230 The formalization of sentence-meaning

nently traditional (and played an important part in medieval logic and grammatical theory). It can perhaps be seen as the antecedent of the present-day formal semanticist's rule-to-rule hypothesis.

So far, I have restricted the discussion to possible worlds that differ from the actual world only in that they have been actua­lized in the past or will be actualized in the future: i.e., worlds, or states of the world, that are only temporally distinguished one from another and succeed, or replace, one another on a single time-line. But there is no need to maintain this restriction. Indeed, the real pay-off from the formalization of possible worlds by Montague and others comes from the fact that it enables one to handle, in a logically respectable way, statements about worlds which may never be actualized: the worlds of one's dreams, hopes and fears; the worlds of science-fiction, drama, and make-believe. It does so by allowing the index by which dif­ferent worlds are identified to be composite and to include non-temporal, as well as temporal, components. I will come back to this point, in connexion with the notion of epistemic modality, in Chapter 10. At this stage, it will be sufficient to note that Montague grammar was more successful than earlier formal systems constructed by logicians for the semantic analysis of some of the features of natural languages. It was more success­ful in the sense that it provided a more perspicuous analysis of the phenomena than standard logical analyses which had held sway until then: in short, it was more respectful of the principle of saving the appearances (see 7.2).

In particular, Montague grammar could handle, in an intui­tively satisfying way, a range of well-known problems in philoso­phical semantics. One of these derives from the fact that in certain so-called intensional (or referentially opaque) con­texts the substitution of expressions with the same extension affects truth-conditionality: i.e., Leibniz's Law (of intersubsti-tutability salva veritate) does not hold. For example,

(11) 'I wanted to meet the first woman Prime Minister of Great Britain'

and

7.6 Possible worlds 231

(12) 'I wanted to mret Margaret Thatcher'

have different truth-conditions, if 'the first woman prime minis­ter of Great Britain' is given an intensional interpretation: i.e., if, to make the point loosely, the speaker wanted to meet who­ever happened to be the first woman prime minister of Great Britain and did not care, and might not have known, who that was. Verbs such as 'want', as well as 'believe', 'hope', etc., are commonly referred to either as intensional verbs (or predicates) or verbs of prepositional attitude. For historical reasons, the extensional (or non-intensional) and the intensional interpreta­tions of sentences such as (11) are often referred to by logicians and formal semanticists as de re and de dido interpretations, respectively.

Another problem which standard, non-intensional, formal semantics has difficulty in handling derives from the fact that many natural-language expressions do not denote anything that actually exists in the (real) world and yet are obviously not synonymous. For example, 'unicorn' and 'centaur', let us assume, do not denote anything - or to put it in terms of set-theory, denote the empty set (the set with no members) - in the world as we know it: i.e., there are no entities in the real world such that they would be truly described as unicorns or centaurs. Granted, these may not be problems which, of themselves, cause non-philosophers to lose sleep. But they are all connected with the more general problem of formulating, as precisely as possible, the principles whereby speakers are able to assign inter­pretations to expressions according to the context in which they are used and to identify the referents of referring expressions.

In what has been said about possible worlds so far in this sec­tion, we have for simplicity adopted a psychological point of view: I have talked as if it is the aim of formal semantics to con­struct models of the mental representations that human beings have of the external world. Looked at from this point of view, a proposition is true or false of the actual or non-actual world that it represents according to whether it is in correspondence with that world or not. This is a perfectly legitimate way of talk­ing about formal semantics, and it is one that is favoured by

232 The formalizfltion of sentence-meaning

many psychologists, linguists and computer scientists interested in artificial intelligence. But it is not the one that is customarily adopted by logicians and philosophers. There are, in fact, sev­eral philosophically different ways in which the term 'possible world' can be interpreted.

Indeed, in the elementary exposition which I have given here of Montague's system of possible-worlds model-theoretic seman­tics, I have not been absolutely consistent in my own use of the term 'possible world'. (I have also been deliberately inconsis­tent, and somewhat vague, in my use of the term 'model'.) Just now I have talked of propositions as being true or false of the world that they represent; elsewhere I have said that proposi­tions are true or false in a world, tautologies being true, and con­tradictions false, in all possible worlds. It is perhaps more in line with everyday conceptions and with traditional usage to say that propositions represent, or describe, a world, rather than that they are, in some sense, in it. However, many philosophers and logicians have adopted the second way of talking. Without going further into this question, I will simply note that some for­mal semanticists have explicitly defined a possible world to be a set of propositions, while others have said that a proposition is the set of worlds in which, or of which, it is true. For purely logi­cal purposes it makes little difference which of these views we adopt, though the choice between them may be motivated by broader philosophical considerations.

It would be impossible, and inappropriate in a book of this kind, to go into the philosophical ramifications of the adoption of one view of possible worlds, and propositions, rather than another. Nor is it necessary as far as the applicability of formal semantics to the analysis of natural languages is concerned, to resolve such thorny philosophical issues as the reality of the external world; the ontological or psychological status of prop­ositions, semantic representations, etc.; or the validity of the notion of truth-by-correspondence. In conclusion, however, I should like to emphasize that model-theoretic, or indexical, semantics provides one, at least in principle, with the means of formalizing many of the phenomena found in natural languages that were not satisfactorily formalized in earlier systems of

7.6 Possible worlds 233

formal semantics. For example, it enables one to formalize various relations of accessibility holding between different possible worlds. To take just one aspect of this: there is an intuitively clear sense in which, in the everyday use of language, we normally operate with the assumption that the past, but not the future, is accessible to us. And this assumption is built into the structure of the system of tenses and moods in many, if not all, languages. Indexical semantics can handle phenomena of this kind. More generally, it allows us to formalize the fact that speakers are constrained by certain kinds of accessibility in their selection, or construction, of the possible worlds that they refer to and in the way that they refer to them; and also of the fact that they necessarily refer to the world that they are describing from the viewpoint of the world that they are in. These two facts, as we shall see in Chapter 10, are crucial for any proper treatment of indexicality and modality in natural languages. We now turn to a consideration of utterance-meaning and, in so doing, move from semantics in the narrower sense to what many refer to these days as pragmatics.

PART 4

Utterance -meaning

CHAPTER 8

Speech acts and illocutionary force