that is, allow a notion of truth to be defined such that the condition for an assertion to be correct will be that for the sentence asserted to be true, but that, while the notion of trutli will not be fundamental... it will be crucial; that is, that it will play an essential role in the account of the connection between the way in which the meaning of a sentence is given and the use that is made of it. To allow, as Dummett does, that the concept of truth can be introduced via the concept of meaning is not necessarily to allow that the concept of truth is such that truth may transcend all possibilities of verification (cf. Dummett, 1976, and Wright, 1976). So, in particular, to introduce the concept of truth via rule {T) is not necessarily to allow that the concept of truth has that feature. We might agree with Wiggins (1980a, p. 208) that truth is a property such that 'every statement which lacks it lacks it independently of a speaker's means of recognizing it; and every statement which possesses it possesses it independently of a speaker's means of recognizing it'. (This is Iiis tliird mark of truth.) For, in general, a speaker's believing that p is both ways independent of its being the case that p. But (as Wiggins points out) this mark of truth does not require that truth may transcend all possibilities o f verification. Nor, of course, does it rule it out.

245

.

•—-Appenciix

J

is not equivalent to s means (in Z.) that p.

APPENDIX 2

What Wallace (1978, p. 50) offers as a definition of's means that p ' is the following: It is a matter of meaning alone that s is true if and only if p and for all q, if it is a matter of meaning alone that s is true i f and only if q, then it is a matter of the laws of meaning applied in the left-right direction only that if q, then p. This definition allows one to proceed from (ii) to

In 'Logical form, meaning, translation' (1978), Wallace begins by pointing out that 'A translation manual cannot be a theory of meaning; neither can a theory of truth', (p. 45) and goes on to construct a theoryi of meaning of a kind slightly different from M9. His main idea is to introduce an operator 'It is a matter of meaning alone that'. As an axiom for i i , for example, he would have It is a matter of meaning alone that [si is t r u e ( i n L , ) « snow is white] and as an axiom for '&' It is a matter of meaning alone that [ ( Va) ( V r ) is true in ( Z i ) (a is true (in A i ) & T is true (inZ-i)))].

{'O&T''

f^i means (in i 1 ) that (snow is white & the earth moves) but does not allow one to proceed from (i) to &i2^ means (in Z-i) that ( i i is true ( i n / , 1) & X2 is true (inZ-i)). There is little to choose between Wallace's proposal and the proposal which leads \.oMQ. It miglit be tliouglit to be an advantage for Wallace's proposal that his axioms do not contain the (slightly) controversial '( V p ) ' and '( Vt?)' quantifiers. But this apparent advantage is neutralized by the fact that those axioms do not by themselves yield meaning specifications. For that one needs the definition of 'x means that p\ And in that definition just such a quantifier ('for all ^ ' ) does appear. So it seems that it cannot be a mistake not to prefer Wallace's theory over Af0.

From axioms such as these one would proceed, by rules which are not specified by Wallace, to (i) It is a matter of meaning alone that [^i I &S2^ i s t r u e ( i n L i ) •w (si is true ( i n L i ) &i2 is true ( i n L i ) ) J and thence to (ii) It is a matter of meaning alone that ['si &S2^ is true ( i n Z i ) snow is white & the earth moves]. The fact that both (i) and (ii) are theorems shows that, in general, It is a matter of meaning alone that [s is true (in L) **p] 246

247

yippctjciix

APPENDIX 3

3

own, and whose meaning (together with the meaning of 're-') determines the meaning of 'revise'. (2) An answer to the question whether, in a given case, the level of input to a semantic theory is to come apart from the level of surface syntax may depend upon answers to large questions about syntactic theory. Consider, for example, the sentence Mary wants John to dance the polka. The content of Mary's want (desire) is specifiable by the sentence John dances the polka

The very simple examples discussed in the text may suggest (what is false) that the application of SC to semantic theories for natural languages is quite straiglitforward. Here are three complicating factors (among many): (1) The question as to what is the business of semantics and what is the business, rather, gf etymology is not always easily answered. It is relatively easy to decide that 'hydro-', for example, does not make a uniform contribution to the meanings of words, such as 'hydrophobia' and 'hydroelectricity', in which it occurs. The occurrence of 'hydro-' in those words is the business of the etymologist rather than the semantic theorist. But the prefk 're-', for example, provides a more difficult case. It does seem to make a uniform contribution to the meanings of're-evaluate', 're-examine', 'rekindle', 'rewire', and so its occurrence in those words seems to be the business of the semantic theorist. It is not clear, however, that 're-' makes the same contribution to 're-enter' (since a spacecraft which re-enters the earth's atmosphere may well not have entered the earth's atmosphere before). So it is not clear that the occurrence of 're-' in that word is the business of the semantic theorist, rather than of the etymologist. And while 're-' as it occurs in 'revise' is etymologically the same as 're-' as it occurs in 'rekindle', its occurrence in 'revise' is not the business of the semantic theorist since 'vise' is not a verb which can be used on its 248

and it is very natural to regard 'Mary wants (that)' as a sentence operator which is semantically similar to 'Mary beUeves that'. But then the sentence Mary wants to dance the polka presents a prima facie difficulty. For what foUows 'Mary wants' is more like a verb phrase than like a sentence. One response to this difficulty is as follows. I f the sentence is true then what Mary wants is that she (herselQ should dance the polka. The content of her want (desire) is specifiable by a sentence. A sentence which Mary could use to specify that content is I dance the polka. A sentence which others could use to go some way towards specifying that content is Mary dances the polka. (This does not give a fully accurate specification since Mary wants to dance the polka is not equivalent to Mary wants Mary to dance tlic polka.) So accordmg to this response the appearance of a verb phrase rather tlian a full sentence after 'Mary wants' is 'so much misleading surface structure'. Such a response might well be accompanied by the suggestion tliat tire surface sentence 249

Appendix

Mary wants to dance the polka

corresponds to a sentence, at the level of input to a semantic theory, something like Mary wants Mary to dance the polka

crucial source of evidence as to what conceptual resources they employ, and so, as to what their sentences mean. (See also Davies, 1981, Section 8.) (In this appendix I am indebted to Simon Blackburn, Geoffrey Pullum, and Deirdre Wilson.)

(although not exactly like it), and that the syntactic rule relating the two is the deletion rule Equi-NP Deletion. Indeed, this suggestion would seem to offer some prospect of an account of the grammatical correctness of 'herself rather than 'her' in Mary wants to improve herself and of 'her' rather than 'herself in Mary wants John to dance with her. But Equi-NP Deletion may itself come under attack for reasons having to do with syntactic theory. And, i f the constraints upon syntactic theory will not allow the rules which would bridge the gap between surface sentences and sentences at the level of input to a semantic theory, then the semantic theorist must think again about allowing such a gap to open. In the case which we are considering he must reconsider the response to the original prima facie difficulty. (3) The answer to a question as to whether a certain language is impoverished may be sensitive to quite small variations in the meaning specifications. It is possible to miagine cases in which (i) a language L ' contains all the sentences of L and some sentences which are not in Z,, (ii) the sentences in common to the two languages would be used in just the same kinds of circumstances by speakers of L and by speakers of/,', (iii) given what the shared sentences mean in Z,' it is possible to project from their meanings to the meanings of sentences of L ' which are not in Z,, but (iv) given what the shared sentences mean in L it is not possible to project from their meanings to the meanings of any sentences other than those in L . In such an imaginable case the facts about a population's linguistic behaviour which might suggest that they speak an impoverished fragment of L ' would also suggest (and ceteris paribus suggest more strongly) that they speak not L ' but Z. The structure of the linguistic competence of speakers is one 250

3

251

Such connections, between the use of a name and the sort of

APPENDIX 4

situation which prompts the behefs it helps to express, can be, not merely idiosyncratic facts about individuals, but partly constitutive of a shared language. To retreat to the idea that all co-referring names have the same meaning would be to ignore the difference between idiosyncratic variations in ways of thinking and conventional variations. (In this appendix I am indebted to Christopher Peacocke.)

The notion of a way of thinking about an object has its home in theories about the content of behefs which are expressed using demonstratives (see e.g. Evans, forthcoming b). The idea would be that if two beliefs, concerning the same object, to the effect that it is thus and so, involve precisely the same way of thinking about the object then the two beliefs have the same content. A name is not associated with such a precise way of thinking about the object named, but with a relatively unspecific way, or a range of precise ways, of thinking about it. This may suggest tliat a resolution of the puzzle about belief, in the case of beUefs expressed using names, will involve distinguishing the contents of beUefs each of which is a belief that, say, Harry is modest. (The suggestion would be all the more attractive i f it were independently plausible that any belief which can be expressed using a proper name can also be expressed using a demonstrative.) Suppose that the puzzle were resolved in this way. Then, someone might say, we should no longer need to claim that 'Hesperus' and 'Phosphorus', for example, are non-synonymous names. For we should have another explanation of the apparent failure of substitutivity salva veritate within the scope of hyperintensional operators such as 'John believes that'. But, while it is correct that, in a certain sense, we should not 'need' to claim that 'Hesperus' and 'Phosphorus' are non-synonymous, we should nevertheless, still claim that. For it is not just an accident that a speaker who expresses one belief using 'Hesperus' and another using 'Phosphorus' thinks about the planet Venus in two different ways. The different (ranges of) ways of thinking are, in the case imagined, conventionally associated mih the different names (McDowell, 1977, p. 176): 252

253

London, Boston and Henley

APPENDIX 6

APPENDIX 5

The axiom f o r ' V in a theory of meaning forXg ( V $ ) ( vr) [MCorr('i>, Y)-* '( Vv,)4>v,i means that V X ) Y A : ]

(

is true even though the ' ( V 7 ) ' quantifier in the expression which 'MCon(^, F)' abbreviates ranges only over names in L ^ . This is in sharp contrast to the following putative axiom for a truth theory for Li, which is in general not true: ( V4.) ( V y ) [ ( YyeL,) ( Vx) {Ref{L„j) =x {Tr{Le, ^$7^) ^ Yx))^{Tr{L„ '{\vd('r,OT,') ^ r,m2 since ' w j ' and 'Wj' are syntactically different. So in the axioms for names a new primitive theoretical notion PRef is needed (cf. Kripke, 1976, p. 360). It might then seem that a theory meeting SC could be provided simply by replacing MRef by PRef in the theory for Lg (and, of course, replacing ' X j ' by ' K j ' , . . . , 'Xio' by 'Fio'). But this thought would be mistaken. In such a theory ' m i ' is governed by a single axiom which is employed in the canonical derivations of biconditionals for both 'Pirrii' and ' F i W i ' . But, ex hypothesi, ' m j ' does not contribute to the meaning of '^1^1' by its semantic properUes but merely by its syntactic form. Since it is not possible to come to know what 'P\mi' means on the basis of knowing what 'Yitrii' means and what some sentences containing ' P i ' such as 'Pim-i' mean, the suggested theory would infringe SC.

Yet it cannot be that '( V v i ) likes Whitlam' means both that everything likes Whitlam and that everything likes itself. In such a case we need to invoke an extended language when expanding abbreviations of the form 'MCon G)' (see p. 123).

A second thought might be to provide two axioms for each name, one axiom to be used in the canonical derivations of biconditionals for sentences containing predicates and the other in canonical derivations of biconditionals for sentences containing pseudo-predicates. But this thought would be mistaken for two reasons. First, the suggestion

254

255

Appendix 6

Appendices

involves the utterly implausible claim that names in such a language are ambiguous. It is a very special kind of perversity that would encourage one to maintain that the expression 'Hesperus' as it occurs in 'Hesperus' contains eight letters or 'Hesperus' is an eight-lettered name of a planet has the same syntactic form but quite different semantic properties from that expression whose semantic properties involve naming the planet Venus. Second, i f ' has the meaning of ' . . . ' is a short expression for example, then it is surely possible to know the meaning of ' r , / ' i ' on the basis of knowing the meaning of 'KiWi', whereas 'YiPi' is not even admitted as well formed on the present suggestion. The most natural way of avoiding these difficulties is to recognize the occurrence within such expressions as ' . . . ' contains eight letters of the quotation functor. Pseudo-predicates (such as ' F j ' ) are composed of genuine predicates ('rf'), true of expressions and perhaps other objects as well, and that functor. The quotation functor is governed by a very simple axiom involving objectual quantification over expressions.

( V a ) ( W ( f ' a ' ^ ) = a) The net effect of this axiom and an axiom for ' K f ' is the following theorem which makes it clear that the semantic properties of names are irrelevant to the meanings of atomic sentences containing pseudopredicates.

(Va) [7>(rr,ai)

Y^a]

The canonical derivation of a biconditional for the sentence '(Evi) (FiVj APiVi)', for example, proceeds as follows (we consider just the left-to-right direction; the converse is similar): 7'r('(Evi)(r,v, & P . V , ) ' )

(aT)7>(rr.7& P i V ) (by the axiom for 'E'). Suppose the name is 70 • Then 256

Tri'Y.jo

&Pi7o^)

(by the axiom for '&'). From the first conjunct we have K*7o by the theorem just mentioned. From the second conjunct we have Pi (Ref (7o)) by the axiom for the predicate 'Pi'. (Since 'Pi', . . ., 'Pio' are predicates the theory need include just reference axioms for names.) The next step requires one of a pair of axioms relating objectual quantification over names and substitutional quantification in the ML, namely ( V 7 ) ( E x ) ( 7 = ' x ' & / ? e / ( 7 ) = x). (For the right-to-left direction the other member of the pair, namely ( A x ) ( 3 7 ) ( 7 = ' x ' & / ^ e / ( 7 ) = x) is needed.) Using that axiom we have from ^ 7 0 &P,

(Ref(Jo))

the substitutionally quantified (Ex)(rr'x'&Pix) that is ( E x ) ( r i x &Pix). The difference which in general is crucial for the truth of quantified sentences of this language is that between one ordered pair of an object and a name of that object and two such ordered pairs. The quantification is quantification over such pairs. I f ' F i ' has the meaning of ' . . . ' is a short expression and 'Pi' has the meaning of 'is modest' then we might specify the meaning of '(Evi) (Yi Vi & Pi Vi)' as that there is an object and a name (in the language) of that object such that the name is a short expression and the object is modest. Similarly, if the base language were to contain predicates, quasi-predicates, and pseudo-predicates then substitutional quantification would be quantification over ordered pairs of names and their meanings. We are now in a position to tie up some ends which were left loose in the discussion of the '( Vp)' and '( Vq)' quantifiers (in Section II.3), the ' ( V i ; ) ' quantifier (in Section V . l ) , and the '( V F ) ' quantifier 257

yl ppcf

ictices

(in Section VI.1). It is implicit in Section VI.4 that the '( Vv)' quantifier which was used in the ML can be interpreted as a substitutional quantifier. Since the opaque contexts into which quantification using '( V i ' ) ' takes place involve opacity of only the first kind the quantification is over the meanings of names (in the Aft). Similarly, the quantificafion using '( V F ) ' , and using ' ( V p ) ' and '( V ^ ) ' , can be interpreted as substitutional quantification into predicate position and into sentence position, respectively. In the latter case, for example, it would suffice to take as the substitution class the class of ML sentences which themselves contain neither semantic vocabulary (such as 'means that' or 'is true') nor substitutional quantification. The quantification would be quantification over the meanings of sentences in the substitution class. (For the conditions which must be imposed upon the substitution class in these cases see Kripke, 1976, pp. 331 and 368.) At the end of Section II.3 (at (2)) qualification 'in and out of quotes' was mentioned. We have just discussed such quantification into name position. Similar remarks apply to such quantification into sentence position, as in what we should now write as

APPENDIX 7

The reason for the parenthetical 'almost' in the claim about the privileges of occurrence of definite descriptions and proper names is this. It is a familiar point tliat a definite description (such as 'tiie elephant') can be followed by a restrictive relative clause as in The elephant that fell down did little damage

(Ap) Cp' means that p). We suppose that the OL is included in the ML and that the substitufion class for the substitutional quantification in the ML is the class of OL sentences. Since one sentence posifion is within quotation and the other within the scope of the hyperintensional operator 'means that' this quantification is over ordered pairs of OL sentences and their meanings. We might specify the meaning of the universally quantified ML sentence as that for every OL sentence s which means that p, s means that p. This shows why the acceptability of the '( Yp)' and XYqY quantifiers (in the theory Md, for example) does not turn upon the acceptability in a theory of meaning of that universally quantified sentence.

while Jumbo that fell down did little damage is not a grammatical sentence. In fact, however, this is not a serious exception to the claim that definite descriptions and proper names have the same privileges of occurrence. For, in this example, the expression 'the elephant' is not functioning as a definite description. Rather, the restrictive relative clause attaches to tlie common noun 'elephant' to form a common noun phrase, and the only definite description is 'the elephant that fell down'. And a proper name can occupy the position occupied by that definite description. Similarly, it would be misleading to say that in Every elephant that fell down did little damage a quantifier phrase 'every elephant' occurs as antecedent to a restrictive relative clause.

258

259

(Qy) \Fy\Y jc) ((Man who loves jt')

loses > ' ) ] .

Rather, we expect that the sentence Every man w h o loves a woman loses her

APPENDIX 8

w i l l be naturally interpreted as equivalent to Every man who loves a woman loses the woman whom he loves. It is easy to check that these expectations, too, are correct. Someone might suggest that, shnply on the basis o f word order, we could expect that Every man who loves a woman loses her The sentence ( M O S T x ) [(Woman w h o m John admires) x; John loves x] surfaces as

would not be interpreted as though i t corresponds to a sentence at the level o f input i n which the 'a' quantifier has wider scope than the 'every' quantifier. But this suggestion, unless i t is accompanied by a general account o f the anaphoric use o f pronouns, simply leaves the occurrence o f the pronoun 'her' i n the surface sentence a semantic mystery. (For some more examples, see Evans, 1977, p. 496.)

John loves most women w h o m he (John) admires. I n this sentence the first name position occupied by 'John' governs the second. So we expect that surface sentences i n which a quantifier phrase occupies the first name position and a pronoun occupies the second w i l l be naturally interpreted as corresponding to sentences o f the form (Qy) [^y; (MOST X) ((Woman w h o m > ' admires) x; y lovesx)]. And

i t is easy to check that this expectation is correct. The sentence ( E V E R Y x) [(Man who loves Mary) x; x loses Mary]

surfaces as Every man w h o loves Mary loses her (Mary). I n this sentence the first name position occupied by 'Mary' does not govern the second. So we expect that surface sentences i n which a quantifier phrase occupies that first name position and a pronoun occupies the second w i l l not be naturally interpreted as corresponding to sentences o f the form 260

261

(2)

where 7 1 , . . ., 7 „ , 5, e, and 0 sue purely trutli functional sentences. We then use the following two schemata which follow from ( i 2 ^ 1 ) - ( . ^ 4 ) :

T l i e T a x i o m f o r ' Si^A'

S^AoL -* a is not a generally valid schema. But the S4 axiom for S^Aa

-> ^A

'^A' ( I ) J^'(a & 15) ^ (S^a ( I I ) S^(a V S^d) ^ i^a

^Aa

and the S5 axiom f o r ' ^ A ' ~i^yl~a ^

By ( I ) , ' the form

^A~^A--a

are b o t h generally valid schemata. Without appealing to the completeness theorem we can show that all instances o f the S4 axiom f o r ' ^A" (strengthened to a biconditional) are provable i n S5A^ . We make use o f the Elimination Theorem (see (3) below) to guarantee, for each sentence a, the existence o f an equivalentCTJi n which ' J ^ ' does not occur. A n d we make use o f the following fact (which is an immediate consequence o f a result proved i n Crossley and Humberstone, 1977, p. 16): (D) For any sentence a not containing '/I'-free sentence a' such that S5A^

there is an \-Aa ^ Aa'

Then the following are equivalent: 3FAa ^Aoy ^Aal •a/

where a / is 'A'-free, by ( D ) by ( ^ 6 )

• •a/ S^AUal SFA^Aal ^AS^Aoy ^A^Aa.

by S4 and T axioms for ' • ' by ( ^ 6 ) by(J^6) by(D)

(3) Elimination Theorem: For any sentence a there exists an 'J^'-free sentence a such WvzXSSA^ h a ^ a'. Proof: We consider innermost occurrences o f ' ^ ' . Let f J ^ r l be any subsentence o f a such that ' ^ ' does not occur in r . Then (by Crossley and Humberstone, 1977, p. 15) r is provably equivalent to a conjunction o f disjunctions o f the form • T I

V . . .

V

U-in

V

05 ^ Ae y Q

264

& S^d) V

is equivalent to a conjunction o f sentences o f

^(nji

V . . .

By ( ^ 2 ) and (•^S) S^iS^Oji

V

Dy„

V

05

V

V

0).

each such sentence is equivalent to V . . . V ^Dy„

V J^05

v .4e v ^ 0 ) .

By ( J ^ 3 ) , ( I I ) , and ( ^ 6 ) each such sentence is equivalent to

(S^aji

V

. . .

V

J^Ojn

V ^08

V

De

V

^9).

By ( . ^ 2 ) and ( J ^ 5 ) all the remaining occurrences o f ' i ^ ' can be deleted, to yield a provably equivalent sentence containing no occurrences o f ' J ^ ' . By repeating tlris procedure all occurrences o f in a can be eliminated. Corollary: For any sentence o f the form ^^T^ , there exists a sentence r ' containing neither nor 'A' such that S5A^ \ - ^ T «• r ' (by inspection o f the above proof). (4) I n order to prove the completeness o f S5A^ we shall use the notion o f a canonical model. I n a canonical model, the set o f 'worlds' is the set o f ah maximal consistent sets o f sentences o f the language in question. Instead o f there being a single designated world, the set o f worlds is partitioned by an equivalence relation R and there is a designated w o r l d w i t h i n each equivalence class. Thus, for the purposes o f this proof, a model will be a quadruple < W, R, f, V> where R is an equivalence relation on W, for cacii w in W, [w\s the /?-equivalence class containing w , and f{[w\ e [w\. I f X and Y are equivalence classes then we say that A'^a 1^just in case there is a one-to-one function g from X onto Y such that, for every w in X , w and g{w) agree on the truth values o f all atomic sentences. To indicate that g is the function in question, we write 'X^ Y'. Instead o f considerhig variant models, we consider ««-related equivalence classes within a single model. The function K i s extended to V* by obvious clauses for 265

o f s e n t e n c e s . T h e basis case a n d tlic i n d u c t i o n cases l o r the

the truth functional connectives and by

t r u t h functional connectives and for ' • ' are as in a complete-

V*(w, T D a i ) = T i f f for every w ' s u c h that R(w, w'), V\w',a)

ness p r o o f for S5 (cf. Lemmon and Scott, 1977). So we

= T

omit them.

V*(w, U a i ) = T i f f V*(f([w]),

a) = T

Suppose that a is U T ^ and that V\w,

V* (w, ^ S^a^) = T i f f for every Y and every g such that Y'ilw], V*(g(w), a) = T .

/ ( [ w ] ) . Thus ^AT^ is in w . The converse is similar. Thus we have a completeness theorem for S5A.

FinaUy, we impose the foUowing condition on models. (U)

Now suppose that a does contain '^\By

For every equivalence class X and every w i n X,

containing

= g(w).

'. Suppose that V* (w, a) = T . Then V* (w, a')

= T and since a' is It is not difficult to confirm that the axioms o f S5A^

are

valid w i t h respect to this modified model theory, and that the rules preserve validity. ( I n the cases o f ( . ^ 5 ) and ( J*'6) we appeal

'-fiee, a' is in w . But S5AS^

ness theorem (or

S5A^.

We now define the canonical model. The set W is the set o f all maximal consistent sets o f sentences o f the language in question. (Consistency is, o f course, consistency w i t h .) I f x andy are i n W thenjR(A:, y) i f f for

every sentence a, i f 'Ha^ is i n

then a is i n ; ^ . I f w is i n W

t h e n / ( [ v v ] ) is the set o f sentences a such that ^Aa^ is i n w. I f w is i n

and a is an atomic sentence then V(w, a) = T i f f

a is in w. That R is an equivalence relation can be established by a familiar argument (cf. Lemmon and Scott, 1977). That / h a s the required properties is a consequence o f the fact that S5A^

includes the axioms (A1)-(A4)

for 'A\d i t can be

checked that the canonical model meets condition (U). I t remains t o show that, for every sentence a and every w in W, V* {w, a) = T i f f a is in w . Suppose that we can establish that. Then, i f a is a sentence which is not a theorem o f S5A

^

then ' ~ a ' is a member o f a maximal consistent set w . Consequently, V* (w, a) = F and a is not vahd w i t h respect t o the modified model theory. Furthermore, Q is not valid w i t h respect t o the original model theory, for the triple < [w] , / ( [ w ] ) , F ' > (where V' is the restriction o f K t o [ w ] ) is a falsifying model i n the original sense. In order to prove that for every a and w, V* (w, a) = T i f f a is i n w , we first restrict attention to sentences which do not contain

h a' -> a.

So a is in w. The converse is similar. Thus we have a complete-

(This appendix is aknost entirely attributable to L l o y d Humberstone.)

to condition (C/).)

respect t o S5A^

the Elimination

Theorem there is a provably equivalent sentence a', not

there is an equivalence class Y and a function g such that r I . X and f(Y)

o) = T. Then

V* ( / ( [ w ] ) , r ) = T. By the inducfion hypothesis r is in

We proceed by induction on the complexity 266

267

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277

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INDEX

actual language relation, 6, 12, 19-25, 30, 3 5 , 5 2 , 5 5 , 7 3 - 4 , 7 9 , 9 1 , 100, 107,110 actuality, 201, 209, 220-42 'actually' operator: logic of, 222-4; need for, 220-2 Altham, J . , 134 ambiguity, 60, 65, 131, 171-3,218-19 ambiguity theorist, 157-60, 181-2 anaphora, 161-76, 261; see also pronouns antecedent sentence, 170-1 assertion, 9, 11,14, 21, 24,107-8, 232 attributive use (of definite descriptions), 154-7 Baldwin, T . , 28 base language (for substitutional quantification), 142 Bennett, J . , 17 Bigelow, J . , 46, 48 Blackburn, S., 100, 106, 108, 237, 251 Boolos, G . , 138 Burge, T . , 105 canonical theorems, 33 Carnap, R., 39 causal explanation (of Unguistic competence), 77-8 C-command, 169 c-determination, 53-4, 75 character, 203 Chomsky, N., 81,83-5

competence (linguistic), 52-4, 59-60, 75-83 completeness theorem for S5Aj?7265-7 concatenation, 31-2, 41, 90-1, 144-5 conceptual analysis, 4-5 content, 203 context dependence, 37, 165, 174, 202-9,237 context shifting operator, 204-7 contextual limitation (of domain of quantification), 160-1 contingent a priori truths, 224, 230-8 contingent existence, 213-19 convention, 10-12, 25, 164, 252-3 Cooper, R . , 174-6 Crossley, J.N., 222, 264 Davidson, D., 18, 22, 28, 34, 39,40, 43,45,59-61,70 d-determination, 53, 55, 63, 75, 79 dealing non-semantically with an expression, 58-9, 71 definite descriptions, 99-104, 149-60, 179-83, 259; jee also pronouns demonstratives, 252 description theories of names, 98-108 descriptive name, 238; see also fixing reference (by description) differential determination, 78-9 differential state, 76-7, 79, 83 direct reference, 99 Donnellan,K., 99, 154-6, 159, 176-83,235-6

279

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Index

Dummett, M . A . E . , 5, 8, 117-19, 122, 202, 231, 237,245 empty names, 98-9, 145 epistemological salience, 96, 110-11, 150, 235-6 etymology, 248-9 Evans, G . , 4 , 2 9 , 3 3 , 7 2 , 1 3 7 , 1 9 6 , 2 2 8 , 252;on the contingent a pr/on, 232, 235, 238; on names, 97, 101, 107; on pronouns, 157,166,170-8,261; on quantification, 115, 119, 122; on tense logic, 202, 205, 208 exclusive disjunction, 68-71 existence dependence: of beliefs, 96, 240; of meanings, 96, 159 extension of predicates, 90, 109-11 feature placing, 137 finite axiomatization constraint, 5, 57-62 fixed actuahty, 225, 231, 239,241, 264 'fixedly' operator, 225; logic of, 226-7, 263-7 fixing reference (by description), 110, 173-1, 230-8 force, theory of, 8-10, 13, 2 2 ^ , 34 Foster,:., 38,43 Frege, G . , 37, 39-40, 99, 101, 203 Frege argument, 210-12 full understanding, 55, 74-81 generation, derivational and causal, 82 genuine singular reference, 94-103, 109, 150, 157, 239-tO good mood function, 23-4 govern, 169-71 Grice, H.P., 1 8 , 1 9 , 2 5 Grice's programme, 11, 15-18, 80 'Grrr', 10, 15 Hausser, R., 174 Hazen, A., 216, 218, 222 homophony, 70-2, 117, 144-5 Humberstone, I . L . , 1 3 3 ^ , 222, 264, 267 identity statements, 100-2, 239-41 implicit beliefs, 84-6; see also implicit lS5,190; r , 189; and weak ' necessity, 214-15 modal operators, 187-93; and predicates, 219; and quantification, 209-19; and temporal operators, 205-9; weak and strong interpretations, 213-14 model theory: for 'actually', 223-4; canonical model, 265-7; for •fixedly', 228-30; and truth theory, 194-6 modes of presentation, 101; see also ways of thinking mood, 8, 1 3 , 2 2 - 4 , 3 5 'more', 132-6

•most', 1 2 4 - 7 Mostowski, A . , 133

quantification : b i n a r y , 1 2 3 - 3 6 ; essential nature of, 1 3 6 - 4 8 ; over objects o f a

kind, 137, 210, 258; predicate, 136-42; standard first-order, 114-23; substitutional, 44, 62, 142-8, 254-8 quantifier phrases in natural language, 130-2,149, 167, 259-61 quasi-predicates, 146 Quine, W.V.O., 39, 65, 82, 137, 193, 210-11 quotation, 146, 193, 255-8

names, 89-113, 149, 252-3; in behef contexts, 105, 252-3; co-referring, 99-103; in an extended language, 115-16; of properties, 141; of sets, 110-11; and truth theory, 90-2;see also empty names natural kinds, 241 necessary a posteriori truths, 224, 238-41 necessity, 28, 48, 95,187-219; two notions distinguished and applied, 225-41 non-Uteral anaphoric uses (of pronouns), 179

reahzation, 77 reference, 90-4, 212 referential use (of definite descriptions), 154-5, 180 relative clauses, 162-5 Rescher, N., 124 rigid designation, 235-6; see a/so truth conditional salience rule (.R),93 rule (D, 21 rules fitting and guiding behaviour, 82 rules of proof: Fix, 226; necessitation, 189; in truth theories, 33, 49-50 Russell, B.A.W., 151 Russellian equivalence, 151,160-1,211 Russellian theorist, 157-60, 165, 176, 182-3

opacity, 142; the first kind, 146-8; the second kind, 255-8; two kinds distinguished, 145-6 passive, 131 Peacock, C , 21, 25, 28, 62, 95, 121, 189-90, 216, 218, 253, 262 phrasebook knowledge, 52, 76, 80 Plantinga, A., 28, 187, 196, 199 Platts, M. de B., 15-16, 39, 80, 127 possible worlds: and model theory, 1938; realism concerning, 198-201, 262 predicates, 108-13; and properties, 111 -13; and sets, 109-11; and substitutional quantification, 144; and theory of meaning, 93-4; and truth theory, 90-1 pronouns: andbound variables, 167-71, 260; and definite descriptions, 166-76, 261; and syntactic theory, 174-6 properties, 111-13, 140-1 propositional attitude attribution, 17-18 propositional attitude constraints, 7-25,35,93;/MC7,9;/'/lC2,

n;PACS,21;PAC4,

23

propositional attitude explanations, 9, 84-6 pseudo-predicates, 255-7 pseudo-reference, 144, 255-6 PuUum,G., 251 Putnam, H., 241

Sainsbury, R.M., 70,151,161 s-asking, 12, 14,23 satisfaction theory: for binary quantifiers, 125-6; for 'more', 133; for 'most', 126-7; for standard firstorder quantifiers, 119-22 saying, 21, 24 Schiffer,S., 1 0 , 1 4 , 2 4 , 2 5 , 3 6 , 9 8 , 1 0 2 , 105,107 s-commanding, 12, 14, 20, 23 scope, 131-2,140, 170, 220, 238 Scott, D.S., 266-7 semantic constituent, 59, 192 semantic primitive, 59, 73-4, 116 semantic state, 73-4, 80 semantic structure, see structural constraint semantically complex expression, 59 sentence operators, 46, 114, 140, 188, 203-5, 210; extensional, 47;

281 280

London, Boston and Henley

sentence operators

icont.')

t r u t h c o n d i t i o n s , 2 8 , 4 4 - 5 0 , 6 3 - 4 , 95 ; see also sentence o p e r a t o r s

hyperintensional,48,140,146,148; intensional, 47-8, 95, 140, 188 sentences as primary semantic unit, 118,122,202 singular belief, 9 6 - 9 , 1 0 6 - 8 , 110, 153, 241,252-3 situation expressions, see t-predicates 'smart bomb', 84-5 s-meaning, 11-12, 14, 1 8 , 2 3 , 35-6, 158,218; concerning an object, 153-4 s-meaning*, 19, 35-6 sortal predicate, 128-30 speaker's reference, 154, 182 Stalnaker, R . C , 198-200 Stich, S., 85 Strawson, P.P., 45, 91, 112, 128-30, 135,141 stress, 131 structural constraint: applied, 64-72, 89-90,93,117,123,128,140,143, 151, 192, 248-51, 255; on theories of meaning, 56-7; on truth theories, 62^ subject-predicate language, 61, 89-94 substitution class, 142,144, 258 'such that', 132 surface syntactic impoverishment, 6 7 - 8 , 1 2 8 , 131-2, 250-1 surface syntactic irregularity, 66-7 tacit knowledge, see impUcit knowledge talking about an object, 157, 177-9 Taylor, B., 121 temporal operators, 205-9 Tennant, N., 134 tense logic, 201 t-predicates, 208-9 translation, 4 truth, 27-51, 245; and the actual world, 201, 209; marks of, 35-7; and meaning, 27, 38-40; and satisfaction, 121-2; of utterances ( T R U T H ) , 36-7, 202, 209, 227-8, 232,239-tl truth conditional salience, 95, 103, 110-11, 150,174, 234-6, 239-40

truth theories: for 'actually', 222-3; for belief operator, 47, 64; for binary quantifiers, 124-6; for definite descriptions, 152; for exclusive disjunction, 68-71; for 'fixedly', 227-8; interpretational, 34-5, 192; and theories of meaning, 37-44, 246-7; for modal operators, 189-93; and possible worlds, 196-8; for predicate quantifiers, 139-40; proof theoretic resources used in, 32-3; for propositional calculus language, 31-2; for quanlified modal language, 212-13; and rules of proof, 33, 49-50; and semantic theorizing, 44-50; for standard first-order quantifiers, 115-19; for subject-predicate language, 90-2; for substitutional quantifiers, 146-7 two dimensional modal logic, 229-30 underspecification, 160-5 understanding, see full understanding validity: general, 223, 229; real world, 223, 229; and truth, 194-6 Vendler, Z . , 162-4,166 verification, 245 Vlach, F . , 234-5,239 WT predicate, 1 0 2 , 1 0 3 ^ ; see also ways of thinking Wallace, J . , 2 8 , 4 6 , 61, 92, 143,199, 246-7 Wasow, T . , 170 {ways of thinking, 101-5, 111, 137, ' 147,240,252-3 weak necessity, 214-18 weak-s-meaning, 20-4 whatever-that-is use (of definite descriptions), 151, 156 Wiggins, D., 35, 125, 126, 214, 216, 219,245 Wilson, D., 251 Wittgenstein, L . , 39 Wright, C , 245

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