INTENSIFICATIONANDATTENUATIONACROSSCATEGORIESByCurtisAndersonADISSERTATIONSubmittedtoMichiganStateUniversityinpartialoftherequirementsforthedegreeofLinguisticsŒDoctorofPhilosophy2016ABSTRACTINTENSIFICATIONANDATTENUATIONACROSSCATEGORIESByCurtisAndersonThisdissertationexaminesthesyntaxandsemanticsofandattenuationinEnglishthroughfourcasesstudies.Thesecasestudiesprovideawayofaddressingtwoquestionsonthenatureofandattenuation.First,whatcomponentscanandattenuationbedecomposedinto,andarethesecomponentssharedacrossvariousconstructions?Second,caninstancesofandattenuationbeunderonetheoreticalframework,orareandattenuationbroadtermsfordisparatephenomena?Chapter2focusesonthesortaandkinda.Thesemareofinterestduetotheircross-categorialnature,beingabletomodifynounphrases,verbphrases,andadjectivephrases.Whencomposedwithagradablecategory,suchasagradableadjective(e.g.,sortatall),thesedegreewordsweakenentailmentstothestandard.Whenusedwithanon-gradablecategory(e.g.,sortaswim),theyweakentheconditionswhenthenon-gradablecategorycanbeused,allowingittobeusedimprecisely.IadapttheframeworkinMorzycki2011,supposingthatnaturallanguageexpressionshavexibledenotationscorrespondingtopragmatichalos,inthesenseofLasersohn(1999).Thesehalosarelinkedtoadegreeofprecisionontheinterpretationfunction.Typeshiftingmechanismsallowthisdegreeofprecisiontobeaccessedthroughgrammaticalmeanings,coercingpredicatesfrombeingnon-gradableintogradable,withthedegreeofprecisionprovidingthescalealongwhichtogradethepredicate.Theanalysisofsortainchapter2isextendedtoveryinchapter3.Canonically,whenveryisusedwithagradableadjective,itassertsthattheadjectiveholdstoahighdegree.However,thereexistothercaseswhereveryisusedwithanominal,suchasintheverycenteroftheEarthandIspokewiththisveryperson,aswellaswithordinals(theverystpersoninline).Iarguethattheseareimprecision-relatedusesofvery,andthat,likewithsorta/kinda,animplicittypeshiftisusedtoconvertthesenounphraseintopredicatesthataregradedbytheirdegreeofprecision.Inkeepingwithitsuseintheadjectivaldomain,veryalsoassertsthatthesepredicatesaretoholdtoahighdegreeŠinthiscase,ahighdegreeofprecision.Inchapter4,Iexaminetheuseofsomeasanumeral,asintwenty-somepeoplewereattheparty.Thesecasescommitthespeakertoignoranceaboutwhichparticularnumbersaaclaim.Moreover,theseexampleshavebothalowerbound,comingfromthenumeralandanupperboundduetothesyntaxofthenumeral.Ibuildasyntaxfortheseconstructions,andadaptAlonso-Ovalle&Menéndez-Benito's2010analysisofalgúninordertoshowhowtheignoranceeffectisderivedfrompresuppositionsonsome.Finally,chapter5focusesonsomeinatypeofexclamativeconstructionusingthedeterminersome.TheseareexamplessuchasJohnissomelawyer!.Ishowthatthesesome-exclamativesareconstrainedinthatthenounphrasethatsomecombineswithmustbeabletobeconstruedsothatsubkindscanbeassociatedwithit.Inanalyzingtheseexclamatives,Iadoptaquestion-theoryofexclamativesinthestyleofZanuttini&Portner(2003),whereexclamativesunderlyinglymakeuseofanalternativesemanticsinthestyleofHamblin1973.Theexistenceofexclamativesbeingbuiltfromansuchassomeprovidesadditionalsupportforexclamativesmoregenerallybeinganalternative-sensitiveconstruction.Thesecasestudiesshedlightonvariouscomponentsthatunderlyandattenuation.First,chapters2and3showhowimprecisionandslackregulationcanbemodeledusingadegreesemantics,aswellasaspecialtypeshiftingmechanismthattransformsnon-gradablepredicatesintogradablepredicatesbygradingthembasedonprecision.Chapter4showshowpropertiesoftheepistemicdeterminersomeareusedingeneratingignoranceeffectswithnumeralsandbuildingapproximatemeanings.Finally,chapter5showshowspeakersexclaimaboutkindsandsubkinds,andhowexclamativeconstructionsdependonalternative-generatingconstituents(whethertheyarequestionsorThevarietyofanalyticaltoolsusedsuggeststhatandattenuationarenotprimitivetheoreticalnotionsandshouldnotbeCopyrightbyCURTISANDERSON2016Tomyfriends,family,andAi.vACKNOWLEDGEMENTSOneofmyfavoritethingstodowhilereadingdissertationsistoreadtheacknowledgementssection.Whilewritingmyowndissertationtheselastfewmonths,onebriefnoteinanotherdissertation'sacknowledgementsectionhasstoodoutinmymind:thatalthoughcircumstancesforcedthatauthor'sdissertationtobecompleted,thatitshouldnotbetakentoimplythattheauthorregardsitasawork.IhavesimilarthoughtsregardingwhatIwritehere,inthatalthoughit'stimeformetomydoctoralstudies,Idon'tconsiderwhatIwriteheretobetheword,butjustmyturninalongconversation.MichiganStateUniversityhasbeenawonderfulplacetohavemanyotherlongconversationsaboutlinguistics,andIameternallythankfulfortheadmissionscommitteeseeingsomethinginmyapplicationallthoseyearsago.Icamefromanundergradbackgroundthatdidn'tincludeanylinguistics,andIamgratefulforhavingthechancetoworkwithsuchgreatlinguists.Inparticular,IwanttothankthefacultyIspentthemostamountoftimewith,myguidancecommittee.MarcinMorzyckihasbeenanexceptionalmentor,andhasmemorethananyoneelseindevelopinganintellectualstyleandtasteinproblems;IalwaysfoundIcoulddiscussallsortsofoddsemanticfactswithhim,andhewouldhappilyfollowmedownblindanalyticalleysbeforegentlyguidingmetowardstestablehypotheses.CristinaSchmittandAlanMunnhavealsohadalargeinhowIthinkaboutlanguage,alwaysaskingmetoconsiderfurtheraboutwhatitwouldmeanforourlinguisticfacultytolookinaparticularway.Moreover,althoughthisdissertationdoesn'tobviouslyit,thetimeIspentintheirchildlanguageacquisitionlabhasalsobeenincrediblyformativeinhowIthinkaboutlinguistictheory,thementalrepresentationsthatchildrenandadultsmusthave,andhowlinguisticsrelatestootherareasofcognitivescience.Finally,AlanBerettahasbeeninhowIthinkaboutlanguageaswell,particularlyinourlongdiscussionsinhisneurolinguisticslababoutChomsky.I'mparticularlythankfulforhavingthechancetothinkcloselywithhim(andothercoauthors)abouttherelationshipbetweenourtheoriesviandwhatwecanobserveaboutbrains.Andofcourse,myfamily(allforty-orofthem)deservethanks,too,forbeingsupportiveofmewhileI'vebeeninschoolalltheseyears.Iespeciallythankmymomanddad,mygrandparents,Quinn,Kim,theirsassylittlecorgiBambi,andalsoIan,Kristen,CaylaandDavid.IalsothankmyoldfriendsJackandKelly,andKurtandEbru(whowouldhaveimaginedwe'dlivesoclosetooneanother!).IalsowanttoparticularlythankAiT.,Greg,Jason,Kali,AndrewM.,Jessica,Steve,Hannah,Damien,Joe,Mina,Karthik,andTuulifortheirfriendship.Withoutthem,livinginEastLansingwouldhavebeenmuchmuchmuchlessenjoyable.AdditionalthanksgoestothemembersoftheMSUsemanticsgroup(fiAwkwardTimeflŠIcalleditthat,Marcin!),theMSULanguageAcquisitionLab,andalsothelinguisticsEEGlab.Ialsocouldn'thavedonethiswithoutthehelpofJenniferNelson,PeteHavlatka,andLoganO`Neil,whowerealwaystheretoguidemethroughtheMSUbureaucracy.Thiswouldhaveneverbeenpossibleintheplace,too,withoutmyundergraduatementors.Inthisrespect,PaulAlbee,JohnMeixner,DaleHartkemeyer,andSonyaSheffertdeserveparticularmention.AdamGobeski,JoshHerrin,CaraFeldscher,andAiTaniguchideserveaspecialthanksforreadingthisdissertationandpointingoutvariousplaceswhereitcouldbeimproved.I'vetriedtoworkinasmanyoftheirsuggestionsaspossible,andthisworkismuchbetterbecauseoftheirdiligence.Aideservesspecialthanksforherextensivecommentsonnearlyeverysinglepage,andCaraandJoshdeserveaheartylaughfortheirfipublisherreviewsflafterreadinganearlydraft.AsI'vebecomepartoftheI'vesemantics,I'vebeenhappytothatthesemanticscommunityisquitegenerallysupportiveandfriendly.Theworkinthisdissertationhasbeenmuchimprovedbyconversationswithmanypeople,andinparticularinteractionswithChrisKennedy,NickFleischer,BernhardSchwarz,LauraWagner,AnaTeresaPérez-Leroux,KyleRawlins,ErinZaroukian,EzraKeshet,HeatherTaylor,LisaLevinson,andAnne-MichelleTessierhavebeenthought-provoking.Theaudiencesatvariousvenueswherebitsandpiecesofthisdissertationhaveviibeenpresentedwerealsohelpful.TheseincludeSALT23,SinnundBedeutung19,the19thPennLinguisticsConference,theWesternConferenceonLinguisticsin2013,ConSOLEXXI,SWAMP2015,andthe2016LinguisticSocietyofAmericaAnnualMeeting.Andmostimportantly,IhavetothankAiTaniguchiforherloveandsupport.ShecarefullylistenedwhileIworkedoutsolutions,calledoutmybadideas,andpushedmetogoonwhenIwantedtocallitquits.Thiswouldneverhavebeencompletedwithouther,andIhopeIcanbeassupportiveofherwhenthetimecomes.viiiTABLEOFCONTENTSLISTOFFIGURES......................................xiiCHAPTER1INTRODUCTION11.1Gradabilityininterpretation..............................11.2.....................................21.2.1Gradabilityand..........................21.2.2Exclamatives.................................31.2.3Increasedprecision..............................31.3Attenuation......................................41.3.1Approximationandslackregulation.....................41.3.2Epistemic.............................51.4Thisdissertation....................................61.4.1Theconnectionbetweenandattenuation...........61.4.2Imprecision..................................61.4.3Approximationandsome...........................81.4.4Exclamatives.................................91.5Decompositionand............................101.6Co-optingmechanisms................................121.7Structureofthedissertation..............................13CHAPTER2SLACKREGULATIONUSINGSORTA142.1Introduction......................................142.2Sortawithgradableandnon-gradablepredicates...................152.2.1Sortaandadjectives..............................152.2.2Sortaandothernon-gradablepredicates...................172.2.3Sortacanaffectnouns............................192.2.4Sortaisnotalmost..............................212.2.5Summary...................................222.3Pragmatichalosandalternativesemantics......................232.3.1Halos.....................................232.3.2Analternatives-basedimplementation....................242.3.3Imprecisionorvagueness?..........................272.4Analysis........................................302.4.1Prelude....................................302.4.2Sortaandgradablepredicates.........................322.4.3Sortaandnon-gradablepredicates......................342.4.4Context-dependenceandsorta........................372.4.5Revisitinggradablepredicates........................392.4.6PRECandalternativeformulationsofsorta..................402.4.6.1Muchworries............................40ix2.4.6.2PRECinsorta?...........................432.4.7Hedgingobjects................................462.5Discussion.......................................482.5.1Ontheconnectionbetweensortaandotherapproximators.........482.5.2Modulatingstandards.............................522.5.3Whatissimilarity?..............................532.5.4Lingeringissuesandspeculation.......................572.6Conclusion......................................60CHAPTER3EXTENDINGTHESLACKREGULATINGANALYSISWITHVERY623.1Non-canonicalwithvery........................623.2Twokindsofapproachestovery...........................653.2.0.1Kleinianapproaches........................653.2.0.2Veryindegree-basedapproaches..................663.3Theslackregulationmechanism...........................673.4Analysis........................................683.4.1Veryasaslackregulator...........................683.4.2andnominalswithinherentlyscalarmeanings........703.4.3Demonstrativesandvery...........................723.4.4Precisionandothernominals.........................773.4.5Veryandordinals...............................783.5Otherformulationsofthesyntaxandsemantics...................803.6Conclusion......................................83CHAPTER4NUMERALSANDSOME844.1Introduction......................................844.2NumSomeasanepistemic.........................864.3Representingcardinalnumbers............................894.3.1Hurford(1975)'sanalysisofnumerals....................894.3.2Ionin&Matushansky(2006)'sanalysisofnumerals.............934.4Myproposal......................................974.4.1Simplecardinalnumbers...........................974.4.2Complexcardinalnumbers..........................1004.5Analysis........................................1024.5.1SyntaxandsemanticsofNumSome.....................1024.5.2PragmaticsofNumSome...........................1084.6Constraintsonnumerals................................1104.6.1ADDanditspresuppositions.........................1114.6.2Hurford'sPackingStrategy,appliedtoNumSome..............1144.7Conclusion......................................117CHAPTER5SOME-EXCLAMATIVES1185.1Introduction......................................1185.1.1Basicdata...................................1185.1.2Aretheyreallyexclamatives?.........................119x5.2Theoriesofexclamatives...............................1215.2.1Questiontheoriesofexclamatives......................1215.2.2Degreetheoriesofexclamatives.......................1235.3Some-exclamativesmakereferencetokinds.....................1255.4KindswithintheDP..................................1275.4.1Zamparelli'slayeredDP...........................1275.4.2Kindargumentsincommonnouns......................1285.4.3Types,tokens,andNumP...........................1305.4.4Weir(2012)'sanalysisofsome........................1315.5Alternativesand..............................1335.6Derivingtheexclamative...............................1345.6.1Someandkinds................................1345.6.2Semanticsofsome..............................1375.6.3Buildingtheexclamative...........................1415.7Apuzzle:frontingofthesome-DPandpejorativity...............1435.8Conclusion......................................145CHAPTER6CONCLUSION1466.1Afewremarks.....................................1466.2PREC:typeshiftorfunctionalhead?..........................1466.3Decompositionofandattenuation...................1506.4On.....................................153BIBLIOGRAPHY156xiLISTOFFIGURESFigure3.1Diagramofaconcert...............................63Figure3.2DiagramoftheinterioroftheEarth........................64xiiCHAPTER1INTRODUCTION1.1GradabilityininterpretationInteachingsemanticsattheintroductorylevel,thesentencesthatareusedareoftenfairlyunin-terestingsentenceswithrelativelycrisptruthconditions,suchasJohnateanapple(truejustincaseJohnateanapple)orMaryisfemale(truejustincaseMaryisinthesetoffemales).Lurkingaroundthecorner,andcarefullyhiddenfromstudents(atleastforalittlewhile),arethesentenceswhereitislessclearastohowtostatetheirtruthconditions,sentenceslikeJohnisverytallandItisabout3pm.Whatdoesitmeantobeverytall,whenbothShaqandtheEmpireStateBuildingareverytall?Howisabout3pmdifferentfrom3pmŠisitabout3pmifit's2:57?Thesekindsofsentencesshowhowsentencescannotonlyhavetruthconditionsthatappearquiteve,butalsotruthconditionsthatarevagueinparticularways.But,makingreferencetohowthosesentencesarevaguestilldoesnotcapturethesensesassociatedwiththem.Whenconsideringverytall,forinstance,wehavenotonlythesensethatverytallishardtopindown,thatitisvague,butthatitisalsomuchstrongertocallsomeoneverytallcomparedtotall.And,ontheothersideofthis,whenthinkingaboutabout3pm,wehavethesensethatabout3pmisaweakerstatementaboutthetimeofdaythat3pm.Thisdissertationisabouttheintuitionthatcertainlexicalitemsstrengthenorweakentheforceofanutterance,thatsomelexicalitemsareandothersareattenuators.Assigninglabelstoparticularlinguisticformsandconstructionsisnotatheory,though,ofcourse.Inthisdissertation,whatIamattemptingtodoisbetterunderstandparticularcasesofandattenuationacrossvariouslinguisticcategories.Byunderstandingtheseparticularcasesofandattenuation,wecanlearnmoreabouthowthesemanifestinnaturallanguagemoregenerally.Inthenextsections,Iprovidesomeadditionalexamplesofintensandattenuationin1English.Theexamplesprovidedrepresentcategoriesofphenomenawheretheybroadlyintothepictureofeitherintensifyingorattenuatingmeaning.1.21.2.1GradabilityandCertainlinguisticexpressionsaregradable,inthattheydonotsimplyholdornotholdofanindividual,butthattheycanholdtodegrees.Thecanonicalexamplesofthisinmanynaturallanguagesaregradableadjectivessuchastall.Asexampleslikethosein(1)and(2)show,anadjectivesuchastallnotonlyholdsofanindividualsimpliciter,butthattwoindividualscanbecomparedbytheirdegreeofheight.(1)Johnistall.(2)JohnistallerthanMary.Gradableexpressionscanoftenbeusingcertainlikeveryandquite,too.Whenthesecombinewithagradablepredicateliketall,theinterpretationisthattallnotonlyholdsofthesubject,butalsothatthedegreeoftallnessisquitehighonthescaleoftallness.(3)Johnisquite/verytall.Thesekindsofexampleshavebeenimportantinthestudyofgradabilityandvaguenessduetothesensethatthegradabilityisarisingfromtheadjectiveitself.Whenweclaimthatsomeoneisverytall,veryisintensifyingalongascalethatisbuiltintotheadjective.InunderstandingthisfactisimportantinthatsuggeststhatsomecategoriesinnaturallanguagecanbeinherentlyBut,thequestionthisraisesiswhatcategoriesallowforthisinherentandwhatarethegrammaticalmeansforaccomplishingthis?21.2.2ExclamativesExclamativesprovideanotherenvironmentwhereisexhibited.Examplesofexclama-tivesincludewh-exclamativesin(4),wherethefeatureistheuseofawh-word,aswellasnominalexclamativeslikethosein(5).(4)a.WhatdeliciouspiesJohnbaked!b.Whatabigcrowditwas!(5)a.Thethingsheeats!b.Thestrangethingshesays!Exclamativesprovideforanotherclearcaseofinthatthenaturalinterpretationforthemisonewheretheexclamativeisexclaimingaboutahighdegreeofsomeproperty.Forinstance,(4a)naturallyexclaimsthatthepiesthatJohnbakesarequitehighonascaleofdeliciousness.Inordertobetterunderstandasaphenomenon,exclamativesareausefulareaofinquiry.1.2.3IncreasedprecisionLasersohn(1999)notesthatlinguisticexpressionsoftenallowforanamountofimprecisionorpragmaticslacktobeaffordedtothem.Forinstance,asentencesuchasthatin(8a)allowsforafewexceptionsinanormaldiscourse(e.g.,we'refreetooverlookacouplenightowlsinthetown),andsimilarlyfor(8b),whichallowsJohntonothavearrivedatprecisely3pm.(6)a.Thetownspeopleareasleep.b.Johnarrivedat3pm.However,certainwordsandphrasesreduceourtoleranceforloosetalk.Anexampleofthisisasin(9a),wheretheuseofallallowsforfewerorevennoexceptionstotheclaimthatthetownspeopleareasleep.And,in(9b),theuseofpreciselymakesusbemuchmoreexactlyabouttheprecisetimethatJohnarrived.3(7)a.Allthetownspeopleareasleep.b.Johnarrivedatprecisely3pm.Caseslikethisprovideanotherkindofcasewherenaturallanguageallowsspeakerstointensifythemeaningofalinguisticexpression.However,thewaythatthisoperatesisintuitivelyquitedifferentthanhowthewecaninverytallworks;whereverytallgradesoverascalethatisinherenttotheexpression(e.g.,thetallnessscalecontributedbytall),increasesofprecisiondonotoperateonascaleinherenttotheexpressionbeingPrecisely3pmisnotsomehowmore3pmthanabout3pmoreven3pm,whateverthatwouldmean,butitisaboutthechoiceofwordsuseditself.Thescaleofprecisionisascalethatisabouttheaptnessofparticularwordsincontext.1.3Attenuation1.3.1ApproximationandslackregulationSection1.2.3noteshowimprecisionandslackregulationcanbeviewedasaformofinsomesituations,wheretheslackregulatinglexicaliteminasensethemeaningoftheexpressionbyrequiringittobeinterpretedmorestrictly.However,therearealsocaseswhereslackregulationcangotheotherdirectionaswell,inallowingforinterpretationsthatarelooserratherthanstricter.Forinstance,well-knowncaseswherelooser(ratherthanstricter)meaningsareconstructedcanbefoundinLakoff1973.Lakoffgathersadizzyingarrayofexamplesofhedging(andiinEnglish,withafewexamplesin(8).(8)a.Achickenissortofabird.b.Inamannerofspeaking,abatisabird.c.Looselyspeaking,awhaleisa4Intheseexamples,thespeakerisspeaking`loosely'Šthatis,thespeakerisusinginsuchawaysothepredicationexpressedinthesentencewillbetrue,oratleasttrueenough;thekindofsystemthatLakoffenvisionsisasystemusingfuzzylogic,atypeofmany-valuedlogic(Zadeh,1965).InclassicalBooleanlogic,therearetwotruthvalues,correspondingtotruthorfalsity.Infuzzylogic,truthcomesinacontinuum,asarealnumberbetween0and1.AsshownbyFine(1975);Kamp(1975),though,fuzzylogicisinadequatetoaccountforsomeinferencepatternsinnaturallanguage,leadinglargelytoitsabandonmentinformalsemantics.CasesofthekinddiscussedbyLakoffareofinterestforthisstudyinthattheyarearelativelyclearcaseofattenuatedmeaning.Quiteintuitively,themeaningsin(8)areweakenedinsomeway.ThisraisestheissueofhowattenuationcanoccurintheplaceŠwhatkindoflogicalrepresentationmightweneedtosupportaweakeningofmeaninginthisway?But,thebiggerquestionthatthesecasesraiseiswhattheirconnectiontocasesofincreasedprecisioninsection1.2.3is:arethesetwosidesofthesamecoin,oraretheyreallyquitedifferentintermsoftheirlogicalrepresentation?1.3.2EpistemicEpistemicarethatconveyignoranceonthepartofthespeakerastothepartic-ularreferentofsomenominalexpression.Theyarequiterobustlyattestedcross-linguisticallywithexamplesinEnglish(some),German(irgendein),Spanish(algún),Romanian(vreun),Hungarian(vagy),andJapanese(theWH-kaseriesofpronouns),tonameafew.ToillustratewithanexamplefromEnglish,considersome,whichimplicatesthatthespeakerdoesn'tknowthepreciseidentityofthepersonbeingreferredto.Theexamplesin(9)and(10)belowdemonstratethis.WhilepersonBcannotaskthequestionaboutwhowasshotintheexchangein(9),duetopersonAhavingusedsome,thisisallowedin(10),duetotheabeingcompatiblewithknowledgeonthepartofthespeaker.5(9)A:Somecabinetministerhasbeenshot!B:#Who?(10)A:Acabinetministerhasbeenshot!B:Who?Epistemicsuchassomeprovideanothercasewherelanguageisabletoattenuatemeanings.Here,theattenuationcomesintheformofbeingtoidentifythereferentofthenounphrase,whichisaweakerclaimthanidentifyingthereferent.1.4Thisdissertation1.4.1TheconnectionbetweenandattenuationWhatisnotclearfromtheoverviewintheprevioussectionofdifferentdomainsofandattenuationiswhetherthetwoshouldbetreatedinsimilarsortsofways.Drillingintotheissuefurther,it'salsonotcleartowhatextentthetypesofphenomenonwemightwanttocallcanbeusingonesortofsemanticanalysis.Thisholdslikewiseforattenuation.Inmydissertation,Ilookatandattenuationinthreedomains:imprecision,approximation,andexclamatives.Myanswertothisquestionisthatthereisnothattheexpressionofandattenuationvaryacrosscategories.Withrespecttoimprecision,Ishowhowandattenuationcanbelinkedtogetherthroughadegreesemantics.Forapproximationandexclamatives,however,nodegreesemanticswillbeused.Thephenomenainthesedomains,instead,structuresetsofalternativesinparticularways.Anoverviewofthechaptersisgiveninthenextfewsections.1.4.2ImprecisionInchapters2and3ofthisdissertation,Ilookatimprecisionintwocontexts.Thecontextiswiththesortaandkinda.Thesecanattachtogradableadjectives,asin(11),6whereIarguetheydotheoppositeoftheposmorphemeandquantifyoverdegreesthatarelowerthanthecontextuallysuppliedstandard.Reinforcingtheideathatsortaandkindaaretargetingdegreesthatarepartoftheargumentstructureofthepredicateisthattheycanmodifygradableverbsaswell,asin(11).(11)a.Johnissortatall.b.Thecoffeeiskindahot.(12)Hekindalovesher.Whentheseareusedwithnon-gradableproperties,theyservetoquantifyoverdegreesthatarelowerthanthecontextuallysuppliedstandard.Someonewhoissortatall,forinstance,doesnotquitemeetthestandardfortallness,butmaycomeclosetodoingso.Asthesepredicatesinherentlyprovideforscales(tallness,heat,andlove,respectively),theuseofsortaandkindaintheseexamplesservestoshowhowattenuationcanoccurwithpredicatesthatlexicallyencodescales.However,sortaandkindadonotonlyoperateoverlexicallysscales.Whenusedwithnon-gradablepredicates,suchasintheexamplesin(13),thescalethatisusedisbestcharacterizedasoneofaptnessintheparticularcontext.(13a),forexample,thatitmightnotbecompletelyapttodescribewhathappenedaskickingtheground,andthatsomeconceptuallyclosemeaningshouldbeusedinstead.(13)a.Isortakickedtheground.`Ididsomethinglikekickingtheground.'b.Hesortaswamovertotheboat.`Hedidsomethingthatwaslikeswimmingovertotheboat.'Inchapter2,thewaythatIwillcashthisoutwillbeintermsofprecision.Iadoptamodelwherepragmatichalos(inthesenseofLasersohn(1999))areavailableinthecompositionalsemantics,andthelexicalitemssortaandkindaareusedtoexpandthehaloassociatedwiththeexpressionthey7modify.Thecentralquestioninthechapterishowthesecanactbothasdegreewords(andattenuatealonginherentscales)andalsoasslackregulators(attenuatingthroughexpandingapragmatichalo).ThemodelIbuildusesdegreesinbothcases,butlexicallydegreeargumentsfortheformercaseanddegreescorrespondingtoprecisioninthelatter.Chapter3expandsonthistoincludecasesofusingvery.Canonically,verygradableadjectives,butinsomecasesitseemstomodifyanominalelement.Examplesofthisarein(14),whereveryservestoincreasetheprecisiontowhichtheelementisinterpreted,narrowingapragmatichalo.(14)a.theverycenteroftheEarthb.theveryspotwhereLincolnstoodc.theverybeginningofthelined.theveryfrontattheconcertExpandingthesysteminthiswayshowsthat,atleastinthecaseofandattenuationwhentheyareworkingoverascaleofprecision,theycanbethoughtofinsimilarterms.1.4.3ApproximationandsomeChapter4ofthisdissertationlooksattheuseofsomeasanapproximatorfornumerals.Someexamplesofthisarein(15),wherethenumeralsbysomehavetheglossedinterpretation.(15)a.Thereweretwenty-somepeopleattheparty.`Therewerebetween21and29peopleattheparty.'b.Hisforty-someyearsofexperienceweredevotedtohumanresources.`Hehadbetweenforty-oneandforty-nineyearsofexperienceinhumanresources.'Theseexamplesproveinterestingforthestudyofattenuationinthattheyshowaconnectionbetweenattenuationintwodifferentdomains:thedomainofepistemicandthedomainofapproximatives.WhatIshowinthischapterishowanapproximativeinterpretationcanbe8formedfromtheepistemicsome.Inmyanalysis,somecombineswithacovertnumeral,inordertoessentiallycreateannumeral.Crucialherearetheepistemictepropertiesofsome,whichforcethespeakertonotbeabletocommittoaparticularnumber.Thischaptershowshowattenuationwithrespecttoapproximativescanbegenerated.1.4.4ExclamativesFinally,thisdissertationalsotakesalookatlesser-studiedexclamativesusingthedeterminersomeinchapter5,asintheexamplesin(16).(16)a.Johnissomelawyer!b.Maryissomefriend!Whatmakestheseexclamativesparticularlycuriousistheiruseofsome,whichisknowntobeanepistemicOtherdonotparticipateincreatingexclamativessoeasily,asmightbeshownbythelackofa(n)-exclamativesin(17).Thesestillcannotberescuedbycopyingtheintonationalcontourthat'spresentonthesome-exclamativesin(16).(17)a.#Thisisadeliciousdessert!b.#Maryisalawyer!Clearly,whatiscrucialinbuildingtheexclamativemeaningintheseexamplesispropertiesofthedeterminersomethatmakeitcontrastwitha(n).Inshort,itseemstobeapropertyoftheepistemicnatureofsomethatitcanbeusedtobuildexclamativemeanings.Paradoxically,it'sthenatureofsomeasanattenuatorthatallowsittoalsobeusedasanexclamative.Inchapter5,Iprovideananalysisofsome-exclamativesthatexplainshowthisisso.Someisanalyzedasobligatorilygeneratinganon-singletonsetofpropositions(incontrastwitha(n)),anditwillbethenon-singletonnatureofthethissetthatallowssome-exclamativestobepossible.Thechapteradditionallyarguesforaviewwherekinds(andnotdegrees,contraothertheoriesofexclamativesuchasRett2011)areimplicatedinthemeaningofsome-exclamatives.Thisprovidesacasestudy9inhowcanoccurwithoutdegrees,andhowthegrammaticalmachineryusedinepistemicforattenuationcanalsoplayarolein1.5DecompositionandAsamajortheme,thisdissertationconcernsitselfwithhowandattenuationcanbedecomposed.Inotherwords,whataremorebasicsemanticcomponentsthatgointoconstructingandattenuation?Arethesecomponentsthesameacrossallorarethereawidevarietyofpiecesthatcangointobuildingthem?Thisworksplitsintensandattenuationintovariouscomponents.Onemainfocusherewillbeonhowdegreescanbeusedtointensifyandattenuatemeanings.Degreesprovideforanintuitivewayofrepresentingmeasurementalongsomescale,whereadegreeisanabstractvariablethatencodesanindividual'sparticularmeasurementalongsomescaleofmeasurement(suchasaheightscale).Degreesarequitefamiliarfromthesemanticsofgradableadjectives,wheregradableadjectiveshavebeenarguedtoeitherhavedegreearguments(asverbshaveargumentsforindividuals)(Cresswell,1976;vonStechow,1984;Bierwisch,1989)ortodenotemeasurefunctionsfromindividualstodegrees(Kennedy,1999),aswellasfromworkoncomparativesandsuperlatives.Degreespresentonecomponentthatisusedindependentlyinotherdomainsofthegrammar.Asecondimportantpieceofthedecompositionthatismademoreextensiveuseofinchapter5(andimplicitinthediscussioninchapter4)isalternatives.ThenotionofalternativesisfoundinHamblin's1973analysisofquestions.Althoughastatementdenotesaproposition,it'sclearthatquestionsdonotdenotepropositions,asquestionsdonothavetruthvaluesassociatedwiththem.Hamblininsteadanalyzesquestionsasdenotingsetsofpropositions,propositionsthatcorrespondtopossibleanswerstothequestion.Morerecently,alternativeshavebeenimplicatedinotherdomainsofthegrammaraswell,suchasinthesemanticsof(Kratzer&Shimoyama,2002).ProposalssuchasGutiérrez-Rexach1996andZanuttini&Portner2003alsoargueforanextensiveroleforalternativesinthesemanticsofexclamativeconstructions.10Finally,chapter5usestoolsfromthestudyofkindsinordertoanalyzesome-exclamativessuchasJohnissomelawyer!.Kinds,atleasttoaapproximation,correspondtotheintuitivenotionofagenus,theconceptofcertainindividualsformingaclassofindividuals.Forinstance,potatointhesentencesin(18)referstothekindpotato,andnottoindividualpotatoes.(18)a.ThepotatowascultivatedinSouthAmerica.b.PotatoeswereintroducedintoIrelandbytheendofthe17thcentury.c.TheIrisheconomybecamedependentuponthepotato.(Krifkaetal.,1995)Moregenerally,though,wecantakekindstocorrespondnotjusttonaturalkindssuchaspotato,buttogroupsofindividualsthatsharecertainregularproperties.Nounssuchaslawyerandteacher,forinstance,wouldmakereferencetothesesortsofkinds.Kindscanalsohavesubkindsassociatedwiththemaswell.Therearesubkindsofpotatoes,suchasRussetsandYukongoldpotatoes,aswellassubkindsoflawyerssuchasdivorcelawyersandbankruptcylawyers.Subkindsalsoformkindsinthattheyalsohaveregularpropertiesassociatedwiththem.KindsareindependentlymotivatedaspartofthelinguisticsystembyworksuchasCarlson1977andChierchia1998.1Thesecomponentsareusedtobuildthesemanticsandpragmaticsofandattenua-tionfortheconstructionsexaminedinthisdissertation,althoughnotallconstructionswillmakeuseofallofthesecomponents.Thisraisesquestionsrelatedtothesecondmajorthemeofthisdissertation,namelyhowmuch(orhowlittle)weshouldattempttounifyinstancesofandattenuation.Broadlyspeaking,andattenuationprovideintuitivepre-theoreticalcategoriesforisacategoryofconstructionsdealingwithmakingutterancesstronger,andacategoryofconstructionsdealingwithmakingutterancesweaker.Giventhatwecanplainlyseethattheseexistatthelevelofdescription,wemightaskifallinstancesofandattenuationcanbeTheanswertothisisthatdoesnotseemtobepossibleatthehighestlevels.andattenuationarenotnotions,aswillbeseenlater1AndseeKrifkaetal.1995foranoverview.11on(andasthelistofcomponentsearlierinthischaptermightsuggest),butaresimplybroadtermsforcertaintypesofphenomenon.AlthoughIwillclaimthatisimpossible,broadlyspeaking,decomposingandattenuationasIdohereprovidessupportformorelimitedofcertaindomains.1.6Co-optingmechanismsLastly,anothermajorthemeofthisworkisthecross-categorialnatureofparticularwordsandmorphemes,andhowsomelexicalitemsseemtobeco-optedinordertoexpressmeaningsthattheymightnothaveoriginallybeenintendedtoexpress.Thisisaconceptthatisseparatefromthatofgrammaticalization,theprocesswherebythegrammaticalfunctionofwordsandmorphemeschangesovertime,orwherelexicalitemscanhavetheirsyntaxandsemanticsshiftedinordertocovercertaingrammaticalproperties.Rather,theprocessthatIamdescribinghereisnotonewherethelexicalitemsgrammaticalizeandareusedinanewenvironment,butonewherethelexicalitems,byvirtueofthesortofsyntaxandsemanticstheyalreadyhave,canbeusedinavarietyofgrammaticalroles.Thebestexampleofthisinthisdissertationissome.Asanepistemicsomeisusedtoexpressignoranceastotheparticularidentityofsomeindividual.But,asIshowinlaterchapters,somehasusesthatfalloutsideofitsnormaluseofanepistemicInchapter4,Ishowhowsomecanbeusedtogenerateapproximatemeaningswhenitisusedwithothernumberwords.Althoughtheuseofapproximationwithsomeseemstobeclearlyrelatedtoitsuseasanepistemicinthattheyarebothattenuatedmeaningsandexpresssomeweakenedcommitmentonthepartofthespeaker,itisnototherwisecompletelyobvioushowtoderivetheapproximativemeaningfromtheother.Thechapterarticulatesawayofthinkingaboutthatconnection.Moreover,theuseofsomeinsome-exclamativesinchapter5alsoshowsanotherwayinwhichsomecanbeco-optedinordertoexpressatypeofmeaningitmightnotprimarilybeusedtoexpress.Thekeyconceptualissuewithsomebeingusedinsome-exclamativesisthat,although12somefallsonthesideofbeinganattenuatorwhenusedcanonically,itsuseinsome-exclamativesshowshowitcantakepartinexpressingmeaningsaswell.Inthatchapter,Ishowhowtheattentuationinherenttosomeisimportantinbuildingupthemeaningofsome-exclamatives.Again,thischapterrecallsthethemethat,althoughlinguisticexpressionsmayhavecanonicalusestothem,thegrammarcanborrowexpressionswiththerightlogicalpropertiesinordertousethemtoexpresskindsofmeaningsthattheywouldnototherwiseexpress.1.7StructureofthedissertationTheindividualchaptersofthisworkareasfollows.Chapter2examinesthesyntaxandsemanticsofsortaandkinda,providingaframeworktoshowhowtheycanincreaseimprecisionwhenusedwithnon-gradablepredicates.Chapter3extendsthissameframeworktocaseswhereverycanalsobeusedtoincreaseprecision.Chapter4looksattheuseofwhatIcallNumSome,caseswheresomecanbeusedtomodifynumeralsandimplicateignoranceonthepartofthespeaker.Finally,chapter5examinesanexclamativeconstructionusingsome,showinghowitrelatestoother,morecanonicalexclamatives.Forthemostpart,thesechapterscanbereadsequentiallyorindividually.Readsequentially,thesechaptersprovideasenseofwhatthecomponentsunderlyingandattenuationare,andhowthesenotionsmightbe(ornot).Chapter6expandsonthattheme.However,chapterscanbereadindividuallyaswell,forreadersthatareinterestedinparticulartopicareas.Forreadersinterestedinimprecisionandvagueness,chapters2and3shouldbereadtogether,alongwithsection6.2,whereIhaveadditionalthoughtsonwhetherPRECisatypeshift.Readersinterestedinnumerals,epistemicindorapproximationcanproceedtochapter4withoutanylossofclarity.And,anyreadersinterestedinexclamativeconstructionscanreadchapter5withouthavingreadpreviouschapters.13CHAPTER2SLACKREGULATIONUSINGSORTA2.1Introductionthatattenuatemeanings,suchassorta,kinda,moreorless,andsomewhat(tonameafew)areapervasiveaspectoflanguage,providingalinkbetweensemanticsandpragmatics,withafootanchoredsecurelyineachdomain.Althoughthetargetofearlyforaysintoformalsemantics(Lakoff,1973),hedgeshavebeenstudiedmuchlesscomparedtootherphenomenathatcutacrosssemanticsandpragmatics,suchaspolarityitems(?Fauconnier,1975,andothers).Thischapterpresentsacasestudyonsorta(anditssiblingkinda)withtheintentofmakingclearsomeofitslexicalsemanticproperties.Chiefamongthepropertiesstudiedwillbeitscross-categorialnatureandhowitcanmodifyadjectivesaswellasverbs,asin(1)and(2),respectively,andeveninsomecasesnouns,asin(3).(1)a.It'ssortahardtoexplain.b.alotofyoungpeoplethinktheirparentsarestartingtoseem,youknow,sortaoldandoverthehill...1c.Gasissortaexpensive.2(2)a.ButIcan'tseehowthatDiazjustsortaevaporated,likesomekid'sbaddream.3b....runningonconcreteandaccidentallysortakickedtheground.4(3)a.asortafairytale51CorpusofContemporaryAmericanEnglish(COCA)(Davies,2008)2http://www.tripful.com/q/v/257295/i_want_to_move_to_south_nm_or_az_advice_please3COCA4http://www.kongregate.com/forums/2/topics/97092?page=25ToriAmos,fiASortaFairytale.flEpic/SonyBMG.(songlyrics)14b.ImaybeyoursortamomnowandI'mpracticallyachildmyself.6Alsoofinterestinthisstudywillbethesourceofthegradabilityforvariouspredicates,andwhysortahastheeffectofmakingverbsandnounsconceptuallygradable.Thishasbroaderreachingconsequencesthansimplythelexicalsemanticsofsorta.Iarguethatthereareatleasttwosourcesofgradabilitythatsortadiagnoses:theinherentgradabilityofscalaradjectivessuchastall,butalsocoercedgradabilityderivedfromsetsofalternativesmodelingLasersohnianpragmatichalos.Thishasthefurtherconsequenceofmakingpragmatichalospartofthecompositionalsemantics,amovethatfollows(Morzycki,2011).Thecentralclaimofthechapterwillbethatsortaoperatesasadegreeword,butinconstructionswithoutalexicalizeddegreeargument,atypeshiftoccursthatbestowsadegreeargumentuponanon-gradablepredicate.Theroleofthistypeshiftistobuildanewscalewherenoscaleexistedpreviously.First,anoteonconventions:throughoutthechapter,Iusesortatorefertotheadverbialelementinexamples(1)Œ(3)above.Iwritethiselementassortaratherthansortofinordertoemphasizeitsdifferencefromthenounsort(i.e.,asortofdog).Sortaisoftenreducedinspeech,whichthewritingisalsomeanttobuttheremaybecaseswhereIhavewrittensortabutitisnotreduciblefortypicalAmericanEnglishspeakers.Finally,Itakesortatobeequivalenttokinda(kindof,morestandardlywritten);insofarasIcantell,thereisnosemanticdifferencebetweenthetwo.Somespeakersdopreferkindaoversorta,forseeminglyapparentstylisticreasons,soforexampleswheresortaisused,kindacanbesubstitutedforthosespeakers.2.2Sortawithgradableandnon-gradablepredicates2.2.1SortaandadjectivesSortareadilyappearswithgradableadjectives,andisabletocombinewithadjectivesinthepositiveasin(4),aswellasthecomparativein(5),andconstructionsinvolvingtooandenoughasin6ModernFamily,fiTheFutureDunphys.flABC.(fromaTVshow)15examples(6a)and(6b).Inthisway,sortalookslikeadegreewordlikeveryorslightly,whichcanalsoappearinmanyofthesesameenvironments.(4)a.Billissortatall.b.Gasissortaexpensive.(5)a.She'ssortamoreintelligentthanheis.b.AfterlosingalotofweightIdofeelsortataller.7(6)a.IwouldcrybutI'msortatooangry.8b.Theyaresortaoldenoughtoappreciateit.9Ifsortaisadegreeword,wemightalsoexpectittobeananswertohow-questions,asveryandslightlycan.Example(8)showsthatthisisinfactpossible.(7)a.HowtallisBill?Verytall.b.Howwetisthesponge?Slightlywet.(8)HowtallisyourfriendBill?Sortatall.Thenaturalinterpretationofsortaherealsosuggeststhatitisdegree-related.Forinstance,example(4a)claimsthattheindividualBillfallsalongthetallnessscale,ameaningwhichiscomparabletothesenseofanotherdegreewordlikevery.Theinterpretationalsomakesreferencetoacontextuallystandard;sortoftallintuitivelyassertsthatanindividualholdsadegreeofheightclosetothestandardforbeingtall.Again,thisiscomparabletoadegreewordlikevery,whichassertsthatanindividualholdsaheightfarabovethestandard.However,sortadiffersfromotherdegreewordsinbeingabletocombinewithnon-gradablepredicatesaswell,asin(9).7http://facepunch.com/showthread.php?t=11801658http://firewifeelly.com/2011/02/19/i-would-cry-but-im-sorta-too-angry/9http://westcoastmuthas.com/2013/07/29/are-we-there-yet/16(9)a.I'vebeensortapregnantfourtimes.Beingsortapregnantsortasucks.It'slikeyou'relate,youtestearly,youseetwolines,yougoforabloodtest,you'repregnant,andthenit'sJUSTKIDDING!10b.It'ssad[Chineseriverdolphins]are(sorta)extinct.They'resuchcoolcritters.11What'simportanttonoteisthatsortalosesitsdegreesense.(9a)doesn'tassertadegreealongascaleofpregnancy(becausethereisnoscale),butinvolvesashiftinmeaning,onefromactualpregnancytopassingthetestforpregnancy.Thisshiftinmeaningcanbeaptlyparaphrasedwithanapproximativesuchasclosetoorlike,andtheapproximativeassertingclosenesstothe`normal'meaningoftheword:beingsortapregnantislikebeingpregnantinpassingcertaintestsforpregnancy,whilebeingsortaextinctisbeingveryclosetobeingextinct.Alsosupportingtheideathatsortaisdegree-relatedisthatitparticipatesinformingscaleswithotherdegreewords.Intuitively,sortaistheweakermemberofthescalehsorta;veryi.(10)Heisn'tjustsortatall,he'sverytall.Summarizing,sortahasacleardegreeusewithgradableadjectives,butcanbeusedwithnon-gradableadjectivesaswell.Whenusedwithnon-gradableadjectives,sortapredicatesundergoameaningshifttowardssomethingapproximatingthepredicate.2.2.2Sortaandothernon-gradablepredicatesSortacancombinewithothernon-gradablepredicatesaswell.Chiefamongtheseareverbs,butforsomespeakers,nounsarepossibleaswell.Likecasesinvolvingnon-gradableadjectives,sortawithaverbalsoinvolvesameaningshiftandcanbeparaphrasedwithanapproximative.Theroleofsortahereistoassertsomeconceptualclosenesstowhatisbeing10http://stowedstuff.com/2012/12/sorta-pregnant.html11http://clockworkstamps.deviantart.com/art/Baiji-15176920517(11)a.Isortakickedtheground.`Ididsomethinglikekickingtheground.'b.Hesortaswamovertotheboat.`Hedidsomethingthatwaslikeswimmingovertotheboat.'Theuseofsortawithnounsdiffersfromthenominalsort,asdemonstratedwiththecontrastsin(12)and(13).12Asortoffairytaleisatypeoffairytale,butasortafairytalecanbetakentomeansomethingthatisonlylikeafairytaleinsomerespect.Similarly,althoughaPorscheisasortofcar,itmostisnotasortacar.(12)a.asortoffairytale`atypeoffairytale'b.asortafairytale`almostbutnotafairytale'(13)a.APorscheisasortofcar.b.*APorscheisasortacar.ImportanttopointoutisthatsortaweakenstheentailmentsofwhatitthereisnoentailmentfromsortaVtoV,whereVisaverb.Tryingtoforceacontradictionshowsthatsortaisabletoweakentheentailmentsoftheverbphrase(Bolinger,1972).Thisshowsthattherearesemantic,truth-conditionalconsequencesinvolvedwiththis.(14)a.Heswamovertotheboat.*Thatistosay,hedidn'treallyswim.b.Hesortaswamovertotheboat.Thatistosay,hedidn'treallyswim.(15)a.Hekickedtheball.*Thatistosay,hedidn'treallykickit.b.Hesortakickedtheball.Thatistosay,hedidn'treallykickit.Finally,sortawithnon-gradablepredicateshastheintuitivefeelingofgradability.Constructions12Somespeakershavetroublewithsortaasanoun.18withsortainvolvelocatingtwopredicates(sortaVandV)alongascaleofresemblance,withonepredicateholdingalesserdegreeofresemblancetotheother.Thisisaderivednotionofgradability.Thegradabilityinvolvedherewithnon-gradablepredicatesisn'tinherenttothelexicalitemitself(asitiswithagradablepredicatesuchastall),butratherisexternaltothepredicate.2.2.3SortacanaffectnounsSortaisabletomodifyverbphrasesheadedbymosttypesofverbs.Formanyverbs,thebehaviorofsortamirrorsthebehaviorin(15b)above,wheresortahedgestheverb.Forsomeverbs,however,asecondreadingariseswheresortacanhedgenotjusttheverbbutalsoitsdirectobject.Someverbsthatcandothiseasilyincludesomeintensionaltransitiveverbs(suchaslookfor),aswellascreationverbs(build),depictionverbs(draw,paint),andperformanceverbs(sing).Toillustrate,in(16)below,thesentenceisambiguousbetweentworeadings:onereadingwheretheverbishedged,butalsoonereadingwherethedirectobjectoftheverbishedged.(17)demonstratesthesamephenomenonwithadepictionverb,and(18)withlookfor.(16)Thecarpentersortabuiltabarn.a.Thecarpenterdidsomethingthatwaslikebuildingabarn(e.g.,puttingtogetheraprefabricatedstructure).b.Thecarpenterbuiltsomethinglikeabarn(e.g.,ashed).(17)Theboysortadrewahouse.a.Theboydidsomethinglikedrawingahouse(e.g.,connectedthedotsinapicture).b.Theboydrewsomethingthatwaslikeahouse.(18)I'msortalookingforahorse.a.I'monlyhalf-heartedlylookingforahorse.b.I'mlookingforsomethinglikeahorse.Withmoredifforsomespeakers,otherverbscanallowtheirverbstobehedgedaswell.For19example,(19a)hasareadingwheresomethinglikeacookiewaseaten(say,abiscuit)and(19b)hasareadingwheresomethingsimilartoacarwaspurchased(say,astationwagon,inasituationwherewhatisimportantishavingalotofspaceforhaulingthings).(19)a.Isortaateacookie.b.Hesortaboughtatruck.Indirectobjectscanbetargetedbysortaaswell:inasituationwhereIamtalkingwithwriterfriendsaboutwherethingswehavewrittenarebeingsubmitted,(20)canbefelicitouslyuttered.Andin(21),ifthespeakerischattingwithothersaboutmeetingtheirspousesatparties,theinsidetheprepositionalphraseadjunctcanalsobetargetedbysorta.Generallyspeaking,thecompositionalsystemseemstofreelyallowsortaaccesstonounphrasesinsidetheVP.(20)IsortasubmittedanarticletoamagazineŠexceptitwasn'treallyamagazine,butajournal.(21)Isortametmyspouseataparty,tooŠitwasreallyaconferencedinnerratherthanaparty,butithadaninformalatmosphere.(cf.*Imetmyspouseataparty,tooŠitwasreallyaconferencedinner)Amatterworthonforthispuzzleishowsortacanaffectadirectobjectatall.Givenstandardsyntacticassumptions,sortaandthedirectobjectneverformaconstituent,andinfact,sortadirectlymodifyingaDPisquiteunacceptable(22).(22)a.*Isawsortaabird.b.*Sheatesortaacracker.c.SortaatruckiswhatIamlookingtobuy.Undercommonassumptionsaboutcompositionality,itshouldbeabitofamysteryabouthowsortacanaffecttheinterpretationofanNPwhenitdoesn'tformasyntacticconstituentwithit.202.2.4SortaisnotalmostOurcourseofactionmightbetotreatsortaasjustavariationonalmost,astheybothhaveanapproximativeinterpretationandbotharecross-categorialHowever,thesetwohavedifferentrestrictionsonwhattheycanfelicitouslycombinewith.First,sortaisacceptablewithrelativeadjectives,butalmostismarginalorunacceptablewithrelativeadjectives.Unlikealmost,sortadoesnotseemtobeendpointorientedwhenusedasanadjectival.(23)a.Floydis8><>:sorta??almost9>=>;tall.b.Gasis8><>:sorta*almost9>=>;expensiveontheisland.Furthermore,sortaisgenerallyabletomodifyactivityverbswithoutfurthercontextuallysupport.Almost,bycomparison,isdistinctlyoddwithactivityverbsunlessthereissomeadditionalcontextualinformation(suchasascenariofor(24b)wherepeoplearebeingjudgedonwhethertheysuccessfullyranornot).Althoughtheexamplesin(24b)and(25b)belowaregoodonthereadingwherethepossibilityoftheeventispresupposed(i.e.,thepossibilityofBillrunningistakenforgranted),theyaremuchlessacceptableonasecondreadingwherewhatisassertedisthattheeventcomesclosetobutdoesnotquitemeetthecriteriaforusingtheeventdescriptionwithoutalmostŠe.g,for(24b),thatBilldidsomethinglikebutnotquiterunning.Thiscompareswiththesortaexamplesin(24a)and(25a),whichareacceptable.(24)a.Billsortaran.b.??Billalmostran.(25)a.Floydsortajogged.b.??Floydalmostjogged.Anotherdifferencebetweensortaandalmostisintheirlicitnesswithmeasurephrases.Almostisreadilylicensedinthepresenceofameasurephrase,butsortacannotcombinewithmeasure21phrases.(26)a.Floydis8><>:almost*sorta9>=>;sixfeettall.b.It's8><>:almost*sorta9>=>;30Ctoday.Finally,almostcanbeusedwithDPsheadedbycertaindeterminers(Horn,1972),butsortacannotcombinewiththoseDPs,oranyDPsatall.(27)a.8><>:almost*sorta9>=>;everydogwaspresent.b.8><>:almost*sorta9>=>;nodogwashairy.Tosummarize,althoughsortaandalmostsharethefactthattheybothincorporateanapproxima-tivemeaning,sortaisnotsimplyreducibletoalmost;thereareobvioussyntacticandsemanticdifferencesbetweenthetwo,asdemonstratedbytheirdistributions.2.2.5SummaryTheobservationsintheprevioussectionsbringupseveralpointsthatananalysisofsortamustaccountfor.Thepointregardsthecross-categorialnatureofsorta.Whyisitthatsortacanappearwithwordsandphrasesofseverallexicalcategories(adjectives,nouns,verbs)?Whatwouldsortahavetodoinordertobeusedwithcategoriesthatareoftenthoughttohavedifferentsemantics?Andwithregardstothesemanticsofgradability,howdoessortainducegradabilitywhereitdidnotarisebefore?Iaddressthesequestionsinsection2.4,buttaketimetointroduceusefulbackgroundassumptionsintheupcomingsection.222.3Pragmatichalosandalternativesemantics2.3.1HalosLasersohn(1999)observesthatmanynaturallanguageexpressionscanbeusedlicitlyeveninsituationswheretheywouldbefalse,strictlyspeaking.Forinstance,considertheutterancein(28)below.Undernormalcircumstances,(28)canbeutteredevenifthereareahandfulofnightowlsstillawake.Lasersohnnotesthatthefewpeoplestillawakeatmidnightinthissituationdon'tseemtomatterforthelicitnessof(28);eventhoughit'sfalsethatthetownspeopleareasleep(someofthemareawake,afterall),thesentenceisstillpragmaticallyacceptable.TheconclusiontodrawfromthisisthathearersaffordotherspeakerswhatLasersohncallsfipragmaticslackflŠspeakersareallowedadegreeofsloppinessintheirspeech.Theheareraffordsthespeakerof(28)pragmaticslackinhowthetownspeopleistobeinterpreted;althoughafewpeopleawakeatmidnightdocountsemanticallyforthetruthconditionsof(28),theyarepragmaticallyignorableexceptions.(28)Thetownspeopleareasleep.(utteredatmidnight)Thisisn'tsolelytopluralNPs.Similarbehaviorcanbedemonstratedwithotherthings:withtime(where(29)canbeutteredifit'snotexactly3o'clock);withasuchaseveryone,asinexample(30),evenifafewstudentsaremissing;andwithpredicatessuchassphericalin(31),eventhoughveryfewthingsareperfectlyspherical.Pragmaticslackisaffordedquiteregularly.(29)It's3o'clock.(utteredat2:58pm)(30)Ok,everyoneishere.(utteredbyaprofessoratthestartofclasswhenafewstudentsareabsent)(31)Theearthisspherical.Lasersohnproposesthatcertainlinguisticexpressionshavesurroundingthemafipragmatichalofl23ofpragmaticallyignorabledifferences.3o'clock(forinstance)mighthaveahalothatincludestimesveminutesbeforeandveminutesafter3o'clock.Aslongasthetruthofthematterfallswithinthehalo,theutterancewillbelicit,and(29)islicitbecausethetruetime,2:58pm,iswithinthepragmatichaloof3pm.Similarly,althoughtheEarthmightnotbeaperfectsphere,sphericalisinterpretedimpreciselyenoughsothatnearspheresfallwithinitspragmatichaloandarepragmaticallyignorable.PragmatichaloscanbebywhatLasersohncallsfislackregulators.flTheseworktocontractthesizeofthehaloŠinotherwords,toallowlesspragmaticslackandrequiremoreprecisioninhowastatementisinterpreted.Iftheslackregulatorallisusedasin(32)inasituationwheretownspeopleareknowntobeawake,thesentenceisfalseandrecognizedbyhearersasinfelicitous.Similarlyfortheslackregulatorsexactlyandperfectlyin(33)and(34),respectively,whichshrinkthepragmatichaloandrequiremoreprecisioninhowthetermsareinterpreted.(32)Allthetownspeopleareasleep.(noexceptionsallowed)(33)It'sexactly3o'clock.(cannotbeutteredat2:58pm)(34)Theearthisperfectlyspherical.(recognizedbyhearersasfalse)Themanipulationofpragmatichaloswillformanimportantpartoftheanalysisinlatersections,withsortaanalyzedaswideningahalo.ButIintroduceinthenextsectionanimplementationofLasersohn'sproposalusingHamblinsemantics.2.3.2Analternatives-basedimplementationMorzycki(2011)providesananalysisofmetalinguisticcomparatives(seealsoMcCawley(1998)).Informally,metalinguisticcomparativescomparehowaptorappropriateaparticularexpressionis.Tocharacterize(35a),forexample,what'sbeingcomparedistheaptnessorappropriatenessofcallingGeorgedumborcrazy,andsimilarlyin(35b),what'sbeingcomparedistheappropriatenessofcallingClarenceasyntacticianorsemanticist.24(35)a.Georgeismoredumbthancrazy.b.Clarenceisasyntacticianmorethanasemanticist.Morzyckicashesoutthedescriptivegeneralizationhereintermsofimprecision.What'sbeingcomparedishowpreciseitistocallGeorgedumborcrazy.AdegreeparameterontheinterpretationfunctionJ:Kcapturesthis,wherehigherdegreescorrespondtoincreasedprecision.Iwillcallthistheimprecisionparameterordegreeofimprecision.Ametalinguisticcomparative,then,comparesthedegreeofimprecisionbetweentwoexpressions.Thisisdemonstratedinformallyin(36),wheremax(D)=id[8d0[D(d0)!d0d]].(36)JGeorgeismoredumbthancrazyKd0=(ld:JGeorgeisdumbKd)>max(ld:JGeorgeiscrazyKd)`ThedegreetowhichwecancallGeorgedumbisgreaterthanthedegreetowhichwecancallGeorgecrazy.'MorzyckisuggeststhatimprecisionshouldbethoughtofintermsofLasersohn'spragmatichalos.Halosarerecastintermsofalternatives(Hamblin,1973;Kratzer&Shimoyama,2002).Denotationsthemselvesarewiththeirpragmatichalo,withtheimprecisionparameterdirectlydeter-miningthesizeofthehalo.Thealternativesinthepragmatichaloarebuiltfromaprimitiverelationˇfiresembles,flwhichcomparesthedegreetowhichtwopredicatesofthesametyperesembleeachother.Thisisin(37).(37)aˇd;Cbiff,giventheorderingimposedbythecontextC,aresemblesbto(atleast)thedegreedandaandbareofthesametype(Morzycki,2011).Adenotationfordumbmightlookasin(10):asetoffunctionsoftypehe;tisuchthateachfunctionfresemblesdumbtoatleastdegreed.(11)illustrateshowthevalueoftheimprecisionparameteraffectsthesizeofthepragmatichalo.Highdegreesdecreasethesizeofthehalo,whilethemaximumdegreeforcesthehalotobeasingleton.25(38)JdumbKd;C=ffhe;ti:fˇd;Cdumbg(39)a.JdumbK1;C=fdumbgb.JdumbK:9;C=fdumb;ignorant;dopey;foolish;:::gc.JdumbK0;C=Dhe;tiThelessonisthatwecanthinkofLasersohnianpragmatichalosasexistingnotinapost-compositionalpragmatics,butaspartofthecompositionalsemantics.Byprovidingahookintopragmatichalosthroughtheimprecisionparameterandbymodelinghalosasalternatives,weareabletoprovideacompositionalaccountofhowpragmatichalosinteractwiththerestofthegrammar.InaHamblinizedsystemsuchasthis,it'susefultohaveamodeofcompositionseparatefromFunctionApplication(FA)(Heim&Kratzer,1998)thatcanputsetsoffunctionstogetherwiththeirargumentsŠnamely,it'susefultohaveamodeofcompositionwherewecanactlikewe'reworkingwithfunctions,butinrealitybebuildinguplargersetsofalternatives.Theintuitionbehindthisnewmodeofcompositionistoapplyalltheobjectsfromonesetofalternativestoalltheobjectsfromanothersetofalternativespointwise,creatinganothersetofalternatives.ThisisformalizedasHamblinFunctionApplicationin(40)below.(40)HAMBLINFUNCTIONAPPLICATION(HFA)Ifaisabranchingnodewithdaughtersbandg,andJbKd;CDsandJgKd;CDhs;ti;thenJaKd;C=fc(b):b2JbKd;C^c2JgKd;Cg(Morzycki(2011),basedonKratzer&Shimoyama(2002))Toillustrate,supposeafunctionA,typehe;stiandasetB,typee,asrepresentedwiththesetsofalternativesin(41)below.26(41)A=8>>>><>>>>:lxlw:f(x)(w);lxlw:g(x)(w);lxlw:h(x)(w)9>>>>=>>>>;B=fa;b;cgSincethesearesets,A(B)proceedsviaHFAandnotFA.EachobjectinthesetAisappliedtoeachobjectinB,resultinginthesetCsuchthatC=A(B).Thisisillustratedbelowin(42).(42)C=A(B)=8>>>><>>>>:[lxlw:f(x)(w)](a);[lxlw:f(x)(w)](b);[lxlw:f(x)(w)](c);[lxlw:g(x)(w)](a);[lxlw:g(x)(w)](b);[lxlw:g(x)(w)](c);[lxlw:h(x)(w)](a);[lxlw:h(x)(w)](b);[lxlw:h(x)(w)](c)9>>>>=>>>>;=8>>>><>>>>:lw:f(a)(w);lw:f(b)(w);lw:f(c)(w);lw:g(a)(w);lw:g(b)(w);lw:g(c)(w);lw:h(a)(w);lw:h(b)(w);lw:h(c)(w)9>>>>=>>>>;CistheresultofthepointwisefunctionapplicationoftheelementsfromsetAtosetB.ThisresultsinthealternativesfrombothAandBbeingrepresentedinC.AninterestingpropertyofHFAisthatthesetcreatedbyapplyingthealternativesfromAtoBpointwisehasallthealternativesofbothAandB.Thinkingaboutthissyntactically,ifamothernodeahastwodaughters,bandg,andbisoftherighttypetoapplytogusingHFA,theresultoftheircombination,a,willhavethealternativesofbothbandg.2.3.3Imprecisionorvagueness?Beforestartingtheanalysisofsorta,weshouldthinkaboutwhatkindofgradablemeaningisimplicatedinthemeaningofsorta.Namely,issortatrulyaslackregulatorandworkingwithpragmatichalos,alaLasersohn,orissortaregulatingvaguenessinstead?Comparingtheintuitionswithsortatobothvaguenessandimprecision,wethatsortabehavesinsomewaysmorelikeavaguenessregulatorthanaslackregulator.First,ifsortawerea27slackregulator,wemightexpectittocombinefreelywithothertypesofexpressionswithexactmeanings,suchasnumerals,expressionsoftime,andIndeed,weapproximatorsandslackregulatorsthatdocombinefelicitouslywithexpressionsofthesetypes,butsortadoesnot.(43)a.Almost/approximatelytwentypeoplewereinline.b.*Sortatwentypeoplewereinline.(44)a.Ataround3pmIwilleatlunch.b.*Atsorta3pmIwilleatlunch.(45)a.More-or-lesseverydogkissedacat.b.*Sortaeverydogkissedacat.However,therearewaysthatitbehaveslikeaslackregulatoraswell.Considertheadjectivestriangularandextinct,whichputativelyhaveexactuses.TriangularandextinctarepredicatesthatallowforwhatPinkal(1995)callsnaturalŠcontextsinwhichthepredicatescanbeeasilyforcedtohaveexactinterpretations.(46)Weneedashapewhichistriangular,butthisShapeBwon'tdo,sinceithasasmallbendononeside.(47)Weneedtoaspeciesthatisextinct,butNorthernWhiteRhinoswon'tdo,sincetherearestillveleft.Asshowninthe(b)examplesin(48)and(49),theseadjectivesdonothavegradablesenses.But,asshowninthe(c)examples,bothtriangularandextinctcanbebysorta,whichmightsuggestthatsortadoeshaveaslackregulatingmeaninghere.(48)a.Theseshapesaretriangular.b.??ShapeAismoretriangularthanShapeB.c.ShapeBissortatriangular.28(49)a.Dinosaursareextinct.b.??Dinosaursaremoreextinctthandodobirds.c.NorthernWhiteRhinosaresortaextinct.13Incontrasttopreciseadjectivesliketriangular,trulyvaguepredicatesdonotallowfornatural(50)??Weneedalongrodfortheantenna,butsincelongmeans`greaterthan10meters'andthisoneis1millimetershortof10meters,unfortunatelyitwon'twork.(Kennedy,2007)ExtinctandtriangularalsodonotgiverisetotheSoritesParadox,whereintheSoritesParadoxthetwopremisesP1andP2donotleadtotheconclusionC(premiseP2isrejectedinboth).Thisfactalsosuggeststhattheydonothavevaguemeanings.Incontrast,avaguepredicatesuchastalldoesgiverisetotheparadox.(51)P1:Apersonwhoissixfeettallistall.P2:Apersonwhoisonesixteenthofaninchshorterthanatallpersonistall.C:Therefore,apersonwhoisthreefeettall(ortwofeettall,oronefoottall,etc...)istall.(52)P1:Aspeciesisextinctifithasnolivingmembers.P2:Aspecieswithonemorelivingmemberthananextinctspeciesisextinct.C:Therefore,aspecieswithonehundred(ortwohundred,orathousand,etc...)livingmembersisextinct.(53)P1:Ashapewiththreesidesistriangular.P2:Ashapewithonemoresidethanatriangularshapeistriangular.C:Therefore,ashapewithfoursides(orvesides,orsixsides,etc...)istriangular.Whatthissuggestsisthatsortacannotonlyberegulatingvagueness;theexistenceofusesofsortawithimprecise(ratherthanvague)predicatesmightsuggestthatsortacanbeinvolvedinregulating13Atthetimeofthiswriting,therewereveNorthernWhiteRhinosstillalive.29bothimprecisionandvagueness.WheredoesthisleaveusinadoptingaformalizationsuchasthatofMorzycki(2011)?Evenifsortahasmixedbehaviorintermsofthetypesofmeaningsthatitregulates(imprecisionversusvagueness),Morzycki'sproposalofputtingadegreeofprecisionparameterontheinterpretationfunctionissuitablehereinthatitcapturesafundamentaldifferencebetweendifferenttypesofpredicates:gradabilityisinherentinsomeexpressions(particularlyofteninadjectives),butnotinothers(suchasverbs).Fortheremainderofthechapter,Iwillmakereferencetoafidegreeofprecision,flbutinthecontextofthisdebateitcanbeunderstoodasindifferenceastotheexacttypeofmeaningatwork:vaguenessorgradability.Rather,whatisatstakeissomethingdifferent,namelywhichexpressionsareinherentlygradable(ornot)andhowsortacancombinewiththoseexpressionswhicharenotgradable.2.4Analysis2.4.1PreludeTheintuitionIpursueistoanalyzesortaasadegreeword.Thereasonforthiscomesfromsorta'scross-categorialbehavior,combiningwithgradableandnon-gradableadjectivesaswellasverbsandnouns.Whencombinedwithagradableadjective,thereadingavailableisakintoadegreereading.Withnon-gradableadjectives,verbs,andnouns,thereadingbecomesoneofapproximationtothepredicatebeingThissuggeststhat,atitscore,sortaisdegree-related,buthascoercivepowerswhenusedwithpredicateswithoutagradableinterpretation.Thecoercivepowerhereisaconsequenceofpragmatichalosbeingsetsofalternativesthatresemblesomecorefunction.Theroleofsortaistoincreasethesizeofapragmatichaloinordertobringinmorefunctionsthatapproximatesomeotherfunction.UsingMorzycki'salternativesemanticsforpragmatichalosallowsustokeepadegreesemanticsforsortawithbothnon-gradableandgradablepredicates.Gradablepredicateslexicalizedegreearguments,whichsortacansaturate.Fornon-gradablepredicates,sorta'scombinatorialneedtocombinewithagradablepredicateforcesatypeshift.Theeffectofthistypeshiftistomakenon-gradablepredicatesgradablebyusingtheir30imprecisionparameterasadegreeargument.Inthisway,sortacansaturatethenewdegreeofprecisionargumentofanon-gradablepredicate.Beforebeginningtheanalysis,Ishouldstatemyassumptions.Iassumeanontologywithdegrees,abstractunitsofmeasurement(Kennedy,1999;Seuren,1973;Schwarzschild&Wilkinson,2002;vonStechow,1984).Ialsoassumethatgradableadjectivessuchastalllexicalizedegreeargumentsandarerelationsbetweendegreesandindividuals(asin(55)).Thismovemakesadjectivesbythemselvesincomplete;theyneedtobesaturatedwithadegree.AnullmorphemePOSisassumedtobepresentintheunmarked(absolutive)constructions(Cresswell,1976;vonStechow,1984;Bierwisch,1989;Kennedy,1999).ThefunctionofPOSistoexistentiallyquantifyoverdegreesandsupplyadegreethatmeetsacontextuallysuppliedstandard.Foragradableadjective,thismakesitsothatnotonlydoessomeonehavesomeheight(whichmereexistentialoveradegreewouldgiveyou),butthatsomeonealsomeetsthestandard.Thismatchesourintuitionsforwhattallmeans;tobetallisn'ttohavejustanyheight,buttomeettheheightforwhichwewouldcallsomeonetall.Afunctionstandardisusedinthesemantics,whichtakesagradablepredicateasanargumentandreturnsthedegreeinthecontextwhichrepresentsthestandard.Here,POSisassumedtobeaDeghead,DegPbeingtheextendedprojectionofAP(Abney,1987;Kennedy,1999;Corver,1990;Grimshaw,1991).Thisisillustratedin(54)Œ(57).(54)DegPtallAPDegPOS(55)JtallK=ldlx[tall(d)(x)](56)JPOSK=lGhd;etilx9d[dstandard(G)^G(d)(x)](57)JPOStallK=lx9d[dstandard(JtallK)^tall(d)(x)]BecauseIamworkinginaHamblinizedsystem,denotationswilloftenbesetsofalternativesrather31thanfunctions.AssumingMorzycki'simprecisionparameterandrepresentingdenotationswiththeirhalos,tallmightbetranslatedasin(58).Theanalysiswillstartwithoutalternatives,butalternativeswillbeaddedwhennecessary.(58)JtallKd0;C=ffhd;eti:fˇd0;Cldlx:tall(d)(x)gFinally,itwillbecrucialformetohaveaccesstotheimprecisionparameter.FollowingMorzycki,IassumeatypeshiftPREC,in(59)below.(59)JPRECaKd=ld0:JaKd0ThePRECtypeshiftbindstheimprecisionparameter,turninganyexpressiontypetintoafunctiontypehd;ti.Whennecessary,I'lllabelPRECasanodeinthesyntax.2.4.2SortaandgradablepredicatesInprevioussections,Ihighlighthowsortabehavesasadegreeword.Iwillconsideritadegreewordatheartandanalyzeitasonemightanalyzeanotherdegreewordsuchasvery.ThesyntacticassumptionherewillbethatsortaheadsaDegP,muchlikePOSorverydoundercertainanalyses,withanAPheadedbyagradableadjectiveasitscomplement,asin(60).DegPsarepredicativeandarepropertiesofindividuals,andbyassumptionAPsarerelationsbetweendegreesandindividuals.Syntacticallyandtype-theoretically,thismakessortacomparabletoPOS.(60)DegPtallAPDegsortaHowmightwethinkaboutthesemanticcontentofsorta?ThemostnaturalmoveistokeeptheparallelismbetweensortaandPOS;sortashouldbeofthesamelogicaltypeasPOS,aswellasdosomethingsimilarsemantically.POSassertstheexistenceofadegreesuchthatthatdegreemeetsacontextuallyprovidedstandard,aswellassaturatingtheindividualanddegreeargumentsoftheAP32itcombineswith.Theentailmenttothestandardwithsortaismurky,however;whatwemightdoissaythatthedegreeoverissimplyclosetothestandard.Ia`closeto'relationin(61),suchthat,fortwodegreesdandd0,dld0istruejustincasedissmallerthand0anddiscloseinvaluetod0,asbythecontext.Sortaisasin(62),whereaisagradableadjective(typehd;eti).(61)8d8d0,dlC;Pd0iffthevalueofdisclosetod0asdeterminedbythecontextC.(62)(Tentative)JsortaKC=lGhd;etilx9d[dlstandard^G(d)(x)](64)demonstrateshowsortatallwouldwork.Forreadability,I'vesuppressedthecontextparameteronlandtheargumenttostandard.(63)Billissortatall.(64)a.JsortaKC=lGlx9d[dlstandard^G(d)(x)]b.JsortatallKC=lx9d[dlstandard^JtallK(d)(x)]=lx9d[dlstandard^tall(d)(x)]c.JsortatallKC(JBillK)=9d[dlstandard^tall(d)(JBillK)]Additionally,althoughtheanalysissofarhasbeendevelopedwithgradableadjectivesinmind,sortaalsocombineswithgradablepredicatesthatarenotadjectives.Averbsuchasrespectorwidenisplausiblygradable,basedonthetheexistenceofadegreereadingwithacomparative.ThereadingavailablewhensortaVPsheadedbytheseadjectivesiswhatwewouldexpect,giventhatthesearegradablepredicates;theexamplesin(66)havedegreereadingsŠsortarespectmeansfitorespectalittlebitflandsortawidenedmeansfitowidenalittlebit.flThisismoresupportforsorta'sstatusasadegreeword.(65)a.Irespecthermorethanyoudo.33b.Thissectionofthestreetwaswidenedmorethanthenextsection.(66)a.Isortarespecther.b.Theroadcommissionsortawidenedtheroad.Tosummarize,sortacanbeanalyzedasavarietyofdegreewordusingthestandardtoolsfromdegreesemantics.Syntacticallyandsemantically,wecanthinkofitasacousintoPOS,butratherthanassertingthatadegreeexceedsthestandard,sortarequiresthatadegreebeclosetobutbelowthestandard.Theanalysisherewillformthecoreoftheanalysisofsortawithnon-gradablepredicatesinthenextsection.2.4.3Sortaandnon-gradablepredicatesIntheprevioussectionIanalyzesortaasavarietyofdegreeword.Theroleofsortaistoassertthatadegreeisclosetobutlowerthanthecontextuallyprovidedstandardandtosaturatethedegreeargumentofthegradablepredicateitcombineswith.Ifsomepredicatehasadegreeargument,thiswouldbesatisfactory.Theissuethatarises,though,isthatmostverbsandnounsaren'tusuallyarguedtolexicalizeadegreeargument.Ifsortaisadegreeword,weneedtoaskwhatdegreeitisoperatingoverwhencombinedwithnon-degreepredicates.Thecluethatwecanextendadegreeanalysistonon-gradablepredicatescomesfromtheapproximativevorofsorta.Recallingpreviousobservations,constructionsinvolvingsortaandnon-gradablepredicatescanbeconvenientlyparaphrasedwithapproximativessuchasclosetoorlike,asin(67).Thewaytolookatthedegreethatsortaoperatesoverwithnon-gradablepredicatesshouldbeasadegreethatrepresentshowcloselyonepredicateapproximatesanother.(67)a.Isortakickedtheground.`Ididsomethinglikekickingtheground.'b.Hesortaswamovertotheboat.`Hedidsomethingthatwaslikeswimmingovertotheboat.'34ApproximationiswhattheimprecisionparameteronJ:KinMorzycki'sformulationofpragmatichalosrepresentsŠadegreethatrepresentshowmuchobjectsinthepragmatichaloareallowedtoapproximatesomeobject.Ahighdegreeofprecisionisawayofforcingobjectsinthepragmatichalotomorecloselyapproximatesomeobject,whileincreasinglylowerdegreesallowforlessprecisionandcorrespondinglylooserapproximations.Thisapproximationisaccomplishedwitharelationˇd;c,whichistruejustincasetwosemanticobjectsresembleeachothertoatleastsomedegreedincontextc.Theinterpretationsofconstructionsinvolvingsortaandnon-gradablepredicatesalsosuggestthatlookingatapproximationinthiswayisontherighttrack.Intuitively,aconstructionwithsorta,likesortaswim,involvessomethingthatresemblestheverbinsomeway.Swimcanbeusedinmanydifferentwaysthatapproximateacoreconceptofswimming(whateverthatmaybe).Whatshouldbesaid,then,isthatsortaswim(forexample)isn'tnecessarilyapproximatetoswim,butapproximatetowhat`counts'asswimminginthecontext.Neededisanotionofstandardsthatincludesnotjustthestandardsassociatedwithadjectivalscales,butalsowithdegreesofprecision.Drawingupthedegreeanalysisofsortafromtheprevioussection,thedegreethatsortaintroducesmustbeclosetoandlowerthanthestandarddegreeofprecisionforthecontext.WhatIwillassumeisthatthestandardfunctionisnotonlytoreturnstandardsassociatedwithadjectivalscales,butalsostandardsassociatedwiththedegreeofprecision.Thisrequiresstandardtonotonlyreturnstandardsforgradablepredicates(typehd;eti),butmoregenerallyforanythingwithadegreeargument,suchaspropertiescoercedintogradablepropertiesviaPREC.(68)JPRECswimKd=ld0:JswimKd0=ld0:ffhe;ti:fˇd0;CswimgWiththisinmind,whatsortadoesisexistentiallyquantifyoveradegreeclosetobutlowerthan35thestandarddegreeofprecision.Thishastheeffectofloweringthedegreeofprecision,inturnwideningthepragmatichalo.Becausewearedealingwithalternativesnow,ourofsortamustbeadjustedinordertopickasinglealternativefromthehaloandapplyittotheindividualargumentofsorta,aswellassettheimprecisionparametertothenewdegreeofprecision.(69)thesechanges,wherethePargumentissaturatedbyaPRECtypeshiftedproperty.14Thedenotationforsortanowalsohassetbracketssurroundingit,themovetohavinganalternativesemanticsforeverylinguisticexpression.(69)JsortaKd0=nlPhd;het;tiilx9d[dlstandard^9f2P(d)[f(x)]]o(70)VPVPswimVPPRECsorta(71)Jsorta[PRECswim]Kd0=JsortaKd0(J[PRECswim]Kd0)=8><>:lx9d264dlstandard^9f2JPRECswimK(d)[f(x)]3759>=>;Forconcreteness,wecansubstituteJPRECswimK(d)withthehaloofswim.ThedegreeargumentofJPRECswimKissaturatedbyd,creatingasetofalternativesthatrepresentswimtoatleastdegreed,asdemonstratedin(72).Examplesofthesealternativesareexplicitlyrepresentedin(73).(Argumentshavebeensuppressedwherepossibleforreadability.)(72)J(70)Kd0;C=8><>:lx9d264dlstandard^9f:f2ffhe;ti:fˇd;Cswimg[f(x)]3759>=>;14TheunusualtypeŠhd;het;tiiŠisaresultoftheVPdenotingasetoffunctionsratherthanasinglefunction.36(73)J(70)Kd0;C=8>>>>>>><>>>>>>>:lx9d266666664dlstandard^9f:f28>>>>>>><>>>>>>>:swim;;wade;:::9>>>>>>>=>>>>>>>;[f(x)]3777777759>>>>>>>=>>>>>>>;Asmentionedinsection2.2.2,sortaVdoesnothaveentailmentstoV.Thereasonsforthisarenowapparent;becausethehaloaroundtheverbwasexpanded,therearemanyfunctionswithinthehalothatsortacanchoosefrom.Notalloftheseoptionsarewithintheoriginalhalooftheverb,assetbythestandarddegreeofprecision.Sincesortaisfreetochooseanyfunction,theentailmenttotheverbdisappears.Tosummarize,sortadoesacoupleofthings.First,itexistentiallyoverdegreesthatareclosetothestandarddegreeofprecisionforthecontext,withthepurposeofwideningthepragmatichalooftheobjectitiscombinedwith.Assortarequiresagradablepredicatetocombinewith,non-gradablepredicatesarecoercedintogradablepredicatesviathePRECtypeshift.Next,thedegreeofprecisionofthenon-gradablepredicatethatsortaiscombinedwithissettothedegreeedoverbysorta.Thiscreatesasetofalternativesthatatleastd-resemblethepredicatethatsortaismodifying.Finally,afunctionispickedfromthishaloandappliedtotheindividualargumentofsorta.Althoughtheexamplesaboveareforverbphrasesoftypehe;ti,wecanseethatthiswillgeneralizetootherexpressionsthatareproperty-denoting,includingnounsandnon-gradableadjectives.2.4.4Context-dependenceandsortaThisanalysispredictsthatsortashouldbedoublycontextsensitive,regardingthestandarddegreeandsecondregardingtheˇrelation.Atanintuitivelevel,thesetwolociforcontextdependencedealwiththedegreeofsimilaritybetweenpredicates(e.g.,aretwopredicatesverymuchsimilaroronlysomewhatsimilar?),andtheparticularwaysinwhichthingscanbesimilar.Let'sconsiderthecontextparameteronˇ.AspointedoutbyGoodman(1972),anytwo37objectshavemanypropertiesincommon,makingsimilarityauselessnotionifwearesimplytalkingaboutcommonproperties.Whatisneededforsimilarityistobesimilarinparticularrespects;inordertodeterminewhethertwoobjectsaresimilar,itisnecessarytohavesomeedrespectsinmind.Whatthecontextparameterinthiscasedoesisdeterminewhatrespectswearetalkingaboutwhenwearejudgingwhethertwoobjectsaresimilar.Takingthepredicatesortaswim,ifwevarycontextswecanseethatthefelicityandinterpretationofsortaswimdependsonwhatrespectsarebeingusedtojudgesimilarity.Fortheverbswim,theserespectsmighthavetodo(forexample)withdoingtheactivityinthewaterandmovingone'sarmsandlegsinaparticularway.Ifweconsiderasituationwhereachildislearninghowtoswiminapool,itisappropriatetousesortaswimevenifthechildwasjustpracticingbecauseissimilartoswimminginthattheybothoccurinthewater.However,differentrespectscanberelevantinothersituations.Ifoneisplayingcharadesanddemonstratingswimming,wecanusesortaswimtodescribethesituationiftheyaremovingtheirarmsinawaythatisreminiscentofswimming.Eventhoughcharadesisn'tbeingplayedinthewater,sortaswimcanbeusedbecausethecontexthasdeterminedthatwasisrelevantinthesituationisnotthattheactiontookplaceinthewater,butthattheplayer'sarmsweredoingsomethingsimilartowhatisdonewhenoneswims.Ifweholdtherespect(s)underconsiderationconstant,theeffectofcontextonthestandardalsobecomesapparent.Toseethis,considertheVPkicktheball.Kickingtheballrequires,intermsofrespects,somemovementofthefootandlegandmakingcontactwiththeball.Infants,semanticists,andprofessionalsoccerplayerscanallkickballsŠtheycanmovetheirfeetandlegsinaparticularfashiontomakecontactwiththeball.Thisisthebareminimumforwhatitmeanstokickaball,theloosestcontextinwhichwewillsaythatsomeonekickedaball.However,ifwewanttotalkaboutwhatprofessionalsoccerplayersdoduringsoccergames,whichhastheeffectofincreasingourstandardastowhatcountsaskicking,itbecomeshardertocountwhataninfantisdoingaskickingaball(particularlyifthereisverylittlemovementoftheballwhentheinfantkicksit).Insum,descriptionsusingsortaarecontext-dependentinatleasttwoways:byvirtueofwhatrespectsmatterforsimilaritywithinacontext,andsecondbyvirtueofthestandardswesetfor38whetherapredicatecountsassimilarornot.Theseareindependentfromeachother.Holdingthestandardconstantwhilevaryingtherespect,wecanseethatdifferentsituationscallfordifferentrespectstobeexamined(asintheswimcase).And,iftherespectisheldconstantbutthestandardmanipulated,thethresholdforwhatcountsforaparticularpredicatecanbechanged(asinthekickcase).2.4.5RevisitinggradablepredicatesInsection2.4.2,sortaisanalyzedasadegreeword.Insection2.4.3,thisanalysisisfurtherdevelopedsothatsortacanplayadegreeroleintheabsenceofalexicalizeddegree.Twotechnicalmovesmakethiswork:thePRECtypeshiftisappliedtoanon-gradablepredicateinordertocoercegradabilitywherenoneexistedbefore,essentiallybuildingagradablepredicateoutofanon-gradableone,andsortaexistentiallyoverasetofalternativesinordertopickasinglealternative.Thequestionthatneedstobeanswerediswhetherthemoveofmakingsortasensitivetoalternativescreatesanyproblemsfortheoriginalanalysisofsortaasadegreeword.AHamblinizeddenotationfortallmightlookasin(74).Somewhatunconventionallyforthischapter,I'vetranslatedtallasasingletonsetratherthanusingthesetbuildernotationandˇ.Onereasonforthisispurelyexpository,awishtokeepthemovingpartstoaminimum.However,thereisalsoalessinnocentbutmoreinterestingreasonhereaswell:it'ssimplynotclearwhatthealternativestotallwouldbe,atleastundernormalcircumstances.Plausibly,thisisrelatedtotallbeinganadjectivewithonlyasingledimensionofmeasurement:thereisonlyonewayinwhichwecandeterminewhethersomeoneistall(i.e.,whattheirheightis).(74)JtallKd0=fldlx:tall(d)(x)gInordertomakesortacombinewithaHamblinizedadjective,thetypeforsortahastochange:sortaneedstocombinewithasetofgradablefunctionsandanindividual,makingittypehhhd;eti;ti;he;tii.Thistypeisdifferentthanthetypeofsortaforwhenitcombineswithanon-gradablepredicate(typehhd;het;tii;he;tii)39(75)JsortaK=lGhhd;eti;tilx9d[dlstandard^9g2G[g(d)(x)]]Thereisawrinklehere,however:althoughsortaisintuitivelylookingforsomethinggradabletocombinewithinallcases,thesourceofthisgradabilityisdifferent.Forgradableadjectivesandothergradablepredicates,thegradabilityislocatedwithinthepredicate,andhenceit'seachmemberofthesetthatsortacombineswiththathasadegreeargument.However,withnon-gradableVPs,thischanges;thegradabilityislocatedoutsideofthealternatives,duetotheapplicationofPREC.Whatthismeansisthatthedenotationsortaisdependentonwhattypeofconstituentitcombineswith.Ifthegradabilityiscoerced,suchasinthecaseofmanyVPconstituents,onedenotationmustbeused.Ifthereisinherentgradabilityinwhatsortacombineswith,however,thenadifferentdenotationisused.Thedisjunctivedenotationin(76)this.(76)JsortaK=8><>:lFhd;het;tiilx9d[dlstandard^9f2F(d)[f(x)]]lGhhd;eti;tilx9d[dlstandard^9g2G[g(d)(x)]]Althoughthissortofambiguityisn'tideal,it'sworthnotingthatthesetwodenotationsstillhavemuchincommon.First,inboth,theintuitionisthatsortaislookingtocombinewithagradablepropertyŠthedifferenceisinwherethisgradabilityislocated.Second,thispropertygetsappliedtosomeindividual.Finally,andmostimportantly,sortalowersthestandardinbothdenotations.Eventhoughthedenotationsaredifferentintheirtechnicaldetails,theintuitionthatsortaisaffectingthestandardremainsinboth.2.4.6PRECandalternativeformulationsofsorta2.4.6.1MuchworriesAddingatypeshifttoourtoolkitisn'tasteptotakelightly;therearewell-foundedworriesaboutwhatmakingthiskindofmovemeansforourtheoryofgrammar.OneworryiswhetheranewtypeshiftsuchasPRECshouldbeused,orifthereisanothertypeshiftthatcanbeusedtoaccomplishsomethingsimilar.Onepossibilityismuch,whichisarguablyagradabilityinducingtypeshift.As40observedbyBresnan(1973)andCorver(1997),muchsurfacesasadummyadjectivalelement(much-support)inexamplessuchas(77)and(78).(77)a.Iloveherverymuch.b.Itwasverymuchasecret.(78)JohnisfondofMary,andBillisverymuchso.(79)Theballoonascendedasmuchasthekitedid.But,therearesomedifferencesthatmakeassimilatingPRECtomuchhard.Forone,sortaappearswithoutmuchinexampleslike(80).Ifmuchispartofthemeaningoftheseconstructions,wehavetoexplainwhyitappearscovertly.Inadjectivalcontexts,much-supportoccurswhenthereisellipsis,butthereisnomuch-supportnecessaryforsorta(see(81)).(80)a.Isortaloveher.b.Itwassortaasecret.(81)a.JohnisveryfondofMary,andBillisverymuchso,too.b.JohnissortafondofMary,andBillissorta(*much)so,too.Anotherpointinfavorofsortabehavingdifferentatthesyntacticlevelisthatitmustappeartotheleftoftheconstituentitunlessithasbeenextraposed(signaledthroughintonationoracommainwriting).Comparingsortatoverymuch,wedonotseesuchasrestriction.(82)*Ilovehersorta.(compareto:Iloveher,sorta.)Finally,accordingtoBresnan(1973),theEnglishadjectivalcomparativeincorporatesacovertmuch,andarelatedproposalcanbefoundforverbalcomparativesin?.In(83),thecomparativegivesusaninterpretationwherewecomparequantities,suggestingthatwhatmuchisdoinginthecomparativeisallowingthecomparativemorphemetoaccessaquantityscale.Thiscanbe41comparedto(84),wheresortabuildsaninterpretationwhereweimplicitlycomparesimilarkindsofevents(say,eventsthatarelikerunningorlikesleepinginsomeway).Althoughaquantityinterpretationdoesn'tappeartobecompletelyruledout15,thecomparativeexamplesdonotallowthefisimilarityflinterpretation.Ifmuchiswhatcoercesgradabilitywithsorta,weshouldexpectthesametypesofreadingswithboththecomparativeandsorta.(83)a.JohnranmorethanMary.XQUANTITY,*KINDb.BillsleptmorethanSue.XQUANTITY,*KIND(84)a.Johnsortaran.??QUANTITY,XKINDb.Billsortaslept.??QUANTITY,XKINDFurthermore,exampleswithverymuch,wheremuchisclearlypresent,alsodonotgiverisetothesamekindofreadingassorta.16(85)hasthesametypeofquantityreadingasin(83a)and(83b).Again,ifmuchwereatplayinexampleswithsorta,weshouldexpectsentenceslike(84a)and(84b)toalsohavesimilarquantityreadings.(85)a.Johndidn'trunverymuch.b.Johndidn'tsleepverymuch.Insum,althoughitwouldbetheoreticallynicetoreducePRECtoactuallybeingacaseofacovertmuch,doingthispresentssomedif15Forinstance,sortasleepseemstohaveareadingavailablethatisakintofididsomesmallamountofsleeping.fl16Thisiscomplicatedbythefactthatverymuchiseithermarkedorunacceptableinnon-negatedsentences:(i)??Johnranverymuch.(ii)*Johnsleptverymuch.422.4.6.2PRECinsorta?Asecondworryaboutthecurrentformulationofsortaiswhetherdegreesofprecisionshouldbeaccessiblefromoutsideofsorta,orwhetheritshouldbesortaitselfthataccessthedegreeofprecision.Inotherwords,dowewantthePRECtypeshift,whichmakesavailablethedegreeofprecision,tobeseparatefromthemeaningofsorta,orshoulditsomehowbeincorporatedintoit?IarguethatPRECreallyshouldbeconsideredasaseparatecomponentfromsortaandnotbeincorporatedintoitsmeaning.TheargumentthatPRECshouldbeseparatefromsortaconcernsitsinterpretationwithgradableadjectives.Asatypeshift,PRECappearswhenthereisatypeincompatibilitybetweensortaandtheexpressionitiscombiningwithŠnamely,sortaistryingtocombinewithsomethingoftypehe;ti17whenitrequiresagradableexpression,typehd;eti.Whatweseeisthatsortainvokesameaningshiftwithexpressionsthatarenotgradable(sortaswiminvokespredicatesthatarelikeswim),butthatnosuchmeaningshifthappenswithpredicatesthatarealreadygradable;itisdiftoexampleswheresortatallcouldmeanwide,forinstance(sortatallinsteadmeansfitalltosomedegreedthatisclosetobutlowerthanthestandardfl).ThissuggeststhatthemeaningofPRECisn'tpartofthemeaningofsorta,forifitwere,wewouldexpectmeaningshiftstobeavailableforwhateversortacombinedwith.Second,wemightworryaboutaproliferationofdegreeofprecisioninterpretationswerePRECtobeseparatefromsorta.Onthefaceofit,thiswouldappeartomilitateagainstPRECbeingaseparatemeaningcomponent.Ifwecanothermorphemesthatseemtoalsohaveadegreeofprecisioninterpretationassociatedwiththem,however,thisbecomesanargumentthatPRECshouldbeseparate,asitcanbeusedmoregenerally.IofferuptwocaseswhereitseemsthatatypeshiftlikePRECmightbeused.Theconcernsthedegreemorpheme-ish(Sugawara,2012).Inadditiontoitsadjectivaluses,where-ishoveradegreethatdoesn'tmeetthestandard,thereareuseswhereitattachestoothercategoriessuchasnouns,numeralsandtime-denotingexpressions,andasnotedbyBochnak17Ormoretechnically,asetoffunctions,eachofwhichistypehe;ti.43&Csipak(2014),propositions.(86)a.He'sveryboyish.b.Heactsverychildish.(87)a.I'llbevisitingintwenty-ishdays.b.Isawhimaroundsix-ish.(88)a.Ilikedthemovie...ish.b.Leedrewacircle...ish.c.Theywonthematch...ish.Sugawaraproposesadegreesemanticsforish,andBochnakandCsipakfollowSugawarainofferingupadegreesemanticsanalysisforish.Toaccountforhowishcanbeapropositionalwhenithasadegreemeaningatitscore,onthisversionoftheanalysistheysuggestthatPRECopensupthedegreeofprecisionparameteroftheproposition,beforethepropositionscombineswithish.Theeffectofishistolowerspeakercommitmenttothepropositionexpressed,duetotheloweringofthedegreeofprecision.In(89),ishappliestoapropositionthathasadegreeofprecisionargumentopenedbyPREC,andreturnsasetofpropositionalalternatives.(89)JishKd=lphd;sti:lw:MAXd0:p(d0)(w)<d^smallc(dd0)(Bochnak&Csipak,2014)Forthesecondcase,weconsidernon-canonicalusesofthedegreewordvery.Althoughveryusuallyhasanad-adjectivaluse,whereitappearswithgradableadjectives(Klein,1980;Kennedy&McNally,2005),therearebothad-nominaluseswithnon-gradablenouns,anduseswithordinalnumbers,whichareconsiderednon-gradable.Toillustrate,certainnounslikecenterallowverytointensifythemeaningofthenoun.Ordinalnumberslikestalsoallowwithvery,againwithareadingwhereverygivestheordinalastricterinterpretation.Whatwemightconsiderthistobeisanimprecision-relateduseofvery,whereveryincreasestheamountofprecisioninthe44interpretationofthenounorordinal.(90)a.theverycenteroftheEarthb.theveryfrontoftheline(91)Heistheverypersoninline.Theobservationthatveryhasadegree-relatedandprecision-relatedsensemakesitbehaveinsomewayslikesorta.Oneanalysisisthatveryinallcasesisdegree-related.Inthenon-canonicalcaseswhereveryactsasanad-nominalandasatoanordinalnumber,verymakesreferencetodegreesabovethestandard.However,thestandardhereisastandardofprecision,andveryhastheeffectofincreasingthedegreeofprecisionfortheexpression.Thiswouldmakeverylookinsomewaysliketheoppositeofvery,whereitincreasesthedegreeofprecisionratherthanlowersit.Iwillpursueafulleranalysisofthisinthenextchapter,makinguseofthesametoolsinthischapter.Furthermore,adjectivessuchasextinctandtriangularareoftenconsideredpreciseandnon-gradable,butitisnotimpossibletowhatlooktobegradableusesofthemaswell,suchasin(92).Forquiteextinct,thescaleappearstoascaleofsimilaritytoextinctness,withquiteextinctfallingatthetopofthescale.Thisalsoappearstobewhatishappeningwithverytriangular,wheretheshapeoftheformationsresemblesatriangletoahighdegree.AnanalysisofthesekindsoffactscouldalsobegivenusingPREC,wherePRECcoercesthenon-gradablepredicateintoagradablepredicatebyopeningupthedegreeofprecisionargument.Thesewouldnotbecasesofscalarcoercionperse,whereanon-gradablepredicateisgivensomegradablemeaningbyreinterpretingit,buttheywouldratherbecaseswherethegrammaticalmachineryallowsforthemtobeinterpretedwithrespecttoadegreeofprecision,duetodegreesofprecisionbeingpartofthegrammar.45(92)a.ItshouldbeassumedthereforethatthisspeciesisquiteextinctinthePieninyMoun-tains.b.AdjacentV-shapedvalleyformationsgivetheremainingfaultspursaverytriangularshape.Thecasesof-ishandveryshowthat,aswemightexpect,PRECmightalsobepresentinothersortsofconstructionswheretheelementbeingedistraditionallythoughtofasbeingnon-gradable.TogetherwiththeconceptualargumentthatputtingPRECinsidethemeaningofsortawouldmakeitdiftogetthestandarddegreeword-likeinterpretation,thissuggeststhatPRECshouldbeatypeshiftseparatefromsorta.2.4.7HedgingobjectsIntheprevioussection,Idevelopedananalysisofhowtheverbmaybehedged.Theanalysisdependsonlinguisticexpressionshavingsetsofalternativesavailable,alternativesthatmodelLasersohn'spragmatichalos.Forinstance,foraverbsuchasswim,eachalternativeisafunctionthatresemblesthecoremeaningofswim,thefunctionswim,tosomedegree.Theentiresetofalternativesisasetofresemblingalternativesthatisorderedbytheirdegreeofresemblancetosomefunction.Whatsortadoesinthiscaseistolowerthedegreeneededtobepartofthesetofresemblingalternatives,bymanipulatingadegreeofprecisionontheinterpretationfunction.But,asdescribedearlier,sortacanalsohedgethedirectobjectsofsomepredicates.Thequestionishowtogetthiskindofbehaviorwithsorta,howsortacanhedgeadirectobjectevenwhenitdoesn'tmergewiththedirectobject.Theanswer,Isuggest,comesfromthearchitectureoftheHamblinsemanticsassumedhere.Inthissystem,denotationsarerepresentedassetsofalternativesthatgroworshrinkdependingonthedegreeofprecision.Intheprevioussection,verbs(andverbphrases)wererepresentedinthisfashion,butweshouldexpectthatnouns(andnounphrases)arerepresentedinthiswayaswell,andthisispreciselyhowMorzycki(2011)handlesmetalinguisticcomparativeswithnominalsrather46thanadjectives.Thedenotationforhouse,forinstance,wouldberepresentedasin(93),asetoffunctionsfsuchthateachresembleshousetodegreed.(93)JhouseKd=ff:fˇd;ChousegIfnominalsalsohavesetsofresemblancealternatives,theproblemofhowsortacanhedgeadirectobjectbecomestheproblemofhowsortahasaccesstothesealternatives.Putsimply,thealternativesforthedirectobjecthavetofiprojectfluptotheVPlevelinordertobevisibletosorta.Themechanismtodothisisalreadyavailableusinganalternativesemantics.TheintuitionformalizedasHamblinFunctionApplicationwastoapplyeachfunctionfromonesetofalternativespointwisetoitsargumentsinanothersetofalternatives.Thiscreatesanewsetofalternativeswiththealternativesofboththepredicateanditsargument.Forconcreteness,JbuildahouseKdwouldberepresentedasin(94),withthealternativesfromJbuildKdapplyingpointwisetothealternativesforJhouseKd.18(94)JbuildahouseKd=fb(h):h2JhouseKd^b2JbuildKdgSinceJbuildahouseKdwillhavethealternativesofbothJbuildKdandJhouseKd,thissolvestheissueofhowsortahasaccesstothealternativesofhouse.Quitesimply,thealternativesfromhousewillcontinuetoprojectupwardstotheVPlevel.Throughthiscompositionalprocess,HFA,thealternativesatalowernodeinthesyntaxcanprojecttohighernodesinthesyntax.Abstractingawayfromtheprecisetranslationofbuildandhouse,thealternativesforbuildahousemightprojectasin(95).(95)8><>:lx[build(x)(house)],lx[build(x)(shack)],lx[pieceŒtogether(x)(house)],lx[pieceŒtogether(x)(shack)]9>=>;8><>:house,shack9>=>;8><>:lflx[build(x)(f)],lflx[pieceŒtogether(x)(f)]9>=>;18Iassumethatthesingulararticleahasnosemanticcontributionhere,sothatJhouseKd=JahouseKd.47IfwesupposethatsortaadjoinsquitehighwithintheVP(notunreasonablegivenitspositionbeforetheverb),itshouldhaveaccesstothealternativesofotherelementsinsidetheVP.As(20)and(21)show,thisistrue,whereindirectobjectsandloweradjunctscanbetargetedbysorta.Thiswouldrequirenospecialmechanism,asthealternativesfromnominalsinthesesyntacticpositionswouldallcontinuetoprojectupwarduntilbeingcapturedbysorta.Tosummarize,sortacanmodifythedirectobjectsofverbsevenwhenithasn'tmergedwiththedirectobjectduetothemechanicsofaHamblinsemantics.ThereasonforthiscomesfromthebehaviorofHamblinFunctionApplication.HFAappliespredicatesfromonesetpointwisetoargumentsinasecondset,creatingathirdset.Thissetcontainsallthealternativesfromtheandthesecondset;inessence,HFAallowsthealternativesfromthedirectobjecttopercolateupwardthroughoutthecourseofthederivation.Worthonisthatthisbehaviorcomesforfree,sinceHFAisindependentlynecessaryinthisframework.Allthingsbeingequal,ifalternativesaregrammaticallyrepresentedandcertainexpressionsaresensitivetoalternatives,weshouldexpectcasesofapparentnon-localrelationshipsbetweensomeexpressionsandalternativesensitiveelements.Findingthatsortaexhibitsthisbehavior(albeitinlimitedways)islesssurprisinginlightofthealternativesemanticsI'veadopted.2.5Discussion2.5.1OntheconnectionbetweensortaandotherapproximatorsInsection2.2.4,Ishowthatsortaisn'tequivalenttoalmost,basedontheirdistributions.However,astheanalyticalintuitionpursuedhereinvolvessortahavinganapproximativemeaning,itisinstructivetoconsiderhowsortaissimilartootherapproximativessuchasalmost,aswellasotherhedgeslikelike.Sadock(1981)proposesanintensionalsemanticsforalmost,involvingarelationbetweentheevaluationworldandasimilarpossibleworldandanassertionthatthepropositionoccursinasimilarpossibleworld(asin(96)).Giventhisformulationofalmost,itshouldbelogically48possibleforthepropositiontoholdintheevaluationworldaswell.Sadocksuggeststhatthesensethatthepropositiondoesnotholdintheevaluationworld(sometimescalledthepolarcomponent(Horn,2002))comesfromaGriceanquantityimplicature:almostpisweakerthanp,andascalarimplicature:parisesduetothefactthatalmostpbutnotpwasuttered.(96)JalmostK=lwlphs;ti9w0:w0isnotverydifferentfromw^p(w0)(Sadock,1981)Penka(2006)criticizesthisimplementationwiththeobservationthatthepolarcomponentofalmostseemsstrongerthanascalarimplicature.(97a)contrastswith(97b),whichsuggeststhatcancelingtheinferencenegativeinferenceofalmostismuchharderthannormallyobservedforscalarimplicatures,andinturnsuggeststhatthenegativeinferencearisesthroughsomeothermechanismbesidesscalarimplicature.(97)a.?NotonlydidBillalmostswimtheEnglishChannel,hedidswimit.b.NotonlydidBilleatsomeofthecake,heateallofit.(Penka,2006)Penkaproposesthedenotationin(98)inordertoaccountforthis.InPenka'sdenotation,thepolarcomponentislexicalizedinthemeaningofalmost,andalmostinvolvescomparisontoalternativesviaˇ`closeto'.(98)JalmostˇK=lwlphs;ti::p^9q[qˇp^q(w)](Penka,2006)What'sinstructivetopointoutarethesimilaritiesanddifferencesbetweenalmostandsorta.Accountsofalmost,suchasthoseofSadockandPenka,generallygiveanintensionalsemanticstoalmost,wherethetruthofapropositionisstatedwithrespecttoaworldsufsimilartotheevaluationworld.Thiscontrastswithsorta,wherethealternativesgeneratedascloselyresemblingpredicates.AlthoughapossibleworldsemanticscouldinpracticebegivenforthemachineryIhidebehindˇ,overtreferencetopossibleworldsisdispensablehere.Focusingonthepolarcomponentofsorta,wecancontrasttheabilitytosuspendthenegativeinferencewithsortaagainstthatofalmost.(99)showsthatthenegativeinferencecaninfactbe49suspended,suggestingthatithastheweakstatusofanimplicatureandisnotentailed.(99)Billisnotonlysortatall,heistall.(100)??Billnotonlysortaswamtotheboat,hedidswimtotheboat.(100)ispuzzlingifitisinfactthecasethatthenegativeimplicationhasthestatusofanimplicature,sinceinthisexampletheimplicaturecannotsoreadilybesuspended.Iarguethatthisisnotproblematic,ifweconsiderthesortofscalethatispresentinthesetwodifferentusesofsorta.Intheuseofsortawhereithedgestheadjectivetall,thereisadegreescalepresent.Animportantfactaboutdegreescalesisthatifanindividualholdsadegreehighonthescale,lowerdegreesalsohold.Thiscontrastswiththeresemblancescalepresentin(100)duetoˇ.Althoughthealternativesformascaleorderedbyresemblanceinthiscase,noalternativenecessarilyentailsanalternativeloweronthescale.Inthecaseof(100),swimtotheboatdoesnotentailsortaswimtotheboat;thesemustbepredicatedofseparateevents.Theoddnessof(100)comesfromthismultiplepredicationofevents.Inessence,whatthespeakerhastriedtodoissaythatbothpredicatesholdofthesameevent.Clearly,thisisimpossible,sinceoneeventcannotbebothafisortaswimmingflandafiswimming.flHowever,theexamplein(99)worksduetotheentailmentpatternspossiblewithdegrees;thereisnocontradictiontosaythatanindividualholdsahigherdegreeandalowerdegreeofsomeproperty.Comparingsortatootherhedges,themostaptcomparisonisbetweensortaandSiegel(2002)'sanalysisoflike.BasingheranalysisontheintuitionofthatofSchourup(1985),whichisthatlikeexpressesaminornonequivalencebetweenwhatissaidandwhatismeant,Siegelproposesananalysisoflikethatiscloselyrelatedtomyownanalysisofsorta,wherebylikeintroducesafreevariablethatisrestrictedtothepragmatichaloofsomeconstituent.However,thedistributionoflikeissomewhatmorefreethanthedistributionofsorta.AsSiegelshows,likecanbeusedtoweakentheforceofadeterminerssuchasevery(see(101a)).Thisisquitesimplyimpossiblewithsorta.Inasluicingcontext,asin(102),itismuchmoreapparentthattheforceofthedeterminerisweakened.Siegel(aswellasSchourup(1985)andUnderhill(1988))showsthatlikecanappearinavarietyofplacesinasentenceandhedge50nearlyanytypeofconstituent,butmyanalysisshowsthatsortaismuchmorerestrictedaswell,appearingonlywithverbphrases,adjectivephrases,andnounphrases(inalimitedfashion).Likecanmoregenerallymodifynounphrasesinawaythatsortacan't,includinganounphrasewithacardinalnumber(103),wherethenumberitselfcanbehedged.Likesorta,however,likecreatestruth-conditionaldifferenceswherenoneexistedbefore;bothsortaandlikeseemtobringsomeaspectofthepragmaticsintothetruth-conditionalsemantics.(101)a.Lanahates,like,everycoach.(Siegel's(54a))b.*Lanahatessortaeverycoach.(102)a.*Theyspoketoeverystudent,butwe'restillwondering(exactly)who.(Siegel's(36a))b.Theyspoketo,like,everystudent,butwe'restillwondering(exactly)who.(Siegel's(36b))c.*Theyspoketosortaeverystudent,butwe'restillwondering(exactly)who.(103)A:Hehas,like,sixsisters.B:Yes,hehasaboutsixsisters.(104)*Hehassortasixsisters.Whatthiskeysintoisadeeperdifferencebetweenwhatsortadoesandlikedoes,consistentwithmyanalysisofsorta.Thecross-categorialfactspresentinmydiscussionofsortastronglysuggestthatsortarequires,agradablepredicateofsomesortandsecond,anobjectthat,onceitsdegreeargumentissaturated,hasaproperty-typedenotation.Likedoesnothavethisrestriction;forwhateverreason,likeisashappywithnon-gradablepredicatesasitiswithgradablepredicates.ThemoralisthatiflikeinvolvesaLasersohnianpragmatichaloatsomelevelofanalysis,themechanismmediatingthehaloforlikecouldverywellbequitedifferentthanthemechanismusedwithsorta,duetothelackofanysortofgradabilityrequirementwithlike.Thedifferences(andsimilarities)betweenthesetwohedgesdeservesfurtherexamination.512.5.2ModulatingstandardsThesuggestioninprevioussuggestshasbeentothinkofsortaasmakingreferencetoacontextuallysuppliedstandard.Thismakessortasimilarinformtoanotherstandardregulatingmorpheme,POS(alsocalledABSinsomework).TheroleofPOSinthevorofdegreesemanticsI'veassumedistosaturatethedegreeargumentofagradableadjectivewithadegreethatmeetsacontextuallysuppliedstandard.SortahasasimilarfunctioninthestoryItellhere,whereitsaturatesthedegreeargumentofagradablepredicate(whetheritisagradableadjectivewithaninherentdegreeargumentorapredicatecoercedintogradabilityviaPOS)withadegreethatismerelyclosetoacontextuallysuppliedstandard.(105)JPOSK=lGhd;etilx9d[G(d)(x)^d>standard]Analysesofotherdegreewordshaveinvolvedcomparisontoastandard.Verycanbeanalyzedinthisway,whereveryassertsthatadegreeisveryhighaboveacontextuallysuppliedstandard(106).(The!>relationcanbethoughtofasgreaterthan.fl)Theeffectistoremoveanyquestionofwhethertheindividualisclosetothestandard.(106)JveryK=lGlx9d[G(x)(d)^d!>standard]BecausePOSisthoughttoentailthatanindividualmeetsorexceedsacontextuallystandard,Fara(2000)suggeststhatPOSisthelocusofvaguenessresolutionwithintheadjectivephrase.ShesuggeststhatnotonlydoestheuseofPOSentailmeetingorexceedingastandard,butthatitalsoentailsexceedingthestandardbyasalientlylargeamountinthecontext,anamountlargeenoughtomeetinterlocutors'interestsregardingthecutoffpointsforgradableproperties.Herformulationisadaptedin(107)below,wherenormisafunctionfromgradablepredicatestodegrees,and!>isafisalientlygreaterthanflrelation.(107)JPOSK=lGhd;etilx9d[G(x)(d)^d!>norm(G)](AdaptedfromFara(2000))If,asFarasuggests,vaguenessisregulatedwithinthePOSmorphemebyassertingthatadegree52issalientlyaboveastandard,wemightexpecttomorphemeswheretheoppositeholdstrue,thatis,morphemeswhereadegreeisassertedtobemerelyclosetothestandardandevenwithinabandofvaguenesssurroundingthethresholdbetweenmeetingandnotmeetingthestandard,asdeterminedbytheinterestsoftheinterlocutors.Intuitively,sortamayactlikethis.TheformulationIproposeforsortarequiresthatsortaexistentiallyquantifyoveradegreeclosetothestandard.Ifwethinkaboutthelrelationastakingintoaccounttheinterestofthespeakerinincreasing(ratherthandecreasingvagueness),itwouldseemtobetheinverseofFara's!>relation.Thiswouldexplainspeakerintuitionsconcerningstatementssuchassortatall;sortatallistruejustincasethespeakerisn'tsurewhetheranindividualcountsastall.Providedthatsortadoesregulateimprecision,itsuggeststhatbothimprecisionandvaguenessneedsimilartypesofmachineryformanagingcontexts.Here,thatmachineryisdegreesemanticsandafunctionfromgradablepredicatesandcontextstodegrees.Thedualroleofsortahereisevidencethatstandardsplayapartinbothimprecisionandvagueness;withintheAP,sortaactsasavaguenessregulatoranddoesnotcareaboutimprecisionatall.However,inacontextwheredegreesmustbecoerced,pragmatichalosandimprecisionmustbeinvolved.Sorta'sdenotationdoesnotchangetothis;rather,thesamemechanismŠastandardfunctionŠworkstomodulatestandardswithbothimprecisionandvagueness.2.5.3Whatissimilarity?Sofar,wehavetreatedsimilarityasaprimitivenotion,alogicaloperationthatcancomparewhethertwoobjectsofthesametypearesimilartoeachother.Whatsimilarityitselfishasbeenunexplored,however.Inthissection,Iwilltrytogiveafewindicationsofwhatsimilarityis.Thiswillhelpusbetterunderstandwhatobjectswe'regeneratingwhenusingsorta.First,similarityisaproblematicnotion,asGoodman(1972)notes.Onereasonforthisisthat,ifwereducesimilaritymerelytothepossessionofcommonproperties,anytwoobjectscanberegardedasbeingsimilartoeachotherduetotherebeingmanypropertiesthatthingscanhaveincommon.Furthermore,similarityisatrivialnotionifnotrelativizedtosomeparticular53aspectsŠindecidingwhethertwoobjectsaresimilartoeachother,certainpropertiesareprivilegedoverothersinmakingthecomparison.Thisisquiteclearifwecomparethecapitalletter'A'andthestandardsymbolfortheuniversalr8.Ifourgoalistosimplycomparethetwobasedonshape,theyareverysimilartoeachother,withthesymbolfortheuniversalbeing'A'witha180degreerotation,butifourgoaliscomparingthemforthepurposesofhowtheybehaveinorderlogic,theyarenotsimilaratall.Prototypeshavebeeninvokedasoneideaofhowsimilaritycanbemodeled(Rosch(1975);alsoseeKamp&Partee(1995)foranexplicitsemantictheoryofprototypes),butthereisaworryisthatprototypesthemselvesarelackinginexplanation,namelyaboutwhatitmeansfortwoobjectstosharethesameprototype.Althoughpenguinsandrobinsarebothbirds,whyarerobinsconsideredtobemoreprototypicalofbirdsthanpenguins?Ananswertothishasbeenthatprototypicalityisbasedondimensions.Dimensionsarefamiliartosemanticistsinworkonadjectivalsemantics:Bierwisch(1989)notesthatsomeadjectivesallowformorethanonewayofbeingmeasured.Anadjectivelikehealthyhasaspartofitssatisfactioncriteriathatanindividualishealthyiftheyarehealthyinallthedimensionsthatgointobeinghealthy,suchasbloodpressure,cholesterol,weight,andsoon.Thiscontrastswithitsantonymsickwhere,althoughtherearealsomanydimensionstomeasurebeingsick,andindividualcountsassickiftheyaresickinanyofthosedimensions.Thismultidimensionalityisalsopresentinotheradjectiveslikelarge,whichwhenappliedtocities,canmeasureeitherthepopulationorthegeographicextentofthecity.Butmultidimensionalityalsoexistsinthesemanticsofnounsaswell.AbirdisabirdbyvirtueofhavingcertainmeasurementsalongthedimensionsofWINGS,BEAK,FEATHERS,WARMBLOODED,andmanyotherdimensions.AsSassoon(2013)pointsout,though,thedimensionsinherenttoanounlikebirddifferfromthoseinanadjectivelikehealthyinakeyrespect.Adjectivaldimensionsappeartobeboundbylogicaloperators:tobehealthymeansthat,acrossallrespectsofhealth,anindividualishealthy;tobesickmeansthatthereisarespectwithwhichanindividualisnothealthy.Sassoonarguesthatnominaldimensionsarenotboundbylogicaloperators,butthat54eachdimensionisgivenaweightandthemeasurementsacrossdimensionsareaveragedtogiveameasureofthedistanceofsomeindividualfromaprototype.Forexample,whatitmeanstobeabirdistonotbemorethansomedistancedfromtheprototypeofbird.WhatUmbach&Gust(2014)pointoutisthatwhatunderliesjudgementsofsimilaritycannotbecomparisonsamongpropertiesthemselvesŠanotionneededindiscussingsimilarityisthatofdimensionsorrespects,waysinwhichindividualscanbemeasured.Dimensionsarenotproperties,however,butcanbetransformedintopropertiesbycombiningthemwithsomevalue.Forinstance,abookcanbemeasuredalongthedimensionofCOLOR,withpossiblevaluesbeing`green',`red',andsoon.However,thedimensionCOLORisdifferentfromthepropertiesgreen,red,andsoon,inthatpropertiesaretrueorfalseofanindividual.Umbach&Gust(2014)considerdimensionalityintheiranalysisofwhattheycallsimilaritydemonstratives,wheretheiranalysisofnominalsissimilartoSassoon's.Theyusetheconceptofageneralizedmeasurefunction,whichmeasuresanindividualalongmultipledimensions(ratherthanasingledimension),mappingtheindividualtoapointinamulti-dimensionalspace(Gärdenfors,2000).functionscorrespondingtonaturallanguagepredicatesdeterminethethresholdsneededforapredicatetohold.Forconcreteness,supposethatthepredicatecarhasasitsdimensionsNUMBEROFDOORS,ENGINETYPE,HORSEPOWER,andsoon.Ageneralizedmeasurefunctionmcarmeasuresindividualsalongthesedimensions,andthefunctioncarcheckswhetheratupleofvaluesmeetsthethresholdforbeingacar.Achallengefortheoriesofsimilarityishowtomakesimilarityagradablenotion.Fordifferentandlike,Alrenga(2006)supposesmeasurefunctionsthatmeasuredifferencesorsimilaritiesbetweenindividuals,makingthemonparwithothergradableadjectives.ForJapaneserashii,yoo,mitai,McCready&Ogata(2007)arguethattheseadjectivesquantifyoverpropertiesthatarestereotypicalofthenominaltheycombinewith.Individualscanthenbeorderedbasedonhowmanypropertiesstereotypicalpropertiestheysatisfy.However,measuringsimilaritybasedonthenumberofpropertiesthatareoverlooksoneissuethatsomepropertiesaremoreimportantfordeterminingsimilaritythanothers.Supposethattherearethreepropertiesthatmatterforbeing55abird:havingfeathers,havingabeak,andhavingwings.Ifthenumberofpropertiesiswhatmatters,wemightrankafeatherless,beaklessbirdasbeinglessbird-likethanawinglessbird.Myintuitiononthismatteristhatawinglessbirdisratherlesslikeabirdthanafeatherless,beaklessone,however,suggestingsimilarityneedstoalsotakeintoaccounttheimportanceofproperties.Additionally,propertiesthemselvesarealsotooparticulartomeasuresimilarity.Avedoorcarandasixdoorcararenotstereotypicalofcarsingeneral,butholdingallotherpossiblepropertiesconstant,ourintuitionstellusthatavedoorcarisclosertothestereotypicalcarthanasixdoorcar.Similaritydependsnotonlyontheweightsoftheparticularrespectsagainstwhichwearejudgingsimilarity,butalsotheirvalues.Thesenotionsaboutsimilaritymustgointowhatˇdoes.Whenaspeakerusesthepredicatessortaswim,whatthespeakerbringstomindisapredicatethatislikeswimminginsomeparticulardimensionordimensions:performedinwater,movementofarmsandlegs,andsoon.Inaparticularcontextwherewhatmatterstothespeakerisperforminganactivityinthewater,sortaswimisonlylicitifitalsousesthesamedimension.Asshownpreviously,though,thedimensionsthatmatterarecontextuallydetermined;ifwhatmattersinthecontextisthearmandlegmotions,sortaswimcancoverswimmingsthatarenotperformedinwater(forexample,apersonactingoutswimminginagameofcharades).Intheformulationofsortainthischapter,thereferencetowhatdimensionsmatterforsimilarityishandledbythecontextparameteronˇ.Finally,apointworthnotingisthatthealternativesthatsortabringstomindfornon-gradablepredicatesdonothavetoberepresentedbyanyparticularlexicalitems.Althoughwemaytalkabouttheactionthatsomeoneperformedusingsortaswim,it'snotrequiredthattheactionthattheyperformednecessarilybeabletobedescribedbyanotherlexicalitem.TheuseofsortaitselfpullsinthisdirectionŠaspeakerusessortatoexplicitlyacknowledgethatitishardtoalexicalitemintheirvocabularythatappropriatelydescribesthesituation.Thisobservationiscompatiblewiththeideathatnotionsofsimilaritymakereferencetodimensions,duetoanysetofdimensionsnotnecessarilybeingcoveredbyasinglelexicalitem.562.5.4LingeringissuesandspeculationThereareafewlingeringissuesaboutsortathatdeservemention.Theissorta'sstatusasapolarityitem;sortacannotbeusedintheimmediatescopeofnegation,unlessthenegationhasbeenreinterpretedasbeingmetalinguisticnegation.Thisisillustratedin(108)and(109),where(109)islicitbecausethenegationisnegatingthespeaker'suseofthewordsortaandnotoperatingaslogicalnegationfortheproposition.(Thecapitallettersindicatethatthewordsarestressed.)(108)a.*Johnisn'tsortatall.b.*Theyoungchilddidn'tsortaswim.(109)a.Johnisn'tSORTAtallŠheIStall.b.Shedidn'tSORTAswimŠsheDIDswim.Asecondissueconcernstheabilityofsortatoshiftthemeaningsofnouns.Althoughsortacanshiftthemeaningofnouns,thisshiftisconstrainedbythedeterminer.Determinerssuchaseveryandtheblocktheabilityofsortatoaffectthemeaningofthenoun,whiledeterminerssuchasadonot.Although(110a)hasareadingavailablethatisparaphrasedbyfidrewsomethinglikeahousefl(thefinounflreadingwheresortathenoun),comparablereadingsarenotavailablefor(110b)and(110c).(110)a.Isortadrewahouse.Xverb,Xnounb.Isortadrewthehouse.Xverb,*nounc.Isortadreweveryhouse.Xverb,*nounInterestingly,McCready(2008)noticesasimilarpatternwiththeEnglishparticleman.Whenmanisusedsentenceinitiallyandprosodicallyintegratedintothesentence,manallowsforDP-internalofadjectives.Likesorta,thisislimited.Somedeterminers,suchasthosein(111),allowtheadjectivetobebutnotothers,suchasthosein(112).57(111)ManJohnate8>>>>>>><>>>>>>>:atwoafewseveral9>>>>>>>=>>>>>>>;bigpiece(s)ofcake.(112)*ManJohnate8>>>>>>><>>>>>>>:few/nomost/manyboth/twooftheevery/the9>>>>>>>=>>>>>>>;bigpiece(s)ofcake.McCreadyarguesthattheproperdescriptionofthisfactisthatallthedeterminersthatallowfortheadjectivetobearemonotoneincreasingontheirargument,whilethedeterminersthatdonotallowlackthisproperty.Moregenerally,integratedmanresistsotherdownward-entailingenvironmentssuchasnegation,invitinganothercomparisonwithsorta.McCready'sexplanationforthisisasfollows.Theanalysisofmanitselfisthatitisusedforshiftingtheutterancetouseamoreextremesetofdegreesthanwouldotherwisebeused,effectivelycreatingastrongerclaim.Undernegation,thisstrengtheningwouldresultinaweakerclaim(see?forany),whichrunscountertotheuseofman.Moregenerallythen,onlyupwardentailingenvironments,includingupwardmonotonedeterminers,willallowbyman.Similarreasoningmaybeavailableforsorta:sortaservestoweaken(ratherthanstrengthenclaims).Asdownwardentailingenvironmentsarescale-reversing(Fauconnier,1975),theutterancewithsortawouldnowbeastronger(ratherthanweaker)statement,alsorunningagainstthefunctionofsorta.Thisanalysiswouldunifyboththedeterminerrestrictionswithbysortaandsorta'sstatusasapolarityitem.Sortacontrastswithveryinallowingsubsequentmeasurement,asshownin(113).Althoughveryallowsthespeakertomorepreciselystateadegree,sortadoesnotallowaspeakertodothis.58(113)HowtallisBill?a.He'sverytallŠ6'7fltobeprecise.b.#He'ssortatallŠ5'11fltobeprecise.Itseemsplausiblethatthisisrelatedtodiscoursessuchasin(114),whereashiftinthestandardofprecisionhastakenplace.Inthisdiscourse,Johnisperceivedtobeneedlesslypedantic,eventhoughhe'sfactuallycorrect.(114)Situation:Billarrivedat2:59pma.Mary:Billarrivedat3pm.b.John:No,hearrivedat2:59pm.c.Mary:You'rejustbeingannoying.Klecha(2014)arguesforaconstraintondiscourseswhereparticipantsmustagreeonasingle,uniformpragmaticcontext.Thisisstatedin(115).Thisconstraintexplainsthefeelingabout(114):MaryandJohnhavedifferentstandardsofprecisioninmind,andthishasbecomeapparentoncethediscoursehasstarted.(115)UNIFORMPRAGMATICCONTEXT(UPC)(Klecha,2014)Speakersmustagreeuponasingleuniformpragmaticcontext,andthepragmaticcontextdoesnotchange,unlesswithexplicitmetalinguisticnegotiation.IfaprinciplesuchastheUPCisassumed,thiscouldexplaintheillicitnessof.In,thespeakerhasapparentlyhadtwocontextsinmind,committinghimselftosalowprecisioncontextwhereitisacceptabletobevagueabouttheprecise,andthenimmediatelyaftertryingtoshifttoahigherprecisioncontextwheretheexactlydegreecan,infact,bespecTheUPCpresumablyrulesthisout,asthespeakerhasnotcommittedhimselftoasinglestandard.Indeed,Klechabringsupanexamplewherethissortofshiftwithinasingleindividualisillicit.59(116)Thefacts:Julianarrivedat2:59;Gallagherarrivedat2:58.(=Klecha's(41),chapter4)a.Itamar:Gallagherarrivedat3.b.Helena:Right,Julianalsoarrivedat3.c.Itamar:#No,hearrived2:59.Finally,onelastlingeringquestioniswhattherelationshipbetweenthenominalsort(asortofcar)andtheadverbialsortais.Icannotofferanyconclusionsonthis,butwemightspeculatethattheadverbialsortaarosethroughareanalysisofthenominalsortplustheprepositionof.Undertheanalysisinthischapter,whensortaaVP,itdoessobylooseningtheinterpretationoftheVPtoallowfortheuseofpredicatessimilartoit.Onewaytothinkaboutthis,perhaps,isthattheseareessentiallyotherfikindsflofeventsdenotedbytheVP;whatsortaswimmingisdoingislettingspeakertalkaboutotherkindsofswimming.Assort(andkind)involvekindssemantically(Wilkinson,1995),thisprovidesatentativelinkbetweenthemeaningofsortandtheadverbialsorta,atleastinit'suseasaofnon-gradablepredicates.Thisisapreliminaryhypothesis,andfurtherworkshouldbedoneonelucidatingtheconnectionbetweensortandsorta.2.6ConclusionThefactthatsortaisabletoappearacrosscategories,appearingwithgradableandnon-gradableadjectives,verbs,andevennouns,mightleadustobelievethatallthesecategorieshadsomecommonsemantics,namelysomesortofinherentgradability.Basedonthemeaningsthatconstructionsinvolvingsortaareabletotake,however,I'vearguedthatthisisn'tthecase.Rather,whattiesthesecategoriestogetherissortaitself;sortahasadegreesemanticsthat,whencoupledwithaspecializedtypeshiftPREC,allowsittogradeoverbothgradableandnon-gradablepredicates.Gradableadjectivesreceiveratherpedestriandegreereadings.Non-gradablepredicatesarecoercedintogradablepredicates;sortalowersthedegreeofprecisioninordertoexpandtheinterpretationsallowedbythepredicateitcombineswith.Theofthissystemisthatitprovidesapictureofhowsortaworks:across60categories,sortamaintainsadegreesemantics,butthedegreeuseddiffersdependingonthelexicalsemanticsofthepredicateGradableadjectivesareinherentlygradable,byvirtueoflexicalizingadegreeargument.However,non-gradablepredicatesareonlyexternallygradable;theymustbecoercedintohavingascalarsemantics.Thisgivesusaclearerpictureofwhatgradabilityisandwheretoit;whileinherentgradabilitymightbelimited,weshouldexpecttoplaceswheregradabilityhasbeencoerced.Lookingatthesemanticsofrssuchassortamaygiveuscluesastowhengradabilityhasbeencoercedorwhenitisinherent.61CHAPTER3EXTENDINGTHESLACKREGULATINGANALYSISWITHVERY3.1Non-canonicalwithveryCanonically,veryisadegreewordthatgradableadjectives,suchasin(1).Inthesecases,verycombineswiththepredicatetoassertthatthedegreetowhichthepredicateisholdingisquitehighonthescale.Verytall,forinstance,meansnotjustthatsomeoneistall,butthatsomeone'sdegreeoftallnessisveryhighontheheightscale.(1)a.Johnisverytall.b.Thisriverisverywide.Insomecases,though,verycanmodifycategoriesthataren'tgradableadjectives,suchasthenominalsin(2).WhatIwillclaimisthattheseusesofveryhaveaslackregulatingvortothem.Whatverydoesinthesecasesislowertheamountofpragmaticslackaffordedtothedescription,orrather,thatveryrequirestheexpressiontobeinterpretedmoreprecisely.(2)a.theverycenteroftheEarthb.theveryspotwhereLincolnstoodc.theverybeginningofthelined.theveryfrontattheconcertToillustratethatthesearetrulyrelatedtoprecision,ithelpstoshowscenarioswhereit'sclearthattheexpressionwithveryisinterpreteddifferentlythantheexpressionwithout.(2d)isaclearexampleofthis.SupposethatthediagraminFigure3.1representsthesetupataconcert,withastageupfrontandaseriesofrows.IfIsitinRow2,Iamentitled(innormalcircumstances)tosaythatIsatatthefrontattheconcert.However,ifsomeoneasksifIsatattheveryfront,I'mobliged62tosayno.OnlythepeoplesittinginRow1weresittingattheveryfront.Figure3.1:DiagramofaconcertThiscanbeshownwithcenteroftheEarthaswell.GeologistsknowthattheEarthhasseverallayers.Thin,rockycrustistheoutermostlayer,coveringamantleofsolidandthenplastic,wingrock.ThisthencoversthecoreoftheEarth.ThecoreoftheEarthisknowntobecomposedofnickelandiron,butitwasn'tuntil1936thatthecorewasdiscoveredtohavealiquidouterlayerandasolidinnerlayer.Inotherwords,althoughthecenteroftheEarthismadeofnickelandiron,itisonlytheverycenteroftheEarththatissolid.ThisisillustratedwiththediagraminFigure3.2,wherethedarkshadedareaistheverycenteroftheEarth,eventhoughthelinedareaandeverythinginsideitisthecenteroftheEarth.63Figure3.2:DiagramoftheinterioroftheEarthVerycanalsobeusedwiththeordinalnumberst,andexpressionslikeitsuchaslast,asshownin(3).(3)a.theverypersontowalkonthemoonb.theverylastpersoninlinec.theverynextdayisunacceptablewhenthearticleoraisused.Togeneratethemeaning,thedeterminermustbepresent.(4)a.*every/averyspotwhereLincolnstoodb.*every/averypersoninlineHowever,notallsensesofverywithnominalshavethesamesenseofThisisillustratedwiththeexamplesin(5)below.Intheseexamples,ratherthangradingthenounalongsomeinherentproperty(likeficlosenesstothecenterflwithcenteroftheEarth),thesearegradedalongsomepropertythatisextrinsictothenoun.I'llcallthisthereading.64(5)a.Thisverypersoncommittedthecrime.b.Hehadbeenhopingformetoreadthatverybookallalong!c.Ispoketothatveryclerkyesterday.Finally,itseemsill-advisedtosimplylumptogetherallusesofverywithcasesofverymodifyingtheDP-internalsame.Supposingthatthereisacovertsamepresentinthestructurewhenveryismodifyinganominalelementseemstomakethewrongpredictions.Examiningthedistributionofcasesofveryandcomparetoverysame,wethattheydoalwaysnothavequitethesamesyntacticdistribution.Verycanmodifysame,asin(6).Ifacovertsamewereimplicatedin(7a),weshouldexpectthesentencetobeacceptable,contrarytofact.Rather,thesentencethatmustbeutteredistheonein(7b).(6)JohnandMaryboughtthe(very)samecar,tenyearsapart.(7)a.*JohnandMaryboughttheverycar,tenyearsapart.b.JohnandMaryboughtthisverycar,tenyearsapart.Toconcludethissection,Iarguethatveryhasaslackregulatingusewhenusedwithordinals,superlatives,andnominals.Inthenextsection,I'llbuildonmyanalysisofsortafromchapter2,andshowhowverycanbeusedtoincreaseprecision.3.2Twokindsofapproachestovery3.2.0.1KleinianapproachesOneapproachtothesemanticsofveryisthatofKlein(1980).InthekindofsystemthatKleinisdeveloping,vaguenessandgradabilityaren'trepresentedusingtypedvariablescorrespondingtodegrees(contrastingwithlaterapproachesbye.g.,Kennedy(1999)).Rather,inthissortofsystem,gradabilityisaproductofhowtheextensionsofinherentlypredicateschangeincontext.Theideainthisapproachisthatvaguepredicates,suchastall,arepartialfunctions.They65aretrueforsomesetofindividuals,falseforanothersetofindividuals,butforotherindividuals.Theseindividualswhereitiswhethertheyaretrueorfalsecanbesaidtofallintheextensiongapoftall.Theindividualsforwhichtallistruearesaidtofallinthepositiveextensionoftall,whiletheindividualsforwhichtallisfalsefallinthenegativeextension.Whatdrivesthecontext-dependenceofadjectivessuchastallistheabilityforthepositiveandnegativeextensions,aswellastheextensiongap,toshiftbetweendiscoursecontexts.Asthestandardforwhatcountsastallmightchangeinaparticularcontext(e.g.,talkofbasketballplayersversusaveragepeople,orskyscrapersversussingle-familyhomes),theindividualswhofallintheextensiongaporthepositiveandnegativeextensionswillalsochange.Adegreewordlikeveryisawayofshiftingwhatshouldcountforthepositiveandnegativeextensionsofagradablepredicate.Verywouldshiftthepositiveextension`upward'sothatfewerindividualswouldfallwithinthepositiveextension,andmorewouldfallinthenegativeextension.Giventheanalysisofsortainthepreviouschapter,however,IwishtosetasidetheideaofusingaKleinianapproachfortheseusesofvery,andinsteaduseadegreeapproach.Thiswillbringtheanalysisofsortaandveryquiteclosetogether.Backgroundonveryindegree-basedapproachestogradabilityisinthenextsection.3.2.0.2Veryindegree-basedapproachesInapproacheswheregradabilityisrepresentedbyatypefordegrees,thetaskofputtingameaningtoverychanges,comparedtotheKleinianapproach.Inmanyofthesetypesofapproaches,adjectivesdenoteeithermeasurefunctions(Kennedy,1999)orrelationsbetweendegreesandindividuals(Heim,2000).Foradjectivesnotembeddedincomparativesorotherdegreeconstructions,nullmorphologyisusedtotransformtheadjectiveintosomethingthatcanbepredicatedofindividuals(pos;Cresswell(1976);vonStechow(1984);Kennedy(1999)),oratypeshiftingruletoshifttheadjectiveintoapropertyofindividuals(Neelemanetal.,2004).663.3Theslackregulationmechanism(Thissectionrecapstheslackregulationmechanismfromthepreviouschapter.)Lasersohn(1999)notesthatlinguisticexpressionsoftenallowforanamountofimprecisionorpragmaticslacktobeaffordedtothem.Forinstance,asentencesuchasthatin(8a)allowsforafewexceptionsinanormaldiscourse(e.g.,we'refreetooverlookacouplenightowlsinthetown),andsimilarlyfor(8b),whichallowsJohntonothavearrivedatprecisely3pm.(8)a.Thetownspeopleareasleep.b.Johnarrivedat3pm.However,certainwordsandphrasesreduceourtoleranceforloosetalk.Anexampleofthisisasin(9a),wheretheuseofallallowsforfewerorevennoexceptionstotheclaimthatthetownspeopleareasleep.And,in(9b),theuseofpreciselymakesusbemuchmoreexactlyabouttheprecisetimethatJohnarrived.(9)a.Allthetownspeopleareasleep.b.Johnarrivedatprecisely3pm.WhatLasersohnproposedwasthatexpressionshadpragmatichalossurroundingthem,pragmaticallyignorabledifferences,andthatloosetalkcouldbethoughtofintermsofthesehalos.Lasersohnprovidesoneimplementationofthiswouldwork,whileMorzycki(2011)providesanother.OneofthesysteminMorzycki2011isthatitoffersaclearwayoflinkingtogethertalkofdegreeswithtalkofimprecision,asimprecisioninhissystemisregulatedviaadegreeparameterontheinterpretationfunctionJ:K.Thepragmatichalossurroundingalinguisticexpressionaretiedtothisdegreeparameterbyarelationˇd;C,whichistrueoftwoobjectsjustincasetheyared-similartoeachother.(10)JdumbKd;C=ffhe;ti:fˇd;Cdumbg67(11)a.JdumbK1;C=fdumbgb.JdumbK:9;C=fdumb;ignorant;dopey;foolish;:::gc.JdumbK0;C=Dhe;tiThenextsectiongoesintofurtherdetailabouthowdegreewordssuchasverycaninteractwiththissystemandalterthesizeofthepragmatichaloassociatedwithlinguisticexpressions.3.4Analysis3.4.1VeryasaslackregulatorInchapter2,Ianalyzedsortaasadegreewordthatoverdegreesthatarelowerthanthecontextuallysuppliedstandardforsomegradablepredicate.WhatIwillpursuehereisanalyzingveryinasimilar(butnotexactlythesame)wayŠthatwhatverydoesiscombinewithgradableexpressionsandsupplyadegreethatishighalongthescale.Standardly,onewayofwritingthiswouldbeasin(12),whereveryoverdegrees.ThisdenotationwouldcombinewithagradablepredicateGandsaturateitsdegreeargument.(12)JveryK=lGhd;etilx9d[high(d)^G(d)(x)]Iwilltakeaslightlydifferentapproachtoveryinthischapter,though,andproposethatverywilldirectlydenoteadegreehighalongthescale.Toseehowthisworksintheadjectivaldomain,let'sconsiderverytall.Inordertohaveverycombinewithanadjectiveliketall,asilentmeasurementheadMEASwillsaturatethedegreeargumentoftallwiththedegreeprovidedbyvery.ThisissimilartoMEASinSvenonius&Kennedy2006.68(13)DegPhe;tidveryhd;etiDeghhd;eti;hd;etiiMEASAPhd;etitall(14)a.JMEASK=lGhd;etildlx:G(d)(x)b.JMEAStallK=ldlx:tall(d)(x)c.JveryK=dc,wheredcisahighdegreeincontextcd.JveryMEAStallK=lx:tall(dc)(x)Ofcourse,withnon-gradablepredicates,thereisnodegreeforverytosaturate.ThisiswherethePRECtypeshift,describedinthepreviouschapterandrepeatedbelow,comesintoplay.Torecall,thedenotationforPRECisasin(15),wherePRECbindstheprecisionparameteronthelinguisticexpressionitisshifting,creatingwhatisessentiallyagradablepredicate,gradedbydegreesofprecision.(15)JPRECaKd=ld0:JaKd0Whenveryismodifyingnon-gradablecategories,Iitsyncategorematicallyasin(16),whereveryaisveryandtheconstituentithasmergedwith,inthiscasetheconstituentbuiltintoagradablepredicateusingPREC.69(16)Whereaisagradableexpression(typehd;ti),JveryaK=JaK(dc),wheredcisahighdegreeincontextcThenextsectionsshowhowthisworksincertainsyntacticenvironments.3.4.2andnominalswithinherentlyscalarmeaningsCertaintypesofnominalsprovidefornaturalwaysofmakingthemmoreprecisewithvery.Exam-plesofthesearecenterandbeginning,asshownin(17).(17)theverycenteroftheEarth(18)theverybeginningofthelineWhatisspecialaboutnounslikecenterandbeginningisthat,foranygivenindex,theyuniquelydenote.TherecanonlybeonecenteroftheEarth,onebeginningofaline,andsoon.IntheterminologyofLöbner(1985),thesenounsprovideforfunctionalconcepts,andarefunctionsfromindices(worlds)toindividuals.AdenotationforcenteroftheEarthwouldlookasin(19).(19)JcenteroftheEarthK=lwix:xisthecenteroftheEarthinwThedrivingideainthischapteristhatverycanbeusedtoraiseadegreeofprecisionassociatedwithalinguisticform.So,althoughthesetypesofnounshavetypesoftheformhs;ei,attheleveloftheirpragmatichaloIwilltreatthemassetsoffunctionsratherthansinglefunctions.Thedegreeofprecisioninthiscasewillbemodulatingthesizeofthelocationreturnedbythefunction,suchthatthesefunctionswillhaveanaturalorderingdeterminedbytheirrange.(20)JcenteroftheEarthKd=(fhs;ei:fhs;eiˇdlwix:xisthesinglepointatthecenteroftheEarthinw)Likesortadidwithnon-gradablepredicates,verycangetaccesstothedegreeofprecisionparameterontheNPviathetypeshiftPREC.Thetreein(21)illustratesthiswithveryandcenteroftheEarth,70wheretheuseofPRECopensupthedegreeofprecisionargumentsothatverycangetaccesstoit.1(21)DPDtheNPveryPRECNPcenteroftheEarthCombiningPRECwithcenteroftheEarthwillresultinthelogicalformin(22).Sinceld0abstractsoverthed0parameteronˇ,thesetofalternativesgeneratedforcenteroftheEarthwillbeasetoffunctionssuchthateachd-approximatesthesinglepointatthecenteroftheEarth.(22)JPREC[centeroftheEarth]Kd=ld0:JcenteroftheEarthKd0=ld0:(fhs;ei:fhs;eiˇd0;clwix:xisthesinglepointatthecenteroftheEarthinw)NowbeingagradablepredicateduetoPREC,PRECcenteroftheEarthcancombinewithvery.TheroleofveryistoensurethatthedegreeofprecisionsettocenteroftheEarthisontheextremeupperendofthescale.Whencombinedwithvery,PRECcenteroftheEarthwillbesaturatedwiththecontextuallysuppliedhighdegreedenotedbyvery,dc.1EventhoughPRECisatypeshift,I'vechosentorepresentitinthetreehere.Thisisfornotationalconvenienceinshowinghowthesemanticderivationproceeds,ratherthanacommitmenttothetypeshiftbeingsyntacticallyrepresented.71(23)Jvery[PREC[centeroftheEarth]]Kd=(fhs;ei:fhs;eiˇdc;clwix:xisthesinglepointatthecenteroftheEarthinw)ThissuccessfullyderiveshowcenteroftheEarthcanbeinterpretedmorepreciselywhenbyvery.3.4.3DemonstrativesandveryVeryisalsoableto(seemingly)combinewithnominalsthatdonothavenaturalwaysofmakingthemmoreprecise.Someexamplesofthisareasin(24).(24)a.Thisverypersoncommittedthecrime.b.Hehadbeenhopingformetoreadthatverybookallalong!c.Ispoketothatveryclerkyesterday.Whatseemstobecrucialaboutanumberoftheseexamplesisthattheyinvolvetheuseofademonstrativedeterminer,e.g.thisandthat.Whatmakesdemonstrativesspecialhereinallowingforverytobeused?AmongtheanalysesofthedemonstrativedeterminerintheMontagoviansemanticstraditionisthatofBennett1978.Bennett(1978)arguesforananalysiswheredemonstrativedeterminersshouldbeunderlyinganalyzedasbeingdeterminerswithlocativeToputthisanotherway,thesentencein(25a)isanalyzedbyBennettasbeinglikethesentencein(25b).(Asimilarideaappliesin(26).)(25)a.Thishouseisforrent.b.Thehousehereisforrent.(26)a.Thatguyistall.b.Theguythereistall.Schmitt(1996,2000)arguesthatinsomecasesanounisnottheargumentofa72determiner,butthatwhatthedeterminerisselectingforisactuallyarelativeclause.Casessuchasthosein(27)and(28)providesupportforthisview,wherebyarelativeclauseisneededinthe(c)examplesinordertomakethesentenceacceptable.(27)a.Iboughtonetypeofbread.b.*Iboughtthetypeofbread.c.Iboughtthetypeofbreadthatyoulike.(28)a.Johnpaintedhishouseanicecolor.b.*Johnpaintedhishousethenicecolor.c.Johnpaintedhishousethecolorhisgirlfriendliked.TheseexamplesareanalyzedastheDtakingaCPcomplement(seealsorelatedproposalsinKuroda1968;Vergnaud1974;Kayne1994),asin(29).Withthenoun(actuallyaNumP)inSpecAgrP,itis`free'fromthedeterminer.Schmittproposesthatthedeterminerentersintoaq-bindingrelationshipwiththerelativeclause(seeHigginbotham1985)andnottheNumP.Thismakestherelativeclausetheargumenttothedeterminer,andnotthenoun.73(29)DPDtheAgrPNumPbooksiAgr0AgrCPOpiC0thatBillwrotetiArelatednotioncanbefoundinBarker2004,whoanalyzescaseslikein(30)wherethedeterminerseemstobe`weaker'thannormalinnotstrictlyrequiringuniqueness(thesecaseswerenoticedbyPoesio(1994)).WhatBarkerproposesisthattherelationalnoun(corner,side)composeswiththedeterminerviafunctioncomposition,beforetherelationalnoun'scomplementcomposeswiththedeterminer.Inthisway,therelationalnountheuniquenesspresuppositionofthedeterminer.(30)a.Ihopethecafeislocatedonthecornerofabusyintersection.b.Inthecenteroftheroomisalargestonecube,about10feetonaside.Engravedonthesideofthecubeissomelettering.Followingtheseproposals,Iwillassumeisthatthecovertindexicalistheargumentofthedeterminerindemonstrativedescriptions,andnotthenoun.Onthefaceofit,thismayseemalittleodd,buttheup-shottothisisthattheuniquenesscontributedbytheisuniquenessrelativetothesituationdenotedbytheindexical,ratherthanuniquenesswithrespecttothenominal74itself.Inusingdemonstrativenounphrases,thenominalitselfdoesnotseemtobeuniquelydenotinginthecontext.Rather,whatisuniqueisthelocationreferredto.Incaseslikethiswithdemonstrativedeterminers,whatveryismodifyingisnotthenominalitself,butthelocativeelementinstead.Ifveryweretobemodifyingthenominal,thenaturalinterpretationwouldseemtobeonewherethenominalisbeinginterpretedmoreprecisely.But,personinthisverypersonisn'twhatisbeinginterpretedmoreprecisely.Rather,veryinthatexampleseemstobenarrowingwhichpeoplecancountforthedescription.Sincethecovertlocativeelementiswhatisbeinginterpretedmoreprecisely,veryisattachingtoitandincreasingitsprecision.Syntactically,thepictureIwillassumeatLFforthisverypersonisasin(31):thedeterminertakesthelocativeasitsargument,andthenounphraseasitssecondargument,withthenounphrasepostposed.(Thiswillbeconsideredtobethespell-outofthe+HERE.)Again,tobeclear,thesyntaxin(31)shouldnotbetakentobethesurfacesyntaxfortheexpression,onlythesyntaxfortheexpressionatLF.(31)DPDPDtheXPXHEREtiNPclerkiWhenthecombineswithacommonnounphraseundernormalcircumstances,Iconsiderthetohavejustasingleargument.Thedeterminerwillbemodeledasachoicefunction,afunctionfromasettoamemberofthatset.Whenthecombineswithacommonnounphraselikedog,the75logicalformwouldlookasin(33).Thechoicefunctionalvariablefisvaluedcontextually.(32)JtheK=lPhe;ti:f(P)(33)JthedogK=JtheK(JdogK)=f(dog)Forthetreein(31),theneedstoaccepttwoarguments,though:itneedsanargumentpositionnotonlyforHERE,butalsoforthepostpostedNP.Inthiscase,thedenotationforthewouldbeasin(34).Thetwoargumentstotheareinterpretedintersectively,andaretheargumenttothechoicefunctionf.(34)JtheK=lPlQ:f(lx:P(x)^Q(x))ThewaythatwecouldstandardlyconsiderthedenotationforHEREwouldbetentativelyasin(35).Itencodesadeicticelementloc,andistruejustincasetheindividualxisatthelocationlocpointstoincontextc.(35)JHEREK=lx:locc(x)(tentative)However,asweareworkinginasystemwheretheprecisionalternativestoexpressionsareimportant,whatweneedtoconsideriswhatalternativesHEREwillhave.IfveryisincreasingtheprecisionforHERE,whatwewantforthealternativesisasetoffunctionsthatpointtomoreandmorepreciselocations.HEREwillstructureitsalternativesinthefollowingwayin(36).Thesealternativeswillbe(partially)orderedwithrespecttohowcloselytheapproximatethelocationofxinc.(36)JHEREKd=nfhe;ti:fˇd;clx:locc(x)oWhenveryiscombinedwithHERE,verywillnecessarilyrequirethatHEREbeinterpretedtoahighdegreeofprecision.76(37)Jvery[PRECHERE]K=JPRECHEREK(dc)=nfhe;ti:fˇdc;clx:locc(x)o3.4.4PrecisionandothernominalsHavingdiscussednominalsthathavenaturalwaysofbeingprecise,anddemonstratives,wheretheincreaseinprecisionisappliedtotheindexicalelementratherthanthenounitself,weturntoothercasesofverywhereveryseemstobeincreasingtheprecisionofanominalelement.Exampleofthisisarein(38)and(39),wherespotfallsintothisclassduetospots(locations)nothavinganaturalorderingtothem.(38)IstoodintheveryspotwhereLincolnstood.(39)Seaturtlesareabletoreturntotheveryspotwheretheywereborn.Likepersonintheprevioussection,though,ifweweretoincreasetheprecisionofspot,whatwewouldwindupwithisbeingmorepreciseaboutwhatitmeanstobeaspot,whichisintuitivelyincorrect.Rather,whatwewanttobemorepreciseaboutintheexamplein(38)istheexactlylocationwhereLincolnwasstanding(notjustsomewherecloseby!),andsimilarlyin(39)wewanttotalkabouttheexactspotonthebeachwheretheturtleswereborn.ThesyntaxforthisatLFwillbeasin(40),whereonceagainthedetermineriscombiningwithsomethingthatisnotthenoun;inthiscase,itcombineswiththeCPwhereLincolnstood.VerythisCP,andthedegreeofprecisionfortheCPisaccessibletoverythroughthePRECshift.77(40)DPDPDtheCPveryPRECCPtiCPwhereLincolnstoodNPspotiWhereLincolnstoodcanbeunderstoodasaconstituentthatcanbemademorepreciseinthiscontextbymakingfunctionsthataretrueoflocationsthataresuccessivelyclosertotheexactspotwhereLincolnstood.Theprecisionalternativesforitwouldbeasin(41).(41)JwhereLincolnstoodKd=nfhe;ti:fˇd;clx:Lincolnstoodexactlyatxo3.4.5VeryandordinalsFinally,veryisalsoabletomodifyordinalnumbersinsomecases.Someexamplesofverymodifyingordinalnumbersandrelatedcategoriesarein(42).Firstorlastaretheordinalsthataremosteasilybyvery,butincertaincircumstancesotherordinalssuchassecondcanbe78aswell.2(42)a.theverypersontowalkontheMoonb.theverylastpersoninlinec.?theverysecondthinghedidthatdayWhatisbeingintheseexamplesisnottheNP,northecomparisonclassprovidedbytheprepositionalphraseorrelativeclause.Rather,itisthatveryismakingtheinterpretationoftheordinalmoreprecise.FollowingBhatt&Pancheva(2012)andBylininaetal.(2015),I'lldecomposetheordinalintoanumeraloftypenandanordinalformingmorpheme-th.Bylininaetal.(2015),breakingfromotheranalyses(Bhatt,2006;Sharvit,2010),proposeasyntaxforordinalswithoutmovementofasuperlativemorpheme.Theirassumedsyntacticstructureforanordinalisbelow,wherenisanaturalnumberandCCisacomparisonclass-denotingrelativeclause.(43)[[[n-th]CC]NP]Iwon'ttakeupthemantleofintegratingmysemanticsforverywiththeirsemanticsforordinals,butitisnaturaltoseehowverycanincreasetheprecisionofthenumeralintheordinal.Numeralsbythemselvesareofteninterpretedimprecisely,butcanalsobeforcedtobeinterpretedmoreprecisely.Thenumeralone,forinstance,mightbeinterpretedashavingthehaloin(44),whereitdenotesasetofnaturalnumbersapproximating1.(44)JoneKd=n:n2Nˇd;c1Onerubinthisisthatthestpersoninlinedoesnotseemtonormallybeinterpretedimprecisely,andneitherdoesthenumeralone,whichbyhypothesisstcanbemorphologicallydecomposed2ExamplesshowthatverysecondispossiblecanbefoundonGoogle.Someincludetheverysec-ondthinghedidwassucceedinblowinguptheearth(http://forums.spacebattles.com/threads/if-dragonball-z-did-not-go-as-far-with-the-powerlevels.329869/)andtheverysecondthinghedidwhenheassumedPresidency/Premiership/DictatorofIraq(http://www.reddit.com/r/Military/comments/28d6b3/somebody_dropped_the_ball/).79into(one-th).3However,Idonotthinkthattheirpreferencetobeinterpretedpreciselyissupportforaviewwheretheyabsolutelymustbeinterpretedprecisely.Rather,incasesliketheverystpersoninline,Iwouldliketosuggestthatthereisrathersomeamountofpragmaticreasoninggoingonregardingtheuseofvery.Whenaspeakerusesverytoincreasetheprecisionofsomeexpression,thisalsoimplicatesthattherewasthepossibilityofinterpretingthatexpressionimpreciselybefore.Eventhoughtheverystpersonandthestpersonmightbetruthconditionallyequivalent,theformer(andnotthelatter)alsoimplicatesthepossibilityofhavinginterpretedthelatterimprecisely.3.5OtherformulationsofthesyntaxandsemanticsInthischapter,I'veassumedoneversionofasyntaxandsemanticsforexpressionsusingvery.But,therearealternativestotheseassumptionsthatcouldalsobeexploredwhilemaintainingtheinsightthatveryinthesecasesisslackregulating.OnesyntacticpossibilitythatcouldbepursuedismorecloselyadoptingthesyntacticproposalsfordemonstrativesinSchmitt2000.Inthisstructure,theNumPcontainingtheNPisthecomplementofacovertprepositionhere.HereraisestotheDhead,passingthroughAgr,whiletheNumPraisestoSpecAgrP.Thiscapturestheintuitionthatthelocativerelationitself(ratherthantheNP)isthecomplementtotheAstheNPisn'tthecomplementoftheuniquenessiscalculatedwithrespecttothelocativerelationratherthantheNP.3AiTaniguchi(p.c.)givesascenariowhereitispossibletointerpretstimprecisely.(i)YesterdaywasmyappearanceonTVasanactor.Well,kindaIwasonTVoncewhenIwas2andIwasinthebackgroundofsomelocaldaycarecommercial.Thatwasmyveryappearance.Thisseemstosuggestthatexpressionslikestreallydosimplyhaveamerepreferencethattheybeinterpretedprecisely,ratherthanthemrequiringabsoluteprecision.ThisiscompatiblewiththestoryIamtellinginthischapter.80(45)DPthisiD'D+[herej+Agr]AgrP[mank]Agr'[herej+Agr]PPLOCtiP'tjtkIfthisisusedasthestructurefordemonstrativenounphrases,itisstillthelocativeelementthatmustbeinterpretedmorepreciselywhenveryisusedasaslackregulator.ThebestoptionfortheinsertionsiteofverywiththisstructureistoadjoinverytothePhead,asbelow.Verywillthenbe81inapositiontoincreasetheprecisionofthelocativeelement,whilenotaffectingtheprecisionwithwhichtheNumPisinterpreted.(46)PPLOCthisP'Pvery+hereNumPmanTheanalysisforcaseswhereveryappearstomodifyanominalwithaninherentwayofincreasingitsprecisionmightalsobegivenadifferentformulation.OnewayofdoingthisthatwouldpreserveinsightsfromBarker2004wouldbetotreattheinthecenteroftheEarthasuniquenessrelativetothecenterrelation,ratherthanasuniquenessrelativetotheentireNPcenteroftheEarth.TorecallBarker'sanalysis,heanalyzescaseswithweaksuchasthosein(47)ascaseswherethedeterminerimposesuniquenessontherelation(corner,side).Barkernotesthattherearemanypossiblerelationsbetweenpossessorsandpossessedobjects(part-wholerelations,ownership,physicalproximity,andsoon),anduniquenesswithrespecttotherelationherecanbeconstruedasthespeakermarkingwiththeethatthereisasinglerelationheorshehasinmind.(47)a.Ihopethecafeislocatedonthecornerofabusyintersection.b.Inthecenteroftheroomisalargestonecube,about10feetonaside.Engravedonthesideofthecubeissomelettering.ReturningtotheverycenteroftheEarth,anotherwayofanalyzingthiswouldbetoanalyzetheasmarkingthatthespeakerhasinmindaparticularrelation,namelycenter(asopposedto,say,the82outsideoftheEarth).Eveninthiscase,though,whatverymarksisthatcentershouldbeconstruedmorepreciselythanitwouldotherwisebeconstrued.Althoughtherearedifferentwaysofanalyzingthesyntaxandsemanticsoftheconstructionsexaminedinthischapter,theparticularmodesofanalysisseemtohavelittlebearingontheobservationthatveryisabletoincreaseprecision.Futureworkontheseshouldexaminefurtherhowveryintothesestructures.3.6ConclusionThischapterexaminedcaseswhereveryisusedoutsideoftheadjectivaldomain.Inthesecases,veryisusedtomarkanincreaseinprecision.Inotherwords,thespeakerusesverytosignalthatsomeexpressionshouldbeinterpretedmorepreciselythanwouldotherwisebethedefault.Manyanalysesofveryproposethatverysuppliesadegreethatisextremeonascale.Imaintainedthisbasiclineofanalysis,butproposedthatverycouldsupplyextremedegreesnotjustforgradablepredicates(suchaswithverytall),butalsosupplyextremedegreeswithrespecttodegreesofprecision.Iextendedtheanalysisofsortafromchapter2totheanalysisofveryinthischapter,usingthetypeshiftPRECtotransformnon-gradablepredicatesintopredicatesthatcouldbegradedwithrespecttotheirdegreeofprecision,withverysupplyinganextremedegreeofprecision.Inthisway,thesamebasictoolsfromchapter2canbeusedtonotonlylowerprecision,asisthecasewithsorta,butalsoincreaseprecision,aswithvery.83CHAPTER4NUMERALSANDSOME4.1IntroductionApproximationinEnglishcanbeexpressedinvariousways.Forinstance,theadverbialsalmostandapproximatelyaresomewaysofexpressingthatanexpressionshouldbeconstruedapproximately.Anotherway,asdiscussedinchapter2,aretheadverbialssortaandkinda.Withnumerals,prepositionsprovideanotherwayofexpressingapproximation,asshownin(1).(1)a.aroundtenpeopleb.betweentenandtwentypeoplec.closetotenpeopleInthischapter,IlookatanapproximativeconstructioninvolvingnumeralsinEnglish.Partofwhatmakesthisconstructiontheoreticallyinterestingisitsrelianceontheepistemicsome.Thissetsitapartsyntacticallyfromotherinstancesofapproximation,inthattheelementthatisexpressingapproximationisnotanadverbialorapreposition.Examplesofthisapproximationconstruction(whichIwillcallNumSome)areshownin(2).Intheseexamples,someappearspost-numerally.TheinterpretationintheseexamplesisonewhereNumSomeexpressesarangeofpossiblenumbers,butwherethespeakerdoesn'tknowtheprecisenumberthattheclaimexpressedbythesentence.(2)a.Twenty-somepeoplearrived.b.Hisforty-someyearsofexperienceweredevotedtohumanresources.c.Icouldhaveitentirelyfullofsmalliconsandahundredsomeiconsononescreen.Othernumeralssuchasatleast10andnotmorethan20haveboundedinterpretations,84eitherlower-bounded(likewithatleast)orupper-bounded(likewithnotmorethan).WhatsetsNumSomeapartfromothernumeralsisthatithasbothalower-boundedandupper-boundedinterpretation;forinstance,thenumeralsintheexamplesin(2)abovewouldbeassociatedwiththeintervalsasin(3).1Thesalientfactaboutthisintervalisthatitslowerboundstartsatthenumeral,andhasanupper-boundasdeterminedbythesyntaxofthenumericalexpression(whichwillbeexplainedshortly).(3)a.[20;30)b.[40;50)c.[100;200)ThismakesNumSomedifferentthatsomeothertypesofapproximators,suchasaround.Althoughtheyseemsimilarinthattheyinvolveanumberthatisclosedtowhatisbeingaroundimplicatesahaloofnumberscenteredaroundthenumber(forinstance,somethinglike[1822]in(4)),whileNumSome'sintervalstartsatthenumberdenotedbythenumeralitself.(4)Isawaroundtwentydogsduringmywalktoday.(=Isawbetween18and22daysduringmywalktoday.)It'ssomewhattrickytoshowthatthereisaparticularnumberthatsetsthelowerboundforNumSome,duetotheepistemicrequirementthatthespeakerdonotknowtheprecisenumberthattheclaim.But,ifwepairanutterancewithafactabouttheworldthatthespeakerlearnslateron,wecanshowthattheutterancewaseithertrueorfalse.Whenwepair(5)with(6a),wherethefactofthematteristhattherewasanumberofdogsincompatiblewithtwenty-some,namely19dogs,thesentenceisjudgedfalse.However,if(5)ispairedwith(6b),wherethefactisthattherewereactually23dogsthespeakersaw,thentheutteranceisjudgedtobetrue.Thisshowsthattheutterancereallyislower-boundedatthenumeralthatisbeing1Theseusetheintervalnotation,wherethenumberisthelowerbound,andthesecondnumbertheupperbound.A[and]specifythattheboundincludesthenumber,while(and)specifythattheboundexcludesthenumber.85(5)Isawtwenty-somedogsduringmywalktoday.(6)a.Speakerlaterlearnshesawonly19dogs:(5)isjudgedtohavebeenfalse.b.Speakerlaterlearnshesaw23dogs:(5)isjudgedtohavebeentrue.Finally,returningtothequestionofhowandwheresomeislicensed,whatweobserveisthatNumSomeisonlypossibleifthenumeralisonethatcancombineadditivelywithanothernumeral.Whenthenumeralcannotcombineadditivelywithanothernumeral,asisthecasewithonethroughnineteen,NumSomeisimpossible.(7)a.*ten-someb.ve-some(8)a.ve(expected:15)b.ve-one(expected:6)Moreover,somedoesnothavetooccuraftertheentirephrasecorrespondingtothenumeral.Ifasmallerconstituentcancombineadditivelywithanothernumeral,somecanappearinthatposition,asin(9).(9)Morethanhalfoftheexpenditureofeighty-somethousanddollarsisforsoftcosts.4.2NumSomeasanepistemicThedrivingideabehindtheanalysislaterinthischapteristhatNumSomeisatypeofepistemicEpistemicarethatconveyignoranceonthepartofthespeakerastotheparticularreferentofsomenominalexpression.Theyarequiterobustlyattestedcross-linguisticallywithexamplesinEnglish(some),German(irgendein),Spanish(algún),Romanian86(vreun),Hungarian(vagy),andJapanese(theWH-kaseriesofpronouns).2Ratherthanexpressignoranceastotheidentifyofanindividual,however,whatNumSomedoesisexpressignoranceaswhichnumberadescription.Inotherwords,whatNumSomeisisatypeofnumeral.TomotivatethatNumSomereallyisanepistemicwehavetocompareitspropertieswithsomeotherknownepistemicTheepistemicthatIcompareNumSometosomeinitscanonicaldetermineruse,aswellasSpanishalgún.Someimplicatesthatthespeakerdoesn'tknowthepreciseidentityofthepersonbeingreferredto.Theexamplesin(10)and(11)below(attributabletoStrawson(1974))demonstratethiscontrastwithaandsome.WhilepersonBcannotaskthequestionaboutwhowasshotintheexchangein(10),duetopersonAhavingusedsome,thisisallowedin(11),duetotheabeingcompatiblewithknowledgeonthepartofthespeaker.(10)A:Somecabinetministerhasbeenshot!B:#Who?(11)A:Acabinetministerhasbeenshot!B:Who?ComparingthebehaviorofNumSometosome,wecanseethatNumSomerequiresthesameexpressionofignorance.Thisisillustratedin(12),wheresomeonecannotfollow-upanutterancethatusesNumSomebyaskingforanexactquantity.(12)A:Twenty-somestudentsaretakingmyclassthissemesterB:#Howmany?Alonso-Ovalle&Menéndez-Benito(2010)notethattheignoranceinferencewithalgúncanbereinforcedwithotherlinguisticmaterial.Thissetsitapartfrompresuppositionalcontentandassertedcontent,whichcannotbereinforced,duetobeingentailed.Thissuggeststhattheinferenceisnotentailed,butisratheranimplicature,asimplicaturesmoregenerallyareabletobereinforced.2SeeHaspelmath1997andAlonso-Ovalle&Menéndez-Benito2013foroverviews.87(13)MaríaMaríasalegoesoutconwithalgúnALGUNestudiantestudentdelofthedepartamentodepartmentdeoflingüística,linguistics,perobutnonotséIknowconwithquiénwhom.`Maríaisdatingsomestudentinthelinguisticsdepartment,butIdon'tknowwho.'Inotethattheignorancecomponentofsomebehavesinasimilarway,inthatitcanalsobereinforced.Likewise,theexpressionofignoranceinNumSomecanbereinforced,drawinganotherparallelbetweenknownepistemiclikesomeandalgúnandNumSome.(14)Mariaisdatingsomestudentinthelinguisticsdepartment,butIdon'tknowwho.(15)Marycookedtwenty-somepies,butIdon'tknowexactlyhowmany.3Toconcludethissection,NumSomeappearstopatternwithotherepistemicinthatitalsoenforcesanepistemicrequirementonthespeakerthatthespeakernotbeabletomakeapreciseclaimastotheidentityofthereferent.Withrespecttonumbers,thisamountstothespeakernotbeingabletocommitastowhichparticularnumberadescription.Thisissimilartothebehaviorofsomeandalgún.Moreover,likealgúnandsome,NumSome'signoranceinferencecanbereinforced,makingitpatternwithimplicaturesratherthanpresuppositionsandassertions.Inthenextsections,I'lldevelopananalysisofNumSomethatbuildsoffofAlonso-Ovalle&Menéndez-Benito(2010)'sanalysisofalgún,andshowhowtheignoranceinferencecanbegeneratedasanimplicature.3Thisexamplegetsworseorevenunacceptableifexactlyisleftoff:*Marycookedtwenty-somepies,butIdon'tknowhowmany.Mysuspicionisthatthisisduetoaclashbetweentwenty-somecommittingthespeakertosomemeasureofpies(justnotanexactmeasure),andIdon'tknowhowmanycommittingthespeakertonothavingknowledgeofanyparticularnumber.Sincethespeakerdoesassertheknowssomenumber,justnotaprecisenumber,hecan'tgoontofurtherasserthedoesn'tknowthenumberatall.884.3Representingcardinalnumbers4.3.1Hurford(1975)'sanalysisofnumeralsOneoftheearliestdiscussionofnumeralsintheformalsyntaxliteratureisthatofHurford(1975).Hurfordprovidesforatheoryofnumeralsusingasetofphrasestructurerules.Usingtheserules,hecangeneratethesetofnumeralsinEnglishandotherlanguages.Thephrasestructurerulesareprovidedin(16).NUMBERisthecategoryofadditivenumerals,and/standsfortheunit(thedigit1).PHRASEisthecategoryofmultiplicativenumerals.LexicalitemsofcategoryMarethemultiplicativebases;inEnglish,theseincludehundred,thousand,and-ty(asintwenty).(16)a.NUMBER!8><>:/(NUMBER)PHRASE(NUMBER)9>=>;b.PHRASE!NUMBERMc.M!NUMBERMThesephrasestructureruleshaveaninterpretationtogoalongwiththemaswell.TheNUMBERruleinterpretsitssubconstituentsascomposingviaaddition,whilethePHRASEruleinterpretsitssubconstituentsascomposingviamultiplication.Thesimplenumeralsonethroughelevencanbeconstructedinthissystembyrecursiveapplica-tionoftheNUMERALphrasestructurerule.Anumeralsuchasfourwouldbeconstructedasin(17).Each/getsinterpretedastheunit(e.g.,1),andsoadditionofeachunitwillgetthenumber4asthemeaningofthenumeralfour.89(17)NUMBER/NUMBER/NUMBER/NUMBER/Anumerallikeelevenwouldberepresentedinthesameway,asarecursivesequenceof/s.Forsimplicity,wecanjustwriteeleveninstead,withtheunderstandingthatit'saplaceholderforthatsequence.(18)NUMBERelevenNumeralssuchastwentyarerepresentedinadifferentway.Theobservationthesetypesofnumeralsisthattheyaremathematicallyandmorphologicallycomplex;twentyismorphologicallytwoand-ty,andmathematically2*10.Thestructurefortwentywouldberepresentedasin(19),wheretheM-tyistakentoalsoberecursivelyconstructedfrom/.90(19)PHRASENUMBER/NUMBER/M-tyMorecomplexnumbers,suchastwenty-fourcanbebuiltupwiththesephrasestructurerulesaswell.Twenty-fourwouldberepresentedasbelow.91(20)NUMBERPHRASENUMBER/NUMBER/M-tyNUMBER/NUMBER/NUMBER/NUMBER/Ifwecollapsethenumbersequencestogetheraswedidwitheleven,thisnumbercanberepresentedequivalentlyasin(21).92(21)NUMBERPHRASENUMBERtwoM-tyNUMBERfourHowdothesenumeralsgettheappropriateinterpretation?Hurfordsupposesthatthephrasestructurerulesalsohaveinterpretativerulesassociatedwiththem.PhrasestructurerulesthatgenerateaNUMBERareinterpretedusinganadditiverule;thevaluesofthesubconstituentsofaNUMBERarecomposedviaaddition.ForaPHRASE,thesubconstituentsareinsteadcomposedviaamultiplicativerule.Thevaluefortwenty-four,24,wouldbecalculatedas(1+1+1+1)+((1+1)10)=24,wherethesequencesofadditionof1representthevaluesforfourandtwo.Hurford'sproposaldoesovergeneratewithrespecttothenumeralsofEnglish(andotherlanguages),however.Forinstance,thereisnomechanisminplacetostopanumeralsuchasthirty-eleven(withtheinterpretationof41)fromarising.Thisobjectionaboutovergenerationisdiscussedlaterinthischapter,insection4.6.2.Inmyanalysis,I'llbuildonaspectsofHurford'ssystem,namelythatsimplexandcomplexnumeralsareconstituents.Beforestartingmyanalysis,though,it'simportanttoalsotalkaboutamorerecentanalysisofnumerals.4.3.2Ionin&Matushansky(2006)'sanalysisofnumeralsIonin&Matushansky(2006)proposeanalternativeanalysisofnumerals,wherecomplexnumeralsdonotnecessarilyformconstituents.First,theyarguethatmultiplicativenumerals,suchastwo93hundred,areformedviacomplementation.Twohundredcatswouldberepresentedasin(22),wheretwohundreddoesnotformaconstituent,butratherwherehundredtakestheNPcatsasacomplement.(22)NPNtwoNPNhundredNPcatsContrastingwiththisisthestructureforadditivenumeralsliketwohundredandthirtycats,asin(23).Thesenumeralsdoformconstituentsviacoordination.Eachofthecoordinatednumeralshastheheadnounasacomplement.Theheadnounistheneitherellidedfromtheconjunct,orbothinstancesundergoright-noderaising(whichI'verepresentedinthestructurein(23)).94(23)NPNPNPNtwoNPNhundredNPcatsConjPConjNPNthirtyNPcatsNPcatsSomeevidenceforastructuresuchasthiscomesfromBiblicalHebrewandLuvale(Zweig,2005),wheretheheadnouncanbepresentinbothconjunctsofanadditivenumeral.(AnexamplefromLuvaleispresentedbelow.)(24)mikokosheepmakumitenatanuvena-mikokoand-sheepvatanuvena-umweand-onesheep'(Zweig,2005)Ifthissortofright-noderaisingviewofnumeralsiscorrect,whatitseemstosuggestforthedefaultanalysisofNumSomeisastructurelikein(25),wheresomehasmergedwiththeheadnoun,and95thenounhasthenraisedoutofthestructure.(25)NPNPNPtwentycatsConjPConjDPsomecatsNPcatsThisanalysiswouldseemtohavesomethingtoofferinthecaseoftwenty-somecats;sincesomecatshasasitsmostnaturalreadinganinterpretationwherethenumberofcatsislow,andtwenty-somecatsmeanstwentycatsplussomelownumberofcats,thisstructurewouldpredicttherightinterpretationforthatphrase.But,Iarguethatthisstructuremakesthewrongpredictionforlargernumeralssuchastwohundred-somecats.Earlierinthischapter,Iarguethatanumberliketwohundred-somehasaninterpretationthatiscompatiblewithanynumberbetween201and299.Sincesomecatsseemstomostnaturallymeansomesmallnumberofcats,it'snotentirelyclearhowtwohundred-somecouldmeannumbersgreaterthan,say,210.Additionally,theuseofsomethatcanbeusedtocountanumberofindividualsisthereducedversion,sm,asin(26).However,thesomethatisusedinNumSomedoesnotseemtobethereduced96some.(26)a.There'ssm/??somecatsintheyard.b.Ihavesm/??somemarbles.Ofcourse,thesearen'tinsurmountableproblems.Fortheformerissue,wecouldappealtocontext-dependenceinsometosaythatsomerequiresalownumber,relativetoanothernumber.Sincenumberslike10,20,andeven50arelowwithrespectto200,thiscouldbethestartofananalysisforhowtwohundred-somecouldmean250.Forthelatterissue,acleartheoryoftherelationshipbetweensmandsome,andhowonemightbederivablefromtheother,mightalsoinformusthatthesomeinNumSomeisreallysm.Withoutsomemoreconcreteideasregardinghowtheanalysisin(25)wouldwork,however,I'llsetasideIonin&Matushansky'sanalysisandbuildananalysisthatisclosertoHurford'sinvor.AspectsofIonin&Matushansky'sanalysiswillbeadopted,though,particularlytheuseofcoordinationinadditivenumerals.4.4Myproposal4.4.1SimplecardinalnumbersInrepresentingthesyntaxandsemanticsofcardinalnumbers,IadaptproposalsfrombothSolt(2015),Ionin&Matushansky(2006)andHurford(1975).First,Iassumeadegreesemanticsforcardinalnumbers,followingasimilarmovebySoltforquantitywordssuchasfewandmany.Itreatsimplenumeralsasdenotingpropertiesofdegrees,typehd;ti.Thismakesacardinalsuchastwentyhavethedenotationasin(27).(27)JtwentyK=ld[d=20]Syntactically,numeralsareinsertedintheofaNumPprojection,asin(28),breakingwiththesyntaxproposedbyIonin&Matushansky(2006).ThisprojectionisabovetheNPprojection,97butstillcontainedinDP.TheroleofNumheadistomeasurethecardinalityofanindividual.Howthisisdoneisshownin(29).(28)DPDNumPNPnumeralNum0NumNPnoun(29)JNumK=lxld[jxj=d]SoltnotesthatthereisacompositionalissueintheNumheadinthisway.Understandardassumptions,theNPthatNumcombineswithissimplyapropertyofindividuals,he;ti.However,NumisofthewrongtypetocombinewiththeNP,beingtypehe;dti.Tosolvethis,SoltusestheDegreeArgumentIntroductionrulein(30)toputtheNPandNumtogether.Theresultingfunctionisnowtypehd;eti.(30)DegreeArgumentIntroduction(DAI):(Solt,2015)Ifaisabranchingnode,fb;ggarethesetofa'sdaughters,andJbK=lxe:P(x),JgK=lxeldd:Q(d)(x),thenJaK=lddlxe:P(x)^Q(d)(x).Atthispoint,thedenotationofanumeralandNumareincompatible(i.e.,Num0needsadegreeandnotapropertyofdegrees,asdenotedbythenumeral).Thesecanbemadetobecompatibleifthe98grammarallowsforxibilityinconvertingbetweentypes.ThispossibilityismotivatedbyPartee(1987),whoarguesfortheexistenceofafamilyoftypeshiftsformanipulatingnominaldenotations.Supposethatwegeneralizethesetypeshiftstodegreesaswellasindividuals.Thiscomesatabitofaprice,butthecostseemstobetostillbequitelow.Ageneralizediotatypeshift,asin(31),canthenbeusedtotakethepropertyofdegreesthatthenumeraldenotestoasingledegree,asthereisasingleuniquedegreethat'llsatisfythatproperty.Thismirrorsthebehaviorofthenominaliotatypeshift,whichtakesapropertyofindividualshe;titoasingleindividual,solongasthereisauniqueindividualinthedomainofdiscoursethatthatproperty.(31)IotaTypeshift(fromhd;titod,wheredisthetypeofdegrees):ShiftPtoid[P(d)]Ordinarynumeralslike,twentyandevencomplexnumeralslikethreehundredandcanhavetheiotatypeshiftappliedtothem.Thefunctiondenotedbytwenty,forinstance,isonlybythedegree20,andsimilarreasoningappliesforotherordinarynumerals.Puttingthistogether,apartialderivationfortwentypeoplewouldlookasin(32).44Theiotatypeshiftisrepresentedinthetreeasanon-branchingnode.Thisisonlymeanttothechangeintypeinvolved,andisn'tacommitmenttoanadditionalnodeinthesyntax.99(32)DPDNumPhe;tid(viaiota)NPhd;titwentyNum0hd;eti(viaDIA)Numhe;dtiNPhe;tipeopleThederivationfortwentypeoplewouldthenproceedasfollowsin(33).(33)a.JNumpeopleK=ldlx[jxj=d^people(x)](viaDIA)b.JtwentyK=ld[d=20]c.JtwentyK=id[d=20](viaiota)d.JtwentyNumpeopleK=lx264jxj=id[d=20]^people(x)3754.4.2ComplexcardinalnumbersCardinalnumberscanalsobecomplex,suchaswithtwenty-twooreighty-nine.Examplessuchasthesearesemanticallyadditive;twenty-twointuitivelyisformedbytheadditionof20and2,100andeighty-nineisintuitivelyformedbyadding80and9.FollowingIonin&Matushansky(2006),Iassumethatadditivecardinalnumbersarebuiltupsyntacticallybycoordinatingconstituentscontainingcardinalnumbers.Ionin&Matushanskysuggestthatcoordinationnaturallygivesthecorrectsemanticsforadditivenumerals.(34)demonstrateshowanadditivenumeralsuchastwenty-threewouldbeconstructedinmyadaptionoftheirproposal.(34)Structureofanadditivenumeral:NPNPtwentyXPXADDNPthreeAkeydifferencebetweentheformulationinthispaperandthatofIonin&MatushanskyistheuseofamorphemeADDintheheadoftheXP,whichtransparentlydoestheworkofadditivelycomposingthetwonumerals.ADDisasin(35).DandD0arepropertiesofdegrees,correspondingtothedenotationsofthenumeralconjuncts(suchastwentyandthreein(34)).ADDassertsthattherearetwodegreesd0andd00,suchthatd0holdsofDandd00holdsofD0,andwhenthesearesummed,theirsumisthedegreeforthenumeral.(35)JADDK=lDlD0ld9d0;d00d=d0+d00^D(d0)^D0(d00)Twenty-threewouldhavethelogicalformin(36).Essentially,twenty-threeissplitintoitscomponentparts,adegreeequalto3andadegreeequalto20,andthepredicateisbydegreesthatareequaltothesumof3and20.101(36)JtwentyADDthreeK=ld9d0;d00d=d0+d00^JthreeK(d0)^JtwentyK(d00)ThisnumeralwouldthenbeinsertedintoSpecNumP,justlikesimplexnumerals.4.5Analysis4.5.1SyntaxandsemanticsofNumSomeAsdemonstratedpreviously,NumSomeisonlypossiblewithadditivenumeralconstructions.Ianalyzethesomecomponentoftheconstructionasbeinglikeanumeral,albeitannumeral.InkeepingwiththepragmaticparallelsbetweenNumSomeandthemorecanonicaldeterminersome,Ianalyzesomehereasadetermineraswell,takinganNPcomplement.IassumethattheNPcomplementtosomeisasilentnounNUMBER.Acovertnominalofthissorthasbeenproposedtobeatworkinotherphenomenonusingnumerals(Kayne,2005;Zweig,2005).ThemeaningforNUMBERwillbeintentionallyquiteweak,beingsimplythedomainofdegrees,Dd.55ItseemsquitedifcultforNumSometodenoteafractionalnumber,suchastwenty-somedenoting25.5.IfsomeNUMBERisjustsimplydenotingthedomainofdegrees,it'ssomewhatunclearwhythisshouldbe,giventhatsomeauthors(Fox&Hackl(2007),forexample)assumethatthedomainofdegreesisasubsetoftherealnumbersR,andnotoftheintegers.There'stwooptionsthatcometomindhere.OnepossibilitywouldbetohaveNUMBERdenoteintheintegersZorinthenaturalnumbersN.Asecondpossibilitywouldbetohaveadditionalentailmentsstemmingfromamoregeneralsemanticsofnumeralsthatnumeralsnecessarilycountatomicindividuals.AnatomicityconstraintofthistypewouldthenforcesomeNUMBERtoalwaysdenoteaninteger.Ihaveverylittleelsetosayaboutthesepossibilitieshere,though,andleavethequestionforfurtherresearch.102(37)NPNPtwentyXPXADDDPDsomeNPNUMBERBasedonthesimilaritieswithalgún,Iproposetreatingsomeinasimilarway,adoptingtheformalizationforalgúnfromAlonso-Ovalle&Menéndez-Benito(2010).(38)JalgúnK=lfhet;etilPlQ:anti-singleton(f):9x[f(P)(x)^Q(x)](Alonso-Ovalle&Menéndez-Benito,2010)However,simplyadoptingthesemanticsforalgúnwillnotquiteworkforNumSome.Inordertocombineadditively,someNUMBERneedstobeapropertyofdegrees(andnotageneralizedThereviseddenotationin(39)forthesomeinNumSome(whichIwillrefertoassomedeg)thesechanges,withtheexistentialforcestrippedoutofsome.Crucially,however,theanti-singletonpresuppositionremains,asthisdrivesthepragmaticeffectsofNumSome.(39)qsomedegy=lfhdt;dtilDld:anti-singleton(f)[f(D)(d)]WhensomedegcombineswithNUMBER,thedenotationwouldlookasin(40),whereDdisthedomainofdegrees.(40)qsomedegNUMBERy=ld:anti-singleton(f)[f(Dd)(d)]103Twenty-some,annotatedwithtypes,wouldlookasbelowin(41).Notethatthesubsetselectionfunction(f)hasbeenrepresentedsyntactically.Thelogicalform,aftersomereduction,wouldlookasin(42).Essentially,twenty-someexpressestwentyplussomenumber.104(41)NPhd;tiNPhd;titwentyXPhdt;dtiXhdt;hdt;dtiiADDDPhd;tiDhdt;dtiDhhdt;dti;hdt;dtiisomedegfhdt;dtiNPhd;tiNUMBER(42)Jtwenty-someK=qtwenty[ADD[somedegNUMBER]]y=ld9d0;d00d=d0+d00^JtwentyK(d0)^qsomedegNUMBERy(d00)105Ournumeral(twenty-someintheexampleabove)isstilltypehd;ti,likeothernumerals.But,thereisstillatypeclashbetweenthetyperequiredofNum0(whichistypehd;eti)andournumerals.Thistimetheiotatypeshiftcannotasolutiontothisproblem;iotarequiresauniquedegree,butthereisnosuchdegreethatcansatisfyournumeral.Thenewstrategyistoraiseratherthanlowerthetype,usingatypeshiftfrompropertiestogeneralized(seealsoPartee(1987)).Here,thistypeshiftisfromdegreepropertiestogeneralizedoverdegrees,asin(43),furthergeneralizingthetypeshiftingsystemproposedbyParteetodegrees.(43)GeneralizedTypeshift(fromhd;titohdt;ti,wheredisthetypeofdegrees):ShiftPtolQ9d[P(d)^Q(d)]Byraisingthenumeraltothetypeofageneralized(shiftingfromhd;titohdt;ti)andRaisingthenumeral,wecancircumventthetypeclash.Thetraceleftbehindbythemovementwillbeinterpretedastyped,preciselywhatisrequiredofNum0.106(44)TPtNPhdt;titwenty-some1TPhd;til1TPtt1peoplearrivedThederivationfortwenty-somepeoplearrivedproceedsasfollowsin(45).First,thenumeraltwenty-someisconstructed,asin(41),andthenmergedinSpecNumP.Next,thenumeraltwenty-someisshiftedviatheGeneralizedtypeshiftin(43).ItundergoesQRandadjoinstoTP,leavingbehindatraceoftypedthat'sboundfurtheruptree.ThistraceisoftheappropriatetypetocombinewithNum0.6(45)a.JSHIFTK(Jtwenty-someK)=lP9d[Jtwenty-someK(d)^P(d)]=lP9d;d0;d00264d=d0+d00^JtwentyK(d00)^JsomeNUMBERK(d0)^P(d)375b.Jt1K=d16The9intherepresentationrepresentsdefaultexistentialclosureovertheindividualargumentHeim(1982).107c.JNumpeopleK=ldlx[jxj=d^people(x)]d.Jt1NumpeoplearrivedK=lx266664jxj=d1^people(x)^arrived(x)377775e.Jl19t1NumpeoplearrivedK=ld19x266664jxj=d1^people(x)^arrived(x)377775f.Jtwenty-somepeoplearrivedK=9d;d0;d00266666664d=d0+d00^JtwentyK(d00)^f(D)(d0)^9x266664jxj=d^people(x)^arrived(x)3777753777777754.5.2PragmaticsofNumSomeHowdoestheanti-singletonsubsetselectionfunctioncreatetheignoranceinferencewithNumSome?TheanalysisofthisparallelsthatofAlonso-Ovalle&Menéndez-Benito'sanalysisofalgún,inthattheanti-singletonconstraintforcesthehearertoconsiderwhythespeakerusesNumSomeandnotsomeparticularnumber.Indoingthis,thehearerconsidersalternativeswhicharerepresentedwithsingletondomains.Asthesearestrongerclaims,andthespeakerdidnotutteranyofthem,thehearercandrawtheinferencethatthespeakercouldnot(orwouldnot)committoanyofthem.First,Alonso-Ovalle&Menéndez-Benitoassume,followingKratzer&Shimoyama(2002),thatsentencesareimplicitlymodalizedwithanassertionoperator.Theytheassertionoperatorasin(46)below,anduseasashorthandforthisoperator.(46)JASSERTKc=lplw8w02Epistemicspeakerofcp(w0)ToseehowtheignoranceinferenceinasentenceswithNumSomeiscomputed,considertheutterancein(47),whichhastheassertionin(a).Thisassertionmerelysaysthatsomenumber108ofpeoplegreaterthan20arrived,andthatthespeakerbelievesit.Theroleoftheanti-singletonconstraint,in(b)istoensurethatasuitablesubsetofthedomainofdegreesDischosenusingthesubsetselectionfunctionf,butthatthissubsetisnotasingleton.InthecontextofNumSome,whatthisdoesisensurethatd0(theunknownnumberthatisaddedto20)willnotbeabletobenarroweddowntoasinglenumber.(47)Twenty-somepeoplearrived.a.Assertion:2666666649d;d0266666664d=d0+20^f(D)(d0)^9x266664jxj=d^people(x)^arrived(x)377775377777775377777775b.Anti-singletonconstraint:jf(D)j>1Forconcreteness,let'ssupposethatf(D)=f1;2;3g.d0couldthentakeasitsvalueanyofthose.Thealternativesfortheutterancein(47)wouldbeasin(48).Inotherwords,thealternativesincludethepropositionsin(a),(b),(c):twenty-onepeoplearrived,twenty-twopeoplearrived,andtwenty-threepeoplearrived.(48)Alternatives:a.9d;d0d=d0+20^d02f1g^d-peoplearrivedb.9d;d0d=d0+20^d02f2g^d-peoplearrivedc.9d;d0d=d0+20^d02f3g^d-peoplearrivedNoneofthealternativesin(48)wereutteredbythespeaker,howeverŠthespeakerutteredthemuchweaker(47).Fromthis,thehearerdrawstheinferencethat,sincenoneofthestrongeralternativesin(48)wereuttered,thespeakercouldn'tcommittoanyofthem,generatingtheimplicaturesrepresentedin(49).Negatingthepropositionsin(49)inthiswayhastheoutcomethatthespeakerwasnotabletocommittothatparticularproposition.109(49)Implicatures:a.:9d;d0d=d0+20^d02f1g^d-peoplearrivedb.:9d;d0d=d0+20^d02f2g^d-peoplearrivedc.:9d;d0d=d0+20^d02f3g^d-peoplearrivedFinally,tocomputetheactualmeaningofanutteranceincludingtheimplicatures,wethestrengthenedmeaning.Thestrengthenedmeaningofanutteranceistheassertionoftheutterance,conjoinedwitheachoftheimplicatures(ifthereareany).Hearingthestrengthenedmeaning,thehearerreasonsthatthespeakerisignorantabouttheparticularnumberofpeoplethatarrivedatthepartybecausethespeakerchosetoutteraformthatcommittedherselftonoparticularnumberofpeople.4.6ConstraintsonnumeralsTheanalysispresentedintheprevioussectionhasacrucialwwithit:itovergeneratesthepossibleinterpretationsofNumSome.Toseewhythis,considerthemeaningofsomeNUMBER,thenumeralthatgetsmergedwiththeadditivehead.Itsdenotationisrepeatedin(50)below.(50)qsomedegNUMBERy=ld:anti-singleton(f)[f(Dd)(d)]WhatsomeNUMBERdenotesissimplyanythinginthedomainofdegrees.ThisisbecauseNUMBERitselfisquiteweakly,alsojustdenotingDd.Inthenextsections,Iproposetwowaysofslippingconstraintsintothenumeralsystem.ThewayI'lldiscussistoencodepresuppositionsintotheADDheadaboutthetypesofnumeralsitcancombinewith.Thesecondwaywillbetoconstrainwhichalternativesaregeneratedbybasingtheirgenerationonpropertiesofthenumeralsystem.1104.6.1ADDanditspresuppositionsOnewayofconstrainingtheinterpretationsforNumSome(andforthenumeralsystemmoregeneral)istoencodethegeneralizationsaboutwhichnumeralsareabletocombineintothefunctionalheadsthatdotheworkofbuildingupnumerals.Forinstance,quitegenerallyinEnglish,numeralsthatdenoteaquantitylargerthan10donotadditivelycombinewithanothernumeralwithamultiplicativebasedenoting10.Thisgeneralization(andothergeneralizationsofthisform)couldbeencodedviapresuppositionsintheADDhead.Torestatethegeneralizationmoregenerally,ADDseemstobeabletoadditivelycomposetwonumeralsjustincasethesecondnumeraldenotesanumberthatisnotlargerthanthenumberdenotedbythemultiplicativebaseofthenumeral.Thisgetsusisanexplanationforwhytwentycanonlycombinewithonethroughnine:onethroughninedenotenumberssmallerthanwhatthemultiplicativebaseoftwenty(-ty)denotes,e.g.10.Thisalsoexplainswhyhundredcancombineadditivelywithninety-nine,thousandcombineswithninehundredninety-nine,andsoon.Althoughthisisquiteeasytostatedescriptively,makingthispartofthemeaningofADDissomewhatcomplicated.Thereareseveralcomplicatingfactors.First,ADDneedsaccesstothemultiplicativebaseofthehighernumeral.Inthecaseoftwenty-two,forinstance,ADDneedstobeabletoseethe-tymorphemethatispartoftwenty.IfADDcan'tseethemultiplicativebase,itwillhavenowayofcheckingthattheothernumeralintheadditiveconstructiondenotesanumberthatissmallerthanadditivebase.Theothercomplicatingfactoristhatthesenseofwrongnesswithnumeralslike*twenty-elevenisn'tthatoffalsity.Forinstance,wecouldrepresenttwenty-elevenasin(51)below,whereJ-tyK=10.7But,if*twenty-elevenisrepresentedinthisway,whatweexpectisforittobefalseofanynumber,since116<10.Thesense,however,isn'tthatwe'resayingsomethingfalseorcontradictory,butthatwe'resimplynotplayingbytherulesofthenumericalsystem.(51)ld9d09d00[d=JtwentyK(d0)+JelevenK(d00)^d00<J-tyK]7AndwecansetasidethequestionofhowJtwentyK=ld[d=20].111Onewaytoencodethissenseofwrongnesswouldbetoencodeitasapresupposition.Where*twenty-elevenwouldgowrongisthatelevendoesn'tmeetthepresuppositionthatthenumeralthatcombineswithtwentydenoteanumberbetween1and9.Intryingtowritethispresupposition,athirdcomplicatingissueappears.Toillustratethis,considerwhatmustbehappeningincheckingwhether*twenty-elevenisbuiltupcorrectly.ADDhasexamineelevenasitsaturatestheappropriateargumentofADD,anddeterminethatitmeetsthepresuppositionimposedby-ty.Inordertodothis,ADDmusthaveinformationaboutthemultiplicativebasebeforegettinginformationabouttheadditivenumeral.Inotherwords,-tymustbeavailabletoADDbeforeeleven,inordertoensurethatthedenotationofelevenissmallerthanthedenotationof-ty.Whatwouldthissyntaxlooklike?Notonlywould-tyhavetobeindependentlyaccessibletoADDfromtwenty,but-tywouldneedtobeanargumenttoADDbeforeeleven.Twooptionsforwhatthiswouldlooklikeareillustratedschematicallyin(52).(52)a.eleventwoADD-tyb.twoelevenADD-tyTwentyisanextremecase,sincewewouldbeforcedintoapositionwherethemorphosyntaxoftheworddoesnotseemtobetrackingthesemanticcomposition.112AnotherwayofaddingthepresuppositiontoADDthatperhapsdoesn'tdoquitesomuchdamagetothesyntaxwouldbetouseafeaturecheckingmechanismtoputafeaturerepresentingthemultiplicativebaseonADD.Thisfeaturecanbeinterpretedasasimpleproperty.(53)twentyADDBase10elevenInthisanalysis,-tywouldbeprovidingthe[Base10]featuretoADD,asdenotedin(54).(54)J[Base10]K=ly:y<10Wecouldassumethatfeaturesarecomposedwiththeheadstheyliveonthroughavariablerule,asin(55).Thisrulemerelymakesthesemanticcontentofthefeatureapresuppositionoftheargumentoftheheadthatfeaturecombineswith.(I'veunderlinedthepresuppositioninordertomakeiteasiertodistinguishfromtheassertion.)(55)If[F]isafeatureoftypehe;tiandXisaheadoftypehe;gi,wheregisanarbitrarytype,thenJ[F]XK=lx:J[F]K(x)[JXK(x)]Again,thissystemhasaovertheotheranalysisinthatitpreservesaparticularsyntaxforadditivenumerals.But,there'sadrawbacktothisanalysisaswell,inthatweneedtoassumetherearefeatureswithsemanticcontentthatareassociatedwithonlyparticularlexicalitemsŠthatthereisafeatureassociatedonlytonumeralsusingthemorpheme-ty,forinstance.ThissectionhasprovidedtwopossibleanalysesforhowtoputtherestrictionsregardingadditivenumeralsintothesemanticsoftheADDhead.Itseemsquitepossibletodoso,buttherearesomeunwelcomeaspectsoftheseanalysesatall.Fortheanalysis,wemustmakesomeunorthodox113assumptionsregardingthecompositionalityoftheadditivenumeral,inordertohave-tyrestrictthenumeralintherightway.Forthesecond,wemustpositanewfeaturethatwehavelittlemorphologicalevidencefor,andalsoclaimthatthisfeatureistiedtoparticularlexicalitems.Neitherapproachseemsparticularlyappealingcurrently,butinvestigatingthespaceofpossibilitiesissomethingthatshouldbeleftformoredetailedresearch.4.6.2Hurford'sPackingStrategy,appliedtoNumSomeAnotherstrategytoconstrainNumSomewouldbetoinvokeprinciplesregardingtherelationshipbetweentheformofanumeralandthenumberthatthatnumeralcandenote.AnexampleofthisisthePackingStrategyinHurford(1975).Hurfordconcedesthatthephrasestructurerulesheproposeshaveaproblem:theyover-generatewithrespecttotheactual,well-formednumeralsinEnglish(andotherlanguages),predictingnumericalcombinationsthataresimplynotseeninthelanguage.Inordertothis,additionalconstraintsarenecessary.Hurfordproposestheconstraintin(56),thePackingStrategy,whichcreatesawell-formednessconditiononnumeralstructures.8(56)PackingStrategy(Hurford,1975)AstructureAgeneratedbythephrasestructuresrulesisill-formedifa.itisofcategoryX,hasvaluex,andhasasimmediateconstituentsaNUMBERandsomeotherstructurewithvaluey,whereb.thephrasestructurerulesgenerateawell-formedstructureBofcategoryZwithvaluez,whereZisontheright-handsideofaphrasestructureruleexpandingXandisnotaNUMBER,andy<zx.Informally,whatthePackingStrategydoesistoensurethatthenon-NUMBERconstituentsŠthatis,theconstituentsthatarenottobeinterpretedadditivelyŠmakethelargestpossiblecontributiontothemeaningofthenumeral.ThePackingStrategyinspectsstructuresgeneratedbythephrase8Thenamereferstohowtheconstraint`packs'asmuchofthe(semanticformofthe)numeralintonon-NUMBERconstituents.114structurerules,andonlyallowsstructureswherethemeaningofnon-additiveconstituentsismaximized.Inthecaseofthirty-oneand*twenty-eleven,whichbothdenote31,thePackingStrategymakesitsothatthenumeralthirtyispreferredovertwenty.Toseehowthisworks,assumethatthesenumbershavethestructuresin(57)and(58).(57)thirty-oneNUMBERPHRASENUMBERthreeM-tyNUMBERone(58)twenty-elevenNUMBERPHRASENUMBERtwoM-tyNUMBEReleven115Inrulingout*twenty-eleven,thenumeral'svalueiscomputed,31,andotherstructureswiththesamevaluewillbewhat*twenty-eleveniscomparedagainst.Inthisexample,thirty-oneisthecompetitor.Thenumeralisinspected,anditisfoundthatthirtyisabetterchoicethantwenty,sincethirtyhasthegreatestnumericalvaluethatisstilllowerthanthevaluefortheentirenumeralstructure.Thisforcesthirty-onetobetheappropriateformforthesemanticvalue31,ratherthan*twenty-eleven,sincethePackingStrategyrequirestheconstituentthatisnotaNUMBERconstituenttohavethehighestvaluepossible.IfwesupposethatsomeNUMBERwouldbegeneratedasaNUMBERconstituentinHurford'ssystem,thenthePackingStrategycouldbeusedtoconstrainthevaluesthatsomeNUMBERcantake.Toillustratehowthiswouldwork,let'sconsidertwenty-some(underlyinglytwenty-someNUMBER),andwhyitcannotdenotethenumber31.Inmyanalysisintheprevioussections,someNUMBERsimplydenotesadegreeinDd,meaningthatsomeNUMBERcouldinprincipledenoteanydegree.Let'ssupposethatsomeNUMBERdenotes11.Then,whencomposedadditivelywithtwenty,twenty-somecoulddenote31.ThePackingStrategyforcesthespeakertoconsiderotheralternativewaysofexpressingthesamenumberusingdifferentnumericalforms.If31isthenumberbeingintendedwithtwenty-some11,onecompetitortotwenty-some11willbethirty-some1(I'vesubscriptedthenumberthatsomeNUMBERwoulddenoteonsome).Toexpress31,thirty-some1ismoreoptimalthantwenty-some11,duetothecontributionofthenon-additiveconstituentbeingmaximizedwhilethecontributionoftheNUMBERconstituentisminimized.Inotherwords,becausethePackingStrategyprefersnon-additiveconstituentstobeaslargeaspossible,theuseofthirtyispreferabletotheuseoftwentysincemoreof31isfipackedflinthirtycomparedtotwenty.Togeneralizeabit,whensomeNUMBERcombineswithtwenty,thirty,andothernumeralswithamultiplicativebaseof10(e.g.,twenty=2*10),someNUMBERcannottakethevalueofanythingotherthan1through9,sincelargervalueswouldbesubjecttothePackingStrategyandwouldhavetoberepresentedbytheotherconstituentinthenumeral.Thisprovidesanexplanationforwhytwenty-somecanonlymean21through29;ifsomeNUMBERtakesthevalueofanumberthatis116greaterthan10,thenthatnumbercouldbebetterexpressedinthenon-additiveconstituent,andanalternativeformwouldneedtosurfaceinstead.4.7ConclusionThischapterinvestigatedtheuseofsomeinformingapproximatemeaningswithnumerals.Inmyanalysis,IproposethatwhatsomedoesinthesekindsofsyntacticismergewithanullnounNUMBERthatdenotesinDd.WhattheNumSomemeans,then,issomenumberwithalowerboundatthenumeralthatwasThisisconstrainedontheupper-boundbyindependentconstraintsonnumerals,whichcouldbecashedouteithersyntactically(throughafeature-checkingmechanism)orsemantically(byassumingasemanticconstraintoftheformofHurford(1975)'sPackingStrategy).117CHAPTER5SOME-EXCLAMATIVES5.1Introduction5.1.1BasicdataTheobservationofsome-exclamativesthatIamawareofintheliteratureisworkbyIsrael(1999,2011).AccordingtoIsrael,themeaningoftheseexclamativesisthatthesubjectisanextremeexemplarofthesomenounphrase.(1)Boy,wasshe(ever)somedancer!(Israel,1999)fiShewasadancerandshewasanexceptionaldancer.fl(2)Thatwassomewineshebroughttotheparty!fiShebroughtwinetothepartyanditwasverygoodwine.fl(3)Somefriendsheturnedouttobe!fiShewasafriendandshewasaparticularlypoorfriend.fl(4)It'sgoingtobesomeparty!(Israel,2011)fiWe'rehavingapartyandit'sgoingtobeagreatparty.flIsraelnotesthattheexclamativemeaningislikelytoberelatedtothehedging(epistemicuseofsome,butdoesn'tprovideacompleteanalysisofhowthiswouldwork.Iwillarguethattheexclamativeusearisesfromaninteractionoftwocomponents.LikeIsrael,Isupposethattheepistemicuseofsomeplaysarolebycreatingasetofalternatives.However,thisisnotquiteenough,sincesomegenerallydoesn'tgiverisetoexclamatives.Thisiswheretheobservationthatsome-exclamativescarryaparticularintonationalcontouronthesomecomesin.118Whenthisintonationalcontourisremoved,theexclamativemeaningisunavailable,andtheordinarymeaningarises.(5)a.Thatwassomewineshebroughttotheparty!b.#Thatwassomewineshebroughttotheparty.(6)a.It'sgoingtobesomeparty!b.#It'sgoingtobesomeparty.Thisisthesecondmajorcomponentofsome-exclamatives,theintonationalcontour.Iarguethattheintonationitselfplaysaroleincreatingtheexclamative.Thisroleistostructurethesetofalternativesdenotedbythesententialcoreoftheexclamative,andassertanattitudetowardsoneofthealternatives.Finally,theexamplesallpreviouslyusedshowthatsome-exclamativesaremosteasilyusedwhenthephraseheadedbysomeisinpredicativeposition,suchasafterthecopula.Thiswouldseemtosuggestthat,intermsofthelogicaltypeofsomeNP,itshouldbethoughtofasasimplepropertyofindividuals,typehe;ti.5.1.2Aretheyreallyexclamatives?IntheliteratureonexclamativesinEnglish,thevastmajorityofattentionhasbeenfocusedonthepropertiesofwh-exclamatives,likethosein(7),aswellasnominalexclamativesliketheonein(8).Astheseformthecanonicalcasesofexclamativesentences,wemightaskwhethersome-exclamativesshouldalsobeconsideredtobeexclamatives.Israelarguesthattheyshouldbe,andIfollowhiminalsoarguingthatsome-exclamativesareexclamativesbasedonthepropertiesthatprototypicalexclamativeshaveaccordingtoMichaelis&Lambrecht(1996).(7)a.Whatalargewatermelon!b.Howbeautifulthebirdssing!(8)Thepeppersheeats!119Zanuttini&Portner(2003)arguethatexclamativesarecharacterizedbytwosyntacticproperties,givenin(9).(9)Syntacticpropertiesofexclamatives(Zanuttini&Portner,2003)a.ExclamativescontainaWHoperator-variablestructure.b.ExclamativescontainanabstractmorphemeFACTintheCPdomain.ByaWHoperator-variablestructure,whatZanuttini&Portnermeanisthatexclamativesareunderlyingquestions,havingaWH-operatorthatbindsavariableinthepropositionexpressedbythesentence.ThisismotivatedbythefactthatWH-exclamativesseemtoweartheirquestionhoodonthetheirsleeveinthattheyclearlyhaveaWH-wordintheirstructure.Next,exclamativesareanalyzedasmakinguseofadomainwideningoperation,conceptuallysimilartothedomainwideningusedbyKadmon&Landman(1993)intheiranalysisofany.Exclamativesentenceshaveattheircoreasetofalternativepropositions,whichiswidenedtoincludepropositionsthatwouldnototherwisebeunderconsideration.(10)ExclamativeswidenthedomainoffortheWHoperator,whichgivesrisetothesetofalternativepropositionsdenotedbythesentence.Zanuttini&Portnerhavetheoreticalreasonsformakingthe(a)partoftheirproposal;theyarguethatexclamativesdenotesetsofalternativepropositions,asaresultoftheoperator-variablestructure.AsIwillargueforlater,exclamativesdenotesetsofalternatives,butthatthemeansbywhichthesealternativesaregeneratedinsome-exclamativesisquitedifferentthanwithothertypesofexclamativeconstructions.Therefore,Iwon'tfollowZanuttini&Portner'ssyntacticcharacterizationofexclamatives,butnotethatmyproposalinquitewellwiththeirsemanticcharacterizationofexclamatives(tobediscussedshortly).Israel(1999)notesthatsome-exclamativeshavetwoofthepropertiesinMichaelis&Lam-brecht'slistofpropertiesofexclamatives:some-exclamativesinvolveanattitudethat'sindexedtothespeaker,andsome-exclamativesinvolveanotionofscalarextent.Michaelis&Lambrecht'slist120oftypicalpropertiesexhibitedbyexclamativesisin(11).(11)Semantico-pragmaticpropertiesoftheabstractexclamativeconstruction(Michaelis&Lambrecht,1996)a.presupposedopenpropositionb.scalarextentc.assertionofaffectivestance:expectationcontraventiond.ofdescribedreferente.deixisSome-exclamativesalsoexhibitthe(a)propertyinthelistaswell.WhatMichaelis&Lambrechtmeanbypresupposedopenpropositionisthatexclamativesarefactive.Some-exclamativesarealsofactive,ascanbeshownbyusingthe`Hey,waitaminute!'testforpresuppositions(Shanon,1976;vonFintel,2004).(12)A:Man,Johnissomelawyer.Healwaysloseshiscases.B:Hey,waitaminute!Ididn'tknowJohnwasalawyer.Giventhesimilaritiesbetweensome-exclamativesandotherexclamativesintermsoftheirmeanings,Iwillcontinuetorefertosome-exclamativesasexclamatives.5.2Theoriesofexclamatives5.2.1QuestiontheoriesofexclamativesOnetypeoftheoryofexclamativestreatsexclamativesasbeingsemanticallyrelatedtoquestions.,thepropositionalcontentofanexclamativeisequivalenttothatofaquestion,butthedifferencebetweenaquestionandanexclamativeliesintheirsententialforce.ThesekindsoftheoriesadoptasemanticsforquestionsinthestyleofHamblin(1973),Karttunen(1977),andGroenendijk&Stokhof(1984).121Undernormalassumptions,declarativesentencesdenotepropositions,functionsfromworldstotruthvalues,typehs;ti.However,ifthisisso,whatdosentencesthataren'tdeclarativedenote?Hamblinproposesthatquestionsaresetsofpropositions,typehst;ti(thisviewisfurtherdevelopedbyKarttunenandGroenendijk&Stokhof).ThequestionWhoiscoming?mightberepresentedasin(13).(13)JWhoiscoming?K=lp9xp(w)^p=lw0come(w0)(x)Gutiérrez-Rexach(1996)adoptsthisviewofquestionsandproposesthatbothquestionsandexclamativeshave,attheircore,essentiallythesamedenotations.WhatsetsexclamativesapartfromquestionsistheuseofanillocutionaryoperatorEXCwhichoperatesonavariableindexedtothespeaker,theworld,andasetofpropositions.Gutiérrez-Rexach'sforthisisasin(14),whereEMOTisasetofemotivepropertiesthatspeakerscanhavetowardspropositions,suchassurpriseandamazement.(14)Letabethespeaker,waworld(typicallytheactualworld),paproposition,andP2EMOT(thesetofemotiveproperties).Then,EXCdef=lalwlphs;ti9Phs;hst;etii[P(w)(p)(a)]AsomewhatdifferenttheoryofexclamativesisthatofZanuttini&Portner(2003).Intheiranalysis,Zanuttini&PortnerfollowGutiérrez-Rexachinanalyzingthecoreofawh-exclamativesentenceasbeingaquestion.WhereZanuttini&Portner'sanalysisdiffersisinthesourceoftheexclamativereadingitself.Theyarguethatexclamativeshaveattheircoreanotionofdomainwidening.TheconceptofdomainwideninghereisrelatedtotheanalysisofanyinKadmon&Landman(1993),whereanyisasimpledeterminer,butshiftsthedomainoftoastrongerdomainwhenembeddedundernegation.InZanuttini&Portner,domainwideningappliesatthelevelofpropositions.Domainwideningappliestothesetofpropositionsdenotedbythesententialcoreoftheexclamative,andwidensthissettoincludepropositionsnotpreviouslyunderconsideration.Theirofwideningisprovidedin(15).122(15)Widening(Zanuttini&Portner,2003)ForanyclauseScontainingRwidening,widentheinitialdomainofforRwidening,D1,toanewdomain,D2,suchthati.JSKw;D2JSKw;D16=0andii.8x8y[(x2D1&y2(D2D1))!x<y]Toillustratehowthisworks,let'sconsidertheexclamativein(16).Zanuttini&PortnerfollowKarttunen(1977)intreatingquestionsasdenotingsetsoftrueanswers,sothesetofalternativesisasin(17).(16)Whatpeppersheeats!(17)JWhatpeppersheeats!K=fp:pistrueinwand9asuchthatp=[`heeatsa']g=f`heeatspoblanos';`heeatsserranos';`heeatsjalapeños'gTobuildtheexclamativeinterpretation,thedomainofthissetofalternativesisexpandedtoincludepropositionsthatweren'tunderconsiderationbefore.Inthesetin(18),whichhasundergonewidening,thepropositionheeatshabanerosisnowincluded.Inessence,whatthewideningoperationdoesisbuildtheinterpretationthatthispersoneatsavarietyofpeppers,andheeveneatstheseextremelyspicypeppers,habaneros.Ifthereareanyotherpeppersheeats,they'renotworthourconsideration,sincethey'vefallenoutsideofthewideneddomain.(18)f`heeatspoblanos';`heeatsserranos';`heeatsjalapeños';`heeatshabaneros'gTosummarize,severallinesofresearchhaveproposedthatexclamativesandquestionsareunderly-ingsimilar,inthatbothhaveastheircoredenotationsasetofpropositions.5.2.2DegreetheoriesofexclamativesIncontrastwithquestiontheoriesofexclamatives,whichtreatexclamativesasbeingunderlyinglyquestions,degreetheoriesofexclamativestreatexclamativeconstructionsasbeingonparwith123otherdegreeconstructions,suchasmeasurephraseonorcomparatives.Inotherwords,ratherthanaccountingforthesemanticsofexclamativesbysayingthattheyaresetsofpropositions,thesemanticsofexclamativesisaccountedforbyassumingthatexclamativesmakeuseofsetsofdegrees.SomeaccountsinthistypeoftheoryarethoseofCastroviejoMiró(2006)andRett(2008,2011).CastroviejoMiróarguesforadegreeanalysisofwh-exclamativesinCatalanbasedontheobservationthattaninexampleslike(19)and(20)occursinbothexclamativeenvironmentsandincanonicaldegreeconstructions.Whatmakesexclamativesdifferentfromothersentencetypesishowtheyupdatethecommonground.Assertionsupdatethecommongroundtoexcludeworldsincompatiblewiththeassertion,whileexclamativesinthisanalysisbackgroundtheinformationcontributedbythedegreeconstruction,andimplicateaspeaker-orientedattitudetowardsadegree.(19)EntheFerranF.haAUX.hepreparatpreparedunapastíscaketansobogoodquethathaAUX.heguanyatwoneltheconcurscontest`Ferranmadesuchanicecakethathewonthecontest.'(20)QuinwhatpastíscaketansobogoodquethathaAUX.hepreparatpreparedentheFerran!F.`WhatanicecakeFerranmade!'Rett(2011)alsoarguesthatexclamativesaredegreeconstructions.Sheobservesthatexclamativesoftenmakeuseofovertgradableexpressions,suchasin(21).Whennogradablepredicateisovert,however,acovertgradablepredicateM-OPisused,whereM-OPmeasuresoveracontextuallysalientdimension(inthecasesin(22)below,thedimensionscorrespondingtodeliciousandexoticmightbelicitincontext).(21)a.WhatdeliciousdessertsJohnbaked!b.TheexoticplacesJohnvisited!(22)a.WhatM-OPdessertsJohnbaked!b.TheM-OPplacesJohnvisited!124Thecoreoftheexclamative,forRett,isasetofdegrees(ratherthanasetofpropositions).Aprocessofdefaultexistentialclosureoverdegreesconvertsthisintoaproposition.AcovertillocutionaryoperatorE-FORCEexpressessurpriseatthatdegree.Thisisschematizedin(23),whered0isthedegreeexistentiallyoverandsCisthespeakerincontextC.(23)HowtallJohnis!a.ld:tall(john;d)b.tall(john;d0)c.E-FORCE(p)countsasanexpressionthat9d0suchthatsChadnotexpectedthatD(d0).5.3Some-exclamativesmakereferencetokindsIarguethat,attheircore,some-exclamativesareultimatelykind-related.Thatistosay,some-exclamativesmakeassertionsinvolvingkinds,asopposedto(say)degrees.Therearetwoimportantpiecesofevidencethatkindsareinvolvedinsomeexclamatives.First,NPsthatdonothaveclear,well-establishedkindsareoddinsomeexclamatives.GoingbacktoCarlson(1977),it'sbeenarguedthatreferencetokindsdependsontheaccessibilityofanestablishedkind.Sincegreenbottles(in(24a))arenotanestablishedkind,theyalsodonotallowforsubkinds,andhenceareillicitinsomeexclamatives.Asimilarlineofreasoningholdsfor(24b),aspeoplethatareinthenextroomdonotformakind.(24)a.??Thisissomegreenbottle!b.#Johnissomepersonfromthenextroom!AsnotedbyConstantinescu(2011),somenounsdonothavereadilyaccessiblestereotypicalpropertiesassociatedwiththem,suchasbuildingorroom.Sincekindscorrespondtogeneralpropertiesthatcharacterizegroupsofindividuals,wemightsupposethatthelackofstereotypicalpropertiesforbuildingandroomwouldmakesubkindsforthemdiftoconstrueinmany125contexts.Thispredictsthatbuildingandroomwouldbedifculttouseinsomeexclamatives,whichseemstobethecase(25).Othernounsthatlackstereotypicalproperties,suchasnon-Methodist(Morzycki,2012),arealsodiftouse.Thisisanotherpieceofevidencethatkindsareinvolvedinsomeexclamatives.(25)a.??Thisissomebuilding!b.??Thisissomeroom!(26)??Heissomenon-Methodist!Finally,anadditionalpieceofevidencesuggestingthatthereisreferencetokindsinsome-exclamativescanbefoundbylookingatpost-nominaladjectiveslikenavigableandvisible.AsnotedbyBolinger(1967),theseadjectivesobligatorygettemporary,episodicinterpretationswhenusedpost-nominally,asin(27).However,whentheseadjectivesareusedinthecanonicalpre-nominalposition,likein(28),theseadjectiveseithergettheepisodicinterpretation,oraninterpretationwheretheyarecommentingoninherent,stableproperties.Larson&Maruıic(2004)goastepfurtherandclaimthatthisisaofastage-level/individual-leveldistinction,inthesenseofCarlson(1977),wherestage-levelpropertiesaretemporarypropertiesapplyingtospatio-temporallylocatedstagesofindividuals,whileindividual-levelpropertiesarepermanentpropertiesapplyingtothewholeindividualstheirselves.Thisideaiscloselyrelatedtokinds,inthatinstantiationsofkinds(butnotkindsthemselves)arethesortsofobjectsthatstage-levelpredicationscanbemadeof.(27)a.thestarsvisible(stage-levelonly)b.theriversnavigable(stage-levelonly)(28)a.thevisiblestars(stage-levelorindividual-level)b.thenavigablerivers(stage-levelorindividual-level)Insome-exclamatives,pre-nominaladjectivesareallowed,asshownin(29),whilethesameadjective126isbarredpost-nominally.IfLarson&Maruıic(2004)arecorrectinidentifyingthepost-nominalpositionasbeingrelatedtostage-levelinterpretation,thenthisisfurthersupportforakind-levelinterpretationbeingusedinsome-exclamatives.Asepisodicstage-levelinterpretationsmustbepredicatedofindividuals,thefactthatthesepost-nominaladjectivesareallergictothenounphraseinsome-exclamativessuggeststhattheNPisalsonotapredicateofindividuals.(29)a.Thisissomenavigableriver!(Webarelymadeittotherivermouthalive!)b.Thesearesomevisiblestars!(Icanbarelyseethem,andIknowwheretolook!)Toconcludethis,Iwillassumethatkindsplayaroleintheinterpretationofsome-exclamatives.Inparticular,I'llsuggestthatsome-exclamativesmakereferencetosubkindsofthekinddenotedbytheNPthatthedeterminersomecombineswith.5.4KindswithintheDPIntheprevioussection,Iarguethatsome-exclamativesinvolvereferencetokinds,atsomelevel.Thelocusforreferencetokindsinsome-exclamatives,I'llassume,iswithintheDP.Imentionafewproposalsthatformthebackgroundtomyanalysisinthissection,whereIwillultimatelyassumeamodelthatissimilarinspirittothatofZamparelli(1995)'sideaofalayeredDP.5.4.1Zamparelli'slayeredDPTherearemanyproposalsthatputreferencetokindswiththeDP.OneproposalisZamparelli(1995).ZamparellisuggeststhattheDPbeexpandedintoanumberoffunctionalprojections(asin(30)).Thiscreatesadivisionoflaborbetweenthevariousprojectsinthestructure;differenttypesofsemanticinformationisavailableatdifferentlevelsintheDPstructure,creatingacloseconnectionbetweenthesemanticderivationandthesyntacticderivation.TheprojectionclosesttotheNP,KIP,isinvolvedinkindpredication.Furtherupthetree,thePDPprojectionisinvolvedinpredicationofordinaryindividuals(itsthelevelcorrespondingtothesemantictypeforproperties127ofindividuals),whiletheSDPlayerisinvolvedwithanddetermination(e.g.,withstrongdeterminers).(30)Zamparelli'sLayeredDPSDPSDPDPPDKIPKINPNIwillnotbeassumingZamparelli'smodeldirectly,buttheconceptthatkindsarerepresentedlowwithintheDPwillbeimportantformyanalysislaterinthissection.5.4.2KindargumentsincommonnounsAnotherkindofapproachisthatofMcNally&Boleda(2004).TheproblemthatMcNally&Boledaaretryingtoaccountforistheinterpretationofnominalswithrelativeadjectives,liketheexamplesin(31).Theseadjectivesposeapuzzleinthattheydonotbehavelikeintersectiveadjectives,asshownin(32),wherethe(b)entailmentonlygoesthroughwiththeintersectiveadjective.(31)a.Martiisatechnicalarchitect.b.Johnisabankruptcylawyer.(32)a.Martiisamalearchitect.(intersectiveadjectivemale)(i)Martiisanarchitect.128(ii)Martiismale.b.Martiisatechnicalarchitect.(i)Martiisanarchitect.(ii)#Martiistechnical.Thesolution,McNally&Boleda(2004)argue,istoimbuenominalswithasecondargumentthatcanbethetargetofIndoingthis,theyborrowamovefromLarson(1998),whoarguesthatcertainnounshaveaDavidsonianeventargument,inadditiontothestandardindividualargument.Thisisbasedontheobservationthatabeautifuldancercanbebothadancerwhoisbeautiful(apredicationoftheindividualdancer),andadancerwhodancesbeautifully(apredicationoftheeventofdancing).ThemovethatMcNally&Boledatakeisn'ttoputeventargumentsincommonnouns,rather,buttoputinakindargument,correspondingtoakindinthesenseofCarlson(1977).Thedenotationforthenounarchitectwouldlookasin(33).1TheRisCarlson'srealizationrelation,whichholdsbetweenanindividualandakindjustincasethatindividualisaninstantiationofthatkind.(33)JarchitectK=lklx[R(x;k)^architect(k)]Moregenerally,commonnounswilladenotationlike(33),wherethenoundenotesarelationbetweenkindsandindividuals,typehk;eti.Relationaladjectives,liketechnicalintechnicalarchitectdenotepropertiesofkinds,likein(34).Thesearecombinedwiththenounusingaintersectiverulein(35).(34)JtechnicalK=lk[technical(k)](35)Ifaisabranchingnodeandbandgarethenode'sdaughters,andbistypehk;tiandgistypehk;eti,thenJaK=lxkly[JgK(x)(y)^JbK(x)]Thedenotationfortechnicalarchitectwouldbethelogicalformasin(36),viaputtingthecommon1I'veslightlyredevelopedtheirformalnotationinthissection.129nountogetherwiththeadjectiveviathecompositionalruleabove.2(36)JtechnicalarchitectK=lklx[R(x;k)^architect(k)^technical(k)]Thisanalysishelpsexplaincertainpropertiesofrelationaladjectives,includingtheirentailmentpatternsandthefactthatrelationaladjectivesseemtobequitelowinthenounphrase.Thereareacoupledrawbackstothissortofsystem,however.Theisthatitisquiteunintuitivetothinkofnounsasbeinginherentlyrelational.Moreover,puttingtheRrelationintothesemanticsofnounsseemstobemissingageneralizationastothenatureoftherelationshipbetweenkindsandobjects.Finally,byputtingthekindargumentinthenominal,weloseanyhopeforacleanmappingbetweenthesyntaxandsemanticswithrespecttothedistinctionbetweenkindsandobjects.Althoughthisproposalisinteresting,theseconsiderationsshouldmakeuswaryofadoptingit.Inthenextsection,Idiscussarelatedproposalthatwillformthebasisfortheanalysisofsomeinlatersections.5.4.3Types,tokens,andNumPGehrke&McNally(2013)argueforasystemsimilartothatofZamparelli(1995),withkindsrepresentedlowwithintheDP.However,ratherthantreatingthenounasdirectlydenotingakind,asZamparellidoes,theysuggestthatthenoundenotesapropertyofkinds.(37)JcarK=lxk[car(x)]Inordertomakethispropertysomethingthatcanbepredicatedofordinaryobjects,itmustbetransformedintoapropertyoftokenentitiesandnotkinds.Theysuggest,followingrelatedproposalsbyDéprez(2005)andMüller-Reichau(2011),thatNumPisthelocusforthisoperation.Thisisillustratedin(38),whereRisavariantofCarlson(1977)'srealizationrelation,whichrelateskindstoindividualsthatinstantiatethem.(38)J[NumP[NPcar]]K=ly9xk[car(xk)^R(y;xk)]2McNally&Boleda(2004)saturatethekindargumentwithafreepronounthatisvaluedwithacontextually-determinedkind.Iseenoreasonthatasimilareffectcouldn'tbeobtainedusingexistentialclosureorachoicefunction.130Thishastheofprovidingatransparentmappingbetweensyntaxandsemantics,unlikethesysteminMcNally&Boleda2004.Iwillassumeaversionofthisinmyanalysisofsome-exclamativeslaterinthischapter,wheresomeplaystheroleofaNumheadandrealizeskinds.5.4.4Weir(2012)'sanalysisofsomeBeforemovingontomyanalysis,itshouldalsobenotedthatWeir(2012)hasalsoproposedthat,incertainenvironments,someissensitivetokinds.Henoticesexamplessuchas(39),wherewhatthespeakerisexpressingignoranceaboutiswhichkindofobjectisbeingreferredto.Theseexamplescannotbeparaphrasedwiththeform`IsawacontraptioninthecopyroomandIdon'tknowwhichcontraptionitwas,'butmustbeparaphrasedwithsomethingmorelike`IsawacontraptioninthecopyroomandIdon'tknowwhatkindofcontraptionitwas.'(39)a.Isawsomecontraptioninthecopyroomthismorning.b.Icamehometosomeplantgrowingthroughaholeinmywall.c.Doctor,somegrowthappearedonmyarm.ShouldIbeworried?TheanalysisproposedbyWeirplaysoncommonnounsbeingpolysemousbetweenbeingpropertiesofindividualsandpropertiesofsubkinds,andthatsomecanquantifyoverboth.First,heassumes,followingChierchia(1998),thatakindisthemereologicalsumofallthemembersofthatkindinagivenworld.FollowingKratzer(2008),heassumesthatnominalrootsdenotethisplurality.Tobuildinthepolysemyofcommonnounsbetweenindividualandkindinterpretations,asystemisused,withforindividuatingandkind-relateduses.TheseareovertinChinese(Krifka,1995),butcovertinEnglish.Theindividuatingassertsthatsomeindividualisamemberofthekinddenotedbythenoun,whilethekindassertsthatakindisasubkindofthekinddenotedbythenoun.(Thesearebothconveyedinthedenotationsbya`partof'relationP.)(40)JplantK=PLANT131(41)a.JCLindK=lxly:kind(x)^individual(y)^yPxb.JCLkindK=lxly:kind(x)^kind(y)^yPxTogetasubkindreadingofaDPsuchasthatplant,theDPwouldbestructuredasin(42).Thelogicalformisprovidedin(43).(42)DPDthatNPCLkindplant(43)a.JCLkindplantK=ly:kind(y)^kind(PLANT)^yPPLANTb.JthatK=lfhe;ti:ix[P(x)]c.Jthat[CLkindplant]K=ix[kind(x)^kind(PLANT)^xPPLANT]Forsome,WeiradaptstheanalysisofalgúnfromAlonso-Ovalle&Menéndez-Benito(2010),butwithacrucialaddition:ratherthanhavethescopeoftheQapplytothexthattherestrictorPappliesto,itisasubpartofxthatQappliesto.Thismoveismadetohavesomequantifyoverinstantiationsofsubkindsratherthansubkindsthemselves.(44)JsomeK=lfhet;etilPhe;tilQhe;ti:anti-singleton(f):9x[f(P)(x)^9y[yPx^Q(y)]]Thisanalysisprovidesananalysisforwhysome,incertainuses,isimplicatingignorancenotaboutaparticularindividual,butaboutwhichsubkindanindividualinstantiates.Moregenerally,thisanalysisisimportantformyanalysisofsome-exclamativesasquantifyingoversubkinds,inthatitshowsinanindependentwaythatsomecangenerallybethoughttobesensitivetokinds.1325.5AlternativesandHamblin(1973)proposedthatthedenotationsofquestionsweresetsofpropositionscorrespondingtoanswerstothatquestion.AquestionoftheformWhocametotheparty?couldbeconsideredashavingthesetofalternativesin(45),forinstance,withwhosignalingthesyntacticpositionthealternativepropositionsshouldhavetheircontentvaried.Thissetraisesanissueastowhichparticularpropositionistrue.(45)JWhocametotheparty?K=8>>>>>>><>>>>>>>:Marycametotheparty;Billcametotheparty;Bobcametotheparty;:::9>>>>>>>=>>>>>>>;Thisviewofquestionshascometobequiteand,withlaterbyKarttunen(1977)andGroenendijk&Stokhof(1984),theviewthatquestionsdenotesetsofpropositionshasbecomeadominantviewintheiranalysis.Theideaoftreatinglinguisticexpressionsasinvokingalternativeshasonlybeenappliedtothesemanticsofquestions,however.Rooth(1985,1992)proposedthatfocuscouldalsobethoughtofintermsofalternatives,withthefocusedconstituentbeingsubstitutedforotherconstituentsofthesametypeinasetofpropositions,similartotherolethewh-wordplaysingeneratingaquestion.Alternativeshavebeenarguedtoalsoplayaroleinscalarimplicatures(Chierchia,2004),disjunction(Alonso-Ovalle,2006),topichood(Büring,1997)and(Alonso-Ovalle&Menéndez-Benito,2003;Menéndez-Benito,2005).Hagstrom(1998)andRamchand(1997)proposethatsentenceswithwh-in-situelementsinJapaneseandBengali,respectively,shouldbegivenaquestion-likesemantics,inthestyleofHamblin(1973).Inthiskindofsemantics,sentenceswiththeseelementsdenotesetsofpropositions(alternatives)ratherthansinglepropositions.Kratzer&Shimoyama(2002)buildonthesekindsofanalysesandshowhowindeterminatepronounsinbothGermanandJapanesecanbegivenacompositionalanalysis,wherealternativesarepartofthecompositionalsemanticsofthesentence,133ratherthaninapost-compositionalsystem.Thisviewthatgeneratesetsofalternatives,raisinganissueastowhichindividualanexistentialclaimholdsof,wasfurtherpursuedforSpanishalgúninAlonso-Ovalle&Menéndez-Benito2003.Morerecently,workinInquisitiveSemantics(Ciardellietal.,2013;Groenendijk&Roelofsen,2009)hasalsoanalyzedasintroducingsetsofalternatives(AnderBois,2012).ThesealternativesplayaroleatadifferentlevelthatthealternativesinKratzer&Shimoyama2002,beingpartofthetop-levelupdatetothecommongroundratherthanbeingacompositionaltool,butthenotionofaspragmaticallyraisinganissueisrelated.MytreatmentofsomeinthischapterwillhavemoreincommonwiththeapproachofKratzer&Shimoyama2002thanofAnderBois2012,whereIanalyzesomebeingimplicatedinbuildingasetofalternatives.Moreover,formypurposes,itwillbecrucialthatalternativesbeavailableaspartofthecompositionalmachineryofthesentence.5.6Derivingtheexclamative5.6.1SomeandkindsMybasicproposalforwhatsomedoesinsome-exclamativeswillbetosaythatsomeoversubkinds.Insection5.3,Iarguethatsomeissensitivetokinds,basedprimarilyonitsbehaviorwithnominalsthatlackkinds.WhatIwillassumeisthatit'snotjustkindsthatsomeover,though,butsubkinds.ThisideahassomethingsincommonwithWeir2012,namelythatincertaincases,whatsomeexpressesignoranceaboutistheparticularsubkindthatisinstantiatedbyanindividual.Insome-exclamatives,thisignorancewillinsteadbeexpressedasanexclamationaboutwhichparticularsubkindtheindividualisinstantiating.Ifsome-exclamativesmerelyinvolvereferencetosubkinds,whatweshouldexpectsome-exclamativestobeabletoexclaimaboutinanaturalwayissubkindsofprofessions.Inotherwords,weshouldexpecttheexclamationin(46)tobeaboutsubkindsoflawyers(bankruptcy,divorce,personalinjury),andtheexclamationin(47)tobeaboutsubkindsofarchitects(landscape,134residential,industrial).Theseexclamationsdon'tseemtoinvolvereferencetothoseparticularsubkinds,orevensubkindsofprofessionsatall.Rather,theyinvolvereferencetotheparticularwaysinwhichtheyexemplifylawyerhoodorarchitecthoodindoingtheirjobs.(46)Johnissomelawyer!(47)Sheissomearchitect!ThiscanbeexplainedbynotingthatthosesubkindsŠbankruptcylawyers,divorcelawyers,land-scapearchitects,residentialarchitectsŠarenotsubkindsoneinstantiatesbyvirtueofparticipatinginevents.Barringcertainoccasionssuchasgraduationceremoniesorbeingaskedataworkplacetodoaparticularjobforaday,divorcelawyersarenotnormallydivorcelawyersbyvirtueofpartici-patinginanevent,andsimilarlyforlandscapearchitects.Ontheotherhand,thepropertiesthatsome-exclamativesseemtotrackŠforlawyers,winningcases,doingprobonowork,orchargingalotofmoney,likethefollow-upsentencesin(48)Šarepropertiesthatcanmoreeasilybeconstruedasbeingassociatedwithevents.(48)Johnissomelawyer!a.Healwayswinshiscasesanddoeslotsofprobonowork.b.Heloseseverycaseandstillchargesalot.Insomeways,thisisasimilarphenomenontoConstantinescu(2011)'snotionoffinaturalconse-quencesflidentifyingandsubkindsinthemeaningofsuch.WhatConstantinescunoticesisthatresultclauseswithinternalsuch,suchasintheexamplesbelow,arelicensedonlyincertainsituations.Whentheresultcanbeconstruedasaneventthatcouldarisefromasubkindofthenounphrasethatsuchmergedwith,theresultisacceptable.Otherwise,ifnonaturalconnectioncanbefoundbetweenthesubkindandtheresult,theresultwillbeunacceptable.Intheexamplesin(49),persondoesnothavereadilyaccessiblesubkindssuchthatthosesubkindswouldresultinnotbeinghired,whileidiotdoes,ontheassumptionthatthesubkindsinvolvedaredegreesofidiocy.135(49)a.*Heissuchapersonthatnoonewillhirehim.b.Heissuchanidiotthatnoonewillhirehim.Beller(2013)alsonoticesthatneutralnounscanbecomepejorativeincertaincontexts,particularlywhenusedwiththeintensifyingsuch,asin(50).Inthesecases,Bellerarguesthattheinterpretationisbasedongettingabehavior-basedreadingforthenoun(e.g.,doctor),wherethepejorativeattitudeiswrappedupwiththebehaviorsassociatedwithbeingofthetypedenotedbythenoun.Heshowsthisbyshowingthatdenyingthattheindividualbehavesin(negative)stereotypicalwaysisunacceptable,whileitisacceptableinneutralcontexts.Thisisshownin(51).(50)Johnissuchadoctor!(51)a.#Johnissuchadoctor,thoughhedoesn'tactlikeadoctoratall.b.Johnisadoctor,thoughhedoesn'tactlikeadoctoratall.Thisisformallycashedoutbyinternalsomemakingreferencetopropertiesthatareheldbyindividualsforwhomthenounapplies(e.g.,doctors)andnotothers,usingthechar(characteristics)functionin(52).Someofthesepropertiesarethensaidtoholdofthesubjectduringaparticulartimeinterval.Anotherwayoftalkingaboutthisthatseemsnearlyequivalentwouldbetotalkofsubkindsinstantiatedbyaparticularindividualduringanevent.(52)a.JcharK=lPlxli:MOSTys.t.P(y);MOSTzs.t.:P(z);9Qhe;tis.t.Q(y)^6=Q(z)^Q(x)atib.JcharadoctorK=lxli:MOSTys.t.doctor(y);MOSTzs.t.:doctor(z);9Qhe;tis.t.Q(y)^:Q(z)^Q(x)atiTheextenttowhichmynotionofsubkindsinstantiatedduringanevent,Beller'sobservationsregardingbehavior-basedjudgements,andConstantinescu'sobservationsregardingnaturalcon-sequencesareseparatephenomenaorsomepropertyofreferencetokindsisstilluncleartome.Whatdoesseemtobethecaseisthatinsome-exclamatives(andperhapsinother136constructionsmoregenerally),referencetosubkindsisnotsostraightforwardastosimplybeanysubkind.Rather,thewaythatsubkindscanbeconstruedisentangledwiththeeventsthatspeakersarealsoconsidering.5.6.2SemanticsofsomeFollowingthediscussiontheprevioussection,I'llassumethatNPsdenotepropertiesofkinds.ThedenotationfortheNPlawyerwillbethepropertycorrespondingtothelawyer-kind.Thispredicatewillbetrueofanykindthatisasubkindofthelawyer-kind.(53)JlawyerK=lk:lawyer(k)FollowingproposalsfromMüller-Reichau(2011),Gehrke&McNally(2013)andothers,I'lltakeNumasbeingthelocusforshiftingpropertiesofkindstopropertiesofindividuals.Whatshiftskindstoindividualsinmyanalysisissome.Accordingly,somewillbemergedlow,asaNumhead,taketheNPasanargument,andyieldapropertyofindividuals,makingsometypehkt;eti.(54)NumPhe;tiNumhkt;etisomeNPhk;tilawyerThedenotationofsomeinthissystemwillbeasin(55)below.ThebasicroleofsomeistotakethepropertyofkindsdenotedbytheNP,andtransformitintoapropertyofindividualsbyquantifyingoversubkinds.137(55)JsomeK=lKhk;tilxe:jpj>1:asetps.t.p=p0:9ks.t.p0=^[Re(x;k)^K(k)]Thisdenotationiscomplexincertainwaysandneedstobediscussedinadditionaldetail.First,someherehastwoarguments,apropertyofkindsKandanindividualargumentx.Skippingaheadtotheassertedportionofthedenotation(ratherthanthepresupposedcontent,whichIwillreturnto),someassertstheexistenceofasetofpropositionsp(asetofpropositionsbasedonthenotionthattriggerthegenerationofalternatives).EachpropositionsassertsthatthekindkisasubkindofthepropertyofkindsdenotedbytheNP,K,andthattheindividualxisarealizationofthiskind.Withkscopingoutsideoftheproposition,pwillbeasetofpropositionsthatvarywithrespecttosubkind.Inlightofthediscussioninsection5.6.1,it'simportanttodiscussR.RhereisavariantoftherealizationrelationfromCarlson(1977),differinginthatitrelatesindividualsandkindsratherthanstagesandkinds.Formypurposeshere,R(x;k)istruejustincasexisamemberofthekinddenotedbyk.Importantly,though,Risrelativizedtoaneventeaswell.Whatthisconveysisrealizationofthekindbyvirtueofbeingaparticipantofsomeevente.Thisisintendedtocapturetheobservationinsection5.6.1thatthekindsassociatedwithsomeexclamativesarethosethataredirectlyconnectedwithanevent.Ratherthanquantifyoverthisvariableimmediately,Ileaveitopenandassumethatitisimplicitlyvaluedbythespeakeratalaterpoint.Finally,Ishouldreturntotheunderlineportioninthedenotation.Asclaimedearlierinthischapter(andalsoseechapter4),someisanepistemicrequiringthatthespeakernothavepreciseknowledgeastotheidentityofsomeindividual.Althoughtheparticularwaythatthisgetscashedoutindifferenttheoreticalanalysesvaries,thereareseveralthatareespeciallyworthattentionhere.TheisananalysisinFarkas2002.Inthispaper,Farkasanalyzessomeasrequiringthatthevariableitcontributesbeis,thatthevaluethatvariableisassignednotnecessarilybethesameacrossallpossibilities.Inessence,thisisawayofensuringthatthespeakercannevercommittoaparticularvaluationforthatvariable.ThesecondproposalthatisnecessarytomentionisthatofAlonso-Ovalle&Menéndez-Benito138(2010).Asdiscussedpreviously,theyproposethattheignoranceimplicatureofSpanishalgúncanbemodeledthroughcompetitionwithun.Theyanalyzealgúnasin(56),wherealgúncombineswithasubsetselectionfunctionf,afunctionfromsetstosets.Theuseofthesubsetselectionfunctionmodelscontextualdomainrestriction.finthisanalysisisrestrictedviathepresuppositionanti-singleton(f)sothatitsrangemustbeanon-singletonset.Whenfcombineswiththerestrictorofalgún,theNP,theeffectistomakeitsothattheremustbeatleasttwoindividualsthatcouldpossiblysatisfytheexistentialclaim.Unisanalyzedasnothavingtheanti-singletonpresupposition,andtheignorancecomponentofalgúnsurfacesasanimplicaturethroughcompetitionwithun.(56)JalgúnK=lflPlQ:anti-singleton(f):9x[f(P)(x)^Q(x)]Finally,athirdproposalthatneedstobementionedisthatofvonFintel(2000).Thisanalysisisnotaboutsomeperse,butaboutwhatever,whichalsoincludesasenseofuncertaintyaboutit.3vonFintelbuildsonDayal(1997)'sanalysisofwhateverinassumingthatwhateverhasapresuppositionofignorance.Thepresuppositionismostrelevantformypurposeshere,inthatitforcesthespeakertonotbeabletoidentifywhichparticularindividualP,justthatthereareatleasttwo.(57)whatever(w)(F)(P)(Q)a.Presupposes:9w0;w002F:ix:P(w0)(x)6=ix:P(w00)(x)b.Asserts:8w02F:Q(w0)(ix:P(w0)(x))Whattheseproposalshaveincommonisageneralanalyticalintuitionthatsomeimposesarequire-mentthatthespeakercannotcommittoaparticularindividual,butrathermustleaveitasanopenpossibilitythattherearemultipleindividualswhocouldsatisfytheclaim.Inmyanalysisofsome,Ifollowthissameidea,andencodeitwiththepresuppositionintheunderlinedportionof(55).Thepresuppositionrequiresthattherebeatleasttwopropositionsinthesetofalternativesgeneratedbysome.Asthesealternativesvarybysubkind,thiswillamounttoarequirementthattherebeatleasttwosubkindsthatcouldpossiblyholdoftheindividualx.Thisbehaviorofsomewillbeimportant3Inclassnotes,vonFintelhasananalysisofsomethatissimilar,accordingtoAlonso-Ovalle&Menéndez-Benito(2010).SeevonFintel1999.139inthenextsectionforbuildingtheexclamativeinterpretation.Thestructureforthesententialcoreoftheexclamativeclausewillbeasin(58).AderivationforthecoreoftheexclamativeJohnissomelawyer!isasin(59).(58)TPDPJohnT0TPredPPredNumPNumsomeNPlawyer(59)a.JsomeK(JlawyerK)=lxe:jpj>1:asetps.t.p=p0:9ks.t.p0=^[Re(x;k)^lawyer(k)]b.JsomelawyerK(JJohnK)=JJohnissomelawyerK=p0:9ks.t.p0=^[Re(j;k)^lawyer(k)]Tosummarizethissection,somegeneratesasetofalternativesthatvarybysubkindsinstantiatedbythesubject.Thissetofalternativesisfurtherconstrainedbyapresuppositionthatsaysthatthissetmustcontainatleasttwoalternativesinit.Thisconstraintiswhatmodelstheepistemicnatureofsomeinothercontexts.Inthenextsection,Iusethisfactaboutsomeinconjunctionwithanexclamativeoperatortobuildthefullmeaningofsome-exclamatives.1405.6.3BuildingtheexclamativeTheprevioussectionsleavesoffwiththecoreofthesome-exclamativedenotingasetofpropositionsthatvaryastowhichparticularsubkindthesubjectinstantiates.Thissetofalternativesisn'tthemeaningoftheexclamative,thoughŠwhatitmeanstoexclaimusingasome-exclamativeisn'tsimplytosaythattherearesomenumberofsubkindsthatcouldbeinstantiated.Rather,theremustbeanattitudetowardsaparticularsubkindthatisbeinginstantiated.Earlierinthischapter,Inotethatsome-exclamativesinvolveaparticularintonationalcontour,andthatwithoutthiscontour,theexclamativemeaningcannotarise.WhatIwilltakethiscontourtobeexpressingisanadditionallayerofmeaningthattransformsthesetofalternativesdenotedbythesententialcoreofthesome-exclamativeintoasentencewiththeappropriatemeaning.OnepossibilityforhowthisoperationisthatwecouldidentifyitwiththewideningoperationusedbyZanuttini&Portner(2003).Iarguethatwideningmightnotbethecorrectwaytothinkaboutwhatishappeningwithsomeexclamatives,though.Onetheory-internalreasonhastodowiththeanalysisofsomeIamassuming.Ianalyzesomeasanepistemicithattriggersthegenerationofatleasttwoalternatives(inordertomodeltheignorancerequiredofthespeaker).Thealternative-generatingvorofsomefollowsworkinalternativesemanticsandotherareasthatarguesthatasaclassareassociatedwithalternatives.Thiswouldmeanthatsentencesusingthesingulara(asinalawyer)wouldalsohaveasetofalternativesassociatedwiththem.Ifwideningistheoperationinvolvedinsome-exclamatives,it'snotclearwhyonlysomebutnotashouldbeinvolvedincreatinganexclamative.Ideally,weshouldpegthelackofana-exclamativeonthefactthatsomeandtheaimposedifferentrequirementsonthealternatives.WideninginZanuttini&Portner(2003)'sanalysisdoestwothings.First,itisawayofcapturingtheintuitionthatexclamativesexclaimabouthighdegreesofaproperty,ashighdegreesareoutsideofthenormaldomainofWhatwideningalsodoesiscapturethenotionofunexpectednessthatalsoseemstobeinherenttoexclamatives,againbywideningthedomainto141includepropositionsthatwereoutsideofthosethatwereexpected.AsomewhatdifferentapproachisusedbyCastroviejoMiró(2008),whoseEI(exclamativeintonation)operatorpartitionsasetofpropositionsintoasingle,strongesttrueproposition,asetofweakerbuttruepropositions,andasetoffalsepropositions.MyapproachwillfollowCastroviejoMiró'sinpartitioningasetofalternativesalongsomedimension.BorrowingfromChernilovskaya&Nouwen(2012),therelevantnotionwillbenoteworthiness.Chernilovskaya&Nouwennotethatnoteworthinessisavagueconcept,buteventhoughit'svague,it'saconceptwherethereareclearintuitionsonwhatcountsasnoteworthyandnot.Forinstance,theypointoutthatablackberry,chickenliverandwercakeisnoteworthyasacake,whilethefontusedintheirpaper(acommonseriffont)isnotnoteworthy.Moregenerally,theybelieve,noteworthinesscanbethoughtofasstandingoutconsiderablywithrespecttosomecomparisonclass.Thisnotionofnoteworthinessissomewhathardertoapplytopropositionsratherthanentities.Drawingupcomparisonclassesofentitiesisafamiliartask,butdrawingupacomparisonclassforpropositionsissomewhatmoredifWhatIwillinvokeissimilarity,whichofcourseisfraughtwithitsownissues(Goodman,1972).Twoobjectscountassimilarifwecantreatthemasbeingsufindistinguishablefromeachother,forwhateverpurposeswehaveinmind.Thinkingofthisintermsofnoteworthiness,objectsthataresufsimilartoeachotherdonothavenoteworthydifferences(withrespecttothedimensions(s)theyarebeingjudgedtobesimilar).Whatitmeanstobenoteworthy,then,istofalloutsideoftheclassofobjectsthataresimilartoeachother.Torelativizethistopropositions,wecanconceiveofworldsasbeingsimilartoeachotheraswell.Insomeworlds,thecoffeecupsittingonmydeskisjustalittletotheleftoralittletotherightofwhereitisnow.Whenjudgingworldsbasedonthelocationofmycoffeecup,thoseworldsaresufcientlysimilartotheactualworld.Ontheotherhand,worldswhereIstudiedgeology,math,orsomeothermightbejudgeddissimilartotheactualworld.Afornoteworthinessisgivenin(60),whichsimplysaysthatapropositionisnoteworthyifit'snotsimilartoanotherworld.142(60)Apropositionpisnoteworthytoanindividualxinworldw(theactualworld)iff8w02Simw;x:w062p(Simw;xisthesetofworldsthataresimilartowforindividualx)Imyexclamativeoperatorusingthisnotionofsimilarityin(62).Thisoperatorcombineswiththesetofpropositionsthatweregeneratedbyusingsomeandassertsthatthesetofpropositionscanbepartitionedintonoteworthyandnon-noteworthypropositions.Thepartitioncreatesacontrastamongpropositionstosaythatsomeareworthremarkingabout,similarlytohowdomainwideninginZanuttini&Portner(2003)naturallybuildsupacontrastbetweentheexpectedpropositionsintheunwidenedsetandtheunexpectedpropositioninthewidenedset.Thispartitionalsohelpsexplainwhysome(butnota)participatesinbuildinganexclamative.DuetoExOpneedingatleasttwopropositionsinordertopartitionthealternativesintonoteworthyandnon-noteworthysetsofalternatives,ExOpmustcombinewithasetthathasatleasttwomembersinit,ensuredbythepresuppositionoftherebeinganon-noteworthypropositioninthatset.Thesingularacannotcreateanexclamativebecauseitwillnotguaranteethatthesetitbuildswillhavetwomembers.Ontheotherhand,somewillguaranteethis,duetoitsanti-singletonpresupposition.(61)JExOpKw=lPhst;ti9p2P::noteworthyw(x;p):9p02P264noteworthyw(x;p0)^w2p0^ATTx(p0)375ExOpalsoassertsanattitudeATTtowardsanoteworthyproposition.Thisattitudeisheldbyanindividualx,whichwillgetvaluedasthespeaker.Thisattitudeisgenerallyapositiveornegativeattitudetowardstheproposition.5.7Apuzzle:frontingofthesome-DPandpejorativityTheexamplesofsome-exclamativesdiscussedsofarallinvolveastructurewheretheDPheadedbysomeappearsafterthecopula,asin(62).(62)a.Johnissomelawyer!143b.SyntacticStructuresissomebook!Thoseexamplescontraststrikinglywithastructurewherethesome-DPhasbeenpreposed,likein(63).y,theexclamativesin(62)havetwointerpretations.Underoneinterpretation,thesubjecthasapositiveattitudetowardsJohnorSyntacticStructures.Underasecondinterpretation,however,thesubjectonlyhasapejorativeattitudetowardsJohnorSyntacticStructures.Whenwecomparethistothesentencesin(63),whatweisthatthesentencesin(63)haveonlythepejorativeinterpretation.(63)a.SomelawyerJohnis!b.SomebookSyntacticStructuresis!Wecanshowthatthisistruebytryingtotheattitudeaseitherpositiveornegative.Whenthesome-DPispost-copular,asin(64),boththe(a)and(b)sentencesareacceptableasfollow-ups.However,whenthesome-exclamativehasapreposedsome-DP,asin(64),the(a)sentence,whichexpressesapositiveattitude,isinfelicitous.(64)Johnissomelawyer!a.Healwayswinshiscasesanddoeslotsofprobonowork.b.Heloseseverycaseandstillchargesalot.(65)SomelawyerJohnis!a.#Healwayswinshiscasesanddoeslotsofprobonowork.b.Heloseseverycaseandstillchargesalot.AsfarasIamaware,thefactthatraisingthesome-DPenforcesapejorativeinterpretationhasnotbenoted.However,thisseemstobeanimportantandinterestingpropertyofthisexclamativeconstruction.1445.8ConclusionThischapterprovidedananalysisofsome-exclamatives,whichhaveremainedunderstudiedinthebroaderliteratureonexclamatives.Some-exclamativesareinteresting,inthattheyshowanotherex-ampleofanexclamativeconstructionwheretheexclamativeisnotderivedfrommorphologyrelatedtotheformationofquestions.TheanalysisIproposesuggestsaofourunderstandingofexclamativesentences.ProposalssuchasthoseofGutiérrez-Rexach(1996)andZanuttini&Portner(2003)analyzeexclamativesashavingaquestionsemantics.Recentworkinthesemanticsofhasarguedthatalsohaveanalternativesemanticsassociatedwiththem,makingthemquitecloselyrelatedsemanticallytoquestions.Thisconnectionallowsustoveryeasilymakesenseofsome-exclamativesandexclamativesasawhole;exclamativeconstructionsarenotaboutquestionhood,asproposedbyGutiérrez-Rexach(1996)andZanuttini&Portner(2003),butareratheraboutmanipulatingsetsofalternatives.145CHAPTER6CONCLUSION6.1AfewremarksThisdissertationhasexaminedseveraldifferentconstructionsthatareexamplesofandattenuationinEnglish.Inthischapter,Iprovidesomeclosingthoughtsonhowandattenuationaredecomposed,whatthismeansforaswellasadditionalthoughtsonthenatureofthetypeshiftPREC.6.2PREC:typeshiftorfunctionalhead?Chapters2and3makeuseofPREC.Inthosechapters,I'vecalledPRECatypeshiftinordertosignalthatitsgrammaticalpurposeistoshiftsomethingfrombeingnon-gradableintobeingsomethinggradable.It'sworthinglingeringforaminuteonhowtobestthinkaboutPREC,though.IsPRECanasyntactictypeshift,abythemeaningcomponentofthegrammarinordertoavoidatypeclash?Or,isitbettertothinkofPRECasbeingamorphemeandinthesyntax?TherearetwowaysofthinkingaboutPRECasatypeshift.First,wecanthinkofitasanoperationthatappliestoalinguisticexpressioninordertochangeitfromonetypetoanother.RepresentativesofthiskindofapproachinthesemanticsliteratureincludePartee(1987)andChierchia(1998),whodevelopsystematicwaysofconvertingexpressionsofonetype(say,typehe;ti)intoexpressionsofadifferenttype(suchastypeeortypehet;ti).(Iusepartofthissysteminmyanalysisinchapter4.)Understoodinthisway,PRECispartofthisfamily,awayofchanginganexpressionofanytypeaintoagradabletypehd;ai.Inthisview,PRECisnotnecessarilysyntacticallyrepresented.PRECappliesasawayofthesemanticrepresentation.Supposethatarequiresagradablecategory,andithasbeen146insertedasthesistertoanon-gradablecategory,asschematizedin(1a).Thiswouldresultinatypeclash,sinceneitherexpressioncouldapplytotheother.WithPRECappliedtotheexpressionontherighthandside,however,thecomputationcanthenproceed,asin(1b).(1)a.Typeclash!hhd;ai;biab.bhhd;ai;bihd;ai(viaPREC)AsecondwayofthinkingaboutwhatPRECdoesistothinkofitasaruleofinterpretation.Functionapplicationcanbethoughtofasthestandardwayofcomposingtwoexpressionsthataresyntacticallysisters,butotherrulesofinterpretationcouldinprinciplebeOnerulethatsemanticistsfrequentlyhelpthemselvestoisaruleforintersectiveinterpretation,Predicate(Heim&Kratzer,1998).in(2),Predicateisawayofcomposingtwoexpressionswherebotharetypehe;ti,suchaswithintersectiveadjectivesmodifyingcommonnouns,likein(3).(2)Predicate(Heim&Kratzer,1998)Ifaisabranchingnode,fb;ggisthesetofa'sdaughters,andJbKandJgKarebothinDhe;ti,thenJaK=lx2De:JbK(x)=JgK(x)=1(3)a.JdogK=lx:xisadogb.JhappyK=lx:xishappyc.JhappydogK=lx:JhappyK(x)=JdogK(x)=1147However,otherrulesofinterpretationhavebeenproposedaswell.Forinstance,Chierchia(1998)aruleofinterpretationDerivedKindPredicationthatexistentiallyoverinstan-tiationsofakindwhenthekindwouldotherwisebeanargumenttoapredicatethatrequiresinstantiations.1And,Heim&Kratzer(1998)aversionoffunctionapplication,IntensionalFunctionalApplication,thatisusedwhenapredicaterequirestheintensionofitsargument(suchasbelieveanditsclausalcomplement).(4)IntensionalFunctionalApplication(Heim&Kratzer,1998)Ifaisabranchingnodeandfb;ggthesetofitsdaughters,then,foranypossibleworldwandanyassignmenta,ifJbKw;aisafunctionwhosedomaincontainslw0:JgKw0;a,thenJaKw;a=JbKw;a(lw0:JgKw0;a)TalkofPRECcouldinprinciplebeunderstoodinthiswayaswell;whenwetalkofPREC,whatwearereallytalkingaboutisaspecialruleoffunctionapplicationthatincludesthesameoperationthatthePRECtypeshiftperforms,namelybindingthedegreeofprecision.Likethepreviousnotionoftypeshift,thisruleisusedtoincompatibletypes,withthedifferencebeingthatitdoesn'tapplytoaparticularlinguisticexpressioninordertoshiftthetypeofthatexpression,butratherisaofhowexpressionsofparticulartypesarecomposed.Anexampleofhowthisrulecouldbewrittenisasin(5).(5)Ifaisabranchingnode,fb;ggisthesetofa'sdaughters,ifJbKd0isafunctionwhosedomaincontainsld:JgKd,thenJaKd0=JbKd0(ld:JgKd)But,therearewaysofthinkingaboutPRECinsyntactictermsaswell.RatherthanthinkingofPRECassomethingthatisusedtothesemanticrepresentationpost-syntactically,wecouldalsothinkofPRECasbeingsyntacticallypresentasamorphemeinoursemanticrepresentation.Inthisview,PRECisanunpronouncedfunctionalcategorythatiseitheradjoinedtoanothercategory(e.g.,adjoinedtoVP,asin(6))ortakesthecategoryasitscomplement(asin(7)).1DerivedKindPredication(Chierchia,1998):IfPappliestoobjects(instantiationsofakind)andkdenotesakind,thenP(k)=9x[k(x)^P(x)148(6)VPXPPRECVP...(7)XPXPRECVP...Tosomeextent,thechoicehereisdeterminedbyone'sbeliefsabouttherelationshipbetweensyntaxandsemantics.Ifyoupreferasemanticsthatcanbetransparentlyreadoffthesyntax,puttingPRECinthetreeispreferable.Ontheotherhand,ifyoupreferasimplersyntaxwithnounpronouncedcategories,theonlychoiceistomakethesemanticsmorecomplicatedandmakePRECatypeshift.But,theredoseemtobesomeavenuesforsettlingthis.Forinstance,ifPRECwererepresentedsyntactically,wemightexpectittobepronouncedinsomecases.AlthoughEnglishdoesnotpronounceit(likemanyotherfunctionalheads),wecouldconceiveofPRECbeingpronouncedinsomelanguage.AmorphemelikePRECthatisovertlypronouncedinsomelanguagewouldthenbeindirectevidencefortreatingPRECaspartofthesyntaxinEnglish.Allthingsbeingequal,treatingPRECasaheadhasainexplainingthelimiteddistributionoftheprecision-affectingveryandsorta/kindaaswell.Asshowninthe(b)examplesin(8)and(9)below,therearelexicalitemsthatcanbeusedbothforincreasingprecision(all,(8b))andfordecreasingprecision(about,(9b)).Ianalyzeveryandsortaasersthatincreaseanddecreaseprecision,respectively,butthesecannotbeusedinthesamewaysthatallandaboutcan149be,asshowninthe(c)examples.(8)a.Thetownspeopleareasleep.b.Allthetownspeopleareasleep.c.*Verythetownspeopleareasleep.(9)a.Twentypeoplewereattheparty.b.Abouttwentypeoplewereattheparty.c.*Sortatwentypeoplewereattheparty.Whatdowemakeofthis?Onepossibilityisthattherearesubtlesemanticdifferencesthatpreventveryandsortabeingusedinthesepositions,althoughit'snotcleartomewhatpreciselythesedifferenceswouldbe.IfwetreatPRECasafunctionalhead,however,andsortaandveryasthatarelicensedintheofthatfunctionalprojection,wecanexplaintheunacceptableexamplesabove.Intheseexamples,presumably,PRECisnotabletotakenounphrasesornumeralsasitscomplement,duesimplytoselectionalrestrictions.It'swell-knownthatcertaincategoriesimposeselectionalrestrictions,andtreatingPRECasamorphemeratherthananasyntactictypeshiftcouldhelpexplainrestrictionsinthedistributionofveryandsortaasatypeofsyntacticselection.6.3DecompositionofandattenuationThephenomenainvestigatedherepresentacasestudyinwhatsortsofpiecesareusedintionandattenuation,atleastforparticulartypesofphenomena.ThepictureIpaintisonewhereimprecision,approximation,andexclamativescanbedecomposedintosmallercomponentsthataresharedacrossparticularinstancesofthesephenomena.Chapters2and3focusonthemechanicsofimprecisionregulation.Thecertainclaimwiththesechaptersisthatacoverttypeshiftingmechanism,PREC,allowsdegree-expressionsaccesstothedegreeofprecisionusedforinterpretinglinguisticexpressions.Fundamentally,thesestories150decomposeintostoriesaboutwhatkindsofdegreesexist,wheretheyareused,andhowtheyareaccessed.Theconclusionisthattherearefundamentallyatleasttwotypesofdegreesinnaturallanguage:degreescorrespondingtomeasurementoninherentpropertyscales,suchasdegreesoftallnessorhappiness,asfoundwithgradablepredicates,anddegreesofprecisionthatmeasuretheexactnesswithwhichthespeakerisusingalinguisticexpression.Correspondingly,thesearealsodistinguishedinwheretheyareusedandhowtheyareaccess.Degreesthatmeasurealonginherentpropertyscalesarefoundwithgradablepredicatesintheformofdegreearguments;certainpredicateshave,aspartoftheirargumentstructure,anargumentforadegree.ThemostcommongradablepredicatesinEnglisharegradableadjectivessuchastallandhappy,butothergradablepredicates,suchasdegreeachievementslikewiden,alsoexist.Thesetypesofpredicatesallmakeuseofdegreesinherently,requiringtheirdegreeargumenttobesaturatedorboundbya.Degreeconstructions,suchassuperlatives,comparatives,anddegreewordslikeveryandslightlyallquantifyoverorotherwiseprovideadegreetothedegreeargumentslotofagradablepredicate.AlthoughtheclaimthatImakehereisthatimprecisionisrepresentedusingdegreesaswell,thedegreesthatcorrespondtoimprecisionarerepresentedinadifferentwaythanthedegreesusedforinherentpropertyscales.Namely,whereasinherentpropertyscalesarepartofthelexicalmakeupofparticularpredicates,degreesofprecisionliveinthesystemthatinterpretsexpressions.Ratherthanbeingabletobeaccessedthroughthenormalcourseoffunctionapplication,degreesarespecialinthattheyrequireadditionalpiecestoaccessthem,suchasthetypeshiftPREC.Thisdissertationprovidesawayofthinkingabouttherelationshipbetweendegreewordsandimprecision,wheredegreewordscanbecomeimprecisionmodulatorsbyvirtueofspecialtypeshiftslikePRECthatcancoercenon-gradablepredicatesintogradablepredicatesbyprovidinganargumentthatcorrespondstoadegreeofprecision.Asecondpieceofthedecompositionofandattenuationisthatofalternatives.First,alternativesarerepresentedinthesemanticsforimprecisioninchapters2and3,inthatthepragmatichalosthatcorrespondtoexpressionsaremodeledusingalternatives.Interpretingan151expressiontoahighdegreeofprecisionmakesthatexpressionhaveasmallhalosurroundingit,whilelowerdegreesofprecisionrequirelargerhalos.Thesehaloscorrespondtoexpressionsthat,forthepurposesofthespeakerinthediscourse,areequivalent.Thatistosay,thealternativesthataregeneratedareexpressionsthatdifferinpragmaticallyignorableways.IalsomakeuseofalternativesinthesemanticsofNumSome.Therolethatalternativesplayhereisdifferentfromtheroletheyplaywithsortaandvery.WithNumSome,alternativesareusedimplicitlyinmodelingtheignoranceeffectthatcomesfromtheuseofsome.TheuseofsomeinNumSomeimplicatesthatthespeakercannotinprinciplenarrowthedomaintoasingletonnumber,duetotheanti-singletonpresuppositionencodebysome.Inotherwords,anexampleliketwenty-somepeoplecommitsthespeakertosayingthattherewereatleasttwentypeople,butdoesnotcommitthespeakertowhatparticularnumberofpeopletherewere.Theinabilitytoeveninprinciplenarrowthedomaintoasingletonimplicitlyraisestheissueastowhichparticularnumberwillsatisfytheclaimmadebythespeaker.Inthisway,thegenerationofthealternativesraisestheissueofwhichparticularalternativeistrue.Alternativesplayaroleintheanalysisofsome-exclamativesaswell.LikeintheanalysisofNumSome,someisimplicatedingeneratingsetsofalternatives.Beingansomegeneratesasetofalternativepropositions,withtheexclamativeoperatorexpressinganattitudetowardsaparticularpropositionfromthisset.Here,thealternativesareusedtoprovidecontrastwiththealternativethatissingledoutbytheexclamativeoperator.Theanalysisofsome-exclamativesmakesuseoftwoothercomponentsthatarenotfoundwiththephenomenaintheotherchapters.First,Iarguethatsome-exclamativescruciallydependonsomecombiningwithanounphrasethatcanbeconstruedasallowingforsubkinds.Kindsplayanintegralroleinthisanalysis,inthatthealternativesthataregeneratedbythedeterminersomearealternativesthatvarywithrespecttothesubkindoftheNPthatisinstantiatedbythesubjectoftheexclamative.Thesecondcomponentusedwithsome-exclamativesbutnottheothercasesofandattenuationinvestigatedhereistheexclamativeoperator.Anexclamativeoperatorisnecessaryinthatitisusedtomapthesetofalternativesthataretheficoreflofthesome-exclamativeintoasingle152proposition,sinceunderstandardviewsasetofpropositionsisnotasuitableobjecttoupdatethecommonground.2Theseanalysesshowthatthereareatleastseveraldifferent,moreprimitivecomponentsthatareinvolvedinthecasesofandattenuationexaminedinthisdissertation.Moreover,withtheexceptionofalternatives,thesecomponentsarenotinanysensesharedbetweenthevariousconstructions;some-exclamativeshavenouseforPREC,forinstance,andkindsdonotplayaroleinNumSome.So,althoughthisdissertationgivesaclueastowhatthebasiccomponentsofandattenuationmightbe,showingusthatthesenotionsinvolveamenagerieofcomponents,whatdoesthissayaboutthehopeforunifyingvariousconstructionsinvolvingandattenuation?6.4OnWhenpresentedwithphenomenathatlookrelativelysimilaronthesurface,theimpulseisoftentotreatthemasunderlyingsimilaraswell.Infact,thetitleofthisdissertationthisimpulse,bycategorizingparticulartypesofconstructionsasinstancesofandattenuationbasedontheirsimilarities.However,thecasesIlookatinthisworksuggestthatweshouldbecautiousinourattemptsatandthatnoteverythinginthesebroadsemanticcategoriesofandattenuationcanbeLookingatthemodesofanalysisforthecasestudieshere,wecanseewhyweshouldnotbeparticularlyhopefulforFirst,lookingatthedifferenttypesofphenomenainvolvedhere,itisclearthatthereisnohopeforatthatlevelŠthereisnosenseinwhichsome-exclamativesareimprecision-related,forinstance.Second,themodesofanalysisforeachoftheconstructionsIlookatherealsosuggeststhat,broadlyspeaking,thereisnohopefornotalloftheanalysisinvolvedegrees(astheanalysesforsortaandveryrequire),notalltheanalysesinvolvekinds(assome-exclamativesrequire),andeventhoughalternativesareusedacrossall2AlthoughseeworkinInquisitiveSemantics(Ciardellietal.,2013;Groenendijk&Roelofsen,2009).153oftheanalyses,theactualwaythatalternativesareusedvaries.Alternativesareusedtomodelexpressionswhicharepragmaticallyequivalentintheanalysesforsortaandvery.Ontheotherhand,alternativesareusedtomodelignorancewithNumSome,andtocreateacontrastsetinthecaseofsome-exclamatives.Thedisparateanalysesheresuggestthatandattenuationshouldn'tbethoughtofasprimitivesinthegrammar.Rather,thesenotionsshouldbebetterthoughtofasdescriptivegeneralizationsaboutdifferentsentencetypesandconstructions;andattenuationdonotnecessarilydenotenaturalclassesofphenomena.But,thereishopeforifwenarrowourfocustosubclassesofphenomena.Byfocusingjustonsubclassesofconstructions,wemighthopetothatthereisatleastwithinthesesmallerempiricaldomains.Twooftheseempiricaldomainsareinvestigatedinthisdissertation:imprecisionandexclamatives.Theanalysisofimprecisioninthisdissertationfocusedonhowimprecisioncouldbeconstruedasadegree-relatedphenomenon.Thiswasbuiltontheobservationthatbothsorta/kindaandveryveryclearlyhaveusesasdegreewords.Theconnectionbetweentheirdegreewordsenseandtheirimprecision-modulatingsenseissomewhatmysterious,unlessweconsiderimprecisiontobeafactthat(atsomelevel)isalsoadegree-relatedfact.Ipresentawayofunifyingimprecision(basedontheframeworkusedinMorzycki2011)withotherdegreeconstructions.Chapter5inthisdissertationalsoimplicitlysuggeststhatexclamativesmightallowforsomedegreeofaswell.Thefactthatsomecanbeusedtobuildanexclamativemeaningwithsome-exclamativesisconsistentifweadopttwoparticularviewsabouthowthenatureofandexclamatives.First,ifweassumethatnounphrasesgeneratesetsofalternatives,asisarguedforinworkbyKratzer&Shimoyama(2002),amongothers,wecanconsidertenounphrasestobeofakindwithquestions,inthatquestionsarealsoassociatedwithalternatives(onaHamblin-Karttunenviewofquestions(Hamblin,1973;Karttunen,1977)).Second,oneparticularviewofthesemanticsofexclamativesarguesthatexclamativesareunderlyinglyquestion-likeintheirsemantics(Zanuttini&Portner2003isonerepresentativeofthisview).Whysomecanbeusedtocreateexclamativesisquiteclearifweadopttheseviews:exclamatives,ratherthanbeingin154thebusinessofmanipulating(thealternativescorrespondingto)questions,areratherinthebusinessofmanipulatingalternativesmoregenerally.Some-exclamatives,byvirtueofsome,alsohaveattheircoresetsofalternatives,andsimplypresentasetofalternativesforanexclamativeoperatortomanipulate.ThissubdomainofnŠexclamativesŠcanbebyconsideringwhatcanonicalwh-exclamativesandsome-exclamativeshaveincommon;here,Iarguewhattheyhaveincommonisanalternativesemantics.Themoralofthestoryisthatshouldn'tbeassumedforbroadtheoreticaldomainsapriori,butshouldinsteadbeconsideredonacasebycase(phenomenonbyphenomenon,construc-tionbyconstruction)basis.Weshouldnottakeiandattenuationisprimitivenotions,butshouldlookatexamplesofthemtodeterminewhatkindsofcomponentsunderlyeachcase.Inthisway,wecanclassesofphenomenathatarequitedeeplyrelatedtoeachotherbyvirtueofusingthesamepieces,ratherthanbeingrelatedatapurelysurfacelevel.Thisdissertationexploreswhatsomeofthesecomponentsmustbe.Forcasesofimprecision,whichcutacrossandattenuation,adegreesemanticsisafruitfulwayofmakingprogress.Forepistemicandapproximation,ignorancecanbemodeledusingdomainrestriction.And,forexclamatives,alternativesandkindscanbeusedtocapturewhatspeakersexclaimabout.Futureworkineachofthesedomainsshouldfocusondecomposingthephenomenaevenmore,inordertogainaclearerpictureastowhattheprimitivecomponentsinthegrammarare.155BIBLIOGRAPHY156BIBLIOGRAPHYAbney,Steven.1987.TheEnglishnounphraseinitssententialaspect:MITdissertation.Alonso-Ovalle,L.&P.Menéndez-Benito.2003.SomeepistemiciInShigetoKawahara&MakotoKadowaki(eds.),ProceedingsoftheNorthEastLinguisticsSociety,vol.33,.Alonso-Ovalle,Luis.2006.Disjunctioninalternativesemantics:UniversityofMassachusettsAmherstdissertation.Alonso-Ovalle,Luis&PaulaMenéndez-Benito.2010.ModalNaturalLanguageSemantics18.1Œ31.Alonso-Ovalle,Luis&PaulaMenéndez-Benito.2013.TwoviewsonepistemicLan-guageandLinguisticsCompass7.105Œ122.Alrenga,Peter.2006.Scalar(non-)identityandsimilarity.InDonaldBaumer,DavidMontero&MichaelScanlon(eds.),Proceedingsofthe25thWestCoastConferenceonFormalLinguistics,49Œ57.AnderBois,Scott.2012.FocusanduninformativityinYucatecMayaquestions.NaturalLanguageSemantics20(4).349Œ390.Barker,Chris.2004.PossessiveweakInJi-yungKim,YuryLander&BarbaraH.Partee(eds.),Possessivesandbeyond:Semanticsandsyntax,GLSAPublications.Beller,Charley.2013.Manufacturedandinherentpejorativity.InToddSnider(ed.),ProceedingsofSemanticsandLinguisticTheory,vol.23,136Œ155.Bennett,Michael.1978.DemonstrativesandindexicalsinMontagueGrammar.Synthese39(1).1Œ80.Bhatt,Rajesh.2006.Covertmodalityincontexts.MoutondeGruyter.Bhatt,Rajesh&RoumyanaPancheva.2012.Twosuperlativepuzzles.HandoutfromatalkgivenattheGISTWorkshoponRelativeClauses,GhentUniversity.Bierwisch,Manfred.1989.Thesemanticsofgradation.InM.Bierwisch&E.Lang(eds.),Dimensionaladjectives,71Œ261.Berlin:Springer.Bochnak,M.Ryan&EvaCsipak.2014.Anewmetalinguisticdegreemorpheme.InToddSnider,SarahD'Antonio&MiaWeigand(eds.),ProceedingsofSemanticsandLinguisticTheory,vol.24,.Bolinger,Dwight.1967.AdjectivesinEnglish:attributionandpredication.Lingua18.1Œ34.Bolinger,Dwight.1972.Degreewords.TheHague:Mouton.157Bresnan,JoanW.1973.Syntaxofthecomparativeclauseconstructioninenglish.LinguisticInquiry275Œ343.Büring,D.1997.Themeaningoftopicandfocus:the59thStreetBridgeaccent.London:Routledge.Bylinina,Lisa,NataliaIvlieva,AlexanderPodobryaev&YasutadaSudo.2015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