Letting negative polarity alone for let alone MaziarToosarvandani UniversityofCalifornia,Berkeley 1. Introduction One of the core questions in the literature on polarity sensitivity is what Ladusaw (1996: 326) calls the Status Question: ‘[W]hat is the theoretical status of a struc- ture containing an unlicensed polarity item?’ The traditional answer has been that, when a polarity item does not cooccur with an appropriate licensor, as with the classicnegativepolarityitemanyin(1b),theresultisungrammaticality—thesen- tence is either syntactically or semantically ill-formed. (For now, I use the asterisk as a general mark of unacceptability; a larger dossier of judgment marks will be introducedin§5.) (1) a. Maxdidn’tseeanyaliens. b. *Maxsawanyaliens. Ladusaw (1980), for example, argues that (1b) is semantically uninterpretable; a polarity licensing requirement disallows the interpretation of this sentence since anydoesnotoccurwithinthescopeofamonotonedecreasingfunction,suchasthe negationin(1a).1 Linebarger(1980,1987)treats(1b)assyntacticallyungrammati- cal,sinceitviolatesaconstraintontheLogicalForms(LFs)ofsentencescontaining negativepolarityitems. More recently, a different view has become influential, one in which the distribution of negative polarity items is derived from a combination of their lexi- cal semantics and general pragmatic principles, e.g. Kadmon and Landman 1993, Krifka 1991, 1995, Israel 1998, 2001, Lahiri 1998, Chierchia 2004, 2006. While these accounts differ in their details, they agree in analyzing a negative polarity item like any as scalar in some way or another; it either makes reference in its de- notation to the bottom of a scale (Israel, Krifka, Lahiri) or it widens the domain of quantification (Chierchia, Kadmon and Landman). Any only occurs in downward entailing environments, then, because its use must have a purpose: it must make a stronger, or more informative, statement.2 Since, as Ducrot (1973) and Faucon- nier(1975)show,inferencepatternsflipwhenthescaletheyarebasedonoccursin I thank Annahita Farudi, Andrew Garrett, Anastasia Giannakidou, Hannah Haynie, Michael Houser,RussellLee-Goldman,YaronMcNabb,JasonMerchant,LineMikkelsen,ChrisPotts,Os- amuSawada,andaudiencesatCLS44,SALT18,andtheBerkeleySyntax&SemanticsCirclefor theirthoughtfulquestionsandsuggestions. 1AfunctionF is MONOTONE DECREASING iff,forarbitraryelementsX andY,ifX Y,then ≤ F(Y) F(X). ≤ 2Being in the scope of a monotone decreasing function must be distinguished from being in a downwardentailingenvironment—aglobalcalculationthattakesintoaccounttheentiresentence. © 2008 by Maziar Toosarvandani. T. Friedman and S. Ito (eds.), SALT XVIII, Ithaca, NY: Cornell University. 730 Maziar Toosarvandani a downward entailing environment, only there will a statement containing any, the lowermemberofascale,bemoreinformativethantheparallelstatementcontaining ahighermemberofthescale. Under the scalar approach, the ill-formedness of unlicensed any in (1b) comes out as a type of pragmatic infelicity, specifically a failure to be informative enough.But,asGiannakidou(toappear)argues,thisisnotthestatusthatsuchsen- tences actually have. They instead seem to be flat-out ungrammatical, an intuition sharedevenbyadvocatesofthescalarapproach(see,forinstance,Israel1998:249– 250, Krifka 1991: 180, Chierchia 2006: 557). Thus, while a scalar analysis may be appropriate for some negative polarity items, it cannot be a universal explanation for their distribution. Instead,Giannakidou (2007) proposes to distinguish between more hard-wired polarity items — which must be licensed grammatically — and expressions whose restriction to some of the same environments is epiphenomenal ofhowtheirscalarsemanticsinteractwithpragmaticprinciples(informally,wecan saythatthesearepragmaticallylicensed). In this paper, I explore the semantics and pragmatics of let alone, an ex- pression whose distribution parallels that of any in many respects. Removing the negation from the let alone sentence in (2a) results in ill-formedness, as shown in (2b). (2) Q: What(mountains)hasOswaldclimbed? A1: Oswaldhasn’tclimbedtheBerkeleyhills,letaloneMt.Everest. A2: *OswaldhasclimbedtheBerkeleyhills,letaloneMt.Everest. I argue that the distribution of let alone in downward entailing environments can be derived from its lexical semantics — which crucially make reference to a scale — and Gricean principles of cooperative conversation. For let alone, then, in con- trast to any, the answer to the Status Question is that unlicensed occurrences are pragmatically infelicitous. The existence of such a negative polarity item thus pro- vides support for a distinction between grammatically-licensed and pragmatically- licensedpolarityitems. 2. Thedistributionofletalone Let alone was first identified as a potential negative polarity item by Fillmore et al. (1988)intheiroriginaldescriptionoftheexpression.Theydonotprovideacompre- hensivelistofthecontextsinwhichitshowsup,but,drawingonnaturally-occuring examples,Ishowthatletaloneoccursonlyindownwardentailingenvironments. AnexpressionαcontainedinasentenceφisinaDOWNWARD ENTAILING ENVIRONMENTiff,for any β, such that β α , φ logically entails φ[α/β] (replacing α with β in φ). Thus, in the ⊆ sentenceLizrarelydoesnoteatanyfishforlunch,anyoccursinthescopeofamonotonedecreasing function,thenega!tion"exp!ress"edbynot,butitisnotinadownwardentailingenvironment(because of the higher monotone decreasing function rarely). From this sentence, we cannot infer that Liz rarely does not eat any trout for lunch. She may hate trout, and so eat some other kind of fish for lunchalmosteveryday. 2 LETTING NEGATIVE POLARITY ALONE FOR LET ALONE 731 Like any, let alone occurs in the scope of negation (3). It also shows up in thescopeofavarietyofantiadditivefunctions(inthesenseofZwarts1998),which are, of course, also monotone decreasing: the negative adverb never (4), the neg- ative adjective difficult (5), the negative quantifier no one (6), the quantificational determinerevery(7),before(8),without(9),andthedegreemodifiertoo(10).3 (3) Like any self-respecting academics, the Brookings authors do not agree onwhattheproblemis,letalonehowtocureit.(ABJ835) (4) Where Musgrove and John Hopkins, who put it all together, got lucky was that they chronicled a period of success that may never have been equalled,letaloneexceeded,byanyBritishgolfer.(AAN70)4 (5) Indeed, the only way in which a society can come to terms with its con- flicting values is to prefer one value in some circumstances and another in different conditions. It is difficult enough for an individual to be con- sistent,letaloneasociety.(A5A124) (6) NoonehadevenheardofPatWeaver,letaloneseenhim.(CE51737) (7) What irks the Brits, and irks far more their Unionist fellow-citizens in Northern Ireland, is that foreigners — in pursuit of domestic votes, not Irish welfare — are using economic pressure to tell them how to behave. EveryAmerican‘fact-finding’visittoUlster,letalonethoseofovertIRA propagandists,rubssaltintothisirritation.(HSF1104) (8) Little attention was paid to it, and 10 years passed before the existence, let alone the exact functions of these receptors, non-committally named alphaandbeta,wasrecognized.(ARF1230) (9) Ihavenowlivedinthesameplacethroughninegeneralelectionswithout onceseeing,letalonebeingaccostedby,aparliamentarycandidate.(AK2 1028) (10) Diana was sympathetic, but did not fully understand his unrest, nor his frantic soul-searching. She was twenty-three and simply too young to comprehend the feelings of middle age — let alone those of a middle- agedPrince.(A7H997) Since these expressions are the only monotone decreasing functions in these sen- tences, this means that, in each, let alone occurs in a downward entailing environ- ment.LetalonecanalsoappearinthescopeofquantifierslikefewAsianadults(11) andatmost20people(12),whicharemonotonedecreasingbutnotantiadditive. (11) InSouthallnow,particularlysincethemurderinsummer1976ofayoung man, Gurdeep Singh Chaggar, by racist thugs, few Asian adults even thinkaboutintegration,letalonewantit.(A6V1961) 3AfunctionF isANTIADDITIVEiff,forarbitraryelementsX andY,F(X Y)=F(X) F(Y). ∨ ∧ 4Thisexample,andotherswithreferencenumbersofthesameform,arefromtheBritishNational Corpus(version2). 3 732 Maziar Toosarvandani (12) By 1928, at most ten people had ever swum the Channel, let alone the Atlantic. There are a number of other contexts where let alone appears that are not straightforwardlydownwardentailing,e.g.inthescopeofonly(13)andbarely(14), intheantecedentofaconditional(15),andinthecomplementoffactivepredicates likesurprised(16). (13) Although Indians had been allowed to join the ICS since 1858, only a handful had actually sat its fiercely competitive examinations, let alone passed.(AKR957) (14) And to think, he wrote, that with all my previous work I barely knew what step to take first, let alone what step to take second, let us not talk aboutthethird.(A0882) (15) Mrs. Clinton once had a big lead among the party elders, but has been steadilylosingit,inlargepartbecauseofhernegativecampaign.Ifsheis evertohaveahopeofpersuadingthesemostloyalofDemocratstocome back to her side, let alone win over the larger body of voters, she has to calloffthedogs.5 (16) However,I’msurprisedthatApplewouldevenannounce,letalonebring online,anewsystemuntilitwasascapableandbug-freeastheold.6 The fact that these expressions also license any has been the object of much atten- tion in the literature, which, for reasons of space, I cannot review here. I would, however,liketopointoutsomeoftheprogressthathasbeenmadeintreatingthese expressions as monotone decreasing.7 Horn (2002), for instance, argues that only andbarelyareindeedmonotonedecreasingifweignorethecontributionofwhathe calls assertorically-inert entailments. For only, the antecedent of conditionals, and factivepredicates,vonFintel(1999)providesasimilarsolutionbydefininganotion ofStrawsondownwardentailingthatfactorsoutthepresuppositionalcomponentof theseexpressions’meanings.8 5‘The Low Road to Victory’, Editorial, The New York Times, April 23, 2008. Retrieved from http://www.nytimes.com/2008/04/23/opinion/23wed1.html. 6http://discussions.apple.com/thread.jspa?threadID=230549&tstart=3702,June27,2008. 7An alternate strand of research, represented by Giannakidou 1998, denies the relevance of monotonedecreasingnessanddownwardentailingnessforpolaritylicensingaltogether,andinstead characterizestheclassoflicensorsintermsof(non)veridicality.Thismoveisperhapsjustifiedfor anysinceitcanoccurinsome(nonveridical)upwardentailingandnonmonotoniccontexts,suchas thosein(18–21),butletalonehasamorerestricteddistribution. 8Letalone,likeany,alsoappearsinpolarquestions(i)andwh-questions(ii). (i) If the caller’s funny and amusing does it really matter whether they’re geniune or not? Doestheaveragelistenerevennotice,letalonecare? (http://www.digitalspy.co.uk/forums/showthread.php?t=348637,June27,2008) (ii) HowmanymodernPrimeMinisterscouldrecallsuchexploitsintheirpast,letalonedare toboastaboutthem?Inaliberaldemocracy‘non-violence’isacherishedvalue,perhaps 4 LETTING NEGATIVE POLARITY ALONE FOR LET ALONE 733 So far, we have seen that let alone can occur in a downward entailing envi- ronment created by a variety of monotone decreasing functions. Now, it remains to be shown that it can occur only in this context. When let alone occurs in a positive episodic sentence, an upward entailing environment, the sentence is ill-formed, as shownin(17).Similarly,itcannotappearinthescopeofanonmonotonicquantifier like exactly three Iranians(18) or of the modal want (19), in an imperative (20), or inagenericstatement(21). (17) *OswaldclimbedtheBerkeleyhills,letaloneMt.Everest. (18) Q: HavealotofIraniansclimbedMt.Everest? A: *Exactly three Iranians have climbed the Berkeley hills, let alone Mt.Everest. (19) Q: DidtheyexpectOswaldtoclimbMt.Everest? A: *They wanted Oswald to climb the Berkeley hills, let alone Mt. Everest. (20) Q: DoyouwantmetoclimbMt.Everest? A: *ClimbtheBerkeleyhills,letaloneMt.Everest! (21) Q: DotouristsgenerallyclimbMt.Everest? A: *TouristsclimbtheBerkeleyhills,letaloneMt.Everest. The generalization thus seems to be that let alone only occurs in downward en- tailing environments: it is disallowed in upward entailing environments (17) and in contextswhereinferencesarenotallowedineitherdirection(18–21). 3. Ascalarsemanticsforletalone The first step towards deriving let alone’s distribution in downward entailing en- vironments is to give it a meaning. I argue elsewhere (Toosarvandani, to appear) thatthesentencein(22)expressesapairofentailments,oneofwhichisanat-issue entailment,whiletheotherisbackgrounded:9 (22) Oswaldhasn’tclimbedtheBerkeleyhills,letaloneMt.Everest. a. At-issueentailment: climb(the-berkeley-hills)(oswald) ¬ b. Backgroundentailment:the-berkeley-hills< mt-everest S themost cherishedof allvalues, forviolence isperceived asthe negationof democracy. (AHG587) Theseare,ofcourse,amongthehardestenvironmentstocharacterizeasdownwardentailing. 9ThismeaningcanbederivedcompositionallyusingaschemeliketheonesthatKarttunenand Peters(1979)andPotts(2005)proposeforconventionalimplicatures.Again,seeToosarvandani,to appearfordetails. 5 734 Maziar Toosarvandani Theat-issueentailmentisconveyedbythefullclauseprecedingletalone.Theback- groundentailment(whatKarttunenandPeters(1979)wouldcallaconventionalim- plicature, Bach (1999) a background entailment, or Horn (2002) an assertorically- inert entailment) expresses a scalar ordering between the constituent immediately following let alone, which I will call the REMNANT, and the parallel constituent in theclauseprecedingletalone,whichIwillcallthe CORRELATE. The precise scale involved depends on the context, as it varies with the as- signment function that values S, a free variable over scales. In an out-of-the-blue context, the default is a scale of mountains ordered by height or climbing difficult. But this can change: imagine that Oswald is the member of a climbing club that ascendsmountainsinalphabeticalorder—firsttheBerkeleyhills,followedproba- bly by a number of other mountains, and then Mt. Everest. In such a scenario, (22) would be felicitous, since the Berkeley hills are again ordered below Mt. Everest (theletterBprecedestheletterE).Reversingtheorderofthecorrelateandremnant inthesamecontextisnotpossible: (23) *Oswaldhasn’tclimbedMt.Everest,letalonetheBerkeleyhills. Theill-formednessof(23)followsfromthesemanticsofletalone.Thebackground entailment comes out false since Mt. Everest is higher on the contextually-salient alphabeticalscaleofmountainsthantheBerkeleyhills. Thereadermighthavetheintuitionthat(22)alsoasserts(24)—or,inother words,thatOswaldhasn’tclimbedMt.Everest.10 (24) climb(mt-everest)(oswald) ¬ At an intuitive level, however, the proposition in (24) seems to follow from the at-issue entailment in (22a): if Oswald hasn’t climbed the Berkeley hills (which are quite short), we can infer that he hasn’t climbed Mt. Everest (which is much taller).Thisinferenceis,ofcourse,notalogicalentailmentsinceitiseasytocome up with countermodels.11 If Oswald is an expert mountaineer from Nepal who has neverbeentoNorthAmerica,thenOswaldwillnothaveclimbedtheBerkeleyhills, though he may very well have ascended Mt. Everest. Nonetheless, the proposition in (24) can be derived as a contextual entailment of the Common Ground after it hasbeenupdatedwiththeat-issueandbackgroundentailmentsin(22).Itthusdoes nothavetobeincludedaspartofletalone’sassertedcontent. The background entailment, when added to the Common Ground, can do morethanjuststateascalarrelationship.Itcantriggerarestrictionofthecontextset to obey the scale, if doing so is relevant to the issue at hand. This follows from the maxim of relevance, which directs the speaker and hearer to make utterances max- imally relevant. When the background entailment in (22b) is added, the speaker and hearer draw on world knowledge, in particular the commonsense fact that, if somebody is not able to climb a very easy mountain, they will not have climbed a 10ThiswastheproposalofFillmoreetal.,whoanalyzeletaloneasassertingtheconjunctionof twopropositions,thefirstofwhich(22a)ismoreinformativethanthesecond(24). 11AsentenceφLOGICALLYENTAILSasentenceψiffψistrueineverymodelinwhichφistrue. 6 LETTING NEGATIVE POLARITY ALONE FOR LET ALONE 735 more difficult one. Since the background entailment states that the Berkeley hills are shorter, and hence easier to climb, than Mt. Everest, the following statement will be included in the Common Ground: if somebody has not climbed the Berke- ley hills, they also have not climbed Mt. Everest. Subsequently, when the at-issue entailment in (22b) is added to the Common Ground, it will entail that Oswald has not climbed Mt. Everest. This type of reasoning crucially makes use of the scalar orderingconveyedbythebackgroundentailment.12 4. Thepragmaticsofletalone With a semantics for let alone in hand, we can now move on to how it is used in actual discourse. As Fillmore et al. observe (pp. 532–533), let alone sentences frequentlyoccurinaparticularcontext,oneinwhichtheprecedingdiscourseraises anissuecorresponding(atanintuitivelevel)totheremnant: (25) You’d have thought your Brian could have found you somewhere a bit more comfortable, interposed Mrs. Harper, seeing her opportunity of in- troducing Brian to his disadvantage, ‘he must know a few folk, it’s not only money that counts...’ and her voice trailed away, as she simulta- neously managed to imply that Brian had the Town Hall in the palm of his hand, and that he had enough money to buy his father a comfortable bungalow in a nice suburb whenever he felt like it. Shirley watched Fred return Mrs. Harper’s grease-smeared, red-nosed gaze: affable, broad, pa- tient,hestaredather,andwipedhismouthonhistablenapkin.Shecould see his decision not to bother to try to explain that Brian hardly knew anybodyinNorthamTownHall,andthatBrian’ssalaryasHeadofHu- manitiesatanAdultEducationCollegehardlyrosetopayinghisown mortgage,letalonetobuyingahouseforhisageingfather.(FB01086) 12Whenthescaleinvolvedisorderedbylogicalentailment,asin(i),noneofthisisnecessary. (i) Oswaldhasn’tclimbedonemountain,letaloneten. a. At-issueentailment: one(mountain)(λx[climb(x)(oswald)]) ¬ b. Backgroundentailment:one(mountain)<S ten(mountain) Givenalower-bounding‘atleast’meaningforthecardinalquantificationaldeterminer,theat-issue entailment is going to entail any parallel statement containing a number higher than one: e.g. ten(mountain)(λx[climb(x)(oswald)]). Again, we can see the effect of the background entail- ¬ mentbyreversingtheorderofthecorrelateandremnant,whichmakesthesentenceill-formed: (ii) *Oswaldhasn’tclimbedtenmountains,letaloneone. Pragmaticscales,likethescaleofmountains,andlogicalentailmentscalescanbeunifiedformally, asshownbyHirschberg(1985),bytreatingthemaspartiallyorderedsets(asetorderedbyarelation that is transitive, reflexive, and antisymmetric). This relation can either be logical entailment or a context-specificrelation. 7 736 Maziar Toosarvandani The context the let alone sentence occurs in here is a discussion about whether Brianhasthemoneytobuyahouseforhisagingfather,anissuethatwasraisedby Mrs.Harper’scomment. This discourse can be modeled formally in Roberts’ (1996) question under discussion(QUD)framework,inwhichtheinformationinadiscourseisstructured byaQUD STACK—asetofquestionsorderedbytheirrelativeinformativeness.The QUD stack for the discourse in (25), just before the let alone sentence is proffered, lookslike(26). (26) Q1:WhatdoesBrian’ssalaryriseto? Q1a:DoesBrian’ssalaryrisetobuyingahouseforhisagingfather? The IMMEDIATE QUD, the topmost question on the QUD stack, is the polar ques- tionQ1a,whichaskswhetherBrian’ssalaryisenoughtobuyahouseforhisfather. There is a higher superquestion, the wh-question Q1, that is partially answered by ananswertooneofitspolarsubquestions. Looking now at the at-issue entailment of the let alone sentence in (25) — that Brian can hardly pay his own mortgage — it does not (directly) address the immediate QUD. Instead, it is the answer to another polar question, Q1b: Does Brian’s salary rise to paying his own mortgage? When the let alone sentence is asserted,Q1bwillbeaddedtothetopoftheQUDstack.13 Butthisnewimmediate QUDisnotcompletelyunrelatedtoQ1a.Becauseofthescalarrelationshipbetween thecorrelateandtheremnantconveyedbythebackgroundentailment—Brianmust payhisownmortgagebeforehecanbuyhisfatherahouse—answeringQ1binthe negativealsoanswersQ1binthenegative. It is also possible for the QUD corresponding to the at-issue entailment to havealreadybeenraisedexplicitly.14Consider,forinstance,thefollowingexample: (27) SeveralcommentatorshaveclaimedthatonthisexpeditionGould’sparty was the first ever to reach the great western bend of the Murray overland fromAdelaide.ButwecannotbecertainthatGouldevengotasfarasthe river at all. He himself says he ‘spent five weeks entirely in the bush in the interior, partly on the ranges and partly on the belts of the Murray.’ Although he had a magnificent view from the top of the Mount Lofty range of the Murray River, winding its course across the flats through a belt of dense dwarf eucalypti, there is no mention of his ever having 13Ihavesofarignoredtherolethatfocusplaysinthesemanticsandpragmaticsofletalone.There arepitchaccentslocatedonboththecorrelateandremnant(whichInotatewithcapitalization):e.g. Oswald hasn’t climbed the Berkeley HILLS, let alone Mt. EVerest. In Roberts’s QUD framework, focushelpstostructurethediscoursebypresupposingthattheimmediateQUDiscongruenttothe sentencecontainingthefocus.Thus,sincethepolarquestioncorrespondingtothefocussedcorrelate in(25)—namely,DoesBrian’ssalaryrisetopayinghisownmortgage?—hasnotbeenexplicitly mentioned,inordertosatisfythepresuppositionoffocus,itisaddedtothetopoftheQUDstack. 14Fillmoreetal.propose(pp.532–533)thatletaloneisaconstructionthatrequirestheimmediate QUD to correspond to the remnant (rephrasing their analysis in QUD terminology). The fact that it is possible for the QUD answered by the at-issue entailment to already be topmost on the QUD stacksuggeststhatthisistoostrongarequirement. 8 LETTING NEGATIVE POLARITY ALONE FOR LET ALONE 737 reached its banks, let alone the remote western bend 100 miles away. (HRB1133) Atthebeginningoftheparagraph,theauthorintroducestheissueofhowfarGould and his party got towards the western bend of the Murray River, and then goes on to discuss whether they even reached the banks of the river (presumably, they would have followed the river to their destination). Thus, by the time the let alone sentence is used, the at-issue entailment — that there is no mention of Gould’s having reached the banks of the Murray river — corresponds to the immediate QUD: (28) Q1:WhatdidGouldreach? Q1a:DidGouldreachthewesternbendoftheMurrayRiver? Q1b:DidGouldreachthebanksoftheMurrayRiver? Again, while the at-issue entailment only directly answers Q1b, because of the scalar relationship between the correlate and remnant — the banks of the Mur- rayRiverprecedethewesternbendinthepathGouldistraveling—italsoanswers Q1a: if Gould didn’t reach the banks of the Murray River, then he didn’t get to its westernbend. In sum, because the background entailment conveys a scalar relationship between the correlate and remnant, the overall effect of a let alone sentence will be, for a given wh-superquestion, to entail answers to more than one of its polar subquestions. In contrast, the simple sentence in (29) places a much more limited requirementonitsdiscoursecontext. (29) Oswaldhasn’tclimbedtheBerkeleyhills. Itonlyanswersthecorrespondingpolarquestion,HasOswaldclimbedtheBerkeley hills? 5. Puttingtogetherthepieces Thepiecesweneedtoderiveletalone’sdistributionindownwardentailingenviron- ments are now in place. Recall that, in the downward entailing examples of §§3–4, the at-issue entailment of Oswald hasn’t climbed the Berkeley hills, let alone Mt. Everestgivesrisetocontextualentailmentsbasedonthescalarrelationshipbetween thecorrelateandremnantexpressedbythebackgroundentailment.Thisisbecause inferencesreversewhenthescaletheyarebasedonoccursinthescopeofnegation —or,moregenerally,inadownwardentailingenvironment(Ducrot1973,Faucon- nier 1975). Thus, in an appropriate context, the statement Oswald didn’t climb the Berkeley hills (the at-issue entailment) implies Oswald didn’t climb Mt. Everest, becausetheBerkeleyhillsarelower onthescaleofmountainsthanMt.Everest. In an upward entailing environment, however, the direction of entailment follows the direction of the scale. Consider the infelicitous let alone sentence in (30),repeatedfrom(2),whichconveysthepairofentailmentsin(31). 9 738 Maziar Toosarvandani (30) Q: What(mountains)hasOswaldclimbed? A: #OswaldhasclimbedtheBerkeleyhills,letaloneMt.Everest. (31) a. At-issueentailment:climb(the-berkeley-hills)(oswald) b. Backgroundentailment:the-berkeley-hills< mt-everest S The background entailment here, as in the downward entailing case, states that the Berkeley hills are lower than Mt. Everest; but the at-issue entailment is different. (31a) states that Oswald did climb the Berkeley hills. Since the Berkeley hills is the lower member of a scale in an upward entailing environment, it does not give risetoanyfurtherinferences.(Instead,itisthestatementcontainingahigherscalar member, Oswald has climbed Mt. Everest, that implies the statement containing a lowermember,OswaldhasclimbedtheBerkeleyhills.)Asaresult,thecontribution of the let alone sentence in (30) towards answering the QUD is equivalent to the simplesentencein(32). (32) Q: What(mountains)hasOswaldclimbed? A: OswaldhasclimbedtheBerkeleyhills. The answer in (32) also conveys that Oswald has climbed the Berkeley hills, but withouttheadditionalbackgroundentailment. Theadditionalcontentofaletalonesentence,whencomparedwiththecor- responding plain sentence in (32), must serve some sort of conversational purpose —thebackgroundentailmentmustberelevantsomehow—orelseitwillbetooin- formative. This would violate the maxim of quantity, which enjoins conversational participantstomaketheircontributionsasinformativeasrequiredbutnomorethan that(Grice1975:45).15 ItshouldnowbeapparentwhyIhavemarkedtheanswerin (30)witha#.Insuchanupwardentailingenvironment,thebackgroundentailment does not serve any conversational purpose, since it cannot license any additional contextualentailments.Theletalonesentenceof(30)thusendsupbeingpragmati- callyinfelicitousbecauseitviolatesthemaximofquantity.(Fromnowon,Ireserve theasteriskforsyntacticorsemanticill-formedness.) WecancomparethisaccountofletalonetoKadmonandLandman’s(1993) classic scalar analysis of any. Their account, while not making explicit reference to scales, does make use of the effect of negation, and other monotone decreas- ing functions, on patterns of inference. The two ingredients of their analysis are a widenedmeaningforany(33)andastrengtheningrequirement(34). (33) Meaningofany In an NP of the form any CN, any widens the interpretation of the com- monnounphrase(CN)alongacontextualdimension. (KadmonandLandman1993:361) 15AsHorn(2001:195)discusses,themaximofrelevanceisessentiallybuiltintoGrice’ssecond maxim of quantity: ‘Do not make your contribution more informative than is required.’ A given utteranceisthusoverinformativewhenitisnotrelevanttotheissueathand. 10