Telicity corresponds to degree of change - PDF document

Thissortofapproachresultsinsomewhatdierentanalysesofthethreeverbclassesin(1)-(3)(cf.Ramchand1997;Tenny1994):Inverbsofcreation/destruction,telicityinvolvesamappingfromthestructureoftheincrementalthemetotheevent(changein(volume/extentof)object).Inverbsofdirectedmotion,telicityinvolvesamappingfromthelocationofthemovingobjectonapathtotheevent(changeinlocation).Indegreeachievements,telicityinvolvesamappingfromadegreetowhichsomepropertyholdsoftheincrementalthemeargumenttotheevent(changeinproperty).Solution1:Stipulatethatthethematicrelation/argument/semanticparameterthatisrelevantforcalculatingtelicityisdierentinthesethreeclassesofverbs:I-THEME,PATH,PROPERTY(cf.Ramchand1997).Thisapproachmissesthegeneralizationthattheseverbsalldescribeeventsinwhichoneparticipant(underlined in(1)-(3))undergoessomesortofgradualchange|involumeorspatialextent,inlocationalongapath,orinthedegreetowhichitpossessessomegradableproperty.Solution2:Handleeverythingintermsof(metaphoric)movementalongapath(Jackendo1996).Isn'tthereamoredirectcharacterizationofwhat'sgoingonhere?Solution3:Analyzealloftheseverbsasdescribingeventsthatinvolveachangeinthedegreetowhichanobject(the`aectedargument'/incrementaltheme)undergoesachangeinthedegreetowhichitpossessessomegradableproperty:achangeindegreeofvolumeorspatialextent,achangeindegreeofprogressalongapath,achangeindegreeofsomearbitraryproperty(providedbyagradableadjective).Theideacanmosttransparentlyillustratedbythecaseofdegreeachievements:(6)[[[VPlengthentheicicle]]]=e:thelengthoftheicicleatthebeginningofe+d=thelengthoftheicicleattheendofeTelicityisdeterminedbywhetherthe`degreeofchange'argumentdisquantizedornot:Ifdisquantized,lengthentheicicleistrueonlyofeventswhoseendpointscorrespondtothatpointintimeatwhichthelengthoftheiciclehasincreasedbyd.Incontrast,ifdisnotquantized,lengthentheicicleistrueofanyeventoficicle-lengthening.Aswewillseebelow,thissortofanalysiscanbeextendedtotheentireclassofverbsofgradualchange.ThisanalysisdierscruciallyfromKrifka'sinthatitdispenseswithstipulationsaboutthemappingfromargumentstructuretoevents|inparticular,theideathatweneedtodeneparticularthematicrolesintermsofahomomorphicrelationbetweenthestructureofthatrole'sargumentandtheprogressionoftheevent.Instead,therelationbetween(non-)quantizationofanargument(thedegreeofchange)and(a)telicityfollowsfromthebasicsemanticanalysisgiventoverbsofgradualchange.2 2BasicassumptionsaboutscalarsemanticsThescalarsemanticsweproposeforverbsofgradualchangeisbasedonthesemanticanalysesofgradableadjectivesthatwehavebeendiscussingforthepastfewweeks.Thecrucialcomponentsareasfollows.1.scales:asetofpointstotallyorderedalongsomedimension(e.g.,length,volume,duration,etc.).WeadoptthetypologyofscalestructuresarguedforinKennedyandMcNally2002:(7)Atypologyofscalestructuresa.hS(0;1);iopenb.hS[0;1);ilowerclosedc.hS(0;1];iupperclosedd.hS[0;1];iclosed2.degrees:positiveornegativeintervalsonascale(Seuren1978;vonStechow1984b;Kennedy1999,2001;SchwarzchildandWilkinson1999).(8)a.POS(S)=fdSj9p12d8p22S[p2p1!p22d]gb.NEG(S)=fdSj9p12d8p22S[p1p2!p22d]gAsastartingpoint,wewilladoptamodiedversionofvonStechow's(1984b)representa-tionsforpositiveandnegativedegrees:(9)Positiveandnegativedegreesa.d+p=fp02Sjp0pgb.d�p=fp02Sjpp0gThiswillbeimportantfortalkingaboutdierencesbetweenpositive/negativedegrees,thoughitmayultimatelybethecasethatwewantadierentformalismfordealingwiththis.3.gradableadjectives:functionsfromobjectstodegrees(Kennedy1999;BartschandVennemann1973.Wecouldpositarelationalanalysis,asinCresswell1977;Seuren1978;Hellan1981;vonStechow1984a;Heim1985,2000andmanyothers,butforreasonsthatwillbecomeclearbelow,assumingafunctionalanalysisissimpler.Sinceaparticularobjectmaymanifestdierentdegreesofthesamegradablepropertyatdierenttimes|andweareinterestedinchangesinpropertiesovertime|weaddatemporalargument.(10)a.[[long(a)(t)]]=thepositiveprojectionofaonthelengthscaleattimetb.[[short(a)(t)]]=thenegativeprojectionofaonthelengthscaleattimetForexample,(11)illustratesthepositiveandnegativeprojectionsontothelengthscaleofanobjectaattimet:(11)length:0|||long(a)(t)||||||short(a)(t)|||13 Thissortofapproachassumesthattherelationalcomponentofpredicatesheadedbygrad-ableadjectivescomesfromthedegreemorphology:(12)DegPDegAP APossibleanalysesoffamiliardegreemorphemes:(13)a.[[[Deg0;]]]=Gdxt:9d:G(x)(t)db.[[[Deg0more]]]=Gdxt:G(x)(t)dTwo(independent)pointstoobserveaboutthesystem:1.Thetreatmentofpolarityallowsustogiveasemanticanalysisofcomparativemorphologythatworksforbothpositiveandnegativeadjectives.2.Ashasbeendiscussedinclass,thisanalysisdoesn'tpositanyquanticationalforceforthecomparative(outsidethecomparativeclause),soweexpectnoscopalinteractionsbetweenthecomparativemorphologyandotherstuinthesentence.(14)a.RodAislongerthanrodB(is).b.long(RodA)(tu)long(RodB)(tu)c.long(RodA)(tu)maxfdjdlong(RodB)(tu)(15)a.RodBisshorterthanrodA(is).b.short(RodB)(tu)short(RodA)(tu)c.short(RodB)(tu)maxfdjdshort(RodB)(tu)(16)length:0|||long(A)(tu)|||||||short(A)(tu)||||1length:0||long(B)(tu)|||||||short(B)(tu)|||||14.differentialcomparatives:Sinceweareinterestedindegreeofchange,wealsoneedtobeabletotalkaboutdierencesinthedegreetowhichdierentthings(orthesamethingsatdierenttimes)havesomeproperty.Dierencesarealsoimportantfor\dierentialcomparatives"like(17a)-(17b).(17)a.RodAis16incheslongerthanrodB.b.RodBis16inchesshorterthanrodA.Following(Hellan1981;vonStechow1984a;Bierwisch1989;Faller1998;Kennedy2001),wewedenedegreeadditionasin(18)(vonStechow1984b),wherethedierentialdegreeisrestrictedtobepositive.(18)Degreeadditiona.d+p+d+q=d+p+qb.d�p+d+q=d�p�qWecannowanalyzedierentialcomparativesintermsofdegreeaddition:4 (19)a.long(A)long(B)+d+16b.short(B)short(A)+d+16Regularcomparativescanalsobereanalyzedintheseterms,providedweexistentiallyquan-tifyoverthedierentialdegreewhenitisunexpressed(seeHellan1981;vonStechow1984aforapproachesalongtheselines,andKennedy2001;SchwarzchildandWilkinson1999forslightlydierentapproaches):(20)[[[Deg0more]]]=Gd1d2xt:G(x)(t)d1+d2Ifthisquantier(oradierentialmeasurephrase)canscopeovercertainpredicates,wemaybeabletoaccountforthescopefactsdiscussedinHeim2000withoutgivingupthenon-quanticationalanalysisofthecomparative.Moreonthisnextweek.3Extendingscalarsemanticstoverbsofgradualchange3.1LexicalsemanticsWeclaimthatallthreeclassesofverbsshouldbeanalyzedinawaythatismosttranspar-entlyrepresentedbydegreeachievements:intermsofchangesinthedegreetowhichanobjectpossessesagradableproperty(i.e.,ameasurefunction).Thecentralclaimsare:1.Allverbsofgradualchangecontaingradablepropertiesaspartsoftheirmeaning|evenverbsofcreation/destruction(cf.Kratzer2000).degreeachievements:apropertydeterminedbytheadjectivalbasedirectedmotionverbs:apropertythatmeasuresmovementalongapathcreation/destructionverbs:apropertythatmeasuresspatialextent.2.Theeventsdescribedbytheseverbsinvolvechanges(increases)inthedegreetowhichoneoftheirargumentspossessesthisgradableproperty.3.Themeasureofchangecorrespondstoa(dierential)degreeargument,whichwerefertoasthe\degreeofchange"(cf.Hay,Kennedy,andLevin1999).Thecoreproposal:foranyverbofgradualchangeV
withassociatedgradablepropertygv,[VPV
xd-much]istrueofaneventeifandonlyifxincreasesingv-nessbyd-much.1(21)a.Thetiltingoftheearthlengthenedthedayby5minutes.b.(Thetiltingoftheearthcaused)thedaytoincreasein(temporal)lengthbyveminutes.(22)a.Theballoonascended100meters.b.Theballoonincreasedinverticalpositionby100meters.(23)a.Kimatetwobowlsofrice. 1Notethatwemostlyignoreexternalargumentsandcausation,sincecausationisnotarelevantfactor:bothcausativeandinchoativeverbsshowthesamebehaviorwithrespectto(a)telicity.Thisisactuallyanimportantfact,sinceitindicatesthatcausationandtelicityareindependent(Abusch1986;Pustejovsky1991;VanValinandLaPolla1997).5 b.(Kimcaused)somequantityofricetoincreaseineatennessbytwobowls.Thelexicalsemanticanalysisismadeexplicitin(24a),wheregvisthegradablepropertyassociatedwiththeverb,disthedegreeofchangeargument,andbegandendarefunctionsfromeventstotimesthatreturnanevent'sbeginningandendpoints,respectively.Forperspicuity,Iwillsometimesusetheabbreviationin(24b).(24)a.V
=xde:gv(x)(end(e))=gv(x)(beg(e))+db.V
=xde:increase(gv(x))(d)(e)ThisanalysisissimilartotheonedevelopedinJackendo1996,butdiersinthatthelatterisbasedonmovementalongapath,ratherthanchangeinagradableproperty.Thefollowinglexicalsemanticrepresentationsillustratetheanalysisasappliedtovariousmembersofthethreeclassesofverbs,where\d-much"correspondstothe(syntacticallyoptional)degreeofchangeargument.(25)Degreeachievementsa.[VPlengthenx(byd-much)]=e:increase(long(x))(d)(e)b.[VPshortenx(byd-much)]=e:increase(short(x))(d)(e)(26)Verbsofdirectedmotiona.[VPxascend(d-much)]=e:increase(up(x))(d)(e)b.[VPxdescend(d-much)]=e:increase(down(x))(d)(e)(27)Verbsofcreation/destructiona.[VPwrite(d-muchof)x]=e:increase(written(x))(d)(e)b.[VPeat(d-muchof)x]=e:increase(eaten(x))(d)(e)3.2TelicitycorrespondstodegreeofchangeItfollowsfromthisanalysisthatthesemanticvalueofthedegreeofchangeargument|whetherornotitisquantized|determinesthepredicate'stelicity.(28)Quantizedd!telicVPa.[VPlengthentheicicleby3centimeters]b.e[long(icicle)(end(e))=long(icicle)(beg(e))+3cm](29)Non-quantizedd!atelicVPa.[VPlengthentheicicle(bysomeamount)]b.e9d[long(icicle)(end(e))=long(icicle)(beg(e))+d]Thisexampleinvolvesadegreeachievement,butthesamesortofanalysisappliestoallverbsofgradualchange,aswewillshowindetailbelow.Wethusachieveourinitialgoalofprovidingafullygeneralaccountofallthreeclasesofverbs.Moreover,onthisapproach,whetherapredicateistelicornotisstrictlyafunctionofthescalarpropertiesofthedegreeofchange|wedonotneedtoestablishamappingfromthedegreeofchange(oranyotherargument)totheevent.6 Ofcourse,itnowbecomesabsolutelycrucialthatweanswerthefollowingquestion:howisthesemanticvalueandcorresponding(non-)quantezednessofthedegreeofchangeargumentdetermined?3.3Aside:Whyincreaseandnot(also)decrease?Wehavecharacterizedgradualchangeasanincreaseinthedegreetowhichanobjectpossessesagradableproperty.Butcouldn'tgraduatechangeinvolveadecreaseinsomeproperty?Wouldn'tthisbetherightwaytoanalyzeverbslikedescend,shortenoreat?Infact,decreasingchangescanbecharacterizedasincreasesinnegativeproperties,aswehavealreadyseen.However,wemightstillwonderwhydon'twendpairslike`lengthen'(increaseinlength)and`lengthess'(decreaseinlength)?Apossibleexplanation?Assumethatchangeinvolvesashiftfrom:PtoP(Wright1963,1968;Dowty1979).IfanobjectpossessesagradablepropertyPtodegreed,thenforanyd0d,thatobjectalsopossessespropertyPtodegreed0.Therefore,changeinthedegreetowhichanobjectpossessessomegradablepropertyshouldinvolveanincrease(ofapositiveornegativedegree).4Capturing(a)telicityHowisthevalueofthedegreeofchangedetermined?Inparticular,whatdetermineswhetherthisargumentisquantizedornon-quantized?Thereappeartobefourwaystodeterminethevalueofthis(possiblyimplicit)argument.Itmaybe:1.explicitlyprovidedbylinguisticmaterial(e.g.,measurephrases),2.inferredbasedonthelexicalsemanticsoftheverboritsarguments(e.g.,open/closedscale,mass/countdistinction?),3.inferredbasedonreal-worldknowledge(e.g.,pantsvs.icicles),or4.itmaybeboundbyadefaultexistentialquantier(the`elsewhere'case).4.1Explicitlyspecieddegreeofchange4.1.1MeasurephrasesAquantizedornon-quantizedmeasurephrasemayexplicitlyprovideavalueford.(30)Somequantizedmeasurephrasesa.5metersb.40fathomsc.10pagesd.ascoope.abowl(ofrice)Ifthemeasurephraseisquantized,wegetatelicinterpretation:7 (31)a.Theyarewideningtheroad5meters.6)Theyhavewidenedtheroad5meters.b.Thelakecooled4degreesintwodays/?fortwodays.(32)a.Thecurtainsarefalling10ft.6)Thecurtainshavefallen10ft.b.Thesubmarineascended40fathomsinanhour/?foranhour.(33)a.Kimiseatingascoop.6)Kimhaseatenascoop.b.Kimwrote10pagesin45minutes/?for45minutes.(34)a.Kimisdrinkingabottleofwater.6)Kimhasdrunkabottleofwater.b.Kimateabowlofricein5minutes/?for5minutes.Thefactthatallthreeclassesofverbstakeovertmeasurephrasearguments|whicharestandardlyassumedtodenotedegrees|furthersupportstheclaimthattheyallhavethesameunderlyingscalarsemantics.Notethatverbsofcreation/consumption,unliketheothertwoclasses,cannotexpressboththemeasureargumentandaectedargumentindependently|wegetoneortheother,ora`combination'ofthetwo(asin(34)).Wewillreturntothispointbelow.(35)Somenon-quantizedmeasurephrasesa.abitb.aquantityc.apartEntailmentsindicatethatnon-quantizedmeasurephrasesgiverisetoatelicpredicates.(36)a.Thesoupiscoolingabit.)Thesouphascooledabit.b.Kimisdrinkingaquantityofmilk.)Kimhasdrunkaquantityofmilk.c.Thesubisascendingapartofthewaytowardsthesurface.)Thesubhasascendedapartofthewaytowardsthesurface.Weappeartorunintoproblemswithfor-PPs.(37)Thesoupcooledabit?for10minutes/in10minutes.(37)Kimdrankaquantityofmilk?for30seconds/in30seconds.(37)Thesubascendedapartofthewaytowardsthesurface?foranhour/inanhour.Thisisnotsurprising|seeZucchiandWhite's(2001)discussionoftwigs,sequencesandquantitiesofmilk.Wewillreturntoanexplanationbelow.4.1.2ScalaradverbsA\maximizing"adverbmayspecifythatsomepointonthescalemustbereached,inwhichcasethedegreeofchangeisquantized,andthepredicatehasatelicinterpretation.(38)Maximizingadverbsa.completelyb.totallyc.halfway8 (39)a.Theyaretotallystraighteningtherope.6)Theyhavetotallystraightenedtherope.b.Thecakeiscoolingcompletely.6)Thecakehascooledcompletely.(40)a.Kellydrankthemilkshakehalfwayin10minutes/?for10minutes.b.Thecurtainsfellhalfwayin10seconds/?for10seconds.Incontrast,\minimizing"adverbs,whichspecifythatthechangecannotgopastsomepointonascale,resultinanon-quantizeddegreeofchangeandanatelicpredicate.(41)Minimizingadverbsa.slightlyb.partiallyc.somewhat(42)a.Theyarestraighteningtheropeslightly.)Theyhavestraightenedtheropeslightly.b.Theindependentcounselisbroadeningtheinvestigationsomewhat.)Theindependentcounselhasbroadenedtheinvestigationsomewhat.(43)a.Thesubmarineisascendingslightly.)Thesubmarinehasascendedslightly.b.Thecurtainsarefallingabit.)Thecurtainshavefallenabit.Again,though,weseemtohaveaproblemwithfor-PPs!(44)a.??Theystraightenedtheropeslightlyfor10minutes.b.??Theindependentcounselbroadenedtheinvestigationsomewhatfor3weeks.4.2LexicallyinferredimplicitdegreeofchangeAswehavealreadyseen,thescaleassociatedwithagradableadjectivemaybeclosedoropen.Thispropertyin uencesthedefaulttelicityofthepredicate.Thiseectisclearestwithdegreeachievementssincetheirscalestructureismosttransparent(seeHayetal.1999,foradditionaldiscussion).Whenthebaseofadegreeachievementisaclosed-scaleadjective,aquantizeddegreeofchangeisinferablefromscalestructure:itisthedegreeofchangerequiredtogettotheendofthescale.(45)a.Theyarestraighteningtherope.6)Theyhavestraightenedtherope.b.Thetubisemptying.6)Thetubhasemptied.Whenthebaseisanopen-scaleadjective,thedefaultinterpretationisatelic(seesection4.4below).(46)a.Theyarelengtheningtherope.)Theyhavelengthenedtherope.b.Theyarewideningtheroad.)Theyhavewidenedtheroad.Preciselythesameeectsareseeninverbsofdirectedmotion.Proportionalmodierscanbeusedheretotestforscalestructure,justaswithgradableadjectves:9 (47)a.Kimenteredthehousecompletely.b.??Kimapproachedthehousecompletely.(48)a.Kimisenteringthehouse.6)Kimhasenteredthehouse.b.Kimisapproachingthehouse.)Kimhasapproachedthehouse.Theopen/closedscaledistinctionmaybeattherootofthemass/counteectontelicityofverbsofcreation/destruction:countnouns(withdeterminers)areassociatedwithaclosedscalarstructure(wherethemaximalvalueisthedegreethatcorrespondstoaectingtheargumentcompletely);massnounsareassociatedwithanopenscalarstructure.(49)a.Kimateasandwichcompletely.b.??Kimatericecompletely.(50)a.Kimiseatingasandwich.6)Kimhaseatenasandwich.b.Kimiseatingrice.)Kimhaseatenrice.Alternatively,wemaywanttosaythatdirectobjectsofcreation/consumptionverbsdirectlysupplythevalueofboththeaectedargumentandthemeasureargument(seethediscussionabove)|thisisaquestionthatstillneedstoberesolved.Moreonthisnextweektoo.4.3ContextuallyinferreddegreeofchangeWhenthemeaningoftheverb'sargumentsaresuchthataquantizedvalueofchangecanbeinferred,atelicinterpretationresults,evenincasesinwhichthesameverbsareatelicintheabsenceofsuchinformation.Intheexamplesin(51),contextandworldknowledgeprovidesinformationaboutwhatthenaldegreeshouldbe|thespeciedlengthofalteration,thewindowsill,thestage|whichmeansthatthedegreeofchangeisquantized.(51)a.Thetailorislengtheningmypants.6)Thetailorhaslengthenedmypants.b.Kimisloweringtheblind.6)Kimhasloweredtheblind.c.Thecurtainisfalling.6)Thecurtainhasfallen.Thisisnotthecaseintheexamplesin(52),andthepredicatesareatelic:(52)a.Thetracislengtheningmycommute.)Thetrachaslengthenedmycommute.b.Kimisloweringtheheat.)Kimhasloweredtheheat.c.Thetemperatureisfalling.)Thetemperaturehasfallen.4.4TheelsewherecaseIfneitherameasurephrase,northescalarpropertiesoftheunderlyingpredicate,norothercontextualfactorsconspiretoprovideavalueford,itisexistentiallyboundattheleveloftheverbalpredicate.Theresultisanon-quantized,atelicpredicate(see(29b)above).(53)a.Theyarelengtheningtherope.)Theyhavelengthenedtherope.b.Themetalcooledforanhour.10 (54)a.Thesubisascending.)Thesubhasascended.b.Kimpushedthecartforanhour.(55)a.Leeisreading.)Leehasread.b.Kimatefor15minutes.4.5TelicityandcontextTheinferencetoaquantizeddegreeofchangeinthecasesdiscussedabovearisesthroughconversationalimplicature(cf.Krifka1989;Filip1999;Jackendo1996;Hayetal.1999):asshownby(56),theinferenceiscancellable.(56)a.Istraightenedtherope,butnotcompletely.b.Thetailorlengthenedmypants,butnotcompletely.Theimplicaturecanbeexplainedintermsofprinciplesofinformativeness.Forexample,inthecaseofscalestructurein uencingtelicity,whatisuniqueaboutclosed-scaleadjectivesisthattheendpointofthescaleisapossiblereferencepoint.Itfollowsthatthemostinfor-mativeinterpretationof,e.g.,Iemptiedthetub,istheoneinwhichtheropeisstraightenedcompletely(cf.Thetubisempty.)Incontrast,whenaquantizedvalueforthedegreeofchangeisexplicitlysupplied,asinthefollowingexamples,telicityisnotcancellable.(57)a.#Theystraightenedtheropecompletely,buttheropeisn'tcompletelystraight.b.#Theywidenedtheroad5feet,buttheroaddidn'tincreaseinwidthby5feet.(58)a.Sheatethesandwichin5minutes.b.Sheatethesandwichfor5minutes.(59)a.Sheatethesandwichbutasusualsheleftacoupleofbites.b.??Sheatethewholesandwich,butasusualsheleftacoupleofbites.(60)a.Sheranaracebutdidn'tquitenishit.b.??Sheranamilebutdidn'tquitenishit.5BitsandquantitiesWhatiswrongwithfor-PPsinthefollowingexamplesifthemeasurephrasesarenon-quantized?(61)a.Thesoupcooledabit?for10minutes/in10minutes.b.Kimdrankaquantityofmilk?for30seconds/in30seconds.c.Thesubascendedapartofthewaytowardsthesurface?foranhour/inanhour.(62)a.??Theystraightenedtheropeslightlyfor10minutes.b.??Theindependentcounselbroadenedtheinvestigationsomewhatfor3weeks.11 ThesearenotaproblemifweadoptZucchiandWhite's(2001)analysisoftwigsandsequences(inpredicateslikewriteasequenceofnumbers).First,weassumethatthedegreevariablesintroducedbytheseexpressionsareexistentiallyboundfromoutsidetheVP(unliketheimplicitargumentexamplesabove,whichareboundinsideVP).(63)a.Thesoupcooledabit.b.e[cool(soup)(end(e))=cool(soup)(beg(e))+d]WhatiscrucialhereisthatdisfreeinsidetheVP.Sinceitsvalueisdeterminedbyanassignmentfunction,theVPisquantized:(63b)istrueonlyofeventsthatinvolveanincreaseincoolnessbyg(d)-much.Assumingthatfor-PPspresupposethatthepredicatetheymodifyisnon-quantized,weaccountfortheincompatibility.6ConclusionVerbsofgradualchangecontaingradablepropertiesaspartoftheirmeaning.Telicityisdeterminedsolelybythesemanticpropertiesofthedegreeofchange;itisnotdeterminedbyalexicaldiacritic(e.g.,[+/{bounded])orsomekindofmorpho-syntacticfeature(s).Contrarytowhatisoftentakentobetheconventionalwisdom(i.e.Dowty1991;Krifka1989),theincrementalthemeargumentdoesnot(directly)determinetelicity.Thein-crementalthemedoesindirectlydeterminetelicitytotheextentthatitsstructureaectspossiblevaluesofthedegreeofchange.Moregenerally,weseethattelicityanddegreeofchange(ourfunctionalanalogueofthetraditionalincrementaltheme)aretosomeextentindependent:averbmayhaveadegreeofchange(andanincrementaltheme)withoutbeingtelic(cf.Krifka1986,1989;Filip1999;Jackendo1996;butseeDowty1991,p.607foradierentview).Mostgenerally,ouranalysisindicatesthatscalarrepresentationsplayamuchbroaderroleinnaturallanguagesemanticsthanhaspreviouslybeenassumed.Theroleofscalarrep-resentationsextendsbeyondthesemanticsofgradableadjectivestoacorepropertyofverbmeaning:thedeterminationofaspectualproperties.Possiblytootherareasofwordmeaningaswell...?ReferencesAbusch,Dorit.1986.Verbsofchange,causationandtime.Technicalreport,CenterfortheStudyofLanguageandInformation,StanfordUniversity,Stanford,CA.ReportCSLI-86-50.Bartsch,Renate,andTheoVennemann.1973.Semanticstructures:Astudyintherelationbetweensyntaxandsemantics.Frankfurt:AthaenumVerlag.Bierwisch,Manfred.1989.Thesemanticsofgradation.InDimensionaladjectives,ed.ManfredBierwischandEwaldLang,71{261.Berlin:Springer-Verlag.Cresswell,M.J.1977.Thesemanticsofdegree.InMontaguegrammar,ed.BarbaraPartee,261{292.NewYork:AcademicPress.Dowty,David.1979.Wordmeaningandmontaguegrammar.Dordrecht:Riedel.Dowty,DavidR.1991.Thematicproto-rolesandargumentselection.Language67:547{619.Faller,Martina.1998.Avectorspacesemanticsforcomparatives.Ms.,StanfordUniversity.Filip,Hana.1999.Aspect,eventualitytypes,andnominalreference.NewYork:GarlandPress.(1993BerkeleyPh.Dthesis).12 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Wright,GeorgH.von.1963.Normandaction.NewYork:HumanitiesPress.Wright,GeorgH.von.1968.Anessayondeonticlogicandthegeneraltheoryofaction.Amsterdam:North-HollandPublishingCo.14 HeimandKennedyTopicsinSemanticsTelicityCorrespondstoDegreeofChange1IntroductionAnalysesofaspectoftenfocusonthevariabletelicityofcreation/destructionverbs(1),butsuchvariabilityisalsoshownbydirectedmotionverbs(2)(LevinandRappaportHovav1995)and(so-called)\degreeachievements"(3)(Dowty1979).(1)a.Kimaterice foranhour.atelicb.Kimateabowlofrice inanhour.(2)a.Theballoon ascendedforanhour.atelicb.Thesubmarine ascendedinanhour.(3)a.Thedrippingwaterlengthenedtheicicle foranhour.atelicb.Thetailorlengthenedmypants inanhour.Krifka(1989,1992)arguesthattelicityisafunctionofthestructureofthe`incrementaltheme'argumentoftheverb,andfollowsfromtherelationbetweenthestructureoftheargumentandthedescribedevent(cf.Dowty1991;Filip1999;Jackendo1996;Tenny1987,1994;Verkuyl1993;Ramchand1997).Focusingspeci\fcallyonverbsofcreation/destruction,Krifkaarguesthatade\fningcharac-teristicoftheincrementalthemeroleisthatitsatis\fes`MappingtoObjects'and`MappingtoEvents':(4)a.MappingtoObjects[MAP-O($8e;e;xxR(e;x!99x0x^R(e0;x)]]]MappingtoEvents[MAP-E($8e;x;xxR(e;x!99e0e^R(e0;x)]]]Given(4a-b),atelicinterpretationofthepredicateariseswhenevertheincrementalthemeargumentisquantized(5)a.Apredicatequantizedifandonlyifnoentitythatiscanbeasubpartofanotherentitythatis(seeKrifka1998,p.200).b.Aneventdescriptiontelicifandonlyifitappliestoeventssuchthatallpartsofthatfallunderareinitialand\fnalpartsof(seeKrifka1998,p.207).Sinceabowlofrice isquantizedin(1b),thepredicateeatabowlofriceistrueonlyofeventswhoseendpointscorrespondtothatpointintimeatwhichabowl'sworthofthericehasbeenconsumed.Sincerice isnotquantized,thepredicateeatricein(1a)istrueofanyeventofrice-eating,regardlessofendpoint.:\Thedistinctionbetweentelicityandatelicityshouldnotbeinthenatureoftheobjectdescribed,butinthedescriptionappliedtotheobject."(Krifka1998,p.207) TelicityCorrespondstoDegreeofChange1IntroductionAnalysesofaspectoftenfocusonthevariabletelicityofcreation/destructionverbs(1),butsuchvariabilityisalsoshownbydirectedmotionverbs(2)(LevinandRappaportHovav1995)and(so-called)\degreeachievements"(3)(Dowty1979).(1)a.Kimaterice foranhour.atelicb.Kimateabowlofrice inanhour.(2)a.Theballoon ascendedforanhour.atelicb.Thesubmarine ascendedinanhour.(3)a.Thedrippingwaterlengthenedtheicicle foranhour.atelicb.Thetailorlengthenedmypants inanhour.Krifka(1989,1992)arguesthattelicityisafunctionofthestructureofthe`incrementaltheme'argumentoftheverb,andfollowsfromtherelationbetweenthestructureoftheargumentandthedescribedevent(cf.Dowty1991;Filip1999;Jackendo1996;Tenny1987,1994;Verkuyl1993;Ramchand1997).Focusingspeci\fcallyonverbsofcreation/destruction,Krifkaarguesthatade\fningcharac-teristicoftheincrementalthemeroleisthatitsatis\fes`MappingtoObjects'and`MappingtoEvents':(4)a.MappingtoObjects[MAP-O($8e;e;xxR(e;x!99x0x^R(e0;x)]]]MappingtoEvents[MAP-E($8e;x;xxR(e;x!99e0e^R(e0;x)]]]Given(4a-b),atelicinterpretationofthepredicateariseswhenevertheincrementalthemeargumentisquantized(5)a.Apredicatequantizedifandonlyifnoentitythatiscanbeasubpartofanotherentitythatis(seeKrifka1998,p.200).b.Aneventdescriptiontelicifandonlyifitappliestoeventssuchthatallpartsofthatfallunderareinitialand\fnalpartsof(seeKrifka1998,p.207).Sinceabowlofrice isquantizedin(1b),thepredicateeatabowlofriceistrueonlyofeventswhoseendpointscorrespondtothatpointintimeatwhichabowl'sworthofthericehasbeenconsumed.Sincerice isnotquantized,thepredicateeatricein(1a)istrueofanyeventofrice-eating,regardlessofendpoint.:\Thedistinctionbetweentelicityandatelicityshouldnotbeinthenatureoftheobjectdescribed,butinthedescriptionappliedtotheobject."(Krifka1998,p.207) TelicityCorrespondstoDegreeofChange1IntroductionAnalysesofaspectoftenfocusonthevariabletelicityofcreation/destructionverbs(1),butsuchvariabilityisalsoshownbydirectedmotionverbs(2)(LevinandRappaportHovav1995)and(so-called)\degreeachievements"(3)(Dowty1979).(1)a.Kimaterice foranhour.atelicb.Kimateabowlofrice inanhour.(2)a.Theballoon ascendedforanhour.atelicb.Thesubmarine ascendedinanhour.(3)a.Thedrippingwaterlengthenedtheicicle foranhour.atelicb.Thetailorlengthenedmypants inanhour.Krifka(1989,1992)arguesthattelicityisafunctionofthestructureofthe`incrementaltheme'argumentoftheverb,andfollowsfromtherelationbetweenthestructureoftheargumentandthedescribedevent(cf.Dowty1991;Filip1999;Jackendo1996;Tenny1987,1994;Verkuyl1993;Ramchand1997).Focusingspeci\fcallyonverbsofcreation/destruction,Krifkaarguesthatade\fningcharac-teristicoftheincrementalthemeroleisthatitsatis\fes`MappingtoObjects'and`MappingtoEvents':(4)a.MappingtoObjects[MAP-O($8e;e;xxR(e;x!99x0x^R(e0;x)]]]MappingtoEvents[MAP-E($8e;x;xxR(e;x!99e0e^R(e0;x)]]]Given(4a-b),atelicinterpretationofthepredicateariseswhenevertheincrementalthemeargumentisquantized(5)a.Apredicatequantizedifandonlyifnoentitythatiscanbeasubpartofanotherentitythatis(seeKrifka1998,p.200).b.Aneventdescriptiontelicifandonlyifitappliestoeventssuchthatallpartsofthatfallunderareinitialand\fnalpartsof(seeKrifka1998,p.207).Sinceabowlofrice isquantizedin(1b),thepredicateeatabowlofriceistrueonlyofeventswhoseendpointscorrespondtothatpointintimeatwhichabowl'sworthofthericehasbeenconsumed.Sincerice isnotquantized,thepredicateeatricein(1a)istrueofanyeventofrice-eating,regardlessofendpoint.:\Thedistinctionbetweentelicityandatelicityshouldnotbeinthenatureoftheobjectdescribed,butinthedescriptionappliedtotheobject."(Krifka1998,p.207)