GARY OSTERTAG

A SCOREKEEPING ERROR

(Received in final form 14 May 1997)

In its naive formulation, Russell’s Theory of Descriptions claimsthat a sentence exemplifyingthe F is Gis true just in case exactlyone thing is F, and all Fs are Gs. Yet, as is well known, this formu-lation fails to account for many of our truth-conditional intuitionsconcerning sentences exemplifying the relevant surface grammar.The current paper proposes an implementation of Russell’s theorywithin a framework that accommodates these intuitions. The generalframework adopted is one according to which quantifiers, includingdefinite descriptions, are to be interpreted relative to a contextually-determined domain of individuals. I am thus assuming a claim thatsome may find controversial – namely, that descriptions, accordingto Russell’s theory, are quantifiers. While I cannot do that issuejustice here, I think the assumption is correct. However, those whopart company with me with respect to my fidelity to Russell maynonetheless find something of interest in what follows, since theproblem I will be discussing, as well as the solution proposed,is applicable to a ubiquitous linguistic phenomenon – incom-plete quantification. Gaining an understanding of this phenomenonwill help to illuminate the relation between the uses we make ofsentences and the meanings these uses carry.

Before discussing the approach I favor, however, I will describean alternative approach and indicate why we should avoid it.In section 1 this approach is developed and criticized. Section2 provides increasingly refined characterizations of the generalapproach I endorse; these are developed in response to a counter-example due to David Lewis. I show that the final formulationis immune to Lewis’s counterexample. Finally, I present possibleobjections that this account faces, and indicates some lines ofresponse.1

Philosophical Studies96: 123–146, 1999.© 1999Kluwer Academic Publishers. Printed in the Netherlands.

124 GARY OSTERTAG

1.

1.1. Naive Russellianism and the Explicit Approach

On a naive Russellian analysis, an utterance of (1):

(1) The table is covered with books

is false if there fails to be exactly one table in the entire universe.And yet, what was said in uttering (1) may be taken to be true byspeaker and hearer, even though it will be mutually known that theproperty of being a table is not uniquely instantiated. Thus, it seems,the naive Russellian analysis fails to comport with facts about howthe language is actually used and understood.

The natural way to circumvent this criticism is to maintain thatan utterance of (1) determines a contextually definite completionof the (incomplete) sentence produced. More generally, we cansay that descriptions are context-sensitive expressions, and thatcontextual supplementation proceeds by providing descriptivematerial sufficient to complete the (incomplete) description uttered.Following Stephen Neale [6], I will refer to this view as the “explicitstrategy” (ES). To facilitate comparison with other accounts, I willdescribe this strategy in the most general terms – namely, as a thesisabout quantifiers. (Recall that I am interpreting definite descriptionsas quantifiers.)

(ES) The context-dependence of quantifiers is captured byassigning utterances of sentences containing them contex-tually definite completions.2

As Howard Wettstein has suggested, however, a defect of ES isthat there is, typically, no non-arbitrary way to complete sentencescontaining incomplete descriptions. That is, in general, a contextwill not supply a unique completion. Let’s introduce a bit of termin-ology to help us characterize the phenomenon in question: calla candidate completiona completion of the description sentenceuttered that is truth-conditionally equivalent to our intuitive assess-ment of the sentence as uttered. Now, as an example, take sentence(1). It is clear that many pairwise non-synonymous completions,drawn from a set of candidate completions, may be raised to conver-

A SCOREKEEPING ERROR 125

sational salience by such an utterance (‘the table in room 209 ofCamden Hall att1’, ‘the table at which the author ofThe Persist-ence of Objectsis sitting at t1’, and so on). But each completionwould result in a different descriptive proposition’s being assignedto the utterance. As Wettstein asks, “The question now arises, whichof these more complete (Russellian) descriptions (or conjunctionof descriptions) isthe correct one, the one that actually captureswhat the speaker intended by his use of the definite description ‘thetable’?” ([14], 41).3

Wettstein poses two difficulties for a Russellian response. Thefirst is epistemological. Even if we assume that the speaker hadintended a definite completion of the description in question, theaudience would not typically be in a position to determine what thatcompletion is. The second response goes further, denying that theassumption is legitimate: the speaker may often have no determi-nate intention with respect to any particular completion. Asked, thespeaker might respond that he did indeed intend to speak about thetable, but that he did not intend to have it thought of as (for example)the table in room 209 of Camden Hall att1, or the table at whichthe author ofThe Persistence of Objectswas sitting att1. Yet, ifthe speaker himself cannot specify what he meant – cannot para-phrase what it is he attempted to convey in additional descriptiveterms – then it seems unlikely that there could have been anythingdescriptive that he did mean. Thus Wettstein:

It now becomes difficult to attach sense to the idea that one of the Russelliandescriptions could be correct. Surely it is implausible in the extreme to supposethat in fact one of these descriptions captures what the speaker intended butthat we cannot, even with the help of the speaker himself, come to know whatdescription that is ([14], 42).

Stephen Schiffer [10] expresses a similar worry about the contextsupplying a unique description or individual concept. He imagines ahypothetical speaker who utters the sentence: ‘I’ll be damned! Theguy’s drunk.’ According to ES, the speaker asserts a proposition ofthe form ‘The8male is drunk’ – where8 is a completing property.But it is likely in such a context that speaker and audience share,and know themselves to share, a number of descriptions uniquelyspecifying the relevant individual. He writes:

126 GARY OSTERTAG

Imagining myself as your audience, I do not see how I could have identifiedany one individual concept, however complex, asthe onewhich figured intothe proposition that you asserted. And yet it would seem that I understood yourutterance perfectly well . . . ([10], 77).

1.2. The Identification Problem

Let us call the problem presented by Wettstein and Schiffer – that, ina typical use of an incomplete description, neither speaker nor hearerare capable of identifying a unique completion – the ‘identificationproblem’. Now, I don’t think that the identification problem shouldbe taken to present a decisive case against ES – at least not yet. Oneway out is to deny that, for example, the hypothesized utteranceuof (1) is in fact semantically determinate. It might be the case that,for each candidate completion8 of u, u indeterminately meansthatthe8 table is covered with books. On this view, there is no uniqueproposition that I meant in utteringu, but there are a number ofpropositions that Iindeterminately meantin utteringu.4

This idea has its most plausible application in the case of vague-ness. If I utter ‘John is bald’, I say something whose meaning,according to our intuitive assessment, is indeterminate. While it iscompatible with a number of possible sharpenings of its meaning(e.g., ‘John is entirely devoid of hair’), the sentence does not selectone such sharpening over any other. Following Kit Fine, we maydefine the truth of a vague sentenceS in terms of the truth of the setof relevant sharpenings, or “precisifications”, ofS (Fine, [3]). Thatis (roughly): S istrue just in case it is true for all (relevant) preci-sifications,falseif false for all (relevant) precisifications, undefinedotherwise.

The Russellian who espouses the indeterminacy proposal seesan analogy between sentences containing incomplete descriptions,such as (1), and vague sentences, such as ‘John is bald.’ The analogyseems strained, however. With a vague sentence, there is a clearintuition of indeterminacy. For example, in ‘John is bald,’ it isundeniable that there are a number of possible sharpenings of ‘bald’,each compatible with the speaker’s intentions, yet none of which issingled out by the utterance. In contrast, there is no similar intuitionsurrounding the hypothesized utterance of (1). On the contrary: theutterance appears to have perfectly determinate content. Now, it

A SCOREKEEPING ERROR 127

seems reasonable to suppose that, if an utterance has determinatecontent, then it has determinate possible worlds truth conditions.And this suggests a way to challenge the claim that a normal utter-anceu of (1) has determinate content – namely, show that we haveno clear intuition, at certain circumstances of evaluation, whetherwhatu says is true or not. That we lacked a clear intuition as to thetruth of what was said at such a circumstance would cast doubt onthe idea that something determinate was said in the first place. Thisis true of ‘John is bald.’ If John is devoid of hair, the sentence willbe true. But we may imagine circumstances at which John is in thepenumbral region between bald and hirsute; here, there will be nodecisive intuition concerning the sentence’s truth.

If u is similarly indeterminate, then there must exist circum-stances at which the question ofu’s truth could receive no deter-minate answer. The problem, however, is that the existence of sucha circumstance would fail to establish the semantical indeterminacyof u. Assume a circumstance C at which only one of the candidatecompletions of (1) is uniquely denoting (e.g., there is more than onetable in room 209 of Camden Hall att1). Is (1) true at C? If ES istrue, there is no definite answer. And this would seem to comportwith the predictions of the ES theorist espousing the indeterminacyproposal. Yet, the conclusion is premature. This consequence maybe attributable to the fact that the speaker, in uttering (1),presup-posesthat there is exactly one table in room 209 of Camden Hallat t1.5 The failure of the presupposition implies the failure of anydefinite judgement concerning the utterance’s content. Thus, thesuggested diagnostic for semantical indeterminacy yields incon-clusive results: the fact that the “content” of a given utterance of (1)fails to have determinate truth conditions at a given circumstanceof evaluation may be attributable to the fact that certain presupposi-tions of the utterance fail to obtain. This possibility seems perfectlycompatible with the utterance’s possessing determinate content.

None of this constitutes a knock-down argument against the ideathat incomplete description sentences are best analyzed on analogywith vague sentences: it simply constitutes an argument that theES theorist has no independent evidence for the indeterminacyhypothesis and an observation that, phenomenologically speaking,sentences such as (1) do not strike us as being semantically deficient

128 GARY OSTERTAG

(to use Fine’s terminology) in the way that sentences such as ‘John isbald’ do. Nonetheless, the considerations are sufficient to motivateour pursuing a Russellianism that avoids indeterminacy.

One way in which a Russellian who accepts ES, but who rejectsthe indeterminacy hypothesis, may respond to the identificationproblem is by specifying a way to isolate the unique, contextuallydefinite completion. This might seem a hopeless endeavor, giventhe intuitive power of Wettstein’s and Schiffer’s arguments. Yet,suggestions due to Brian Loar [5] show that their worries may beoverstated. Loar provides reasons for thinking that the speaker, inuttering (1), might implicitly intend one of the suggested completingdescriptions. The completion would be derived in the followingmanner: determine whether the speaker could have meant what hedid if circumstances had been otherwise along contextually relevantparameters. For example, imagine a situation in which I utter (1)and in which the completions suggested by Wettstein are candidatecompletions of my utterance. Could I have meant what I did inuttering (1) if it had turned out that ‘the table in room 209 of CamdenHall at t1’ and ‘the table at which the author ofThe Persistenceof Objectsis sitting att1’ are not co-instantiated – they each pickout a distinct table? Let’s say that I could not. This would suggestthat what I intended in uttering (1) was something along the lines of:

(1′) [the x: x a table in room 209 of Camden Hall att1 & x atable at which the author ofThe Persistence of Objectsissitting att1] (x is covered with books)

As Loar writes, discussing a similar example:

That in such a case it is [the]conjunction[of the candidate completions] whichis the essential individual concept is made plausible by the fact that, if throughsome bizarre contingency those individual concepts . . . are discovered not to beconjointly instanced, then one will be inclined to think that there is nothing whichclearly was one’s referent ([5], 361).

While Loar’s conclusion is about reference, it is a corollary toa conclusion that is of interest to us. The reason that thereis no referent in this case is precisely because the individualconcepts provided by the context were implicitly assumed to beco-instantiated; and if it was assumed that the relevant individualconcepts were co-instantiated, then it surely was assumed that the

A SCOREKEEPING ERROR 129

two candidate completions were co-instantiated. (And to say that thetwo descriptions were co-instantiated is to say that the conjunctivedescription [in (1′)] was the relevant completion.)

Of course, many details need to be worked out if this proposalis to be achieve plausibility. For example, it has not been shownthat the relevant utterance of (1) actuallysayswhat (1′) says. Itmay be, for example, that (1) only presupposes (1′). This alonewould suffice to explain the counterfactual properties of the relevantutterance. Moreover, Loar’s remarks seem to apply with equal forceto demonstrative constructions – indeed, his paper is concernedwith both descriptions and demonstratives – and this suggestsan unattractive dilemma. Either (i) the counterfactual propertiesthat are being tested for are, in fact, merelypresuppositionsof the utterance and not part of the utterance’s content;or(ii) demonstratives must be analyzed similarly to descriptions.Justification for the latter derives from the fact that, there is noreason to think that utterances of (1) and (1′′) at identical contextswould possess different counterfactual properties of the relevantsort.6

(1′′) That table is covered with books.

(I.e., if it’s true that I would withdraw (1) upon learning that therelevant concepts were not co-instantiated, it should also be true thatI would withdraw (1′′) for the same reason.) Since the Russellianmakes a sharp distinction between the propositions expressed by (1)and by (1′′), the latter horn must be avoided. On the other hand,the Russellian has gained nothing if he clings to the first horn. Hewas concerned to use Loar’s strategy to make a claim about what anutterance of (1)says, not about what it simply presupposes.7 Thus,more work needs to be done if Loar’s proposal is to be of use to theRussellian.

1.3. The Uniformity Problem

ES also gives rise to the following worry, due to Scott Soames. Thisis that the Russellian provides no account of how descriptions arecompleted by contextual information:

130 GARY OSTERTAG

An important and vexing problem for the traditional [explicit] theorist is thatof finding significant semantic uniformity in the process of contextually supple-menting the contents of incomplete descriptions ([11], 369, note 7).

For future reference, I will refer to the problem Soames identifiesas the ‘uniformity problem’. The problem, I take it, is that (forexample) on one reading, ‘the table’ has an argument place forlocation (the table at l), on another reading it has an argumentplace for the person or persons seated (the table at which x isseated). One can imagine countless variations. As Soames suggests,this leaves it unexplained exactly how content selects a completion;more precisely, it fails to explain how it arises that certain elementsof the context of utterance, and not others, play a role in selectinga completion. The looked-for uniformity Soames mentions couldbe achieved by locating, for each simple predicateF, a contextualparameter such that all descriptions of the formthe F are sensi-tive to that parameter. Thus, uses of ‘the murderer’ might plausiblybe held to be sensitive only to the patient (i.e., victim) parameter.‘The murderer is insane’ would thus always be completed by ‘themurderer ofα is insane’, where ‘α’ refers to a contextually defineindividual. This is implausible. I might have very good reason forthinking that Jones is a murderer, that other murderers exist, andthat Jones is insane, without having the slightest idea whom it wasthat he murdered. Since I can say, in such a context ‘The murderer isinsane’ and not intend to be understood as saying that the murdererof α is insane (for someα), it seems that our hypothesis fails. Itmight be objected that I have simply selected the wrong contex-tual parameter for ‘the murderer’. But it seems to me that the mostobvious choice is, in fact, the victim. In any case, it is clear thatsimilar counterexamples will be forthcoming no matter what choiceone makes on this matter.

It is worth noting that the data presented by Wettstein suggests,in advance of any investigation, that there is no uniform contribu-tion that context makes to a description. For, if there were, thena speaker should be capable of specifying what she intended inuttering (1). But, as we have seen, it is implausible to suppose thatshe could. This point is worth emphasizing: If there exists, for eachsimple predicateF, a uniform contribution that context makes to thedescriptionthe F, then this should be known by the speaker in virtue

A SCOREKEEPING ERROR 131

of her mastery of the language. If we asked her what she meant inutteringthe F is G(with F incomplete), she should be able to tell us.(This is certainly the case with ‘It’s raining’, a sentence-type thatcontains an unarticulated argument place for location. A speaker,in virtue of her mastery of the language, will know the contribu-tion that context makes to an utterance of ‘It’s raining’ (i.e., thecontextually salient location – which may not be the location of theutterance). And this provides evidence that tokens of this sentencedo make tacit reference to location.) Of course, Wettstein’s worrystill remains even if we solve the uniformity problem: there may bea number of ways to specify one and the same parameter. To take ourrecent example, there may be no choice of completion betweenthemurderer of Smith, the murderer of the man we saw yesterday, themurderer of your cousin, etc. Thus, solving the uniformity problemwould not solve the identification problem: there is still some roomfor indeterminacy in the process of identifying the intended comple-tion. Nevertheless, the scope of the indeterminacy is significantlydiminished here – perhaps to a point where it is not sufficient torefute the theory. Yet, since it seems unlikely that there is a uniformway in which context supplements incomplete descriptions, at leastin the manner suggested by ES, the question is beside the point.

Another proposal has received some attention.8 This proposalclaims that an incomplete description is completed not by furtherdescriptiveinformation, but by the speaker’s implicit specificationof an individual. To fix ideas, consider the following example. Iam watching the final set of the final match at Wimbledon; I utter,‘The winner will have a chance at the Grand Slam.’ On the currentproposal, this is completed by an implicit reference to the match;the descriptive material, supplemented by this reference, creates a“singular individual concept”.9 It is claimed that this proposal is notsimply an instance of ES. While ES is fully compatible with theidea that, in the utterance in question, there is an implicit referenceto the match, ES assumes that such reference invariably occurs inthe context of unstated descriptive material (e.g., in the context of‘the winner of x’). The current proposal suggests that the supple-mentary material may be non-descriptive – i.e., referential.10 Notethat this proposal, if true, would solve the uniformity problem.Context makes a uniform contribution to incomplete descriptions

132 GARY OSTERTAG

and, presumably, incomplete quantifiers more generally: it is limitedto supplying “completing” referential material to such quantifiers.

Yet, even if this proposal is distinct from ES – which is verydoubtful – it is vulnerable to precisely the same criticisms. Considermy utterance of ‘The winner will have a chance at the GrandSlam.’ Do I make implicit reference to the current set, the match,or the tournament? Each of these completing references are equallyacceptable, but none is more salient than the others. Once again, weare faced with the identification problem.

This completes my evaluation of the explicit approach and itsmost important variations. I have rejected the approach for tworelated reasons: (i) No account is given of how a speaker, in utteringan incomplete description, can intend for her audience to identifyone of a number of conversationally salient completions. (ii) Noaccount is given – nor, it seems, can be given – of which contex-tual parameters a particular description (-type) is sensitive to, andwhich it is not. An adequate response to (ii) would provide a partialresponse to (i) – perhaps as much of a response as we can reasonablyhope to achieve or, even, as much as is necessary. But, as I havesuggested, no such response seems to be forthcoming.

I now consider an alternative strategy, one according to whichcontext contributes to the determination ofwhat is saidby anutterance containing an incomplete description, but where thecontribution is not in terms of descriptive content.

2.

2.1. The Implicit Strategy

It is often suggested that incomplete quantifiers make implicitreference to a contextually-determined domain of quantification.This idea is motivated by the fact that a speaker, when uttering‘Everyone had a great time’ after a party, doesn’t assert thecontextually irrelevant falsehood that every person in existence hada great time, but only that every person relative to a given domaindid. Questions arise as to how best to relate quantifiers to theirdomain. A natural suggestion is that for each quantified utteranceu, there is a contextually definite domain D of individuals suchthat the quantifiers inu are to be evaluated relative to D.11 This is,

A SCOREKEEPING ERROR 133

nearly enough, Jason Stanley and Timothy Williamson’sSententialQuantifier thesis, which they state as follows:

(SQT) The context-dependence of quantifiers is captured byassigning utterances of sentences containing them tocontexts ([12], p. 291).12

The strategy is a version of what I shall refer to, again followingNeale, as the “implicit strategy”. I frame the strategy in termsof context-relativity and notdomain-relativity since reference toa context will become crucial when we consider incompleteattributive descriptions. Given that reference to a context determinesreference to a domain, nothing is lost by making this modification.

Note that the following sentence (derived from [9]) raisesproblems for this thesis:

(2) Everyone had a great time, althoughsome people whodidn’t have a great timecalled the police.

(2) is potentially true, yet it is unsatisfiable (in the extended senserelevant here) even on SQT.13 According to SQT, the quantifiers in(2) must each be evaluated relative to the same context, and thus thesame domain, yet, intuitively, they draw from distinct sets of persons(for example, the party-goers, and the neighbors, respectively).

Stanley and Williamson suggest the following weakening ofSQT:

(CQT) Distinct occurrencesi and j of quantifiers must be evalu-ated with respect to the same context wheni andj are notseparated by clausal boundaries ([12], p. 294; reworded).

Unlike SQT, CQT is compatible with the satisfiability, and thus thepotential truth, of (2). It is worth noting that (2) is trivially satis-fiable on ES, so long as both quantifiers are not assigned identicalcompletions.

2.2. A Problem for CQT

A deeper problem for CQT, and, by implication, SQT, derivesfrom David Lewis’s ‘Scorekeeping in a Language Game’ [4]. Theproblem concerns SQT considered in conjunction with the thesis,

134 GARY OSTERTAG

which I have assumed, that definite descriptions are quantifiers(DDQ). The standard semantical treatment of description sentencesrelative to the assumption of DDQ is THE below (taken almostverbatim from [12], p. 292):

(THE) A sequences satisfies ‘[the x: Fx] (Gx)’ (relative to adomain D for that quantifier) iff: the sequences* suchthat:

(a) s* differs from s at most in what it assigns to ‘x’;(b) s* assigns a member of D to ‘x’;(c) s* satisfies ‘x’

also satisfies ‘Gx’.

THE recapitulates Russell’s theory of descriptions, since it claimsthat ‘[the x: Fx] (Gx)’ is true just in case exactly one member of Dsatisfies ‘Fx’ and whatever satisfies ‘Fx’ satisfies ‘Gx’.14

Lewis provides the following example:

(3) The dog got into a fight with another dog.15

Surely, (3) has potentially true tokenings. Yet, if the standard quan-tificational analysis of definite descriptions is assumed (i.e., THE),then (3) is unsatisfiable even on CQT.16 This strongly suggests theconclusion that DDQ is false. Of course, it is always possible torecognize descriptions as the only quantifiers for which CQT failsto hold, thereby avoiding the conclusion. There is, however, little tomotivate such a view aside from a desire to retain DDQ at any cost.

Yet, rather than recommend dropping DDQ, Stanley andWilliamson recommend dropping CQT. They argue that CQT isfalse for independent reasons, noting the incompatibility of CQTwith the potential truth of certain tokenings of (4):

(4) A group of evangelists met in the square, whereuponeveryone converted someone.

We can imagine that those converting and those converted formdisjoint sets: the evangelists do not convert each other, but ratherthey convert the unconverted. However, this possibility is precludedby CQT, which requires the respective quantifierseveryoneand

A SCOREKEEPING ERROR 135

someone, being within the same clause, to draw from the samedomain of persons. The upshot is that, on CQT, the hypothesizedutterance of (4) fails to say what we would, at the context, recognizeit as saying.17 The implication is that CQT is false, since it fails toaccommodate sentences containing logical quantifiers.

2.3. The Quantifier-Occurrence Thesis

Given the falsity of CQT, the fact that (3) is unsatisfiable on thejoint assumption of CQT and DDQ fails to challenge DDQ. Yet, weare still lacking an account of the relation between the occurrenceof a quantifier in an utterance and the context relative to which thatquantifier is to be interpreted. That is, while the DDQ-theorist ismomentarily out of trouble, she still owes us an account of how toresolve incompleteness for quantified sentences generally.

A helpful suggestion on this score is due to Scott Soames [11].Soames writes that what examples such as (3) and (4) show isthat “contextual supplementation works at the level ofconstitu-entsof sentences or utterances, rather than the level of sentencesor utterances themselves” ([11], p. 357, emphasis added). Thisseems true. However, Soames appears to think that the only viablemethod of incorporating contextual information is by adding furtherdescriptive material to incomplete quantifiers and descriptions,àla ES – or, more precisely, a weakening of ES that conforms toSoames’s suggestion.18 For (3), this method might produce ‘The dogin front of megot into a fight with another dog;’ for (4), we wouldget ‘Every oneof the evangelistsconverted someone.’ Since ES hasbeen ruled out as an adequate method of resolving incompleteness, Iwill pursue Soames’s suggestion independently of his appeal to thismethod.

The following thesis (the Quantifier-Occurrence thesis)incorporates Soames’s suggestion that contextual supplementationoperates at the level of sentence constituents, without abandoningthe implicit approach:

QOT The context-dependence of the occurrencei of a quantifierQ is captured by assigningQ a context relative toi.

QOT simply states that each occurrence of a quantifier in a givenutterance can be assigned a particular context. THE, above, provides

136 GARY OSTERTAG

an example of how a satisfaction-definition for a quantified utterancemight comply with QOT. In particular, clause (b) of THE states thatfor a sequences to satisfy ‘[the x: Fx] (Gx)’ the sequences* thatagrees withs except for whats* assigns to ‘x’ must assign ‘x’ anelement of the domain of the contextrelevant to that quantifier.

Note that on QOT the same quantifier type can have multipleoccurrences in a single utterance and be assigned distinct contexts– and thus distinct domains – for each occurrence. This is the caseeven when the occurrences are within a single clause. We can thusaccommodate utterances of the following:

(5) A band recording its first album was assisted by a groupof musicians; when it was completed, everyone thankedeveryone for contributing.

One reading of the second sentence in (5) is that everyone in theband thanked each musician who assisted her or him, there beingno need for the band members to thank their colleagues, nor for theassisting musicians to thank each other.

2.4. The Adequacy of the Implicit Approach

In [4], Lewis does not consider ES. Despite its inadequacies onother counts, ES is compatible with the potential truth of both(3) and (4). (I have already noted that ES is compatible with thepotential truth of (2).) To see this, consider a treatment of (3)according to ES. This would yield an instance of the following:

(3a) The dog that is8 got into a fight with another dog,

with 8 being a contextually determined completion of ‘the dog’.The logical form of (3a) is represented by (3a′):

(3a′) [the x: x a dog & x is8] ([the y: y a dog & (y 6= x)] (xfought y)).

We observe that (3a′) is satisfiable.19

The reason I bring this up is that, once it is recognized that ESis compatible with (3) and (4), it is a very short step to seeing thatQOT must also be immune to these and to similar counterexamples.

A SCOREKEEPING ERROR 137

Note that for any treatment of an utterance of (3) conforming toQOT – i.e., one in which the respective descriptions are evaluatedwith respect to distinct domains – there is an equivalent explicittreatment of the form (3a′′):

(3a′′) [the x: x a dog & x∈ D] ([the y: y a dog & (y 6= x)] (xfought y))

(where D is a context set in Westertåhl’s sense; see note 11). (3a′′) isof course satisfiable, as it is an instance of (3a′).20 Similar reasoningapplies to (4).

The foregoing considerations show that QOT and the explicitstrategy are equally effective in accommodating Lewis-stylesentences. Thus, the implicit approach is,contra Lewis, fullycompatible with the quantificational analysis of definite descrip-tions. We now turn to some difficulties QOT faces.

2.5. Attributive Incompleteness

The implicit strategy was originally pursued in order to develop aRussellian response to a phenomenon that was taken by some tomotivate an anti-Russellian treatment of descriptions. On the latterview, descriptions often function as referential singular terms, andnot as quantifiers. The view was argued for by appeal to the iden-tification problem. Since Russell’s theory (at least, on its “explicit”construal) is incompatible with the fact that a speaker, in utteringa sentence such as (1), has said something determinate, and sincethe view that incomplete descriptions are referential singular termsdoes account for this fact, it is claimed that the utterance of (1) inquestion is referential.

The Russellian has responded by acknowledging that incompletedescriptions are oftenusedreferentially, but denying that this usereflects any semantically referential role for definite descriptions.He claims that a referential use ofthe table, as it occurs in anutteranceu of (1), is one on which an object-dependent, or singular,proposition is conveyed byu. Indeed, this singular proposition is, insuch a case, the primary object of the speaker’s intention. Yet, thetraditional Russellian maintains, at the same time, that it is in virtueof u’s expressing an object-independent, quantified proposition thatthe referential proposition gets conveyed.

138 GARY OSTERTAG

To see how this works, it is easiest to consider either naiveRussellianism, or the explicit approach. Let us consider the latter.On ES, u will express an object-independent proposition of theform the8 table is covered with books(where8 is a completingproperty). If this proposition is true, then there will be one table (T)that satisfies the description. Thus, on ES,u is true just in caseTis covered with books. Since we may assume that the speaker, inthe example, utters (1) precisely to get the audience to recognizethatT is covered with books – and not simply to inform her that theproperty of being the single8 table that is covered with books is,in fact, instantiated – and since this fact is recognized by the hearer,the import ofu will be taken to be the singular proposition thatT iscovered with books.

On the other hand, the case in which descriptions are used non-referentially – or “attributively” – is one for which the traditionalRussellian analysis is adequate. On the attributive use, both theliteral meaning of the utterance as well as the primary intentionwith which the utterance is made are correctly analyzed alongRussellian lines. (This is a point to which both Russellians andnon-Russellians agree.) Yet,incompleteattributive cases presenta special problem for the implicit theorist. In all the cases wehave considered so far, the domain or context relative to which weinterpret a description is accessible to the speaker and her audience.In the case of incompleteattributive descriptions, the context ordomain that is accessible to the speaker and audience does notsuffice to provide an interpretation of the description in question.Consider, Donnellan’s example, (6), uttered in the presence of thefoully-murdered Smith:

(6) The murderer, whoever he is, is insane.

We assume thatthe murdereris incomplete; it thus demands inter-pretation relative to a contextually determined domain. The problemis that the domain to which the speaker and hearer have access– either perceptually, or through mutual knowledge – contains nomurderer. How, then, do we provide an interpretation for (6)? Onesuggestion is to expand the notion of context to include “situations”that are not accessible, perceptually or otherwise, to the speaker.

A SCOREKEEPING ERROR 139

Obviously, the expansion cannot be so inclusive so as to make thedescription incomplete. (I.e., we don’t expand the context to includemultiple murderers.) In addition, the expansion must berelevanttointerpreting the utterance. (We don’t require an expansion of thecontext relative to which (6) is to be interpreted that contains nomurderers, or, just as bad, murderers not responsible for the murderin question.) Thus, contextual expansion will be determined by theexigencies of the utterance situation – in particular, by a Lewisianstrategy of accommodation. We expand the context in such a waythat it makes the utterance both true and relevant.

Recall that, on CQT and QOT, the context of utterance provides adomain of objects, relative to which quantifiers are to be interpreted.This implies that, when the domain changes, the interpretation mustchange with it. Now imagine two utterances of (6),u and u*. uis uttered in a context C (in the expanded sense) at which Jonesmurdered Smith;u* is uttered in a context C* (in the expandedsense) at whichJohnsonmurdered Smith. Let us assume that thecircumstances surrounding the respective utterances are otherwiseidentical – in particular, the accessible domains are identical. Inour original sense of context, C and C* are one and the same;yet, they “expand” differently, in the ways just suggested. Now,it seems implausible thatu and u* can say different things; butthis is just what our recent suggestion implies.u says, in effect,that the murderer in the expanded context containing Jones isinsane, whereasu* says that the murderer in the expanded contextcontaining Johnson is insane. Thus, the suggestion that utterancesof incomplete attributive descriptions should be interpreted relativeto an expansion of the context must be rejected.21

One might resist this conclusion, and maintain that the respectiveutterances really do say different things. Yet, this is not an optionfor the Russellian, who is committed to the idea that descrip-tion sentences, and, indeed, quantified sentences in general, areobject-independent. Since the current analysis fails to meet thisrequirement, the Russellian must reject it.

Is there a way to provide the intuitively correct account of thecontents of the utterancesu andu* in a way that does not violatethe spirit of the implicit strategy? One promising suggestion is notto expand the notion of context, but rather to modify the relation

140 GARY OSTERTAG

that a description bears to the context of utterance.22 Rather thansaying thatthe murdereris to be understood asthe murderer in Cwe must say that it is to be understood asthe murderer relevantto C. This allows us to accommodate the following intuition: whentwo contexts of utterance C and C* are identical with respect to theirdomains, then, for any quantified sentenceS, whatSsays relative toC will be equivalent to whatSsays relative to C*. This amounts toa condition of adequacy for any implementation of Russell’s theoryof descriptions. (Note that, in cases wherethe F is not attributive,the F relevant to C will simply be the F in C. Thus, the strategyexemplified by CQT and QOT is a special case of the strategy weare now adopting.) In our examples, we assumed that the respectivecircumstances of utterance were identical – in each case, Smith isdiscovered foully murdered. Where they differed was in the factthat, in the one case, Jones murdered Smith, in the other Johnsonmurdered Smith. Unlike the former strategy, our recent strategyassigns the same truth conditions to the respective utterances of (6).

There is the following worry. I have suggested that the properanalysis of (6) is: the murderer, relevant to C, is insane (where ‘C’refers to the context of utterance). But the context that expandsinto a more inclusive context at which Jones murdered Smith mustbe distinct from the context that expands into a more inclusivecontext at which Johnson murdered Smith – even if the originalcontexts contain the same individuals standing in the same rela-tions. This must be the case: contexts are parts of more inclusiveentities – worlds or situations; two distinct worlds (or situations)cannot contain, as component contexts, one and the same context.The upshot is that my analysis assigns distinct propositions tothe respective utterances of (6), and this the Russellian must findunsatisfactory.

The solution is close at hand, however. What distinct worlds canshare are contexts that aretype-identical (these are essentially thesituation-types of [1]). What I refer to in uttering (6) is not thecontext, but rather the context- or situation-type that is made salientby my utterance (in this case, a context- or situation-type whosetokens all contain a unique individual who murdered Smith). Howdoes this proposal help? As we have seen, if it is assumed that utter-ancesu and u* of (6) make implicit reference to their respective

A SCOREKEEPING ERROR 141

contexts, then they will possess distinct truth conditions. On theother hand, if it is assumed that they make implicit reference to acontext- or situation-type, then we may assume that they possessequivalent truth conditions, since it is reasonable to expect that theywill make reference to the same context- or situation-type.

Some may feel that this proposal is rather counter-intuitive –surely speakers don’ttakethemselves to be referring to theoreticalentities such as types of situation when uttering sentences such as(6). I am sympathetic to the spirit of this objection. But in fact, I takea context-type to be a context as we normally understand that notion.It is the notion of a context as a component of a possible worldthat is really the more technical notion. On the current analysis of(6), I am, in essence, appealing to a notion of context accordingto which it is a repeatable entity. While the traditional notion ofcontext is indispensable to semantics, it cannot play the role ofcontext- or situation-type. Moreover, the latter notion seems equallyindispensable when evaluating certain classes of utterance, such asincomplete quantifiers.

2.6. The Identification Problem Again

A final worry concerns a variation on the identification problem.Can we assume that, in a given utterance of, say, (1), the audiencecan make a precise identification of the context relative to whichthe speaker intends to be understood? Can’t it be the case thatmy implicit specification of a context or domain is indeterminate?Surely, my utterance of (1) may not enable my audience to selectfrom a number of “candidate” domains or contexts. Perhaps myintentions are not even determinate on that score. If they are not,how have we advanced from ES?

This objection has some force.23 Notice, however, that the currentapproach does locate a uniform parameter relative to which adescription or, more generally, quantifier, must be interpreted. Thatparameter is the entire context. Thus, we interpretthe F as the Frelevant to C, where ‘C’ is a placeholder for the context or context-type at which the description is produced. Similarly foreach F,some Fs, etc. This reduces the scope of indeterminacy significantly.Moreover, the remaining indeterminacy seems quite compatiblewith usage. If I utter, ‘Everyone left early’ after a party, I might,

142 GARY OSTERTAG

in fact, be understood as saying, indeterminately, of a number ofdistinct sets of persons, that each member of each of those sets leftearly. There may be no fact of the matter as to which set I did intend.

The indeterminacy predicted by ES seems, in contrast, of a quitedistinct nature. It allows the assignment of entirely different typesof completion to a single utterance. As I suggested in section 1.2,there is no motivation for such a hypothesis from the standpoint ofusage. The same is not true with respect to the implicit reference to adomain. Indeed, our judgements as to what a person intended, whenuttering a quantified sentence, are often in need of slight adjustment.

It might be objected that I have conceded the indeterminacytheorist’s claim that utterances of incomplete quantified sentencesare, typically, indeterminate, and have, in addition, shown that it issupported by intuition. Obviously, this involves an overstatement.The indeterminacy in question is, as I have suggested, relativelymild. Even so, it is an indeterminacy; the objection has its point.Yet, the crucial difference between the “mild” indeterminacy thatI acknowledge that uses of incomplete quantified sentences oftenpossess and the indeterminacy exemplified by utterances of vaguesentences is that the latter is a semantic feature of the utterances inquestion, whereas the former is merely pragmatic. If I utter ‘Tallmen are good at basketball’ I say something vague. Its vaguenessis due to the fact that the standards for being tall are not definite. Itis surelynot due to the absence of definite standards at the context.Rather, it is due to the fact that definite standards are unavailable,no matter what the context.24 This is not to deny that standards oftallness vary across context. My point is simply that there are nocontexts at which ‘tall’ has a definite intension.

If I am right, then what distinguishes vague utterances is thattheir indeterminacy is a matter of their semantics: no tokening of avague sentence can have a determinate meaning. (Equivalently: notokening of a vague sentence can have determinate possible worldstruth conditions.) This is not the case with incomplete quantifiedutterances. Their indeterminacy is a purely pragmatic matter.

The above distinction – between semantic and merely pragmaticindeterminacy – is worth making for the following reason. If theindeterminacy of a given form of utterance is inherited from itssemantics, then a semantic analysis of that utterance should obvi-

A SCOREKEEPING ERROR 143

ously reflect that indeterminacy. In contrast, if the indeterminacyof a given form of utterance doesnot derive from its semantics,then there is no need to complicate its semantics by reflecting that(potential) indeterminacy.

Perhaps it will be said that I have inadvertently vindicated ES.After all, ES is a proposal that avoids complicating the semantics ofquantifiers; on ES, indeterminacy is a purely pragmatic notion. Yet,my initial resistance to ES was simply that the kind of indeterminacyit would give rise to, if indeed it were the correct account of incom-plete descriptions, is not reflected in our use of descriptions. In brief:acceptance of ES entails a level of pragmatic indeterminacy that isnot reflected in facts about usage – indeed, it is contraindicated bysuch facts. The pragmatic indeterminacy entailed by acceptance ofthe implicit strategy, on the other hand, seems quite compatible withusage.

CONCLUSION

I have indicated where I find weaknesses in the explicit approach.These weaknesses concern what I have called theidentificationproblemand theuniformity problem. As I have suggested, solvingthe latter problem will at least partially solve the former problem –indeed, perhaps as much as it needs to be solved. It is here that thestrength of the alternative – implicit – approach is most apparent. Onthis view, an utterance of an incomplete description is supplementedby the context (or context-type). We thus answer the question:what feature of the utterance situation determines the completionof a quantified sentence? The answer is always, the context (orcontext-type). I have also shown that Lewis’s objection to theimplicit approach can be overcome by weakening the approach ina manner that seems intuitively appropriate. This weakening alsoaccommodates Stanley and Williamson’s apparent counterexampleto the implicit approach. The counterexamples affect only unneces-sarily restrictive formulations of that approach. Of course, certainaspects of the theory do call for further inquiry – there is surelymore to be said concerning the proper treatment of incompleteattributive descriptions, for example. Nonetheless, the approachpresents an intuitively satisfying account of the context-sensitivity

144 GARY OSTERTAG

of definite descriptions, and of quantifiers more generally, vindi-cating, albeit from a framework utterly alien to Russell, the theoryof descriptions.25

NOTES

1 Note that I am assuming that Russell’s theory can be made to account for thereferential use of definite descriptions. My concern is not with defending Russell’stheory against the challenge posed by such usage, but with determining the besttreatment of Russell’s theory relative to the assumption that descriptions are quan-tifiers.2 My formulation derives from Stanley and Williamson [12].3 The explicit strategy is often formulated in terms of the quasi-syntactic notionof ellipsis (that is, as claiming that an utterance of a sentence containing an incom-plete quantifier iselliptical for a completing sentence). It seems to me that thisconstrues the notion of context-sensitivity too narrowly. There seems no reason tosuppose that the relation between, say, (1) and its completion is anything like thatbetween: ‘John left and Bill did too’ and ‘John left and Bill left.’ For discussion,see Recanati [8].4 This is, in fact, Schiffer’s suggestion; see Schiffer [10], pp. 115–116, and Black-burn [2].5 An utteranceu presupposes a propositionp iff: if u is true thenp is true and ifu is false thenp is true.

Note that the indeterminacy of ‘John is bald’ cannot similarly be explained byappeal to presupposition-failure.6 On this point, see Schiffer [10].7 Not least because it threatens a collapse of the distinction between (1) and (1′′).8 See especially Recanati [8], pp. 449–450, note 1.9 The expression is Soames’s, who, as I will show, doesn’t endorses the view.10 In fact, I doubt that this proposal is really different from ES. (Here I agreewith Neale [6], p. 99.) Recanati claims that it is different from ES, but he nevermakes intelligible the thought that adding an individual to a description createssomething that can function as the semantical value of a quantified noun phrase.In addition, Recanati is mistaken in his attribution of this proposal to Soames;on the very page Recanati cites ([8], p. 352), Soames clearly equates singularindividual concepts with complete descriptions:

On this approach, the content of ‘the murderer’ in the context of our examplewill be a “singular individual concept” involving the victim as one of itsconstituents.Thus, the content of ‘the murderer’ in this context will be thesame as that of ‘the murderer of him’, or ‘the murderer of that one’, with thevictim as the referent of the indexical([11], p. 352, emphasis added).

11 Following Westertåhl [13], we can conceive of the domains in question as‘context sets’, or sub-domains of the relevant discourse universe. Relativizing a

A SCOREKEEPING ERROR 145

quantifier to a context set has the same effect as restricting it with a predicate trueof all and only things in the relevant context set. That is, relativizing ‘everything’to the set of natural numbers will have the same effect as evaluating ‘every naturalnumber’ relative to the entire discourse universe.12 Note that the assignments must be to a particular context – one implicitlyreferred to or otherwise specified by the relevant utterance. Otherwise, certainquantified sentence forms are too easily satisfied. For example, the followingclause concerning definite descriptions omits the suggested qualification, with theresult that the truth conditions ofthe F is Gare identical with those ofan F is G:

An utterance ofthe F is Gis trueiff: there is a context C such that theunique F in C is G:

Similar worries arise concerning other non-persistent quantifiers, such asno Fs,exactly seven Fs, etc. See Soames [11] for discussion; also Barwise and Perry [1].13 A note about my terminology: I am using ‘potentially true’ to apply to Englishsentences that have non-vacuously false tokenings (I acknowledge that vacuousfalsity, unlike unsatisfiability, is not rigorously definable); I am using ‘satisfiable’to apply to sentences in a formal language that are true-in-a-model (and, whencontext makes this clear, to English sentences whose first order translation is true-in-a-model).14 In fact, Stanley and Williamson deny that THE is equivalent to Russell’s theoryof descriptions. I cannot pursue their reasons here; see the Introduction to Ostertag[7] for discussion.15 Attributed by Lewis to James McCawley.16 Note that THE is more general than the standard quantificational accountrequires, allowing for – but not itself requiring – the possibility that distinctoccurrences of quantifier expressions be assigned distinct domains.17 Actually, the conclusion can be disputed. It can be argued that the content thatStanley and Williamson ascribe to the relevant utterance of (4) is an implicature,and not part of (4)’s literal content/truth condition at all. This alone wouldchallenge their claim that CQT is false. I will not pursue this defense of CQT,however.18 The following weakening of ES would suffice:

(ES*) The context-dependence of the occurrencei of a quantifierQ inan utterance is captured by assigningQ a contextually definitecompletion relative toi.

Note that (ES*) is only necessary for contexts in which the same quantifier occursmore than once (e.g.,The dog bit the dog).19 Assuming, of course, that8 is. Note that the internal description ‘another dog’requires a completing predicate distinct from8 if (3a′) is to be true for models inexcess of two dogs.20 Note that the domain for the internal description is the entire discourseuniverse.21 This argument derives from Soames [11], 355–356.

146 GARY OSTERTAG

22 Here I follow Soames [11], 358–359.23 It was suggested, independently, by Stephen Schiffer and Michael Devitt.24 Of course, at a context we mightstipulatethat ‘tall’ means, e.g.,over six feet,seven inches. But in that case, we are no longer concerned with the semantics of‘tall’. Stipulated meanings may be suggested or inspired by linguistic meanings,but they are not determined by them.25 A version of this paper was delivered to the Departments of Philosophyat SUNY-Albany and at SUNY College at Buffalo. I would like to thank theaudiences at these lectures for their comments and questions. Thanks to EileenO’Neill, Stephen Schiffer, Russell Dale, an anonymous referee, and (especially)Friederike Moltmann for helpful comments on a previous draft. Thanks also toMark Crimmins, whose comments on a related paper of mine have influenced mythinking on this matter.

REFERENCES

1. Barwise, J. and J. Perry (1983):Situations and Attitudes, Cambridge, Mass.:MIT Press.

2. Blackburn, W.K. (1988): ‘Wettstein on Definite Descriptions’,Philosoph-ical Studies53, 263–278.

3. Fine, K. (1975): ‘Vagueness, Truth and Logic’,Synthese30, 265–300.4. Lewis, D. (1979): ‘Scorekeeping in a Language Game’,Journal of Philo-

sophical Logic9, 339–359.5. Loar, B. (1976): ‘The Semantics of Singular Terms’,Philosophical Studies

30, 353–377.6. Neale, S. (1990):Descriptions, Cambridge, Mass.: MIT Press.7. Ostertag, G. (ed.) (1998):Definite Descriptions: A Reader, Cambridge,

Mass.: MIT Press.8. Recanati, F. (1996): ‘Domains of Discourse’,Linguistic and Philosophy19,

445–475.9. Reimer, M. (1993): ‘Incomplete Descriptions’,Erkenntnis37, 347–363.

10. Schiffer, S. (1995): ‘Descriptions, Indexicals, and Belief Reports: SomeDilemmas (But Not the Ones You Expect)’,Mind 104, 107–131; reprintedin [7].

11. Soames, S. (1986): ‘Incomplete Definite Descriptions’,Notre Dame Journalof Formal Logic27, 349–375; reprinted in [7].

12. Stanley, J. and T. Williamson (1995): ‘Quantifiers and Context Depend-ence’,Analysis55(4), 291–295.

13. Westertåhl, D. (1984): ‘Determiners and Context Sets’, in J. van Benthamand A. ter Meulen (eds.),Generalized Quantifiers in Natural Language,Foris: Dordrecht, 45–71.

14. Wettstein, Howard (1981): ‘Demonstrative Reference and Definite Descrip-tions’, Philosophical Studies40, 1981: 241–257; reprinted in [7].

New York University, U.S.A.