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Explaining referential/attributive.

Kaplan, Stalnaker and Weustein all urge a two-stage theory of language whereon the propositions expressed by sentences are generated prior to being evaluated. A new ambiguity for sentences emerges, propositional rather than syntactic or semantic. Kaplan and Wettstein then propose to explain Donnellan's referential/attributive ambiguity as simply being two-stage propositional ambiguity. This is tacitly seen as further confirmation for two-stage theory. Modal ambiguities are prime motivators for two-stage theory, which distinguishes local from exotic evaluation to explain them. But if sentences can be found which exhibit both modal and referential/attributive ambiguity, an apparent paradox arises for a two-stage account. The theory recognizes both singular and general propositions, in Kaplan's senses. But reflecting one sense of such a doubly ambiguous sentence, two-stage theory would seem to need a proposition both singular and general with respect to a definite description attributively used. Since modal operators will come into rendering the problem sentences, an obvious idea is to let scope distinctions rescue two-stage theory from the apparent paradox. But while a rescue based on multiple renderings is proposed, it is not strictly a scope rescue, though different scopes are involved. Readers are asked to trust the author on missing formalities of an intuitively transparent two-sorted modal language that is employed. Two-stage theorists explicitly oppose scope treatments of modal ambiguities seeing them as rivals. Stalnaker, in particular, argues against them. But his arguments are shown not to count against the proposed rescue, on which the anticipated rivalry proves to be minimal.

1. Introduction

My topic here will be an account of Donnellan's referential/attributive distinction favoured by proponents of what Almog (1986) calls a two-stage theory of language. Such a theory allows a new ambiguity, neither syntactic nor semantic but rather propositional, as they say, for sentences containing definite descriptions. But this new ambiguity makes almost irresistible, to its discoverers, a reading of Donnellan's ambiguity simply as it: an account of referential/attributive falls out of a theory whose impetus lies elsewhere. This is tacitly claimed as further confirmation, another plus for the theory.

As far as I know, this account has gone unchallenged. But I think I see a problem, for which I will argue after presenting the account. A familiar move may seem to promise a quick solution. But issues arise around this move that should at least keep its solution from being quick. Putting them under scrutiny will lead me to a proposal I hope two-stage theorists might accept.

2. Two-stage accounts: Stalnaker's and Kaplan's

We can usefully start with Stalnaker's pioneering sketch of a two-stage theory:

... the syntactical and semantic rules for a language determine an

interpreted sentence or clause; this, together with some features

of the context of use of the sentence determines a proposition, this

in turn, together with a possible world, determines a truth-value.

(Stalnaker 1972, p. 179)

Almog (1986) calls the two stages generation, of the proposition, and evaluation, determining its truth-value. Kaplan (1989a) gets remarkable mileage out of this approach for sentences containing indexicals and other demonstratives. But Stalnaker anticipates at least some of his arguments for "the extra step on the road from sentences to truth-values" (Stalnaker 1972, p. 179).

Two-stage propositional ambiguity arises because definite descriptions, unlike other singular terms, have two ways of contributing, at the generation stage, yielding different propositions for later evaluation. Let us consider an example, originally Linsky's, which Donnellan develops as a paradigm of referential/attributive ambiguity (Donnellan 1966, p. 244):

(1) Her husband is kind to her.

What two contributions could be made, in generating a proposition, by the definite description "her husband"? With Stella as referent of the deictic "her", it could contribute, as Stalnaker (1972, p. 182) says, the rule for picking out Stella's husband, if any, in an arbitrary context. This yields what Kaplan (1989a) calls a general proposition, which, as Stalnaker would agree, is the proposition expressed by (1) when its description is attributively used.

On the other option for generation, (1) could express what Kaplan (1989a) calls a singular proposition, with the description contributing its denotation. This is the proposition expressed by (1) when its description is referentially used. But Stalnaker and Kaplan diverge sharply here. If Boris is Stella's husband, must he not be the denotation? Maybe not, as Stalnaker (1972, p. 182) sees it. For let the speaker take Ken to be Stella's husband. While Kaplan's singular proposition will still contain Boris, Stalnaker's will now contain Ken. Kripke (1977) distinguishes speaker's from semantic referents, and in effect, without using the phrases, speaker's from semantic truth. Briefly, he believes in peaceful coexistence, for speaker's and semantic notions, through segregation within an overall theory. If Ken is kind to Stella and Boris is cruel to her, Donnellan's popular intuition that the author of (1) has said something true of or about Ken simply acknowledges speaker's truth--which Kripke sees as not precluding semantic falsity. (Donnellan overlooks intuitions of falsity through keeping Stella as Linsky creates her, a spinster, while Kripke is more circumspect, and hardly unfair, in giving her a cruel husband.) Stalnaker (1972) in effect adopts Kripke's distinction for referents, his denotations, but denies it for truth. In putting speaker's denotations into singular propositions, he defies Kripke's peacemaking strategy, upholding within theory Donnellan's blindness to contrary intuitions. Speaker's truth thus becomes the only truth reached on his two-stage road from (1) when its description is referentially used.

In choosing semantic denotations instead, Kaplan makes his propositional ambiguity intriguingly elusive. For he then reaches only semantic truth, to which referential/attributive, as he stresses, cannot matter. With display references to be explained:

Now note that the verbal form of (3) might have been adopted ...

to express what is expressed by (17). We seem to have here a kind

of de dicto-de re ambiguity in the verbal form of (3) and without

benefit of any intensional operator. There is no question of an

analysis in terms of scope, since there is no operator. The two

sentence types (3) and (17) are such that when uttered in the same

context they have different contents but always the same truth

value where uttered. Donnellan vindicated! (Kaplan 1990, p. 326)

His (17) contains "dthat", his device for marking a definite description as purporting to act as a demonstrative, putting its denotation into what is thus a singular proposition. By constrast, his (3), with its unmarked description, is ambiguous, and is able to express a general proposition too. "Under no circumstances could the choice of disambiguation for an utterance of (3) affect the truth-value. Still there are two distinct propositions involved ..." (Kaplan 1990, p. 324). Wettstein is especially lucid here. When the sentence is Donnellan's "Smith's murderer is insane", he has the singular proposition "true with respect to a possible world w just in case the very individual demonstrated in the actual world is insane in w", while "the general proposition is true with respect to a world w just in case Smith was murdered in w by exactly one person and that person is insane in w" (Wettstein 1983, p. 188). These are different truth-conditions, embodied in the two propositions, but with only the actual world relevant to evaluation, their two evaluations to a truth-value must agree if "the very individual demonstrated" is the semantic denotation of "Smith's murderer". Endorsing this last proviso, Kaplan must qualify Donnellan's vindication:

Donnellan and I disagree on how to bring the intended demonstrating

into the picture. To put it crudely, Donnellan believes that

for most purposes we should take the demonstratum to be the intended

demonstratum. I believe that these are different notions

that may well involve different objects. (Kaplan 1990, p. 326)

3. Evaluation: local versus exotic

Siding with Kaplan against Stalnaker and Donnellan here, I consider only his two-stage theory. Its propositional ambiguity shows up best when exotic evaluation, as I will say, as opposed to merely local, is in prospect. Modal sentences are popular examples:

(2) Her husband might have been a mechanic.

For both propositions (2) might express, its "might have been" has the evaluator scanning a range of possible worlds for one where the predicate "x is a mechanic" fits the semantic denotation for "her husband". (Stalnaker, Kaplan and Wettstein would all accept this familiar "quantification over possible worlds" reading of the modal phrase.) The singular proposition has this denotation as a part, put in at generation, when it was fixed by local facts, namely, those of the context of utterance. The general proposition replaces this part by the rule for fixing that denotation, which rule applies at evaluation, and so uses exotic facts, namely, those of any possible world the evaluator must consider in assessing the predication. With local facts fixing a denotation prior to evaluation, (2) expresses a singular truth if a possible world exists in which Boris, locally a cruel lawyer, became a mechanic instead. With exotic evaluation for a rule for fixing a denotation for "her husband", (2) expresses a general truth if a possible world exists in which Stella married a mechanic.

Nonmodal examples are available too, sometimes invoking a single exotic venue rather than a range: I can ambiguously say that in 1957 my wife was only 12 years old.

4. Predicting and discovering a problem

On two-stage theory, sentences can be ambiguous, but the propositions they express, which disambiguate them, are not. So propositions cannot have parts open to either local or exotic evaluation. Yet sentences like (2) have parts, namely, their descriptions, that are ambiguous as to whether local or exotic facts are to fix their denotations. Now two-stage theory makes evaluation uniform, either local or exotic for a whole proposition and all its parts. And where exotic evaluation for the whole is called for, by a modal phrase as in (2), for example, but a sentential sense calls for having the denotation of a part fixed by local facts, the elegant solution is to apply a denotation-fixing rule at generation, with none but local facts at hand, leaving only the denotation itself, a nonevaluable part, as input for further steps of uniformly exotic evaluation. The rule, always evaluable as a part, is not seen by evaluation.

Singular/general, with either denotation or rule as propositional part, thus bestows the local/exotic flexibility needed to explain modal ambiguity, even with uniform evaluation. And singular/general is also held to explain referential/attributive ambiguity: roughly, to use a description referentially as opposed to attributively is simply to generate a singular as opposed to a general proposition. But could these explanations not clash? Attributive use, if Kaplan is right, is as bound to local facts as referential. Undeniably, such local attributive use is at least typical. When it occurs, both of Donnellan's uses will fall on the local side of local/exotic, if that distinction can apply too. But might there not be a sentence like (2) in demanding exotic evaluation for modal propositions it can express, and also containing a description open to local attributive use even within such modal expression? Given such use and expression, the proposition must be general, for attributivity. But it must also be singular, for locality: otherwise, the denotation will be fixed at evaluation by exotic facts. We cannot expect this paradox to confront us often, for the two usages that must combine are both special. While this surprisingly goes unacknowledged, paradigms of attributive use hardly leap at us from the pages of novels or newspapers we read. Nor do mere undeniable possibilities make natural "might have been" speculations: people who might have been named "Gertrude" seldom insist on it. Still, I think examples can be found:

(3) Smith's murderer might not have murdered Smith.

For a noncontradictory sense, the denotation for "Smith's murderer" in (3) must be fixed by local facts. With referential use of that description a two-stage account would yield a singular proposition, generated with that locally fixed denotation as a part. But local attributive use is surely an option too. Let all agree that Smith's unknown murderer is indeed insane. (3) could then follow as expert comment on a species of insanity indicated by details of the murder: if Smith had shown no fear or alarm, the expert might hold, at the approach of a stranger in the park, he would be alive today. Readers should feel free to improve this example, or to find better ones of their own. But if local attributive use can ever thus occur within modal speculation, the paradox is realized: a proposition both singular and general, with respect to the part a description contributes, is predicted by Kaplan's two-stage account.

Making Smith's murderer unknown, so as to deny the speaker a particular person in mind in using that description, may not guarantee an attributive use. If Kaplan (1990) is right, the proposition can still be singular and the use referential:

It is now clear that I can assert of the first child to be born in the

21st century that he will be bald .... (Kaplan 1990, p. 327)

This precisely reverses the position of Kaplan (1968), and I think he was right the first time. Briefly, Donnellan (1977) convinces me that we cannot have beliefs about this child, and would I not be expressing a belief about him in the assertion whose viability Kaplan finds clear? But this issue is not crucial here. For what follows from this discovery of new referential uses? Does it show there to be no attributive uses? Not for explainers of referential/attributive, who need something to explain. Then does it disqualify an attributive use at least in (3)? But how could it do this while leaving Donnellan's paradigms of attributive use unscathed? For even in their settings Kaplan could find referential uses, invoking such forms as

(4) Dthat ["Smith's murderer"] is insane.

Donnellan made Smith's murderer unknown too, in his setting for (4). While this may not guarantee an attributive use, it surely at least makes one likelier, as is even tacitly granted toward the end of Kaplan (1989b). Nor can I see how Donnellan's syntactically simpler paradigm and my (3) differ on this score. And the bare possibility, not even a likelihood, is all my argument needs.

5. Scope to the rescue?

(3) is indeed less simple than other sentences held to show referential/ attributive ambiguity. In particular, noting its modal "might", Kaplan's earlier italics could be given this reverse twist: since there is an operator, (3) is open to an analysis in terms of scope. Can two-stage explainers of referential/attributive use such analysis to meet the challenge of my example?

As Kaplan's italics suggest, champions of two-stage propositional ambiguity see scope analysis as a rival. The rivalry is old: two-stage theory seeks the effect of direct reference, introduced by Kripke as rigid designation, and Dummett (1981a, 1981b) appeals to scope to oppose Kripke's argument that proper names, as rigid, differ from definite descriptions in how they refer. Kaplan (1989a) jumps at chances to limit the scope rival. Closer to our concerns, Stalnaker explicitly opposes it for the likes of (2) and (3). He finds scope ambiguity "highly implausible" for them: "There are no natural syntactical transformations ... which remove the ambiguity" (Stalnaker 1972, p. 183). In our context, scope theory could only be a partner, not an external rival. With referential/attributive paradigms not open to scope analysis, it could only augment, not replace, a two-stage account of that ambiguity. This realization, and the prospect of help with (3) and its ilk, might soften two-stage resistance. Internal rivalry could still be a problem: if there are purely modal ambiguities, as (2) might be held to exemplify, who gets to explain them? More urgent, however, is to see what the partnership has to offer on (3). I will flesh that out roughly here, and then ask, in my next section, about its implementation in languages whose syntax and semantics can be explicit.

So as to stay in the right ballpark, we should note that in two-stage theory definite descriptions are referential devices. (The quarrel with Frege is only over how they can refer.) Roughly, they will be constituents in deep syntax. Surface syntax, or "grammatical form", will at least not be "misleading" as to deep syntax, or "logical form", in this regard. So a two-stage account of referential/attributive cannot seek rescue in Russellian scope disambiguation for sentences like (3), which has the description "broken up" in deep syntax. Russell's theory fails here anyway: the scope ambiguity it predicts for (3), through primary/secondary occurrence options for its description, is dual, not triple as needed. (The missing sense corresponds to the singular proposition two-stage theorists find, vindicating Donnellan (1966) on where referential/attributive challenges Russell.) But this is failure as a rival. As a partner, Russell's explicit denial of referential status makes his theory, and its style of scope disambiguation, incoherent even to entertain.

Another familiar model is also out. When every girl dances with some boy, for example, we have two operators competing for widest scope. But in (3), unless we posit a hidden second operator, no such competition can arise. So (3) can exhibit scope ambiguity in just one way: its description must have options of falling within the scope of its one operator or not. (People, Kripke and Dummett for two, freely ascribe scopes to singular terms, which is incoherent since only operators have scopes. Being sympathetic, it is my options that they have in mind.) For marking these, as Donnellan (1977) does in treating a stand taken in Dummett (1981a), for example, we can expect roughly this stilted English:

(3A) Smith's murderer is such that: it might have been that he didn't murder Smith.

(3B) It might have been that: Smith's murderer is such that he didn't murder Smith.

Singular/general options let us generate four propositions, two each from (3A) and (3B). Let (3Ad) and (3Ar) be the two respectively containing the denotation and the rule for "Smith's murderer", and similarly for (3Bd) and (3Br). Then while (3Br) is contradictory, (3Ar) is the outcome of an attributive use that solves my problem for (3). Except for having both (3Ad) and (3Bd), the referential/attributive ambiguity of (3), despite this appeal to scope, remains the two-stage kind: between a singular proposition containing Smith's murderer and a general one containing a rule, image to that description placed in deep syntax as per (3A). But with the contradictory (3Br), placing the rule rather as per (3B), we have triple ambiguity for (3). Its ambiguity between two general propositions, on this analysis, turns solely on scope.

(Does having both (3Ad) and (3Bd) predict quadruple ambiguity for (3), and falsely, since triple is all we intuit? Not if our theory entails that despite scope differences, evaluations of (3Ad) and (3Bd) cannot differ. Illustrating such a formal outcome, consider (i) "Every girl danced with some boy", (ii) "Every girl danced with Fred", and (iii) "Every girl danced with someone who is Fred". While (i) has two symbolizations, marking its scope ambiguity, the unambiguous (ii) has only one. Now (iii), also unambiguous, has two symbolizations mirroring those for (i). But no false prediction of scope ambiguity arises, since these two are equivalent in quantificational logic with identity.)

6. Two formal modes

The modal operator in (3) might be rendered formally as "<>", within sentences of quantified modal logic. Seeking scope disambiguation for (3), we could give this operator a second role of forming complex predicates through a device called [Lambda]-abstraction. Explaining this for standard logic, where A is a formula, like "Fx" or "??[Lambda]Gxy", whose only free variable is "x", we can augment the language by prefixing "[Lambda]x" to "[A]" to yield a predicate, like "[Lambda]x[Fx]" or "[Lambda]x[??yGxy]", with the syntax of a predicate-letter. Thus "[Lambda]x[Fx]a" and "[Lambda]x[??yGxy]b" are sentences, respectively equivalent, as a suitable semantic clause for their complex predicates insures, to "Fa" and "??yGby". (As we will see, however, such conversion to eliminate "[Lambda]" can fail in a modal language when A in "[Lambda]x[A]" contains a modal operator like "<>".) This device is used by Soames (1989) and by Dummett (1981a), for example, for purposes much like ours here.(1) But its associations within pure logic can be ignored: any way of getting a predicate from a formula with one free variable-type gives the modal operator in (3) a suitable second role, if some formal counterpart to that operator can head the formula. Disambiguating (3) calls for marking singular/general ambiguity too: I will replace the usual upside down "i" in formal definite descriptions by either "d" or "r", for denotation or rule as put into the proposition at generation. (But how is the two-stage novelty of evaluating propositions to occur within a formal language whose semantics is geared to evaluating sentences? Briefly, we can evaluate propositions, rather than sentences, only for the atomic sentences the semantics finally reaches in its pursuit of truth, where sentences containing descriptions can count as atomic.) So using a language for quantified modal logic augmented by [Lambda]-abstracts, and following Soames and Dummett concerning scope options, we could thus disambiguate (3):

(3 AMd) [Lambda]x[<>{??Mxs}]((dy)Mys)

(3 AMr) [Lambda]x[<>{??Mxs}]((ry)Mys)

(3 BMd) <>{[Lambda]x[??Mxs]((dy)Mys)}

(3 BMr) <> {[Lambda]x[??Mxs]((ry)Mys)}

The definite description falls within the scope of "<>" in the (3BM) pair but not in the (3AM) pair. And (3AMr) captures my problem sense for (3): it will be true iff the referent of its description, reached by local evaluation since "(ry)Mys" falls outside the scope of "<>", has the modal property symbolized by "[Lambda]x[<>{??Mxs}]". In a surprising irony, we can look to Stalnaker for a semantics clause for these: Stalnaker and Thomason (1968a) establishes, within a language for modal logic, the apparatus used in (3AM) and (3BM) for a scope disambiguation he would oppose. (In so doing, he replaces "[Lambda]x" by "x ", trading one set of ignorable associations for another.) Informally, "[Lambda]x[<>{??Mxs}]" will hold for an object O iff "[Lambda]x[??Mxs]" holds for O in some possible world.

So all goes swimmingly, it might seem, with (3AMd)-(3BMr) indicating a happy marriage between scope analysis and two-stage theory. But however happy the marriage, a doubt arises as to the identity of one of the partners. For arguably, (3AM) and (3BM) do not reveal a scope ambiguity at all. This idea may seem bizarre: can we not see the same ultimate constituents in the two, simply put together to form a sentence in different ways? But scope ambiguity surely further requires that different truth conditions for the two sentences thereby arise. And in modal logic, truth attaches not to sentences alone but rather to pairs consisting of a sentence and a possible world.

This is clear from Kripke (1971). Where K is the set of all possible worlds: "Formally, a model ?? . . . is a binary function (P,H), where P varies over atomic formulae and H varies over elements of K, whose range is the set {T,F}" (Kripke 1971, p. 64). (In fact, ??, is also defined for nonatomic "formulae" (or sentences) by inductive clauses.) Within the possible worlds idiom, a sentence is often called true at a world. But on Kripke's definitive conception of a model, there is as much reason to call a world true at a sentence. These two usages simply put different derivative slants on the basic triadic notion: truth on a model symmetrically involves both a sentence and a world.

Can this technicality about truth really be a basis for rejecting (3AMd)-(3BMr) as a scope disambiguation? Pursuing the issue, the ultimate constituents of the sentences (3AMr) and (3BMr) can be seen to be the same. But the extensions of the predicate letter "M" in their descriptions, used by the semantics in fixing the* truth-values on a given model, differ: for (3AMr) it is just the real world extension while for (3BMr) it is the whole range of extensions for possible worlds. What the model assigns to the predicate-letter in the description is indeed the same for (3AMr) and (3BMr). However, this is not an extension, as it would be in standard logic, but rather a function from possible worlds to extensions: just as truth attaches not to sentences alone but rather to sentence-world pairs, extensions attach not to predicate-letters alone but rather to letter-world pairs. So even accepting truth for (3AMr) and (3BMr) as paired with the real world, as opposed to truth for the sentences alone, as what is being determined, the extensions that ultimately determine this truth are not the same. And this is an ultimate sameness that paradigmatic scope ambiguity never lacks.

Kripke's inductive clause for "[]", clearly making "[]" "a quantifier over possible worlds", augments the intrinsic appeal of another modal project: to frame a formal language in which such quantifiers, and variables for them to bind, are explicit. (Lewis 1968 and Lewis 1986 develop two, as usefully discussed by Sainsbury 1991.) A two-sorted quantifier language may offer the most perspicuous way of building worlds into sentences, as it were. I must ask readers to trust me that a viable syntax and semantics can be had for a language, to be called PWQ, whose following sentences disambiguate (3). (Seeing how they manage this may make my resistance to scope ambiguity in (3AMd)-(3BMr) seem more than a quibble.) In these sentences, "??MxsW,' is to be read as "x murdered Smith in W", and the constant "G', following Kripke, names the real world.

(3AWd) [Lambda]x[??W{??MxsW}]((dy)MysG)

(3AWr) [lambda]x[??W{??MxsW}]((ry)MysG)

(3BWd) ??W{[lambda]x[??MxsW]((dy)??MxsG)}

(3BWr) ??W{[lambda]x[??MxsW]((ry)??MxsG)}

(Parallelism might suggest "??W{[lambda]x[??MxsW]((dy)MysW)}" as (3BWd). But the definite description operator "(dy)" heralds a singular proposition, with a referent put in at generation, and generation occurs in the real world in two-stage theory. It will thus never employ "(dy)MysW".)

No scope ambiguity emerges here. While "??W" has different scopes in (3AW) and (3BW), all but one pair of these four sentences differ in their ultimate constituents. And the exception here, (3AWd) and (3BWd), are the two that must be equivalent to block a false prediction of quadruple ambiguity. Scope options were supposed to explain an ambiguity between the two general propositions expressed by (3AWr) and (3BWr). But while those options do show up here, the difference in ultimate constituents makes it not a scope ambiguity that they explain.

Nor are sentences showing scope options even needed. For conversion of [lambda]-abstracts, while failing in a standard language for quantified modal logic, is unproblematic in PWQ, yielding:

(3AWdC) ??W{??M(dy)MysG)sW}

(3AWrC) ??W{??M(ry)MysG)sW}

(3BWdC) ??W{??M((dy)MysG)sW}

(3BWrC) ??W{??M((ry)MysW)sW}

The needed equivalence of (3AWd) and (3BWd) is confirmed by the identity of (3AWdC) and (3BWdC). And two suitable general propositions correspond to (3AWrC) and (3BWrC), through the difference in their ultimate constituents, though the scope of "??W" in them is the same.

While I will not prove that conversion works in PWQ, it should convince us to see that what makes it fail in quantified modal logic cannot arise here. It fails for "[lambda]x[<>Fx]((ry)Hy)" and "<>F((ry)Hy)", for example. The description lies within me scope of "<>" in the second sentence but not in the first. In modal logic, semantic treatment of any predicative content, including that of a description, depends on that feature of context. Within the scope of "<>", itself treated as a possible worlds quantifier "??W", the description is treated as if it contained a free possible worlds variable "W". Outside the scope of "<>", it is treated as if it contained instead a constant "G" naming the real world. This use of context by the semantics characterizes even classical modal logic, before quantifiers or descriptions come along, as is easily verified by working out the validity condition in Kripke (1971) for the axiom-schema "[]A ?? A", for example. But context plays no such role in the language whose counterpart to the modal logic conversion failure takes "[lambda]x[??WFxW]((ry)HyG)" into "??WF((ry)HyG)W". Whether within the scope of "??W" or not, the semantic treatment of the description, with its explicit constant "G" naming the real world, will be the same.

7. Conclusions

Two sections back, I said that (3) can exhibit scope ambiguity in just one way: its description must have options of falling within the scope of its one operator or not. Arguably for one and clearly for the other, neither of our formal modes yields a scope disambiguation of (3). (Thus a suspicion is tempting: that scope ambiguity demands at least two operators, as in its paradigms.) Since they seem to be the only two in sight, it is at least arguably not scope that can help with my problem sense for (3). Still, either (3AMd), say, with (3AMr) and (3BMr), or else (3AWdC), say, with (3AWrC) and (3BWrC), do offer a disambiguation that works. Can two-stage theorists happily accept it?

Besides finding no "natural syntactical transformations", Stalnaker lists this "limitation" to scope treatment of modal ambiguity as seen in (2) and (3): "Modal and propositional attitude concepts may be involved, not only as parts of statements, but as comments on them and attitudes toward them" (Stalnaker 1972, p. 183). Cognate with (2), for example, we could comment on the proposition expressed by "Her husband is a mechanic" that it might have been true. This comment could have either of two propositions, one singular and one general, in mind: therein lies its ambiguity, which cannot be laid to scope since no sentence with a modal operator need occur. (It could be ambiguous while referring to the proposition thus: "What you just said is in fact false--but it might have been true".) And Stalnaker could argue for the same singular/general ambiguity as showing up in (2). But while this may reveal singular/general as needed for disambiguation, (3) still shows that it does not suffice. It can by itself explain either (i) paradigmatic referential/attributive ambiguity, where modality is not involved, or (ii) modal ambiguity arising without referential/attributive being involved. But neither (i) nor (ii) fits (3). Identifying its ambiguity with the singular/general ambiguity of a modal comment on its subsentence, as Stalnaker presumably would with (2), yields only two senses. My problem sense for (3) gets left out.

Stalnaker and Kaplan may see scope treatments of sentences like (2) as undermining the singular proposition, at least as generable by sentences containing definite descriptions. Our current proposal still needs singular/ general for such sentences, both for ones without operators and even for some with them, like (3). But as noted earlier, internal rivalry could arise over (2) if its ambiguity were purely modal, not involving referential/ attributive too, as we had with (3). For we could then use either singular/ general or local/exotic (with "c" naming "her") to explain it:

(2S/Ga) ??WM((dx)HxcG)W

(2S/Gb) ??WM((rx)HxcW)W

(2L/Ea) ??WM((rx)HxcG)W

(2L/Eb) ??WM((rx)HxcW)W

Choosing the (2L/E) pair would diminish the explanatory role of the singular proposition. But should two-stage explainers of referential/attributive accept sentences like (2) as being incapable of referential/attributive ambiguity? Are they not committed to our having, for each utterance of (2), either a referential or an attributive use of its description, and so either a singular or a general proposition generated? And if a general one corresponding to (2L/Ea) is possible, a singular one corresponding to (2S/Ga) is surely possible too. So our current version of two-stage theory should treat (2) as it treats (3), using both singular/general and local/exotic since neither suffices alone. Neither the (2S/G) pair nor the (2L/E) pair is apt, nipping this internal rivalry in the bud. The sense for (2) counterpart to my problem sense for (3) may well be one it is unlikely a speaker would intend. But this could be owed to a Gricean stricture not touching syntactic options and their semantic upshots: a speaker's intention to convey a meaning cannot be too unlikely to succeed.

Laboring this crucial point, if my problem sense for (3) is even possible, the syntax and semantics of a language designed for regimenting the English we speak must provide it, not only for (3) but for any sentence, like (2), of relevantly similar form. How likely speakers are to intend that sense, for such a sentence, does not concern syntax or semantics, and cannot relieve them here.

If this is right, Stalnaker's "limitation" aims at an illusory internal rival, and two-stage theorists can forget both. Within the style of disambiguation currently proposed for (3), singular propositions will play an undiminished role. Still, for sentences containing definite descriptions, a prominent general theme of possible worlds theory, that singular terms can be modally stable, will indeed depend on them less. Let us first trace the theme and then see why.

Kripke's early version featured rigid designation, and arose from such intuitions about proper names as this: "We can simply consider Nixon and ask what might have happened to him had various circumstances been different" (Kripke 1980, p. 47). Kaplan, studying demonstratives, found a need instead for the notion of a device of direct reference (Kaplan 1989a, section IV). Almog (1986) also develops this need. But this notion is wrong for definite descriptions when Kaplan (1990) assimilates them to demonstratives. Direct reference is supposed to be "without the mediation of a Fregean Sinn as meaning" (Kaplan 1989a, p. 483). And describing, even as "a form of pointing", must rely precisely on such mediation, on descriptive content, to make its pointing succeed. This is not to deny a demonstrative aspect for most definite descriptions we employ, as urged in Wettstein 1981, 1983. Still, given their descriptive aspect, they are hardly devices of direct reference, as that notion is defined. But a definite description at least emulates such a device when it serves to generate a singular proposition as opposed to a general one. Even here, its Fregean Sinn cannot be denied any role whatever. But these two-stage options for generation at least allow it to be denied any role in evaluation, and Kaplan's assimilation can rest on that. For different reasons, rigid designation and direct reference are both flawed notions for explaining the modal stability a definite description can have. But two-stage theory can invoke singular propositions in particular explanations that escape those flaws.

However, my problem sense for (3) reveals more modal stability than singularity can explain: we have it attaching there to a description used to generate a general proposition. Without making it turn on scope distinctions, PWQ, our possible worlds language for two-stage theory, upholds this. It does so by allowing evaluation to be flexible, not uniform for a proposition and all its parts.

Always fascinated by Donnellan's distinction, Kaplan reports also being maddened by it, in part because "the notion of having someone in mind is not analyzed but used" (Kaplan 1990, p. 317). The two-stage account of referential/attributive appeals instead to uses of definite descriptions as demonstratives to generate singular propositions. But this is not simply out of one frying pan into another: while a theory of demonstratives can hardly avoid Donnellan's notion, Kaplan's study of its paradigms makes solid progress here, which the two-stage account can share through assimilating descriptions to these. Wanting to share it, two-stage theorists could not be happy with a modified account, responding to my example around (3), that undercut the singular proposition and its role. But with neither external nor internal rivalry in prospect, and only a corner on modal stability for definite descriptions needing to be given up, no such threat would seem to arise.

8. Postscript on a familiar issue

In this passage, Dummett concludes a lengthy rebuttal of the attack in Kripke (1980) on Frege's views on how proper names refer:

When modal discourse is in question, there is little obvious alternative

to representing modal expressions as operators on sentences or

predicates; but it is far from evident that our theory is to be

framed in terms of particular possible worlds. We do not come

already equipped with a conception of such possible worlds, which

must therefore be introduced in the course of formulating the

semantic theory; explaining it gives rise to considerable difficulties.

If, despite these difficulties, we do frame our theory in terms of

possible worlds, we shall need to invoke scope distinctions in

regimenting sentences of natural language. We may wish also to

incorporate the device of rigid designation into our semantic

theory. It has here been argued that the mechanism of scope is capable

of entirely replacing that of rigid designation; whether or

not we choose to employ the latter is a question of pure convenience.

(Dummett 1981b, p. 593)

PWQ offers an alternative to modal operators that is made obvious by Kripke's semantics for a formal language that employs them. And in PWQ, as we have seen, scope distinctions are not needed for the regimenting Dummett has in mind. (I noted that he employs forms like the (3AM) and (3BM) pairs.) No device of rigid designation is built into the syntax and semantics of PWQ. Following Almog (1986), I would drop Kripke's notion in favor of two-stage generation of singular and general propositions. My dual notation for definite descriptions in PWQ implements this for them. But my problem sense for (3) reveals that singular/general, the PWQ replacement for rigid designation, is not at best a "pure convenience", given PWQ's handling of counterparts to ostensible scope distinctions for modal operators in a formal language for quantified modal logic. While my problem sense reveals modal stability that singularity cannot explain, (3) has another pair of senses that PWQ's handling of such counterparts cannot explain. (Neither can ostensible scope distinctions in the other formal language, as we saw: this is not a problem peculiar to PWQ.) And if more than dual ambiguity must be represented for sentences like (2), which share a form with (3) if not its aptness for a plausible attributive use, these sentences refute the "pure convenience" tag as well.(2) (1) Cf. also Evans (1979). He notes some of the phenomena which I discuss but draws different conclusions. (2) I am indebted to referees for this journal, whose comments on previous submissions on this topic obliged me to rethink.


Almog, Joseph 1986: "Naming Without Necessity". Journal of Philosophy, 83, pp. 210-42.

Almog, Joseph, Perry, John and Wettstein, Howard K., eds., 1989: Themes From Kaplan. Oxford and New York: Oxford University Press.

Cole, Peter, ed., 1978: Syntax and Semantics, volume 9. New York: Academic Press.

Davidson, Donald and Harman, Gilbert, eds., 1972: Semantics of Natural Language. Dordrecht: D. Reidel.

Donnellan, Keith S. 1966: "Reference and Definite Descriptions", in Martinich 1990, pp. 235-47. Originally published in The Philosophical Review, 75, pp. 281-304.

-- 1967: "Putting Humpty Dumpty Together Again". The Philosophical Review, 77, pp. 203-15.

-- 1977: "The Contingent A Priori and Rigid Designators", in French, Uehling and Wettstein 1977, pp. 45-60.

Dummett, Michael 1981a: Frege: Philosophy of Language, 2nd edition. London: Duckworth.

-- 1981b: The Interpretation of Frege's Philosophy. London: Duckworth.

Evans, Gareth 1979: "Reference and Contingency". The Monist, 62. Reprinted in his Collected Papers, Oxford: Clarendon Press, 1985, pp. 178-213.

French, Peter A., Uehling, Theodore E. and Wettstein, Howard K., eds., 1977: Contemporary Perspectives in the Philosophy of Language. Minneapolis: University of Minnesota Press.

Kaplan, David 1968: "Quantifying In". Synthese, 19, pp. 178-214. Reprinted in Martinich 1990, pp. 370-91.

-- 1978: "Dthat". Originally published in Cole 1978, pp. 221-53. Reprinted in Martinich 1990, pp. 316-29, 1990.

-- 1989a: "Demonstratives", in Almog, Perry and Wettstein 1989, pp. 481-563.

-- 1989b: "Afterthoughts", in Almog, Perry and Wettstein 1989, pp. 565-614.

Kripke, Saul 1971: "Semantical Considerations on Modal Logic", in Linsky 1971, pp. 63-72. Originally published in Acta Philosophica Fennica, 16, pp. 83-94.

-- 1977: "Speaker's Reference and Semantic Reference", in French, Uehling and Wettstein 1977, pp. 6-27. Reprinted in Martinich 1990, pp. 248-67.

-- 1980: Naming and Necessity. Oxford: Basil Blackwell.

Lewis, David 1968: "Counterpart Theory and Quantified Modal Logic". Journal of Philosophy, 65, pp. 17-25.

-- 1986: On The Plurality Of Worlds. Oxford and New York: Basil Blackwell.

Linsky, Leonard, ed., 1971: Reference and Modality. London: Oxford University Press.

Martinich, A. P., ed., 1990: The Philosophy of Language, 2nd edition. Oxford and New York: Oxford University Press.

Sainsbury, Mark 1991: Logical Forms. Oxford: Basil Blackwell.

Soames, Scott 1989: "Direct Reference and Propositional Attitudes", in Almog, Perry and Wettstein 1989, pp. 393-419.

Stalnaker, Robert C. 1972: "Pragmatics", in Davidson and Harman 1972, pp. 380-97. Reprinted in Martinich 1990, pp. 176-86.

-- and Thomason, Richmond 1968a: "Abstraction in First-Order Modal Logic". Theoria, 34, pp. 203-07.

-- and Thomason, Richmond, 1968b: "Modality and Reference". Nous, 2, pp. 359-72.

Wettstein, Howard K. 1981: "Demonstrative Reference and Definite Descriptions". Philosophical Studies, 40, pp. 241-57.

-- 1983: "The Semantic Significance of the Referential-Attributive Distinction". Philosophical Studies, 44, pp. 187-96.

THOMAS E. PATTON Department of Philosophy University of British Columbia 1866 Main Mall, E-370 Vancouver, British Columbia V6T 1Z1 Canada
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Title Annotation:two-stage theory of language
Author:Patton, Thomas E.
Date:Apr 1, 1997
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