Model Theory and the Pragmatics of Indexicals

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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. Cresswells 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 refer- ence models are shown to be necessary to cope with the intricacies of the use of tense in natural language. Benvenistes 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 utterances time and the indexicals is anal ysed.

    RCsum6 Larticle 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 Iobjet. La thbse ddfendue par 1A. 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 Ion veut rendre compte de la complexitt de lusage du temps dans la langue naturelle. La classification du temps en temps physique, chronique et linguis- tique due B Benveniste est examinte. I1 lui est reprocht de mtconnaitre le mtcanisme de Ianaphore temporelle. Pour terminer, le problkme de Iinteraction entre le temps de Itlocution 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 prag- matics 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 opera- tors. 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 pos- sible 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,

  • 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 coordin- ate independent of the others. It will be determined, on a given occasion of utterance of a sentence, by mental factors such as the speakers 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 ambi- guous 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 Scotts 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 descrip- tion 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: Lakoffs 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 sev- eral 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 coordi- nates (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 seman- tics by what we have called textual coordinates, one would have turned the successive additions to the list into a harmless procedure. This is Lakoffs 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 in- dexicals 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 as- signment 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 Lakoffs solution

    Unquestionably, Lakoffs treatment of indexicals is more satisfactory than Scotts. 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 predi- cates. 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 Lakoffs 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 dis- course, the universes of discourse in natural language change all the time

  • Model Theory and the Pragmatics of Indexicals 395

    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 Dahls 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 jeopard- ized 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, do...

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