In this chapter I want to discuss whether the things said in Putnam 1975 affect the kind of possible-worlds semantics illustrated in the case of the very simple language ℒ introduced on pages 5f. Since Putnam's principal target is the use of the intension/extension distinction in semantics, and since that distinction is one which can be defined in if, at least in the case of predicates (see p. 29), it is important to see how Putnam's remarks affect what has so far been said. In the latter part of the paper (pp. 183–8) Putnam offers a critique of what he calls ‘California semantics’. The semantics I offered for ℒ is clearly within this tradition. This section of Putnam's paper is, however, less helpful than other parts. Putnam's principal argument against California semantics is that treating an intension as a function from worlds to extensions requires supplementing by giving an account of what it is to ‘grasp’ an intension. The reason this is for him an important criticism is that the role of intension in semantics that he is concerned with is that it is the means by which a speaker is able to determine the extension, and treating it merely as a function from worlds to extensions gives no help in explaining how it can fill this role. I need take no issue with this criticism since I have already stressed that nothing in the possible-worlds semantics offered for ℒ gives any help in saying what it is about speakers’ behaviour that determines which of the many possible interpretations for ℒ is the correct one.

The purpose of this chapter is twofold. First I shall shew how to extend ℒ to include quantification and variable-binding, and then I shall look at the question of whether the quantifiers should be interpreted possibilistically or actualistically. A language like ℒ is usually extended by symbols which mean ‘every’ and ‘some’. These are called quantifiers and are customarily represented by ∀ and ∃. We also extend the category of names to include individual variables usually written as x, y, z,…,etc. As far as formation rules go individual variables are treated exactly as Adriane, Bruce, etc. The new formation rule is

FR6 If α is a sentence and x is an individual variable then ∀xα is a sentence.

(The terminology of FR6 differs slightly from standard usage in that the word ‘sentence’ in quantificational logic is sometimes used a little more restrictively.)

An example of a sentence requiring FR6 is

(1) ∀x x whistles

1. (1) is interpreted as meaning ‘everyone whistles’. More literally

2. can be read as: for every value of x

3. xwhistles

4. true.

Calling x a variable means that its value is not fixed once and for all, even in a given interpretation (W,D,V). Rather, we add to an interpretation a value-assignment to all the individual variables. If v is such an assignment then for any variable x, v assigns t o x a member of D; i.e. v(x) ∈ D. The interpretation now gives values to all expressions with respect to some v.

This book is concerned with what makes one interpretation of a language the correct one and another the wrong one. I will be discussing this problem in the context of possible-worlds semantics and so, in order to set the scene, and by way of introduction for those who have not come across possible-worlds semantics for natural languages, I shall, in the first two chapters, set out a simple fragment so that we can see what is going on.

I hope that most of you will have a familiarity with at least the language of the first-order predicate calculus. (sometimes called the lower predicate calculus or LPC). I shall set out here a simple version of this, but without quantifiers, which I can generalize to a language rich enough for the points I want to make. So here is a language ℒ

Sentences or well-formed formulae of ℒ are finite sequences of what are called symbols. Although, in logical languages, symbols are often represented by letters, it is best to think of them as corresponding to words in natural language rather than letters. The sentences of ℒ are those allowed by the formation rules. The formation rules are sensitive to the syntactic category of each symbol. It is time to be specific.

1. ℒ contains a category of names. Let these be Adriane, Bruce, Julie and David.

2. ℒ contains a category of predicates. Let these be runs, whistles and sees.

3. ℒ contains a category of sentential functors (sometimes called connectives). Let these be not, and and if.

4. ℒ contains a left parenthesis, (, and a right parenthesis,).

Categories (2) and (3) may be further subdivided.

The last chapter raised the problem of deciding which interpretation is the correct one. I want now to raise a particular case of what is in fact the same problem. To do this I will take ℒ and pretend that its intended interpretation is extremely small. I shall assume that W contains only two worlds w1 and w2 and that D contains only two individuals, say Adriane and Bruce, whom I shall refer to as a and b. I will assume that, for the interpretation of possibly, w1Rw1 and w1Rw2. That is, each world is possible relative to itself and w2 is possible relative to w1. Assume that a runs in w1 and b runs in w2 while a sees b in w1 and b sees a in w2. I shall ignore whistling. It is convenient to refer to running and seeing as w1 and w2 where

What this means is that the set of worlds in which a runs is just {w1}, i.e. the set whose only member is w1, while the set of worlds in which b runs is {w2}. To state w2 we need the symbol ø, which stands for the empty set, the set which has no members.

In previous chapters various procedures have been discussed for reducing semantic facts about public languages to facts about propositional attitudes, and facts about propositional attitudes to physical facts. In all cases there seemed a large amount of underdetermination. Some of those who advocated these reductions, David Lewis in particular, have acknowledged this and are prepared to live with it. While I have no conclusive arguments that the amount of underdetermination is too great to be acceptable I am impressed with the difference between how little these theories deliver and how definite we seem able to be about what a person's propositional attitudes are and about what the expressions mean in the language they speak. How can this be?

One feature of the views we have looked at is that they all seem to be reductive. Thus, for Lewis, an interpreted language ℒ is the language of a population P in w iff a convention of truthfulness and trust obtains in w in accordance with ℒ among members of P. And belief is defined in terms of a theory that explains behaviour. The question I want to raise is this. Suppose that there is a complex pattern of behaviour which constitutes a's believing that p. Why should we expect that there should be any theory in which ‘believes’ is a theoretical term whose meaning is defined by the physical consequences of the theory? Suppose the behaviour of a's and facts about a's environment, perhaps including facts about other people, is so complex that no theory can describe it. Maybe this is just a practical limitation, or maybe no physical language can provide a finite description of the behaviour.

In this chapter I want to take up some issues in the metaphysics of possible worlds. Although not strictly connected with the main theme of this book, it might help to get clear just what kind of metaphysical framework I am assuming, particularly since not all possible-worlds theorists adopt the same views. The view I shall be outlining is the one I called transmundism on page 43 and briefly outlined there. The first question I want to discuss is what Kaplan 1975 calls haecceitism and I want to see what this doctrine amounts to in a transmundist framework. Kaplan (Loux 1979, p. 217) defines haecceitism as the view that the same thing can exist in different possible worlds, and that a common ‘thisness’ may underlie extreme dissimilarity and distinct thisnesses may underlie great resemblance. Now the first feature of transmundism is that things as-such are not located in worlds. For some entities, as discussed on pages 45–8, there is to be sure a property ωactual such that a can be said to exist in world w iff w ∈ ωactual (a) But ωactual just happens to be one property among many, and it is no more metaphysically privileged, in a transmundist framework, than any other property. So the question of whether or not individuals can exist in more than one world turns out not to be a metaphysical question at all, but simply a question of whether the property ωactual, that we express by using the word ‘exists’, allows there to be w ≠ w′ such that w ∀ ωactual and w′ ∀ ωactual(a). I don't mean to claim that the question turns out to be simply a linguistic question.

Meanings of whole sentences of ℒ are sets of worlds. Actually this isn't quite right since a sentence like (6) on page 6 could be true at one time and false at another. We must pretend that all the sentences of our restricted little language ℒ are understood as referring to some particular time. But whole sentences are complex expressions, and according to Frege's Principle, their meanings depend on the meanings of the symbols in them, together with the rules for combining those meanings. It is here that the categorial description of the syntax of ℒ becomes relevant. Consider the one-place predicates of ℒ. They are runs and whistles. In a categorial description one-place predicates turn a name into a sentence. Now among the set of all possible worlds there will be those in which (at the particular time that we are assuming ℒ to be talking about) Adriane is running. Call this set p. There will also be the set of worlds in which Bruce is running. Call this set q. At this point we have to remember that worlds, whatever they are, are not linguistic things. That Adriane is running in a world, or that Bruce is running in a world, is something which in some sense is ‘out there’ and which can be referred to in ℒ.

In chapter 8 I argued that the possible-worlds account of causation provided the right model for our everyday explanation of behaviour in terms of beliefs and desires. If possible-worlds semantics is to be justified in the manner advocated by Lewis, as discussed in chapter 7 above, by reducing semantic facts to facts about belief and other propositional attitudes, then it will be necessary to reduce facts about propositional attitudes to facts which do not make reference to content. Both Lewis (1986a, pp. 27–40), and Stalnaker (1984 chapter 1) advocate the reduction of the content of attitudes via belief-desire psychology. Stalnaker contrasts what he calls the pragmatic picture, whereby the ascription of possible-worlds content to attitudes is made directly in terms of the role of beliefs and desires in explaining behaviour, with what he-calls the linguistic picture, whereby the content of attitudes is explained via the content of sentences or sentence-like objects. The linguistic picture is best represented for Stalnaker in Field 1978, so before I discuss the pragmatic picture I shall look at what Field has to say, and what Stalnaker thinks of it.

Field's analysis of

(1) x believes that p

is a conjunctive one. He supposes that when you believe something you are related to a sentence S (or, as he later amends the account, to some kind of representation) which means that p. He calls the relation to 5 belief* and the analysis of (1) is

(2) There exists S such that

(a) x believes*S

(b) S means that p

Initially he accepts that p is a proposition in the sense of a set of possible worlds.

We know a lot about the semantic structure of natural language. If you think that semantics is about the connection between linguistic entities, words, sentences and such, and non-linguistic entities, things ‘in the world’, then the way to do semantics will be to specify the linguistic entities, then specify the ‘things in the world’ which are to be their meanings, and then connect up the two. Chapters 1 and 2 illustrate this by setting out in detail a very simple formal language together with its semantics. This semantics allows us to address the philosophical issues with a particular example in mind. (These chapters can be omitted by those who already have a background in formal semantics.) The kind of semantic theory set out is what is called possible-worlds semantics, and is based on the idea that the meaning of a sentence is the conditions under which it is true, and that these conditions are simply the class of possible worlds in which the sentence is true.

Many years ago, in Cresswell 1978, I defended this approach to semantics by arguing that speakers of a language know the truth conditions of the sentences they utter, and that it is this knowledge which constitutes their semantic competence. It was David Lewis who, when I gave this talk at Princeton in 1975, convinced me that there was a problem. I had argued that to know meaning is to know truth conditions. Lewis asked what it is to know truth conditions. If an interpretation to a language is a pairing of expressions with their meanings then the fact that certain expressions are paired with certain meanings will be a mathematical (or logical) fact.

One of the few authors who has attempted to address the question of what it is about the linguistic behaviour of a population which justifies our saying that some particular model-theoretic interpretation is the right one for the language they speak is David Lewis (1975). Since I have already used ℒ for a syntactically specified language I will use ℒ+ for a language together with its interpretation rather than Lewis's ℒ. Lewis's proposal is (Lewis 1975, p. 7)

the convention whereby a population P uses a language ℒ+ is a convention of truthfulness and trust in ℒ+. To be truthful in if is to act in a certain way: to try never to utter any sentences of ℒ+ that are not true in ℒ+. Thus it is to avoid uttering any sentence of ℒ+ unless one believes it to be true in ℒ+. To be trusting in ℒ+ is to form beliefs in a certain way: to impute truthfulness in ℒ+ to others, and thus to tend to respond to another's utterance of any sentence of ℒ+ by coming to believe that the uttered sentence is true in ℒ+.

Where Lewis speaks of an interpreted language, which I have represented by ℒ+ in quoting him, I prefer to speak of a language if, together with an interpretation (W,D,V). I shall assume that speakers of ℒ+ are members of D and that their properties and the relations among themselves and to other things are all appropriate set-theoretical entities constructed out of W and D. In particular, their beliefs may be construed as relations to propositions.

This book was begun in January 1991, initially as a set of course notes for a graduate course in the philosophy of language which I taught in the fall semester of 1991 at the University of Massachusetts at Amherst. In addition to my UMass students, Adriane, Bruce, Julie, David, and others, whose names appear in these pages, my lectures were attended by Lynne Baker, Ed Gettier, Phil Bricker and Barbara Partee, all of whom made valuable comments of which some even made it into the text.

A draft of the book was written up in the first three months of 1992 in the comfortable and welcome environment of the Centre for Cognitive Science at the University of Edinburgh, and some of the material was presented in a seminar there. Many people in Edinburgh made those months profitable. In particular regular sessions with Robin Cooper were especially helpful and encouraging. I would like to thank the Science and Engineering Research Council for financial support in Edinburgh.

In April of 1992 I moved to Cambridge and enjoyed the experience of living in college for the Easter term. I would express my heartfelt thanks to the Master and Fellows of St John's College for the Visiting Overseas Scholarship that I held that term. I am also grateful to Hugh Mellor and the other philosophers in Cambridge for the opportunity to give six lectures on the material in this book and for the willingness of my colleagues to engage in philosophical discussion.

Finally, to the Victoria University of Wellington for giving me 1992 as a sabbatical year, and to my department for doing without me for eighteen months, I express sincere thanks.