Part 12 (1/2)

3.5.3.

Russell's Equivalence To pursue the topic of formal semantics from yet another direction, recall that we have so far agreed that the use of logical notation may help represent the data of linguistic intuitions somewhat perspicuously. On favorable occasions such as (79) above, logical representations might even suggest directions for linguistic inquiry. Obviously, only those representations will be taken notice of (or deliberately constructed) that fall within the current scope of grammatical theory. To that extent, formal semantics supports grammatical theory without enlarging its scope.

From this limited perspective, maybe we can think of formal semantics just as a ''mapping'' device concerning three symbol systems: linguistic expressions, expressions of logic, and expressions of set theory with arbitrary elements-''a study of symbolic objects and their properties,'' as Chomsky put it. It seems that this was Montague's only interest in the project, as noted. The task of formal semantics then is to set up two sets of relations-between linguistic and logical expressions, and between log- Grammar and Logic 107.

ical and set-theoretic expressions. Thus, we relate every man walks to (every x: man x) (walk x), which in turn is linked to jMan a Walkj 0.

A systematic matching of three symbol systems for a suciently large fragment of, say, English under the overall constraints imposed by syntax is no mean feat, whatever be the point of the exercise.

To emphasize, we are no longer concerned with what expressions of formal semantics denote. That is, we are ignoring the relations.h.i.+p of the last of the triad-set theory-with nonsyntactic objects such as concepts or ent.i.ties in the world. The current perspective essentially means that we are viewing the model-theory part of formal semantics, at best, as highlighting some general set-theoretical intuitions; such intuitions accompany linguistic intuitions anyway. In fact, studies of these intuitions have an eminent precedence. Although, as noted, Russell (1905) did not have an explicit model theory in his theory of descriptions, he appealed to intuitive set theory whenever needed. Recall his famous remark on the sentence The present king of France is bald: ''If we enumerated the things that are bald, and then the things that are not bald, we should not find the present king of France in either list. Hegelians, who love a synthesis, will probably conclude that he wears a wig'' (p. 485). In this light, the model-theory part of formal semantics is to be seen as visual aids to the (set-theoretic) intuitions we already have, not as an account of those intuitions. Even there, the resources of formal semantics seem severely restricted in representing linguistic intuitions.

Formal semantic treatment of English definite descriptions ill.u.s.trates the point. I do not have the s.p.a.ce to develop a positive theory of descriptions (Mukherji 1987, 1989, 1995). I will only make some brief remarks on why I think that the resources of logical theory fail even to represent the linguistic intuitions concerning definite descriptions, notwithstanding over a century of intense eort. (I must add that positions on this turbulent topic are so hardened by now that nothing is even remotely settled.) To begin, it is natural to think that the original proposal for logical form must have been based on some intuitive understanding of some natural-language sentences of a rather simple sort: Socrates is wise, All men are mortal, Tully is Cicero. So it is no wonder that, given stipulation, at least these sentences will display their meanings via their logical forms since the logical forms ''display'' their meanings via these sentences.

Therefore, we need to show that, beyond the initial stipulations, certain theoretically interesting aspects of the sentences of a language fragment fall under the scope of logic. This much, I a.s.sume, is maintained at least since Frege; it is certainly a.s.sumed by Montague.

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Bertrand Russell (1905) identified such a language fragment. Beginning with the stipulated resources, he proposed an innovative canonical form for English sentences with definite descriptions. The canonical form enabled him to make an empirically significant distinction between the surface and the logical forms of English sentences, as we saw. Armed with the distinction, he proposed a solution within logical form to a semantic problem that arose in the surface form. Definite descriptions thus were something of a test case for the canonical power of formal logic.

The problem is that, in over one hundred years of voluminous discussion on this topic, there is still no consensus on how to treat definite descriptions: the has been viewed as a singular quantifier, universal quantifier, referring expression, term operator, abstractor, Hilbert's epsilon operator, and so on. As a result, the test case has continued to be the problem case. Nevertheless, even if there is disagreement about the operational character of the, there is wide consensus on the basic meaning of the definite article via what David Kaplan (1972) has called Russell's ''fundamental equivalence''; it is also called the ''uniqueness condition.''15 I will argue that the fundamental equivalence gives an entirely wrong account of the intuitions of English speakers when they use/ interpret definite descriptions.16 Russell's fundamental equivalence required that an English sentence of the form (80) The F is G is equivalent to two other English sentences of the form (81) and (82), (81) One and only one F is G (82) Exactly one F is G a.s.suming the equivalence between (81) and (82), Russell argued that, say, (82) could be rewritten as (83), (83) (bx)(Fx & (Ey)(Fy ! x y) & Gx) as we saw, or equivalently as (84), (84) (by)(Ex)((Fx $ x y) & Gy)) So, the ''quantificational'' treatment of the depends crucially on the equivalence of (80) with (81) and (82)-that is, the translation of (82) into (83) or (84) requires the fundamental equivalence between (80) and (81) or (82). As an aside, I note that the canonical forms (83) and (84) are hardly perspicuous for triggering set-theoretic intuitions. For that Grammar and Logic 109.

purpose, their quasi-English rendition and, in fact, the original (80) seem better suited, unsurprisingly.

As noted, most formal semantics approaches take the stated equivalence for granted, even if they disagree with the specific canonical form of (83)(84). To take some examples, Montague held that the role of the definite determiner is to make two a.s.sertions: (i) that there is one and only one individual that has the property of being F, and (ii) that this individual also has the property G (Dowty, Wall, and Peters 1981, 197).

Montague brought out this role by translating the as (85) by applying l-abstraction over (84).

(85) lF[lGby[Ex [Fx $ x y] & Gy]]

According to Neale 1990, 45, The F is G is true i (i) all Fs are Gs and (ii) there is exactly one F. Thus the truth clause for The F is G is (86) '[the x: Fx] (Gx)' is true i jF a Gj 0 and jFj 1 Although Larson and Segal (1995, chapter 9) recognize the ''namelike''

or ''referring'' character of some the-phrases, generally they seem to favor a quantificational treatment along Russellian lines; otherwise, they need to hold that the, a closed item, is widely ambiguous. Thus, The F is G is true just in case there is exactly one F and this F Gs (Larson and Segal 1995, 320). In their formal notation, The F is G translates as (87).

(87) Val(hX, Yi, the, s) i jY a X j 0 and jY j 1 meaning, roughly, the semantic value of the is such that, given a sequence of objects s, the the relation holds between (the cardinality of ) two sets X and Y just in case Y is a subordinate of X and Y is 1.

In eect, both Neale, and Larson and Segal, implement Chomsky's idea that the F is to be viewed as a universal quantifier with the special condition that the set of Fs is a unity when F is in the singular, and more than one when F is in the plural. This enabled Chomsky (1977, 51) to say that the ''meaning of the, then, is not that one and only one object has the property designated by the common noun phrase to which it is attached.'' As shown in the citations, both Neale and Larson-Segal miss this important qualification while implementing Chomsky's idea. In any case, as Evans (1982, 59) points out approvingly, Chomsky's formulation turns the into a straightforward numerical quantifier. It is the ''numerosity'' picture of the that is central to Russell's equivalence.

In contrast to the quantificational treatment, Kaplan (1972) introduces a primitive operator, called the ''definite description operator,'' which 110

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generates a term t in a.s.sociation with a description, such that t denotes one and only one object satisfying that description. Thus Kaplan treats the F as a term (a designator) rather than as a quantified phrase, although his semantic rule obeys Russell's fundamental equivalence. I will hold on to this point exclusively to enquire if the is to be viewed as a quant.i.ty-generating operation at all, in whatever guise. Since quantifiers, especially numerical quantifiers, can certainly be viewed as ''importing'' quant.i.ty (Quine 1980, 169), the question whether the is a quantifier becomes a special case of a more general question that arises even if we treat the-phrases as terms obeying Russell's equivalence.

By focusing on the fundamental equivalence, therefore, I am setting aside the standard controversy between namelike and quantifierlike treatments of definite descriptions. As such I will not be concerned with scope distinctions, anaphoric properties, referential uses, functions across possible worlds, and the like. To raise these theoretical issues, we need some pretheoretical idea of the role of the in language. My contention is that people get into these theoretical issues because it is thought that the pretheoretical issue has already been settled in Russell's equivalence.17 Furthermore, almost all these theoretical issues are raised within a restricted set of choices. That is, it is taken for granted that if you are not happy with the quantificational treatment of the, it is your burden to show that the-phrases are namelike, failing which you return to the quantificational picture somehow (or, settle for ambiguity of a closed item).

This a.s.sumes that there must be a satisfactory account of the within the broad framework of logic. By suspending the theoretical issues, then, we are leaving open the possibility that the closed item the-perhaps the most frequently used closed item of English-escapes the broad framework of logic; the may not be a logical operation, in any clear sense of ''logic,'' at all (Mukherji 1987, chapter 3).

To create interest in this issue, I wish to just raise a number of queries of varying degrees of salience regarding the fundamental equivalence, more or less at random; I have no s.p.a.ce for addressing them individually.

First, while the semantic value of (the singular) The F is one in the frameworks of Neale, Chomsky, and Larson and Segal, Russell's equivalence required the quant.i.ty to be not just one, but exactly one or one and only one. How do we capture these additional things set-theoretically? Second, one item of English, the, is said to be synonymous with two other items of English, one and only one and exactly one. Why should there be such a proliferation of synonymy among the closed items of a language? Third, Grammar and Logic 111.

turning to plural descriptions, when I say The world wars were catastrophic events, do I mean that exactly two things were world wars and each was a catastrophic event? If yes, then what do I mean when I say The claws of a tiger are dangerous? I do not even know how many claws a tiger has. If not, why not? Why don't we have definite articles for exactly two, exactly three, and so on? Fourth, we know that the-phrases can sometimes ''grow capital letters'' (Strawson 1950, 341) and turn into names: The White House, The Good Book, The Old Pretender. Can any other determiner phrase, including exactly one house, ever do so? Fifth, Kripke (1972) suggested that singular descriptions and complex demonstratives may be used to ''fix the reference'' of a name: the teacher of Plato may fix the reference of Socrates without being synonymous with it, that guy with dark gla.s.ses may fix the reference of Karunanidhi. Can a numerically quantified phrase such as exactly one teacher fix the reference of a name? Sixth, we noted that Quine (1980, 169) held that quantifiers import quant.i.ty; why did he treat descriptions separately as importing ''uniqueness''? Is there a distinction between importing quant.i.ty and uniqueness? We can go on like this (see Mukherji 1987 for more).18 Hoping that the issue of fundamental equivalence is now open and setting other issues aside, consider how Strawson (1961, 403) compares numerically quantified phrases with the-phrases: One who says that there exists one thing with a certain property typically intends to inform his hearer of this fact. Thereby he does indeed supply the hearer with resources of knowledge which const.i.tute, so to speak, a minimal basis for a subsequent identifying reference to draw on. But the act of supplying new resources is not the same act as the act of drawing on independently established resources.

Observations like this are typically interpreted in the literature as introducing a ''pragmatic'' new-given (or new-old) distinction; however, the ''semantics'' ( intuitive set-theory) continues to be the same. For example, Jackendo (2002, 397 n.) holds that ''the definite article expresses a claim . . . that a unique individual satisfies this description (more or less as in Russell's 1905 explication of definite descriptions).'' However, if a speaker antic.i.p.ates a situation in which ''the purported referent is not present'' in the hearer's knowledge base, a definite description or an ''un-adorned'' proper name won't be used. Also, we need to ''fall back on some repertoire of repair strategies'' if it so happens that the speaker says the apple on the table, but the hearer fails to see any apples, or sees two of them (Jackendo 2002, 325). So, the fundamental equivalence holds along with the new-given distinction.

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No doubt, Strawson does want to introduce the new-given distinction in the pa.s.sage cited: the so-called familiarity theory of descriptions. But in doing so, he is making a much deeper point-routinely missed in the literature-on the role of the definite article. I also think that Strawson's own earlier-and more famous and controversial-view of definite descriptions (Strawson 1950) is partly responsible for this systematic mis-interpretation. In that work, Strawson suggested that although the F does not mean one and only one F as Russell thought, nonetheless, one and only one F gives the condition/presupposition for a.s.serting the F. I have argued elsewhere that this weaker claim does no damage to the basic spirit of Russell's theory (Mukherji 1995). Without repeating the arguments here, it is clear that Strawson did not detach himself completely from Russell's fundamental equivalence.

The distinction between identifying and resource-presenting functions advocated in the pa.s.sage cited, I will argue, amounts to a distinction between all typically quantified phrases including, in particular, one and only one F, on the one hand, and definite descriptions of all varieties (and perhaps proper names and demonstratives as well, but I will not argue this point here), on the other.

At a minimum, Strawson is claiming that the expressions the F and one and only one F signal very dierent speech acts. To proceed, let me try to understand this claim with straightforward linguistic intuitions. Let us suppose a schoolteacher asks in a history cla.s.s (scenario 1), ''How many kings of France were guillotined?'' a.s.suming just one king of France was guillotined, an appropriate and correct response would be, ''One.'' If the teacher pursues the matter by asking, ''Isn't that more than one?'', an appropriate answer would be, ''No, exactly (or just or only) one.'' The point is, the question requested a number, possibly a unique one, and that request is not fulfilled by uttering the king of France. Suppose now the teacher asks, while showing pictures of kings from dierent countries (scenario 2), ''Which one of them ruled from Versailles?'' Now an appropriate and correct answer would be, ''The king of France.'' In this case, it would be totally inappropriate to respond with one and only one king of France.

Before I proceed to build up on these intuitions, notice that it is too late for formal semantics to claim that these intuitions show, at best, that the king of France and one and only one king of France dier in felicity conditions rather than in truth conditions.19 John Austin (1961, 231) observed that to be true (or false) is not the ''sole business'' of utterances; utter- Grammar and Logic 113.

ances can also be ''happy'' or ''unhappy'' in a variety of ways. There are ''conventional procedures'' for using specific linguistic expressions, and ''the circ.u.mstances in which we purport to invoke this procedure must be appropriate for its invocation'' (p. 237). These circ.u.mstances will be the felicity conditions for the use of the relevant expressions. To take Austin's example, suppose someone says, while playing a game at a children's party, ''I pick George,'' and George says, ''I'm not playing'' (p.

238). The felicity condition for the (correct) use of I pick George requires that George is playing; his refusal makes the use of the expression, on that occasion, infelicitous.

Suppose that Austin's distinction applies beyond what he called ''per-formative utterances'' such as I promise, I name, I pick, I congratulate, and the like. Suppose also that the felicity conditions for uses of the F and one and only one F are as described in scenarios 1 and 2 respectively.

Finally, suppose that the truth-conditional contribution of these expressions is the same via the fundamental equivalence. In sum, we grant the formal semanticist her best ground. This is the best ground because the felicity condition for definite phrases proposed, say, in Heim 1982, 165, is not sucient for distinguis.h.i.+ng the-phrases from one and only onephrases, though Heim's condition may be sucient for distinguis.h.i.+ng definite and indefinite phrases. This is because Heim views the uniqueness condition itself as part of the felicity condition rather than the truth condition; as noted, the uniqueness condition applies to one and only onephrases as well. Supposing that the-phrases and one and only onephrases dier in their felicity condition as above, what follows?