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Model Theory and the Pragmatics of Indexicals * by Paul Gochet

Summary The paper is a critical survey of the semantics and pragmatics of Indexicals. Both

the coordinate-approach due to Lewis and the semantization of pragmatics attempted by Lakoff are shown to be inadequate. Cresswell’s more dynamic approach is shown to withstand the objections raised against it. Sophisticated accounts such as a two dimensional tense logic, or a semantics involving pragmatic models and multiple reference models are shown to be necessary to cope with the intricacies of the use of tense in natural language. Benveniste’s division of time into physical, chronic and linguistic time is assessed and criticised for missing the phenomenon of tense anaphora. Finally, the problem of the interaction between the utterance’s time and the indexicals is anal ysed.

RCsum6 L’article est une Ctude critique de la stmantique et de la pragmatique des em-

brayeurs et indexicaux. La mCthode des coordonn6es dtfendue par Lewis et la lexica- lisation de la pragmatique proposte par Lakoff sont critiquCes. On montre cnsuite que le traitement plus dynamique offert par Cresswell peut &re dtfendu contre les cri- tiques dont il est I’objet. La thbse ddfendue par 1’A. est que des outils conceptuels aussi sophistiquts que la logique temporelle ?t deux dimensions ou une stmantique comportant un modile pragmatique et un modkle ?t a rtftrence multiple n sont indis- pensables si I’on veut rendre compte de la complexitt de l’usage du temps dans la langue naturelle. La classification du temps en temps physique, chronique et linguistique due B Benveniste est examinte. I1 lui est reprocht de mtconnaitre le mtcanisme de I’anaphore temporelle. Pour terminer, le problkme de I’interaction entre le temps de I’tlocution et la rCfCrence des indexicaux est trait6 du point de vue de la logique.

Zusammenfassung Die vorliegende Arbeit enthalt eine Untersuchung iiber die Semantik und die Prag-

matik der indexikalischen Ausdriicke. Es wird gezeigt, dass sowohl die Methode von Lewis, die auf Koordinaten beruht, als auch diejenige von Lakoff, in welcher eine Semantisierung der Pragmatik angestrebt wird, inadaquat sind. Es wird dann die mehr dynamische Behandlung dieser Fragen durch Cresswell gegen vorgebrachte Einwande verteidigt. Der Autor vertritt die Auffassung, dass subtilere begriffliche Instrumente wie eine zweidimensionale Zeitlogik oder eine Semantik, die ein pragmatisches Modell

* This work was supported by a Fellowship of the American Council of Learned Societies 1974-1975. Some materials of it were used for a lecture delivered in the University of Salzbourg and Graz. Miss Sear1 M. A. has kindly checked my English.

Dialectica Vol. 31, No 3 4 (1977)

390 Paul Gochet

und ein Model1 mit multipler Referenz hat, erforderlich sind, um die Behandlung der Zeit in naturlichen Sprachen in ihre Komplexheit zu erfassen. Benvenistes Einteilung der Zeit in physikalische, chronische und linguistische Zeit wird kritisiert: sie verkennt den Mechanismus des Phanomens der Zeitanaphora. Am Ende wird das Problem der Interaktion zwischen der Zeit der Aeusserung und der Referenz der indexikalischen Ausdriicke logisch analysiert.

Q 1.- Introduction

In this paper I intend to assess the merits of a model-theoretic account of the pragmatics of indexicals. The application of model theory to pragmatics occurred as a step in a certain development and can best be evaluated against the background of that development. The development which led to model theoretic pragmatics initiated with possible world semantics applied to the interpretation of modal operators. The next step consisted in the extension of possible world semantics to temporal operators.

Tense operators such as “It has been the case that. . .”, “It will be the case that. . ,” display a structure closely similar to that of the modal operators. In other words, if one accepts the analysis of

into then, a fortiori, one should be willing to agree with the analysis of

into

(1) “It is possible that it should rain” (2) “It rains in a possible world”

(3) It will be the case that it rains (4) It rains in a state-of-affairs which lies in the future at the time

On the other hand, the extension (in this case the truth-value) of “It will be the case that p” depends upon a moment of the time sequence (the point at which the utterance is made) just as much as the extension of “It is possible that p” depends upon a possible world. Between possible worlds and moments in time there is a striking similarity of role which fully justifies us into treating them in a parallel manner, i. e., in treating them as indices which the extension of ‘p’ depends upon.

of the utterance.

Q 2. The coordinate approach to pragmatics

The extension of model theory to cover tense logic took the form of introducing a set of temporal points or indices (T) together with a relation defined on that set. Incremented in this way, the model appears as an ordered sextuple:

where ‘D’ stands for a domain of individuals, ‘f‘ for an assignment function < D, f, W, R, T, < >

Model Theory and the Pragmatics of Indexicals 391

mapping proper names onto individuals, ‘W’ for a set of possible worlds, ‘R’ for a relation defined on the set W, ‘T’ for a set of moments of time, ‘<’ for a relation defined on the set T.

With tense logic, we are coming closer and closer to pragmatics, since among the terms of the tense lexicon we find words such as “now” or words which behave like indexicals such as “present”. The study of these words belongs to the pragmatics of indexicals, i. e. of pragmatics which Hansson called “Pragmatics on the first level”. One has therefore good grounds for expecting that a new extension of the model (the introduction of spatio-temporal coordinates) together with indices designating the agent will be tried by some semanticist. As a matter of fact, the attempt was made and failed. It is worth our while to investigate the reasons for that failure.

Scott suggests that it might be possible to extend the model almost in an automatic manner (Scott, 1970, 149-150).

He considers sentences such as “During that period, all of them have had the property p ” .

Obviously a sentence of that kind acquires truth-value only after we have specified the interval referred to. Such a specification requires the use of an index. But the index i e I is not necessarily a temporal index. “For more general situations, Scott writes, one must not think of the i E I as any- thing as simple as instants of time or even possible worlds. In general we will have

i = (w, t, P, a) where the index i has many coordinates, for example, w is a world, t is a time, p is a “3-dimensional position in the world, a is an agent, etc.. . . all these coordinates can be varied, possibly independently and thus affect the truth values of statements which have indirect references to these coordinates”.

8 3. Objections to the Cmrdinate-approach

The first difficulty raised by Scott’s approach arises when we try to impose a limit to the number of distinct coordinates we have to reckon with. D. Lewis starts with eight coordinates (Lewis, 1972, 176)

“Thus an index is tentatively any octuple of which the first coordinate is a possible world, the second coordinate is a moment of time, the third coordinate is a place, the fourth coordinate is a person (or

392 Paul Gochet

other creature capable of being a speaker), the fifth coordinate is a set of persons (or other creatures capable of being an audience), the sixth coordinate is a set (possibly empty) of concrete things capable of being pointed at, the seventh coordinate is a segment of discourse, and the eight coordinate is an infinite sequence of things”.

Unfortunately, this list, which seemed to be final, is not so. Consider the sentence:

(5 ) The door is open As Lewis notes, this sentence does not mean that the one and only door which is not far from the place where the utterer is located, or the one and only door pointed to by the utterer or which is mentioned in a previous stage of the discourse, is open. The sentence rather means that the one and only door which belongs to the set of the proeminent objects is open.

That is why Lewis concludes (Lewis, op. cit., 254) “We need a proeminent-objects coordinate, a new contextual coordinate independent of the others. It will be determined, on a given occasion of utterance of a sentence, by mental factors such as the speaker’s expectations regarding the things he is likely to bring to the attention of his audience.”

Even incremented in that way, however, the list is not yet final. In any sentence whatever in which an expression occurs which is textually ambiguous and which can be disambiguated by exploiting the context, we shall be compelled to add new indices. For instance, in order to interpret the sentence

(6) . . . I am so dry Fetch your Jim another quart

We need, as Cresswell has pointed out, a ‘previous drinks coordinate’ (Cress- well, 1972, 8).

There seems to be no such thing as a definite limit to the number of coordinate we might need. Lewis and Scott’s method appears to be very heavy and static. Once the list of coordinates has been stretched there is no means at our disposal for us the narrow it down again. If, for instance, we bring in a ‘college’ coordinate in order to interpret the definite description ‘This college’ in

(7) I am master of this college we must retain it even when it is of no use any more. As Cresswell puts it “we should have to have such a coordinate in all value assignments” (Cress- well, ibid).

393 Model Theory and the Pragmatics of Indexicals

9 4. An alternative to the coordinate approach: Lakoff’s lexicalization of the

How can we block the generation of new coordinates? Lewis’ coordinates belong to different categories. He divides the class of coordinates into several subclasses. Coordinates which confer a value to any variable which may occur free in expressions such as “ x is large” or “ x is a son of y”, he calls “assignment coordinates”. Those coordinates which specify the speaker, the hearer, the time or the place of the utterance, he calls “contextual coordinates” (s, h, t, u). We shall call the former coordinates mentioned in this classification “textual coordinates” (Lewis, 1972).

The coordinates of the first kind do not contribute to the proliferation denounced above. As a matter of fact, they can be found already in the very poor models of the non-modal predicate calculus. If one succeeded in replacing the contextual coordinates which undoubtedly complicate semantics by what we have called ‘textual coordinates’, one would have turned the successive additions to the list into a harmless procedure. This is Lakoff‘s policy (Lakoff, 1972, 655, 1974, X-17). Lakoff, however, is committed to subscribe to a very controversial theory, the so-called performative analysis of the illocutionary force. According to that analysis, the deep structure of a sentence such as

should be analysed as having the following form

context coordinates

(8) Bring me what you now have over here

Predicate Argument Argument Argument 3- 3- 3- X Y s, u- u u.

J order

I you bring what y now has

One will notice that in this analysis neither personal pronouns nor indexicals belong to the deep structure. But Lakoff argues that model theory should be applied to deep structure only: “they are meant to apply to logical structures not to surface structures”. One therefore understands why Lakoff claims he has simplified semantics: “Given the analysis given in (9)”, he writes, “the contextual coordinates become superfluous, since the job that they would do in Lewis’ system would be done automatically by the assignment coordinate together with the analysis in (9)”. And he concludes,

to Y

394 Paul Gochet

“What we have done is to largely if not entirely eliminate pragmatics, reduc- ing it to garden variety of semantics”.

$j 5 . Objections to Lakoff’s solution

Unquestionably, Lakoff’s treatment of indexicals is more satisfactory than Scott’s. Contextual coordinates are replaced by texlual coordinates. The shift enables Lakoff to get rid of the unwanted contextual coordinates. Un- fortunately there is a price to be paid for this. The reduction obtained on the level of the coordinate system is accompanied by an ad hoc increase of the number of place in the predicates. Simplicity in one respect is thus paid for by complication in another. In order to account for the fact that marriage can be dissolved in time, Lakoff classifies the predicates “husband of” or “wife of” among triadic predicates: “x is the husband of y at time 2”. But we should remember that there are seamen who get married in two countries without taking the trouble of going through a divorce. It looks as though we ought to turn the predicate under examination into a tetradic predicate, as Dahl has suggested (Dahl, 1975, 60, footn. 7). In that case the logical form of the above-mentioned predicate would become “ x is the husband of y at time t and place z”.

This new kind of ‘inflation’ is nearly as troublesome as the former. Predicates whose places have been increased in number are atomic predicates. If we complicate these predicates, we impoverish the explanatory value of ‘the theory’. A language made up of complicated predicates could hardly be learned at all by a child. Only somwne with an axe to grind would ever dream of treating the sentence

(10) a is the husband of b in the place p at time t as made out of a tetradic predicate and four proper names.

He would rather describe it as made up of a dyadic predicate together with al tense adverb and a location adverb.

A more serious objection can be made to Lakoff: one might argue that Lakoff’s move is useless. Let me spell out this argument a bit more fully. The switch from contextual coordinates to textual coordinates will not be significant if textual coordinates themselves depend on the context. But, unfortunately for Lakoff, this is precisely the case when we deal with natural languages. As Dahl points out (Dahl, 1975, 51)

“In contradistinction to formalised languages, where the universe of discourse is mostly regarded as fixed in advance for the whole discourse, the universes of discourse in natural language change all the time”


and I shall add that the change is determined by the context. In the case of the personal pronouns, it is obvious. As Linski rightly stresses (Linsky, 1966, 117) the question

remains meaningless as long as the context has not been specified. We shall not, however use that counter-example since Lakoff throws the pronouns out of the deep structure. We shall instead show that Dahl’s argument can be made to work just as well if we apply it to quantifiers. Consider for instance the following sentence borrowed from Dahl.

(12) In Great Britain, everybody drinks tea, in France, everybody drinks

It is obvious that the universe of discourse of the quantifier “everybody” varies with the sentence to which it belongs. The logical form of (12) can be represented in this way:

(11) To whom does the pronoun ‘he’ refer?

coffee.

(13) (Vx/x is in G. B.) x drinks tea & ( V y/y is in F.) y drinks coffee.

An objector to this might counter-claim that the universe of discourse can be unified and the ontology of our language simplified provided we are prepared to compensate the ontological impoverishment by an increase of the lexicon. If we follow that line, we ought to ascribe to (13) the following logical form

(14) (Vx) [ (x is in G. B. =I x drinks tea) & ( x is in F. 3 x drinks coffee)]

which requires the use of new predicate constants such as ‘x is in Great Britain’, ‘x is in France’. This easy way out, however, will not do if the sentence under consideration contains modal terms. Suppose we wish to formalize the following sentence:

(15) For everybody in Great Britain, drinking tea is a social obligation

If we adopt the second sort of formalisation, the formula obtained reads as follows

and for everybody in France drinking coffee is a legal obligation.

(16) (Vx) {[x is in G. B. 3 0, ( x drinks tea)]. [ x is in F. 3 0, ( x drinks coffee)]}

But, as was pointed out before, we cannot interpret “0” (“it is obligatory”) unless we bring in possible worlds. “It is obligatory that p” ought to be analyzed “In every world in which obligations are fulfilled, it is true that p”. Not only should we bring in possible worlds, but we should bring in also individuals. It follows that the unity of discourse obtained by introducing

396 Paul Gochet

new predicates such as “x is in Great Britain”, “x is in France” is jeopardized again: the domain of variation for the first occurrence of “x” is not the same as the domain of variation of the second.

One might be tempted to underrate the weight of the objection. It looks as though the unity of the universe of discourse could be restored simply by using a supply of possible individuals. Real individuals can be seen, after all, as a subset of possible individuals. This simple solution, however, does not work. It is open to the objections raised by Hintikka (Hintikka, 1974,47) against the postulates of a “fixed supply of prefabricated individuals”. This postulation entails counterintuitive results in epistemic logic: for instance sentence (17) which is blatantly false must become valid:

(17) (x) ((9 y) (x = y) 2 (3 y) [(y = x) (9 z) John knows that (y = z)]} The reduction of pragmatics to formal semantics attempted by Scott and

Lakoff has failed. We shall see that it is nevertheless possible to build formal pragmatics within the framework of model theory, but on another basis.

0 6 . Two more dynamic accounts

In the coordinate approach adopted by Montague, Scott and Lewis, all indices are put on the same level. This is not the case in Stalnaker’s treatment (Stalnaker, 1972). The latter shows that the distinction traced by Don- nellan between referential and attributive use of a definite description cannot be accounted for if along with Montague or Scott, we take up “the simpler account of pragmatics which merges possible worlds with contexts”, i. e. the account of pragmatics according to which sentences are to be evaluated at an ordered pair of indices (designating a possible world and a context respectively).

Stalnaker offers a more refined treatment. He contends that two steps are to be distinguished in the evaluation of a sentence that contains a definite description displaying the kind of ambiguity considered above: one must separate the determinants of truth into two parts: “the context which determines a proposition given a sentence, and a possible world which determines a truth value given a proposition (Stalnaker, 1974, 4)”. In other words, context and possible words operate at different stages in the process of evaluating a sentence. First one computes which proposition is expressed by the sentence under consideration. One deals with a function from context to proposition. The next step consists in computing the truth-value of the proposition in a certain possible world.

Cresswell shares with Stalnaker the belief that contexts map sentences onto propositions instead of mapping them directly onto truth value, but


he diverges more deeply from the classical coordinate approach advocated by Montague and Scott. Cresswell offers an even more dynamic account of indexicals than Stalnaker.

We owe to Cresswell and to Goddard and Routley (Goddard and Rout- ley 1973, 565) a sharp diagnosis of the problem and also the first steps toward a new solution (Cresswell, 1973, 111)

“The trouble with the ‘coordinate’ approach to contextual dependance is that it seems to require that we give in ladvance a finite list of contextual features to be taken into account when evaluating a sentence. It is my opinion that there is no such list and that the contextual features to be taken into account depend on the meaning of the sentence.”

In other words, the idea that there exists a process of accumulation (i. e. the idea that we call upon more and more coordinates) presupposes that the two kinds of information are independent of each other and add up to one another. This presupposition, however, is false. That which is the relevant part of the context is not independent of the text. It is determined by the text and varies accordingly. In his aim of showing that the context depends on the text Cresswell takes a decisive turn in formal pragmatics: he suggests that we should conceive of the context as being a property of the utterance, rather than a store-house of indices.

If the context is conceived as a property of the utterance, several phenomena which looked mysterious in the classical theory of coordinates become amenable to a satisfactory explanation. One can, for instance, define the lower bound, below which contextual information is insufficient. For instance, for the sentence

(18) I am master of this college which contains three indexicals, “any property of utterance which specifies a speaker, time and indicated institution will be a suitable context for (18) and all utterances of (18) having that property will express the same proposition (Cresswell, 1973, 112)”.

There is a lower bound but there is no upper bound. For instance “a property will still be .a suitable context for (18) if it gives other information as well, and moreover the proposition expressed by (18) will still be the same proposition, (Cresswell, 1973, 115)”. In order to account for this fact, Cresswell introduces the notion of “context family generated by property which constitutes a context”.

It even happens that several indexicals can be used in the same sentence. For instance, in

398 Paul Gochet

(19) I sleep two indexicals (are operated with: tense and a pronoun. In the coordinate theory, the indices referred to by these two indexicals would receive the status of items in a sequence. But the only operation defined would be con- catenation.

Cresswell’s theory, on the contrary, is much more compositional than its alternatives. It enables us to define operations which combine contextual information brought in by the various indexicals. In the case of the sentence (19), “it is easy to see that the intersection of two families of this kind will be a family generated by a property which specifies a time t and an utterer u. Now, if we combine that result with a) the semantic rule which says in which conditions a given utterance expresses a given proposition and b) the definition of “sleep” in terms of function, one can easily prove that “any utterance of (19) by u at t expresses the proposition that u is asleep at t” a proposition which is always false since all genuine utterances occur when the speaker is awake (Cresswell, ibid.).

8 7. Objections to Cresswell’s approach We have recourse to context to disambiguate a text which as it stands

is open to conflicting interpretations. But according to Cresswell, this appeal to context is a two-way traffic, for “the contextual features to be taken into account depend on the meaning of the sentence”. Apostel claims that this interdependence between text and context involves a “threat of circularity”. He requires of Cresswell “a method for selecting the relevant indices and a procedure which determines in which order the coordinates must be used” (Apostel 1975, 86)

Apostel’s qualms about a threat of circularity can be allayed, however, if we remember that on Cresswell’s view even expressions whose meaning depends upon the context contain a context-free ingredient. For instance, the semantic value of the sentence type

is an open proposition. In other words, its meaning is independent of the context. It is a function - i. e. something constant - which takes the context as arguments. Its values are propositions which vary with the argument chosen. At this stage, one might be tempted to conclude that the bearer of a complete meaning (of a “proposition” as opposed to an “open proposition”) is the sentence-token and that, in this view, meaning becomes a very unstable and fleeting phenomenon indeed. This is not the case, however, as can be seen from the fact that two distinct sentence-tokens (i. e. pairs of a sentence type and a context) can express the same proposition: sen-

(20) I am standing


tence (20) uttered by Cresswell, for instance, can be synonymous with sentence (21) uttered by, let’s say, Lewis

(21) You are standing. On the other hand, Cresswell (in conversation) has objected that Apostel’s

demand for a method which would determine in which order coordinates come into play is not a legitimate request. According to Cresswell-time, position and speaker coordinates are not ordered. What matters is to know whether position, for instance, is necessary besides time and speaker. There si no ordering relation between coordinates, no composition, but sometimes - and then only seldom - interaction.

As to the request for la method enabling us to select the relevant indices, this too seems hard to justify. There is no general and autonomous method but a whole set of particular methods which are part and parcel of the meaning of indexicals. For instance, there is one systematic convention that ties a feature of the context (the speaker) with the type-word I and another one that ties a feature of the context (the addressee) with the type-word You. The Zexical meaning of these type-words directs the search for a property of the context which will enable us to fill the gap in open propositions and turn them into propositions.

It is worth stressing here that Cresswell borrows from Stalnaker the two- step procedure according to which a proposition is a function which maps possible worlds onto truth-values and a sentence meaning is a function which maps contexts onto propositions. Cresswell, however, can be credited with the introduction of the very useful concept of open proposition, whose significance we have already assessed.

5 8. A refined version o f the time index In (19)’ the truth-conditions are computed from the truth-conditions of

the components within the same context. Admittedly, in order to evaluate the truth-value of a complex sentence in a context, we generally need to know only the values of the parts of the sentence in that context. But this is not always the case. Consider the sentence

i. e. The truth-value of that sentence depends not on the truth-value of “John

is asleep” at t where t denotes the time of the utterance. I t rather depends on the truth-value of the sentence “John is asleep” at t’ < t i. e. the sentence (22) will be true at t if and only if John is asleep at some t’ earlier than t.

(22) John slept (23) It was the case that John is asleep.

400 Paul Gochet

In its early days, tense logic was nothing more than an extension to modal logic, which had hardly any bearing at all on pragmatics. But it should be borne in mind that a tense logic which remains in that state of depend- ency is altogether unsatisfactory. Tenses have as Benveniste has pointed to a pragmatic dimension (Benveniste, 1974, 73).

Benveniste distinguishes three kinds of time

Will”,

in the calendar and finally,

1) the physical time, which is a “uniform continuum, linear, divisible at

2) the chronic time, i. e. the time of the events which are reported about

3) the linguistic time, which he characterizes in these terms: “What is peculiar to linguistic time is this: linguistic time is organic- ally connected with the speech practice, it can be defied as a function of speech. Its center - its generating center and definitional axis - is the present of the speech utterance”.

That third sort of time obviously falls within the scope of pragmatics.

In the beginning logicians ignored it, as can be seen from the fact that the early systems of tense logic contained no operator designed to express the present but they erroneously subscribed to the thesis that the use of the adverb “nowyy is a redundancy. That gap in tense logic was later filled by Prior and Kamp who worked out an axiomatisation of the ‘Present’- operator. But there is more. Recent researches in tense logic and tense semantics have led to the uncovering of pragmatic phenomena which compel the logicians to revise claims made by some outstanding linguists.

Vlach (1973) succeeded in establishing that the meaning of “now” cannot be exhaustively described if the meaning of that word is conceived as a function which maps it onto the speech utterances in which it is uttered. Let US consider the following sentence.

(24) Jones is going to cite everyone now driving too fast. It looks as if that sentence could be analysed within a tense logic con-

sisting in a first-order predicate calculus to which three tense operators have been added (a Future-operator: “it will sometime be the case that”, a Pmt- operator: “it bas sometime been the case that” and a Present-operator: “it is the case that”).

The logical form of (25) in that symbolism (25) I t will sometime be the case that John is going to cite. . .

would be

Model Theory and the Pragmatics of Indexicals 40 1

(26) F (Vx) ( x is driving too fast now I) Jones is going to cite x )

(27) F ( V x ) ( N D x ~ C j x )

or, more formally:

But, if that formalization were correct, how should we represent the following sentence (28)?

(28) Jones was once going to cite everyone then driving too fast. If we avail ourselves of the tense logic which we put to use in the

(29) It has been the case that it will be the case that ( V x ) ( x is driving too fast now =I Jones cites x )

former sentence, we obtain the following formalization

or formally: (30) PFV x(NDx 3 C j x ) That formalization is however unsatisfactory on various scores. First

(31) It has been the case that Jones is going to do something

(32) It has been the oase that Jones was going to do something. is not synonymous with

But there is another and worse difficulty, which has been pointed out by Vlach, namely the fact that the proposed formalization does not succeed in representing the shift of temporal reference operated by switching “now” into “then”. In other words, the tense logic described above cannot express in symbolic terms a plain sentence of natural language obtained by turning a future into a past.

Vlach stretched the expressive power of tense logic by introducing a new operator, the index-operator K “whose function is simply to indicate which previously established context the ‘then’ operator refers back to”. He calls the ‘then’ operator ‘R’ and the index ‘K’. R will always shift the temporal reference back to the point of the nearest (syntactically) occurrence of K within whose scope the occurrence of R lies. If the occurrence of ‘R’ does not lie within the scope of ‘ K , then ‘R’ behaves exactly as N does. The sentence (28) will therefore be represented by

(33) It has been the case at K that it will be the case that ( V x ) (x is driving too fast at the aforementioned instant =, Jones cites x).

i. e. by (34) PKF (Vx) (RDx 2 Cjx). If syntax is extended by the introduction of two new operators, semantics

will have to be developed also. As Vlach writes “the primary change necessary is that we must evaluate formulas with respect to ordered pairs of moments rather than just one individual moment (Vlach, 1973, 4)”. We shall have to reformulate the truth-conditions of the sentences which con-

402 Paul Gochet

tain the new operators “K” and “R” in a way which enables us to express the fact revealed by sentence (28), namely in a way which takes into account the fact that “the truth-value of a given formula with respect to a given moment of utterance depends on the truth-values of its subparts at moments other than the moment with respect to which the whole formula is being evaluated (Vlach, 1973, 4-5”). Technically, that goal can be reached “by letting ‘the second term of the ordered pair be the moment at which formulas beginning with R are to be evaluated, and by letting K change the second term of the ordered pair (ibid., 5)”. The very existence of the phenomenon of ‘tense anaphora’, exemplified by the sentence (28) and reflected in the semantic mechanism which we have just described, escaped Benveniste’s notice as oan be seen from the following statement (Benveniste, 1974, 74) in which he is speaking about tenses other than the present. Benveniste writes

“Language does not locate them in time according to their own position, nor in virtue of a relation which would differ from the coincidence between the event described and the speech-event, but as points in time seen behind us or in front of us from the viewpoint of the present (Behind or in front of because man moves forward in the direction of time or time moves toward him, as the picture of our representation suggests). The language must, necessarily, define the present on an axis #and this unique reference point is always the speech present.”

Tense anaphora as described above obviously compels us to mitigate Benveniste’s statement on that score. Admittedly the present remains a privileged reference point, but it ceases to be the only one. Other phenomena than tense anaphora also require that we avail ourselves of two reference points. Consider for instance the two following sentences, quoted by 0. Dahl (Dahl, 1975,47-48)

(35) - Last year, the leader of the British Labour Party was in London

These two sentences are ambiguous: the definite description “The Labour Party” can denote the individual who was the leader of that political party last year or the one who is its leader this year. Again “the Pope” can refer to Leo X or to Paul VI. It is worth mentioning that the technical apparatus Vlach has developed enables us to analyse that ambiguity in a satisfactory way by calling upon operators such as “then” and “now” tacitly understood. These operators interact with the definite description and modify its meaning.

- Luther’s ideas did not please the Pope.


It may happen that in order to evaluate the truth-conditions of a sentence, we must keep track of more than two reference points. A case in point is offered by Professor Moravcsik’s example mentioned by Gabbay (Moravcsik, 1974, 184)

(36) She regretted that she married the man who was to become an officer of the bank where she had had her account.

5 9. A new kind of pragmutical model There are also tense sentences whose pragmatic pecularities cannot be

analysed satisfactorily, even within the refined model-theoretic semantics which Vlach affords. In order to be in a position to treat these recalcitrant sentences, we shall have to modify the basic concepts of pragmatics in the way Cresswell does. Consider the sentence

(37) They went up and down hill 603 To free that sentence from the charge of being inconsistent in the sense of analytically false, nothing more is required than to interpret “and” in the sense of “and later on”; and to suppose that “later on” was tacitly understood. That reconstruction, however, creates a problem: it gives to the conjunction “and” a non truth-functional meaning. It is therefore advisable to take ‘another course, i. e. to understand “and” as a truth-functional connective and to posit an implicit tense-indexical alongside “went up” and “went down”.

(38) They went up at time t and went down at time t’

(39) Now the artificial satellite is above Cape Kennedy and now it is

That sentence, like the former, is self-contradictory in the literal sense. It is tempting to apply the same policy as we did before and to translate it into.

(40) At time t,, the artificial satellite is above Cape Kennedy and at

That translation, however, is not satisfactory because (40) does not give the ‘spirit’ of sentence (39). Sentence (40) contains a chronic time in Ben- veniste’s sense, whereas the initial sentence (39) illustrates a linguistic time, i. e. the ‘linguistic present’ which Benveniste (Benveniste, 1974, 74) characterizes in these terms:

“That present moves forward as the discourse proceeds and remains actual.”

Now consider the following sentence

far away from Cap Kennedy.

time t, it is already far away.

404 Paul Gochet

In other terms, in the sentence (39), temporality is not temporality seen from outside. There is some sort of interaction between the content of the sentence and the utterance. This is why (39) differs from (40) and belongs to pragmatics. The troublesome sentence (39) cannot be analysed along the same lines as (40).

The modification which has to be brought about in the key-concepts of model theory in order to make it suitable for the description of the above- mentioned sentence seems to be this: we need to work with new kinds of models. Instead of operating with semantic models which map type-words or type-sentences onto objects, we have to work with pragmatic models which map occurrences onto extralinguistic objects.

This new way of conceiving models is motivated independently by the problems tackled by Cresswell and by the problem we have just considered. Still another reason for this suggested modification is afforded by the problem of accounting for the kind of ambiguity that attaches to a word which occurs twice in the same sentence, but whose meaning varies.

To solve all these problems in one stroke, Warner suggests as Cresswell did in another context, that meaning should be attached to utterance rather than to sentences. “TO implement this idea we must not take the function I in < A, I > simply as a mapping of elements of dom L onto appropriate entities. The reason is that a speaker might use a word W E dom L * twice in the same sentence to refer to two different entities - e. g. SMITH LOVES SMITH. To represent a speaker’s references at a time, the function I in a model <A, I > should assign entities to occurrences of words and sentences (Warner, 1975, 92)”.

Ambiguity can bedevil a sentence even when no word occurs twice in it. Chomsky has accustomed us to the phenomenon of a single sentence having two syntactic structures.

oan be understood in two ways. Pragmatic models should be conceived in such a way that they can afford for that phenomenon. This is why Warner defines an occurrence as a triple containing among its elements ‘p’ which stands for a phrase structure: “an occurrence of w is a triple < p, v, w > such that p is a phrase marker. . . v is a mode of p, and p(v) = w.

Words like “Smith” or “now” in the above-mentioned examples occur during the utterance of a sentence. An utterance is a process which takes time. Occurrences are thus more akin to stages in a process than to elements in a static structure. It seems therefore that in attaching reference to occurrences rather than to type, Warner provides us with a nice way of accounting for sentence (42) without turning the linguistic time into chronic time.

(41) visiting parents can be boring


(42) Now the artificial satellite is above Cape Kennedy and now it is

One might evince some misgivings even against this approach. If we concede to Warner that truth attaches to token-sentences and reference to token-words, how shall we account for the invariance of meaning? This is not a serious problem, however. What holds for reference and truth does not hold for intension. Intension is the function which attaches an entity to each occurrence of a referring expression or a truth-value to each declarative sentence. On the one hand, if the function correlates different individuals with different occurrences of the referring expression, the function itself does not change. On the other hand, non-indexical expressions do not have different denotations. Therefore the idea that meaning is connected with universal concepts is not jeopardized by Warner’s account.

Compare these two successive uses of ‘now’ (43) Now I have caught the trick, now I could repeat it again. (44) Now I utter the word ‘x’ for the first time, thus now I do not utter

Sentence (43) admits an interpretation in which it is only the type of ‘now’ that signifies, not the token. The same moment of time is referred to in the two occurrences. The meaning of ‘now’ can be accounted for in semantic terms. ‘Now’ designates what Thomason calls “time of evaluation”. The truth-value of the sentence depends on that time.

Sentence (44), on the contrary, can only be given an interpretation which accounts for its analyticity if we focus on the occurrences and utterances. The extension of the sentence depends on the time of utterance, i. e. on the pragmatic time.

Warner’s model is one which does account for the difficult sentence (44). There is, however, an alternative way of doing this which is more in line with the Montague-Scott-Lewis conception of a model. Groenendijk and Stockhof (1975) have tried to overcome the limitation of classical pragmatics, i. e. its inability to account for multiple reference. Their new solution consists in dividing the index in the model into sub-indices. Initially they conceived a model as an tentuple

where A, I, J, are a set of possible individuals, possible worlds and possible contexts respectively, < is a temporal relation, S denotes the speaker, h the hearer, etc. . , , ‘ts’ is “an index which determines for each point of reference which sentence is uttered at that point of reference by whoever is the speaker at that point of reference” and ‘Cm’ is “a function which determines for

far away from Cape Kennedy.

the word ‘x’ for the first time.

<A, F, J, j,, <, F, s, h, ts, Cm>

406 Paul Gochet

each pair < i, j > between which possible individuals and sentences there exists a relation of communication”. In this model, j, is an element of J. If we want to account for multiple temporal reference, we should replace that element by an ordered-ntuple of elements

<A, I, J, <jo, jl . . . ji . . .>, <, F, S, h, ts, Cm> If the authors had left the matter in that state, they could be accused of

reiterating the ad h c procedure adopted by Scott and Lewis. But fortunately, they pushed the matter further. They developed their model theoretic apparatus to the point where recursive clauses in a definition of truth become available for pragmatic sentences. This is, I think, the decisive step in a theory of linguistic competence. If someone succeeds in spelling out rules which enable him systematically to compute the meaning of an arbi- trary compound out the meaning of its parts, then he will be entitled to contend that he has supplied a theory of semantic or pragmatic competence as opposed to a mere description of the facts to be explained.

Let us now sum up the successive stages in the development of pragmatics.

In order to be able to account for pragmatic phenomena displayed by atomic sentences, such as the fact that the sentences (40) and (41) are pragmatically although not semantically valid, we have to distinguish, as Montague does, between two kinds of indices: possible worlds and contexts.

(45) I exist (46) Yesterday is past. To be able to explain a wider set of pragmatic phenomena such as for

instance the breakdown of the law of necessitation in demonstrative logic, we have to go one step further. After having split up our index points into two bundles (contexts and possible worlds), we have to distinguish two kinds of functions in our account of sentences such as (45) and (46), namely a function which maps contexts onto propositions and a function which maps propositions onto truth-values. This step has been made by Professor Stalnaker and by Professor Kaplan. The latter has formulated recursive rules of truth-conditions for pragmatic sentences containing a single reference point.

If we want to build up some sort of generative pragmatics capable of accounting for the meaning of molecular sentences containing multiple reference, we have to complicate our technical apparatus still a little more. We have to provide recursive clauses of truth-definition for pragmatic sentences containing several reference points. This is precisely what Groenen- dijk and Stockhof have succeeded in doing. First they substitute a sequence


of temporal indices < j, . . . j, > for a single index j,. Second, they intro- duce a few technical concepts such as the concept of submodel and the relationship of priority obtaining between two submodels. Third, they supply a recursive definition of truth.

A submodel is, roughly speaking, a model in which the sequence < j, . . . j, . . . > is a subsequence of the n-tuple < j,, . . . j, . . . >. A submodel ME is prior to a submodel ME’ if all the items j in the sequence of temporal references (< ji . . . j, > of the former are prior to the items in the sequence of temporal references of the latter (< j, . . . j, >).

Groenendijk‘s and Stockhof‘s definition of truth for conjunctive statements containing several reference points reads as follows

‘‘a & Y” is true in M if there exist submodels ME, ME’ of M such that is true in ME, Y is true in ME’ and ME’ is not prior to Ma. With the aid of such a truth-definition an adequate account of the meaning

of a compound sentence containing multiple reference such as (47) can be given.

(47) Now it is possible to see the satellite in the sky, and now it is not

We require of an account of such a sentence that it fulfil the three following conditions: a) The account offered should explain why (47) is not self-contradictory; b) The account ought not to sacrifice the truth-functional character of the

connective “and”; c) The account ought not to require that the occasional sentence (47) be

an eternal sentence for such replacement would result in a loss of information content.

These three requirements are fulfilled by the $analysis offered by Groenendijk and Stockhof. The pragmatic theory they offer goes far beyond the treatment of indexicality since it includes a model-theoretic account of what B. Hansson has called pragmatics on the third level, namely the theory of speech acts but this is a topic which falls outside the frame of this critical survey.

possible to see satellite in the sky.

Dpt. of Philosophy, University of Liege 32, place du X X Aoat, B-4000 Liege (Belgium)

408 Paul Gochet

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Dialectica Vol. 31, No 3 4 (1977)