[under review]

Dualnumberandthetypologyofthenumeral-nounconstruction1LuisaMartíQueenMaryUniversityofLondonluisa.marti@qmul.ac.ukMay2020Commentswelcome!InthispaperIlaydownthetheoreticalgroundworkforanextensionofMartí’s(2020a)theoryofthenumeral+nounconstruction(e.g.,Englishthreedogs)tolanguagesthatdrawadistinctionbetweensingular,dualandpluralintheirnominaldomain.Martí’saccounthypothesizesthatthe number marking we see on nouns in this construction is the result of the interactionbetweenthecompositionalsemanticsofnumberfeatures,asconceivedofinHarbour(2014),andof cardinal numerals, as conceivedof in Scontras (2014) andothers. ExtendingMartí’saccount to singular-dual-plural languages makes concrete predictions about the types ofnumbermarkingweshouldobserveontheirnounswhentheycombinewithnumerals,andthequestionthatarisesiswhetherthesearethepatternsthatweindeedfindcross-linguistically.Iargue below that the numeral+noun construction in Yimas and Hopi conformsstraightforwardlytothesepredictions.IalsodiscussImereandLjubljanaSlovenian,languageswhichcanbeshowntoconformtothepredictionsonceaproperunderstandingofcomplexnumerals(inthecaseofLjubljanaSlovenian)andnumberprefixes(inthecaseofImere)isinplace. The consideration of Ljubljana Slovenian requires an analysis for complex numerals,aspectsofwhichIborrowfromIoninandMatushansky(2006,2018)andadapttofitMartí’sproposal.Theanalysismakesadditionalpredictionsthatremaintobeinvestigatedandthatarespelledoutaswell.1 IntroductionTwocross-linguisticallycommonpatternsforthenumeral+nounconstructioninlanguagesthatdistinguish singular fromplural onnounsare illustrated in (1)-(3). (1)-(2) illustrateoneofthosepatterns,asrealizedinEnglish,and(3)illustratestheotherpattern,asrealizedinTurkish(Bale,GagnonandKhanjian2011):(1) English

One{boy|*boys}

(2) EnglishTwo/three/twenty-three{boys|*boy}

(3) Turkish

Bir/ iki/ üç/ yirmi üç {çocuk|*çocuk-lar}One/ two/ three/twenty three boy.SG|boy-PL‘One/two/three/twenty-threeboy(s)’

1VerymanythankstoSerahChilia(Imere),MashaEsipova(Russian),BillFoley(Yimas),KenHill(Hopi),NatashaKorotkova(Russian)andRokŽaucer(LjubljanaSlovenian)fortheirinvaluablehelpwithdata.ThanksalsotoKlausAbels,LisaBylinina,DanielHarbour,membersoftheaudienceattheLinguisticsColloquiumattheUniversityofYork,whereIpresentedsomeoftheseideasinthefallof2019,andtothereviewersofthepaper,forcomments,questionsandcriticism.Iwouldalso liketothanktheeditorsofthisspecial issue,BobanArsenijevićandOlgaBorik,notonlyfortheirkindinvitationtocontributeitbutfortheirpatienceandgenerosityataverydifficulttimeinmyfamily,owingtoCOVID-19—withoutit,Iwouldn’thavebeenabletofindthetimeandpeaceofmindtofinishthepaper.Itisdedicated,withmuchlove,tomymother,wholived.

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IntheEnglishpattern,thecardinalnumeralonecombineswithanounthatismorphologicallymarkedassingular,andothercardinalnumeralscombinewithnounsmarkedforplural.IntheTurkishpattern,allcardinalnumeralscombinewithanounthatismorphologicallymarkedforsingular.Note thatTurkishandother languages that instantiate thispatterndo inprincipleinflecttheirnounsforplural(e.g.,withthesuffix-lAr,subjecttovowelharmony,inTurkish),butchoosenottousethepluralformofthenouninthenumeral+nounconstruction(inbothofthelanguagesexemplifiedhere,singularnumberisnotrealizedphonologically,butnothinginwhatfollowshingesonthat).2

Themorphologicalrealizationofthenouninthenumeral+nounconstructionisusuallyconsideredamatterofnumberagreement,andthesemanticsoftheconstructionisderivedbyaseparatesetoftoolsfromthat(see,e.g.,Alexiadou2019,BylininaandNouwen2018,orIoninandMatushansky2006,2018forrecentinstantiationsofthisapproach).InMartí(2020a,underreview), however, a different analysis is entertained, one in which the morphologicalrealizationofgrammaticalnumberandthesemanticsoftheconstructionarisefromoneandthe same set of tools. There are reasons to think that the second approach deserves to beexplored,whichiswhatIdohere.Oneimportantreason,discussedalsoinMartí(2020a:4-5),isthatthesecondapproachsignificantlyreducesthenumberoftoolsthatareneededtoaccountforthenumberpropertiesofthenounintheconstruction.Inthisapproach,thereisnoneedtoappealtoadditionalnumberagreementrulesorprinciplestoaccountforthenumbermarkingonthenouninthenumeral+nounconstruction,sincethatfollowsalreadyfromthetoolsusedto derive its semantics. In other words, the semantic analysis of the construction alreadypredicts the shape that the noun should take, so appealing to any additional principles isunnecessary. It is this economical aspect of the proposal that makes it worth pursuing inprinciple. ThesetoftoolsthatMartí(2020a)appealstois,inbrief,asfollows.First,sheassumesHarbour’s (2014) theory of number features. In particular, she assumes that atmost threebinary features can appear in NumberP, the locus of grammatical number: [±atomic],[±minimal] and [±additive]. These are featureswith a semantics that does not vary cross-linguisticallyandwithaspecificmorpho-syntacticrealizationindifferentlanguages.Second,shefollowsScontras’(2014)assumptionsaboutthesyntaxandsemanticsof(bare)numerals,whichare treatedasspecifiersofNumeralP thatdenotenumbers(i.e., type<n>).NumeralPitselfisheadedbyacountingpredicateCARDandbearsaspecificsyntacticrelationtoNumberP,namely,itisdominatedbyit.Withtheseassumptionsinplace,thepatternsweobservedabovefollow.3 Thetheoreticalgoalofthispaperistoworkoutthepredictionsthatanapproachlikethismakeswithrespecttolanguagesthat,inadditiontosingularandplural,alsodistinguishdualinnouns.TheextensionstothetheorythatIproposehereentailthat,generallyspeaking,thelocus of cross-linguistic variation for the phenomenon at hand rest in two places: (a) thenumber feature(s) a particular language generates in NumberP, and (b) the structuralrelationship between NumberP and NumeralP—I will assume that, in a given language,NumberPdominatesNumeralP(NumberP≫NumeralP),asinScontras’proposal,ortheotherwayaround(NumeralP≫NumberP). Thetheoryisquiterestrictiveinwhatitpredictsforsingular-dual-plural languages,asexplainedindetailinsection3.InwhatIwillcallpredictedpattern1,shownin(4),thenumeral

2ItiswellknownthatanotherrelevantpatternisthatexemplifiedinWesternArmenian,wherenumeralsgreaterthanonemay combinewithnounsmarked for singular or for plural in thenumeral+noun construction,withinterpretativeeffects(seeIoninandMatushansky2018,Martí2020a,Scontras2014,Sigler1997).Martí(2020a)showshowthatpatterncanbeunderstoodwithintheframeworkdefendedthere.Forreasonsofspace,IwillnotbeabletoconsiderherehowthepossibilityofoptionalityinteractswiththeproposalImakebelow.3Martí(underreview)showsthatthesameassumptionscanexplainthepatternsthatwefindwithzeroasthenumeral.

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onecombinesonlywithanouninthesingular,thenumeraltwo,onlywithanouninthedual,andothernumerals,onlywiththenounintheplural:(4) Predictedpattern1:

One+N-singularTwo+N-dualOthernumeral+N-plural

Predictedpattern2,shownin(5), is just likePredictedpattern1exceptthatwithnumeralsotherandoneandtwo,thedualformofthenounisused:(5) Predictedpattern2:

One+N-singularTwo+N-dualOthernumeral+N-dual

Ontheempiricalside,thegoalistofindoutwhethertherearelanguagesthatexemplifythesepatterns,andwhethertherearelanguagesthatconstitutecounterexamplestothepredictionsmadebythetheory.Ishowinsection3thatpattern1isstraightforwardlyexemplifiedinYimasandHopi.

Predictedpattern2mightseemstrangeatfirstbutcanbeaviewedasageneralizationoftheTurkishpatterninthat,ifattested,we’dhavealanguagethatinprinciplemarkspluralityonnounsbutthatchoosesnottousethatmarkinginthenumeral+nounconstruction,usingothernumbermarkinginstead.AsfarasIamaware,thereisnoconfirmationthatalanguageexemplifiesthispattern,soitisnotyetpossibletoknowwhetherthetheoryovergeneratesinthisrespectornot.

I have so far found two languages that are superficially problematic for the theorypresented here. In Ljubljana Slovenian, complex numerals that end in one or two do notcombinewithapluralnoun,aspredicted,butwithasingularoradualone,respectively.Iarguebelowthatthislanguageisnotarealcounterexampletothetheoryaslongasthesyntaxandsemanticsofcomplexnumeralsisproperlyunderstood,anunderstandingthat,Isuggest,mayborrowfromIoninandMatushansky’s(2006,2018)analysisofcomplexnumerals.AsecondcasetoconsiderisImere,whichdisplaysthefollowingpatterndespitebeingasingular-dual-plurallanguageaswell:

(6) PatternattestedinImere:

One+N-singularTwo+N-pluralOthernumeral+N-plural

Iarguethatthislanguagedoesnotactuallyconstituteacounterexampletothetheoryeither.That’sbecausethemorphemethatmarksdualinImere,thenounprefixruu-plausiblyspellsoutdualnumbermorphologyandalsomaterialinD.Giventhis,weexpectitnottobeabletoco-occurwithnumerals,suchasthenumeraltwo.Adifferentnumbermarkingisthenusedwiththatnumeral. Theorganizationofthepaperisasfollows.Section2introducesthetheoreticaltoolsfromMartí(2020a).Section3isthetheoreticalcoreofthepaperanddiscussesthepredictionsthatanextensionofthesetoolsmakesforsingular-dual-pluralsystems.Section4presentsthedatafromYimasandHopithatillustratepattern1.Section5presentstheargumentsthat(Ljubljana)SlovenianandImerearenotcounterexamplestothetheory,despiteappearances. Ioninand

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Matushansky’s(2006,2018)proposalregardingcomplexnumeralsisdiscussedindetailinthissectionaswell.Section6concludes.2 Martí’s(2020a)theoryThis section focuses on singular-plural systems (or one-feature systems) and on Martí’saccountofthem,basedonHarbour(2014)andScontras(2014).

Let’sbeginbyspellingoutMartí’sassumptionsonnumberfeaturesandtheirsyntaxandsemantics,basedonHarbour(2014).Thesyntaxofnounswhentheyarenotaccompaniedbynumeralsisassumedtobeasin(7)(cf.Borer2005andmanyothers):(7) NumberP qp Number0 nP

qp n0 √𝑥Here,anominalcategorynP(whichresultsfromcombiningarootwithn0,anominalizer)isthesister to theheadofNumberP.ThedenotationofnP isassumed to containbothpluralandatomicindividuals(cf.Link1983):(8) ⟦nP⟧={a,b,c,ab,ac,bc,abc}Itisonsuchadenotationthatthesemanticsofthenumberfeatures[±atomic],[±minimal]and[±additive]operateon.Thesemanticsofthetwofeaturesthatwillconcernushere,[±atomic]and[±minimal],isassumedtobeasfollows:4(9) ⟦+atomic⟧=lP<e,t>.lxe.P(x)&atom(x)

⟦−atomic⟧=lP<e,t>.lxe.P(x)&¬atom(x)

(10) ⟦+minimal⟧=lP<e,t>.lxe.P(x)&¬$yP(y)&y⊏x ⟦−minimal⟧=lP<e,t>.lxe.P(x)&$yP(y)&y⊏x

[±atomic] is sensitive towhether something is anatom ([+atomic])ornor ([−atomic]), and[±minimal]issensitivetowhetherthesetdenotedbyitssistercontainselementswithproperpartsinthatset([−minimal])ornot([+minimal]).Possiblenumbersystemsarethosewherenoneofthesefeaturesareavailable(sothelanguagewouldnotmarkgrammaticalnumber),where just one feature is available, or where certain combinations of these features areavailable. Singular-plural systems may be analyzed, in principle, as either [±atomic] or[±minimal].Usually,unlessthelanguagemakesadistinctionbetween1stpersoninclusiveand1stpersonexclusiveinitspronominalsystem(seeHarbour2011),asingular-plurallanguageistreatedasa[±atomic]system.English,forexample,wouldbeonesuchsystem,with[+atomic]spelledoutasnulland[−atomic]spelledoutas–s:5

4‘⊏’isthepropersubpartrelation.Lowercasevariablenamesrangeoverbothatomicandnon-atomicindividuals.ThethirdofHarbour’sfeatures,[±additive],playsnoroleinsingular-dual-plurallanguagesandisthereforenotintroducedhere.5(12)givesrisetoaso-calledexclusivesemanticsforEnglishplurals,thatis,toasemanticsconcernedonlywithpluralindividuals.Thereisalong-standingdebateintheliteratureastowhetherthisisthecorrectsemanticsforthem,giventhemeaningofsentencessuchasIhavenochildren,whichareconcernedbothwithatomsandnon-atoms(otherwisethesentencewouldbepredictedincorrectlytobetrueaslongasthespeakerhasonechild).

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(11) NumberP qp Number0 nP [+atomic]qp n0 √𝑥 (12) NumberP qp Number0 nP [−atomic]qp n0 √𝑥[±Minimal]can,inprinciple,alsogiverisetoasingular-pluralsystem,but,becauseofitsrelativesemantics, this feature can give rise tomore distinctions than [±atomic]. [±Minimal] is thefeature at the heart of the pronominal paradigm of languages like Ilocano (Austronesian),showninTable1(seeCorbett2000:168,Rubino1997:55-6): minimal augmented1excl -ko -mi1incl -ta -tayo2 -mo -yo3 -na -da

Table1Ilocanoencliticpronouns

[+Minimal]picksthespeaker+hearerdyad(cruciallynotanatom)fortheminimal1stpersoninclusive pronoun −ta, giving rise to a pronoun that picks two referents (not one). That’sbecause the speaker+hearerdyad is anelementwithoutproperparts ina set that containsspeaker as well as the hearer; [−minimal] picks three or more referents(speaker+hearer+other(s))forthe1stpersoninclusiveaugmentedpronoun–tayo,sincetheseallcontainproperpartsfromtheset(thespeaker+hearerdyad).Intheotherpersons,whichdonot include the hearer, one (for minimal pronouns) or more than one (for augmentedpronouns) referents are picked. Thus, though close in their semantics, [±minimal] and[±atomic]arenotthesamefeature. Martíargues that thissystem,put togetherwithScontras’ (2014)assumptionsaboutnumerals,predictstheEnglishandTurkishpatternswesawinsection16.Scontrasassumesthefollowingsyntax:

Twomain positions exist in this debate: (i) either plural nouns only have an inclusive semantics, unlike thatobtainedfrom(12),andexclusivemeaningsarisepragmatically(seeDvorakandSauerland2006,Ivlieva2013,Krifka1989,1995,Lasersohn1998,2011,Sauerland2003,Sauerland,AnderssenandYatsushiro2005,Spector2007,Yatsushiro,SauerlandandAlexiadou2017,Zweig2009),or(ii)pluralnounsareambiguousbetweenaninclusiveandanexclusive semanticsand theiruse is regulatedpragmatically (seeFarkasanddeSwart2010,Grimm2012).Whereasargumentsexistforandagainstbothpositions(seeKiparskyandTonhauser2012foranoverview),Martí(2020b)arguesthatonlyanambiguityapproach(suchas(ii))iscompatiblewithHarbour(2014).Giventhatargument,andthatthegoalofthispaperis,inpart,toextendtheempiricalcoverageofHarbour(2014),wemuststicktoanambiguityapproachhere.6 Other assumptions about the semantics or syntax of numerals might also work here. Scontras’ analysisdecomposesthenumeralbutisnottoofarremovedfromnon-decompositionalanalysesthattreatnumeralsasbeingoftype<<e,t>,<e,t>>,thatis,ofmodifiertype(see,e.g.,Baleetal.2011,IoninandMatushansky2006,2018,Link1983,amongothers).SeeMartí(2020a)andsection5.1.3belowformoreonthis.

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(13) NumberP 4

Number0 NumeralP 4

numeral Numeral’ 4

Numeral0nP CARDNumeral words are generated in the specifier position (cf. Gawron 2002, Gärtner 2004,Haegeman and Gueron 1999, Jackendoff 1977, Li 1999, Selkirk 1977, Zweig 2006, a.o.) ofNumeralP and have, uniformly, the semantics of numbers (of type <n>; cf. Rothstein 2013,2016,2017,Ouwayda2014).Forexample:(14) ⟦one⟧=1

⟦two⟧=2ThesemanticsofCARDisasfollows:(15) ⟦CARD⟧=lPlnlx.P(x)&#x=nThat is, CARD takes a property P and a numeral n and returns the set of entities that havepropertyPandnumerosityn.FortheNumeralPs ‘oneCARDnP’and ‘twoCARDnP’,wewouldobtainthefollowing:(16) ⟦oneCARDnP⟧=lx.⟦nP⟧&#x=1(17) ⟦twoCARDnP⟧=lx.⟦nP⟧&#x=2NumberP,thelocusofnumberfeatures,sitsaboveNumeralPinthissyntax.MartíproposesthatHarbour’sfeatures,suchasthosein(9)and(10),operateonmeaningssuchasthosein(16)toderivethegrammaticalnumbermarkingonthenoun,asfollows. Englishisa[±atomic]system,with[+atomic]spelledoutasnulland[−atomic]spelledoutas–s.When[±atomic]operatesonNumeralP,weobtainthefollowingresults:Feature Numeral Nounmorphology[+atomic][−atomic]

oneone

singular✕

Feature Numeral Nounmorphology[+atomic][−atomic]

two,three,four…two,three,four…

✕plural

Table2[±Atomic]withnumerals

Startingwiththetoprowofthetable,when[+atomic]operateson(16),itcreatesanewsetcontainingthosemembersof(16)whichareatoms.Allofthemembersof(16)areatoms,soallofthembecomemembersofthesetdenotedbyNumberP.[+Atomic]isspelledoutasnullinEnglish,so,forarootlikeboy,thismeansthattheformboysurfaces(oneboy).Furthermaterialuponthetreewillusethesetofatomicboysdifferently,dependingonitssemantics;e.g.,ifanexistentialquantifieroverindividualssitsinD,anelementofthissetwillbeassertedtoexist.Importantly, the derivation is not as smooth if the feature that operates on the set of boyindividualswhosenumerosityis1is[−atomic],fornoneofthemarenon-atoms.Thus,NumberP

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denotestheemptysetinthiscase,and,byassumption,thismakesthiscombinationill-formed(seeMartí2020aformoreonthisissue)—thisisthereasonwhyoneboysisungrammaticalinEnglish.Allofthemembersof(17)havenumerosityotherthanone(2fortwo,3forthreeandsoon),so[+atomic]willleadtoungrammaticality,whichisthecorrectprediction(*twoboy,*threeboy,andsoon).Ontheotherhand, [−atomic]returnsasetcontainingallof thenon-atomsofsetslikethatin(17).[−Atomic]isspelledoutas–sinEnglish.Thisiswhytwoboys,threeboys,andsoonaregrammaticalinEnglish.7 Turkish is a [±minimal] system, with [+minimal] spelled out as null and [−minimal]spelledoutas–lAr.When[±minimal]operatesonNumeralP,weobtainthefollowingresults:Feature Numeral Nounmorphology[+minimal][−minimal]

bir‘one’bir‘one’

singular✕

Feature Numeral Nounmorphology[+minimal][−minimal]

iki,üç,…‘two,three,…’iki,üç,…‘two,three,…’

singular✕

Table3[±Minimal]withnumeralsWhen [+minimal] operates on (16), it creates a new set containing thosemembers of (16)whichdonothaveproperpartsin(16).Allofthemembersof(16)lackproperpartsin(16),since theyareallofnumerosityone, soallof thembecomemembersof thesetdenotedbyNumberP.[+Minimal]isspelledoutasnullinTurkish,so,forarootlikeçocuk‘boy’,thismeansthattheformcocuksurfaces(birçocuk‘oneboy’).[−Minimal]createsanewsetcontainingthosemembersof(16)whichdohaveproperpartsin(16)—noneofthemdo,sothesetdenotedbyNumberPinthiscaseisempty,andtheungrammaticalityof*birçocuklarfollows,assumingthat–lArspellsout[−minimal]inTurkish.Noneofthemembersof(17)haveproperpartsinthatset—hence,[+minimal],whichspelledoutasnullinTurkish,willcreateanewsetcontainingallofthemembersof(17),andçocuk‘boy’willco-occurwithiki‘two’(andüç‘three’,andsoon),givingrisetoikiçocuk‘twoboys’(andüççocuk‘threeboys’,andsoon).[−Minimal]yieldstheemptysetwhencombinedwith(17),asnoneofthemembersofthatsethaveproperpartsinit,so*ikiçocuklar(and*üççocuklar,andsoon)iscorrectlypredictedtobeungrammatical.8 Aswecansee,positingthatEnglish-likelanguagesandTurkish-likelanguagesareone-featuresystems,one[±atomic],theother[±minimal],andcombiningthatwithScontras’syntaxand semantics for numerals, explains the relevant patterns in languages that distinguishsingularfromplural. The next question is what the predictions are that are made for singular-dual-plurallanguages,whichiswhatweturntointhenextsection.

7Noticethat[+atomic]doesn’tchangethesemanticsofNumeralPincasedepictedinthefirstrowofTable2:thedenotation ofNumeralP in that case, in (16), is already composed of only atoms. Likewise, [−atomic] doesn’tchangethesemanticsin(17),since(17)alreadycontainsonlynon-atoms.Itwouldbewrongtoconcludefromthis,however, that [+atomic] and [−atomic] play no role here, since [+atomic] is what blocks the ungrammatical*two/three…boy, and [−atomic] iswhat blocks *one boy.NumberP is present in thederivationof all of theseexamplesasamatterofprinciple.Asamatterofprinciple,then,[+atomic]ispresentinthederivationofoneboy,and[−atomic],inthederivationoftwo/three…boys.8Thereisindependentevidencethat[±minimal]occursintheTurkiclanguagefamily(cf.Nevskaya2005),butsearchforindependentevidenceinTurkishinparticularisstillongoing.

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3 Extendingthetheorytosingular-dual-pluralsystems(ortwo-featuresystems)Two ideas are crucial in the extension ofMartí (2020a) I propose here. First, the numberfeaturesthatareusedinHarbour(2014)toderivesingular-dual-pluralsystemsalsoplayaroleinaccountingforthesemanticsandmorphologyofthenouninthenumeral+nounconstructionin languageswith such systems. Second, andmore innovatively, the structural relationshipbetweenNumberPandNumeralPmayvaryacrosslanguages.Thissecondideaiswhatallowstheproposaltopredictpattern1,forwhichIpresentpositiveconfirmationinsection4.Thederivationsprovided inTable4andTable5belowwillbecrucial.Theassumption that thestructural relationship between NumberP and NumeralP may vary cross-linguistically willrequireustorevisittheanalysisinsection2forsingular-plurallanguages,whichIalsodohere.

Toaccount forsingular-dual-pluralsystems,Harbour(2014;seealso2011,andNoyer1992)assumesthatalanguagemaychoosemorethanonefeaturetobegeneratedinNumber0.Choosing both [±atomic] and [±minimal] allows us to generate a systemwith the requirednumberdistinctions.Thesyntaxforthesesystemsisassumedtobeasin(18):(18) NumberP1 qp Number0 NumberP2 [±minimal]qp Number0 nP [±atomic] Thisgivesrisetothefollowingpossiblefeaturecombinations:(19) a.[+minimal,+atomic]

b.[−minimal,+atomic]c.[+minimal,−atomic]d.[−minimal,−atomic]

Thefeaturecombinationin(19)agivesrisetoasingularsemantics.Toseethis,consider(20):(20) [⟦+minimal⟧[⟦+atomic⟧[⟦nP⟧]]][+Atomic]selectsalltheatomsfrom⟦nP⟧;[+minimal]thenselectsallofthemembersofthatsetwithnoproperpartsinit,whichresults,again,inthesetofatomsin⟦nP⟧.Thisisasingularsemantics.(19)bleadstoill-formedness:therearenomembersofthesetofatomsin⟦nP⟧withproper parts in ⟦nP⟧. (19)c gives rise to a dual semantics, because [+minimal] selects themembersofthesetofnon-atomsin⟦nP⟧whichdon’thaveproperpartsin⟦nP⟧—thesearethenon-atomsofnumerositytwo.(19)dgivesrisetoanexclusivepluralmeaning,with[−minimal]selectingfromthesetofnon-atomsin⟦nP⟧ those that do have proper parts in ⟦nP⟧—thesearethenon-atomsofnumerositythreeandabove.Notethatthepluralsemantics(19)dgivesrisetoisonewherepluralnounsaretakentobeaboutpluralitiesofnumerositythreeandabove.Thisseemstobecorrectforlanguagesthatdistinguishdualfromplural.9,10

9Thereareimportantargumentsforthisdecompositionaltreatmentofthedual(cf.Nevins2011),havingtodowithpatternsoflanguagechangeandwiththeacquisitionofthedual.Thesepatternsshowthatthedualisalwaysdependentontheplural,whichiscapturedinthisanalysisviatheirsharingofthefeature[−atomic].10Harbour’s(2014)argumentthatthetheoryshouldpostulateboth[±atomic]and[±minimal]isasfollows.Ifthetheoryonlyhad[±minimal],singular-dual-pluralsystemswouldhavetobegeneratedbyrepeating[±minimal](e.g., the dual would arise from the feature combination [+minimal, −minimal]) (repeating [±minimal] is a

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Predictedpattern2iswhatresultsfromthecombinationofa[±minimal,±atomic]withnumerals.ConsiderTable4:Feature Numeral Nounmorphology[+minimal,+atomic][−minimal,+atomic][+minimal,−atomic][−minimal,−atomic]

oneoneoneone

singular✕✕✕

Feature Numeral Nounmorphology[+minimal,+atomic][−minimal,+atomic][+minimal,−atomic][−minimal,−atomic]

twotwotwotwo

✕✕dual✕

Feature Numeral Nounmorphology[+minimal,+atomic][−minimal,+atomic][+minimal,−atomic][−minimal,−atomic]

three,…three,…three,…three,…

✕✕dual✕

Table4[±Minimal,±atomic]withnumerals(NumberP≫NumeralP)ThedenotationofNumeralPinthecaseofthenumeraloneisthesetofelementsof⟦nP⟧ofnumerosityone,thatis,thesetofatomsin⟦nP⟧.Theapplicationoffirst[+atomic]andthen[+minimal]tothatsetstillyieldsasetofatoms.Ifweassumethatinalanguagethatinstantiatesthis setting, the feature combination [+minimal, +atomic] is realized as singular morpho-phonologically,wewillhavesingularnumbermarkingonnounswhentheycombinewiththenumeralone.Anyotherfeaturecombinationyieldsanill-formedresultwiththenumeralone:[−minimal,+atomic]becausetherearenoelementsinasetofatomswithproperpartsintheset,and[+minimal,−atomic]and[−minimal,−atomic]becausetherearenonon-atomsinasetofatoms.

ThedenotationNumeralPinthecaseofthenumeraltwoisthesetofelementsof⟦nP⟧ofnumerositytwo,thatis,thesetofdyadsin⟦nP⟧.Neitherthefeaturecombination[+minimal,+atomic]nor the feature combination [−minimal,+atomic] canyieldwell-formednesswhencombinedwithsuchaNumeralP,sincetherearenoatomsinitsdenotation(thelatter,asweknow,nevergivesrisetowell-formedness).Thefeaturecombination[+minimal,−atomic]does,however,becauseitispossibletochoosethemembersofasetofnon-atomicdyads(dyadsarealwaysnon-atomic)whichhavenoproperpartsinthatset—that’sallofitsmembers.Assumingthatthisfeaturecombinationisspelledoutasdualmorpho-phonologically,thisgivesrisetoanounwithdualnumbermarkingthatcombineswiththenumeraltwo.Thefeaturecombination[−minimal,−atomic]givesrisetoill-formednessagain,sinceitisnotpossibletochoosefromasetofdyadselementswithproperpartsinit.

The reasoning we just went through for the numeral two generalizes, in fact, to allnumeralsgreaterthanone.Takethecaseofthenumeral3.Neitherthefeaturecombination

possibilitythathistheoryallows,inordertoaccountforlanguagesthatdistinguishminimal,unitaugmentedandaugmented pronouns, for example). For languageswith trials, though,we need a kind of repetitionwhich, ifallowed,over-generatesnumbersystems.Trialwouldarisefromthefeaturecombination[+minimal,−minimal,−minimal]—butifafeaturewiththesamevaluecanrepeat,youcangeneratenon-attestednumbervaluessuchasquadral ([+minimal, −minimal, −minimal, −minimal]), pental ([+minimal, −minimal, −minimal, −minimal,−minimal]),etc.Wecangeneratetrials(andduals)butnoquadrals,pentals,etc.ifthefeaturecombinationfortrialis[+minimal,−minimal,−atomic]instead.

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[+minimal, +atomic] nor the feature combination [−minimal, +atomic] can yield well-formednesswhencombinedwithaNumeralPthatdenotesasetofthreesomes,sincethereareno atoms in its denotation. The feature combination [+minimal, −atomic] does, as before,becauseitispossibletochoosethemembersofasetofnon-atomicthreesomes(threesomesarealwaysnon-atomic)whichhavenoproperpartsinthatset—that’sallofitsmembers.Thefeaturecombination[−minimal,−atomic]givesrisetoill-formedness,sinceitisnotpossibletochoosefromasetofthreesomeselementswithproperpartsinit.Thus,allnumeralsgreaterthanonearepredictedtocombinewithdualnumbermarkingonthenoun.

IdonotknowwhetherPredictedpattern2isattestedbut,withoutanyfurtherchanges,thisisallthatourtheorycurrentlypredictsforsingular-dual-plurallanguages.However,asIwillargueinsections4and5,pattern1isindeedattested.Itisinterestingtonotethatjustsucha pattern is predicted if the hierarchical relationship between NumberP and NumeralP isallowedtochange:thatis,ifNumeralPdominatesNumberP,asin(21):(21) NumeralP

4 numeral Numeral’

4 CARD NumberP

4 Number0nP

Theresultingnumeral+nounpatternsareinTable5:Numeral Feature Nounmorphologyoneoneoneone

[+minimal,+atomic][−minimal,+atomic][+minimal,−atomic][−minimal,−atomic]

singular✕✕✕

Numeral Feature Nounmorphologytwotwotwotwo

[+minimal,+atomic][−minimal,+atomic][+minimal,−atomic][−minimal,−atomic]

✕✕dual✕

Numeral Feature Nounmorphologythree,…three,…three,…three,…

[+minimal,+atomic][−minimal,+atomic][+minimal,−atomic][−minimal,−atomic]

✕✕✕plural

Table5Numeralswith[±minimal,±atomic](NumeralP≫NumberP)The feature combination [+minimal, +atomic] gives us a denotation for the now-lowerNumberPthatisasetofatoms.NumeralPwiththenumeraloneinitsspecifierwillresultinawell-formedsetofatoms,sincetheyareallofnumerosityone.If[+minimal,+atomic]spellsoutwithsingularmorphology,wethenobtainasingularnumbermarkednounincombinationwiththenumeralone.Noothernumeralwillworkhere:membersofasetofatomshavenoothernumerosity besides one, so this feature combination will yield an ill-formed result whencombinedwithanynumeralotherthanone.Thefeaturecombination[−minimal,+atomic]isill-formedonitsown,asbefore.Thefeaturecombination[+minimal,−atomic]yieldsasetofdyads.Sincetheseareelementsofnumerositytwo,thenumeraltwowillbeabletocombine

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with it. No other numeral will be able to do so, since dyads have no other numerosity. If[+minimal,−atomic]spellsoutwithdualmorphology,wewillobtainadualmarkednounincombinationwiththenumeraltwo.Finally,thefeaturecombination[−minimal,−atomic]willyieldasetofnon-atomsofnumerositygreaterthantwo.Thissetcancombinewithanynumeralgreaterthantwo,butnotwithtwoorone.Ifthisfeaturecombinationspellsoutasplural,wewillobtainapluralmarkednounincombinationwithallnumeralsgreaterthantwo. DepartingfromMartí(2020a,underreview)andfromScontras,wethusneedtoconsiderthepossibilitythatthesyntacticrelationshipbetweenNumberPandNumeralPmayvarycross-linguistically,thatis,thatthederivationsinbothTable4andTable5areallowed.Ifwedoso,pattern1isapredictedpatternforsingular-dual-plurallanguageswhereNumeralPdominatesNumberP, and Pattern 2 is a predicted pattern for singular-dual-plural languages whereNumberPdominatesNumeralP.This,Icontend,istheonlyinnovationthatisneededinordertoextendMartí’stheoryofthenumeral+nounconstructiontosingular-dual-pluralsystems. Indevelopingthishypothesisfurther,weshouldlookforindependentevidencefortherelationshipbetweenNumberPandNumeralPinparticularlanguages.Thisevidencemaytakemanyformsandcomefromavarietyofphenomena,andisacrucialpartoftheaccountthatIamproposinghere.Mygoalhere,however,is,morehumbly,tounderstandthepossibilitiesandthelimitsthatthetheoryofthenumeral+nounconstructionunderconsiderationaffordsus.Iwill, nevertheless, point at the numeral+noun construction with complex numerals as apossiblesourceofindependentevidenceattheendofsection5.1.3. Animportantquestionmustbeansweredbeforeweproceedwiththemoreempiricalpartofthepaper.IfthehierarchicalrelationshipbetweenNumberPandNumeralPcanvarycross-linguistically, are there new predicted patterns for the numeral+noun construction inlanguagesthatdistinguishonlysingularfromplural?Recallfromsection2that,inderivingtheEnglish-type and the Turkish-type patterns, we only considered one possible relationshipbetween these two phrases, namely, the one where NumberP dominates NumeralP. Whathappensinsingular-plurallanguageswhentheirrelationshipisreversed?Theanswer,inshort,isthatnonewpredictionsaremade,butthatthereisnowspaceforconsideringthatEnglishmaybea[±minimal]languageafterall. Considerfirstthepossibilityof[±atomic]inaNumberPthatisdominatedbyNumeralP:Numeral Feature Nounmorphologyoneone

[+atomic][−atomic]

singular✕

Numeral Feature Nounmorphologytwo,…two,…

[+atomic][−atomic]

✕plural

Table6Numeralswith[±atomic](NumeralP≫NumberP)Thesubsetofelementsfrom⟦nP⟧whichareatomsisasetofelementsofnumerosityone,socombinationwiththenumeraloneiswell-formedandyieldsasetofatoms,thatis,asingularsemantics.Suchasetofatomscannotcombinewithanyothernumeral,sinceitsmembersonlyhave numerosity one. The subset of elements from ⟦nP⟧ which are non-atoms is a set ofelementsofnumerositygreaterthanone,socombinationwiththenumeraloneisill-formed,andcombinationwithothernumeralsiswell-formed.Thesepredictionsareasinsection1,sowe can conclude that, for languages that are [±atomic], different assumptions about thehierarchicalrelationshipbetweenNumberPandNumeralPdonotyielddifferentpredictionsforthemorphologicalrealizationofnumberonthenouninthenumeral+nounconstruction.Thingsaredifferentfor[±minimal]languages.ConsiderTable7:

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Numeral Feature Nounmorphologyoneone

[+minimal][−minimal]

singular✕

Numeral Feature Nounmorphologytwo,…two,…

[+minimal][−minimal]

✕plural

Table7Numeralswith[±minimal](NumeralP≫NumberP)Interestingly,thepredictionsdonotvaryfromTable6.Ifthefeature[+minimal]appliesdirectlytonP,itwillineffectselectalltheatomsin⟦nP⟧.Thiscancombinewellwiththenumeralone,butnotwithanyothernumeral, sinceatomshavenumerosityone.Thus,nounsmarked forsingularmorphologicallycombinewithone.Asforothernumerals,theywillonlyyieldawell-formedresultfor[−minimal],sinceonly[−minimal],whenapplieddirectlytonP,willselectallandonlythenon-atomsin⟦nP⟧.Nounsmorphologicallymarkedforpluralwillcombinewithnumeralsotherthanone.Again,thisistheEnglish-typepattern. Tosumup,allowingforvariationinthehierarchicalrelationshipbetweenNumberPandNumeralP still predicts the English-type and the Turkish-type patterns for singular-plurallanguages—itnowbecomesaquestionoflanguage-internalevidence(regardingthesyntaxofNumberP and NumeralP), and/or other considerations, whether we take English to be a[±atomic] or a [±minimal] language. The Turkish-style pattern, however, necessitates[±minimal] in NumberP and for NumberP to dominateNumeralP. This entails that a givensingular-pluralsystemhasinprinciplethepossibilityofchoosingthederivationsinTable2,Table3,Table6orTable7forthenumeral+nounconstruction.11Asforsingular-dual-plurallanguages,thisvariationplaysacrucialroleinpredictingpattern1(seederivationinTable5).Pattern2alreadyfollowsfromthesyntacticassumptionsmadeinMartí’sandScontras’work(seederivationinTable4). HavingreviewedinthissectionthebasicpredictionsofourextensionofMartí’stheory,wenowturntothefirststepsintheinvestigationofwhetherthetheory’spredictionsaremetempirically.4 YimasandHopiinstantiatepattern1Thefirststepinthatinvestigationistheconfirmationofpredictedpattern1.IshowherethatYimasandHopi,languageswithasingular-dual-pluralsystemonnouns,exemplifypredictedpattern1straightforwardly.

Consider first Yimas,12 whose nouns are organized into noun classes and distinguishsingular,dualandpluralviasuffixation(orlackthereof,inthesingularofsomeclasses),withnumberandclasssuffixesspecifictoeachclass.AfewexamplesofnounsinthislanguageareprovidedinTable8(Foley1991:91):13

11Arevieweraskswhetherthefactthat,inthistheory,theTurkish-stylepatternhasoneanalyticalsource(seeTable3),whereastheEnglish-stylepatternhasthree(seeTable2,Table6andTable7),suggeststhattheEnglish-style pattern should bemore common cross-linguistically. Thismight indeed be taken as a prediction of theproposedtheory,thoughonemustalsoconsidertheconsequencesthatmightfollowfromalanguagechoosingNumberP≫NumeralPvs.NumeralP≫NumberP.Dependingonwhatevidenceitispossibletofindforthischoice(seeendofsection5.1.3foranexample),settlingtheissueofthecommonalityofonepatternoveranothermightrequiremorenuance.12YimasisPapuanlanguagespokeninPapuaNewGuinea.AllYimasdatapresentedhereisfromFoley(1991)orfromBillFoley,p.c.13Manycommonnounsaresuppletiveinthatsingularandpluralformshavedifferentstems(Foley1991:91).NounsinYimasalsomarkobliqueCase,anissueignoredbelow.

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singular dual plural translationwakn wakn-trm wakn-tt ‘snake’(classV)trŋ trŋ-kl trŋ-k ‘tooth’(classVI)tan-m tan-pl tan-pat ‘bone’(classVII)Table8SomeYimasnounsandtheirnumberNounsagreewithverbsfornumber(viasingular,dualorpluralprefixesontheverb).Thus,Yimasmarksgrammaticalnumberofnounsproductivelyandisa[±minimal,±atomic]systeminHarbour’stypology.

Yimasisanexampleofalanguagewithpredictedpattern1.Thenumeralonecombineswitha(preceding)nounthatismarkedforsingular((22)),thenumeraltwocombineswithanounmarkedfordual((23)),andallothernumeralscombinewithnounsmarkedforplural((24)-(26));noothercombinationsofnumeralandnumbermarkingonthenounareallowed(Foley1991:101-2andBillFoley,p.c.):14(22) Tan-m mpa-m

Bone-VII.SG one-ADJ‘Onebone’

(23) Tan-pl p-rpal

Bone-VII.DU VB-two‘Twobones’

(24) Tan-pat p-ramnawt

Bone-VII.PL VB-three‘Threebones’

(25) Tan-pat tam mawŋkwat p-rpal

Bone-VII.PL five other.side VB-two‘Sevenbones’

(26) Tan-pat namarawt munta-k-n p-rpal

Bone-VII.PL person whole-IRR-I.SG VB-two‘Twenty-twobones’

NoticethatnumeralsinYimasmaydisplayverbaloradjectivalagreementmarkers(suchasthenumeralsmpam‘one’,prpal‘two’andpramnawt‘three’),maybequitecomplexinternally(likethosein(25)and(26)),andmaythemselvesinflectfornounclassandnumber((26)).15Noticealso,importantly,thatdespitethepresenceofthenumeralprpal‘two’intheformationofthenumeral tammawŋkwatprpal ‘seven’ (lit. fiveother side two)ornamarawtmuntaknprpal‘twenty-two’(lit.wholepersontwo),thesenumeralscombinewithnounsintheplural,notinthedual—thisissuewillbediscussedagaininthecontextofSlovenianinsection4. Hopi16isanotherexampleofalanguagethatdisplayspattern1.Hopihasasingular-dual-pluralnumbersystemonanimatenounsandasmallsetofinanimatenouns(Hilletal.1998:

14Keytoglosses:ACC=accusativecase;ADJ=adjectiveagreementmarker;DEM=demonstrative;DU=dualnumber;FEM=femininegender;GEN=genitivecase;INSTR=instrumentalcase;IRR=irrealis;MASC=masculinegender;NOM=nominativecase;NFUT=non-future;PL=pluralnumber;SG=singularnumber,VB=verbalagreementmarker.Romannumeralsindicatenounclass.15Numeralnumberinflectionmaybeagenuinecaseofagreement,ormayconstituteadifferentphenomenon,anissueIwillnotbeabletosettlehere.16HopiisanUto-AztecanlanguagespokeninnortheasternArizona.AllHopidatapresentedhereisfromHilletal.(1998)andhasbeencorroboratedbyKenHill.

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870); most inanimate nouns do not have dual or plural forms and thus do not vary forgrammaticalnumber.Nounsvaryalsobycase,distinguishingNominativefromAccusativecase.Table9showssomeof itsnouns,which, likeYimas,usesuffixation (or lack thereof, for thesingular)todistinguishsingular,dualandplural:singular dual plural translationkawayo kawayo-t kawayo-m ‘horse’sino sino-t sino-m ‘person’pahaana pahaana-t ahaana-m ‘Anglo’Table9SomeHopinounsandtheirnumber(nominativecaseforms)Itisnotuncommonforlanguagestotreatsubsetsofnounsdifferentlyregardinggrammaticalnumber,especiallyalongtheanimate/inanimatedivideweseeinHopi(seeCorbett2000:ch.3fordiscussionandexamples).Thus,wecansaythatHopiisasingular-

Hopi nouns in the numeral+noun construction appear in their singular formwith thenumeralone,asshownin(27),intheirdualformwiththenumeraltwo,asin(28),andintheirpluralformwithanyothernumeral,asshownin(29)and(30)forthenumeralselevenandtwelve,respectively;noothercombinationsareallowed:(27) Suukya kawayo pinto (Hilletal.1998:552)

One.NOM horse.NOM.SG spotted.NOM.SG‘Onespottedhorse’

(28) Lööyöm kawayo-t (Hilletal.1998:215)

Two.NOM horse-NOM.DU‘Twohorses’

(29) Pakwtsuukw sìikya‘ytaqam kawayo-m17 (Hilletal.1998:382)

Ten one.ACC plus horse-NOM.PL ‘Elevenhorses’

(30) Pakwtlööq sìikya‘ytaqam pahaana-m (Hilletal.1998:382)

Ten two.ACC plus Anglo-NOM.PL‘TwelveAnglos’

Notethatnumeralsmaythemselvesinflectforcaseorevennumber,andthat,asbefore,theycanbeinternallycomplex,asin(29)or(30).Eventhen,however,theshapeofthenounisnotdictatedbywhatthecomponentpartswouldcombinewithontheirown(e.g.,singularforone,ordualfortwo,asin(27)and(28)),butbywhetherthenumeralisgreaterthantwo—ifitis,thenthenounappearsinitspluralform.Thisis,inotherwords,anexampleofpredictedpattern1. The analysis for both Yimas and Hopi is then as explained in Table 5, withNumeralP≫NumberP((21)). Thus,predictedpattern1isattested.NextIdiscusstwocaseswhereneitherpredictedpattern1norpredictedpattern2seemstoobtain, though Iargue thatcomplications in thegrammarofcomplexnumeralsanddeterminersinthelanguagesinquestionmasktwofurtherinstancesofpredictedpattern1.

17Theaccusativeformofthenumeralmaybeusedinnominativepositionwhensìikya‘ytaqamisused(Hilletal.1998:895).Ihavenotbeenabletofindasatisfactoryexplanationofwhatsìikya‘ytaqamis,oragloss/translationforit. Itentativelyglossitas ‘plus’here.Hilletal.call itamodifierandsayit isoptional inexampleswiththenumeralspakwt‘ten’andsunat‘twenty’.

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5 ImereandLjubljanaSloveniandoconformtothepredictionsofthetheoryInthissectionIdiscusstwoadditionalsingular-dual-plurallanguages,LjubljanaSlovenianandImere.Thenumbermarkingonthenouninthenumeral+nounconstructionintheselanguagesseems problematic from the perspective of the theory introduced in section 3. LjubljanaSlovenianconformstopattern1foritslowernumerals,buttheempiricalpicturefornumeralsgreaterthanoneismorecomplex.InImere,dualmarkingonthenounisneverusedwiththenumeraltwoandthuscannotbeconsideredaninstanceofeitherpattern1orpattern2.Iargueinthissectionthatneitherlanguageisacounterexampletothepredictionsofthetheoryonceadditionalcomplicationsintheirgrammarsaretakenintoaccount.5.1 LjubljanaSlovenian18The numeral+noun construction for lower numerals in Ljubljana Slovenian looks like astraightforwardinstantiationofpattern1,butcomplexnumeralspresentamorecomplicatedpicture. I argue below there are good reasons to think that Ljubljana Slovenian is still aninstantiationofpattern1.BelowIreviewtheSloveniandataandmakeaproposalabout itsanalysis that incorporates important insights from Ionin and Matushansky’s (2006, 2018)proposalaboutcomplexnumerals.5.1.1 ThedataLjubljanaSloveniandistinguishessingular,dualandpluralonnouns(andonothercategories).Table 10 shows a (partial) nominal declension paradigm for two nouns in this language(LjubljanaSlovenianhasanadditionalgenderandmakesmorecasedistinctionsthanshownhere)(RokŽaucer,p.c.): singular dual plural translationNOM stol stola stoli chair(masc.)ACC stol stola stoleGEN stola stolov stolovINSTR stolom stoloma/stoli stoliNOM banana banani banane banana(fem.)ACC banano banani bananeGEN banane banan bananINSTR banano bananama bananami

Table10SomeLjubljanaSloveniannounsFor numerals less than one, Ljubljana Slovenian follows pattern 1, as illustrated in (31)-(35)(LjubljanaSlovenianalsomarkscaseonitsnumerals)(RokŽaucer,p.c.):(31) En stol

one.NOM/ACC chair.MASC.NOM/ACC.SG‘Onechair’

18LjubljanaSlovenianisadialectofSlovenianspokeninandaroundthecapitalcityofLjubljana.Foralanguagetocountasa[±minimal,±atomic]system,itmustdistinguishsingular,dualandpluralproductively.ThedualisbeinglostincertaindialectsofSlovenian,butnotinLjubljanaSlovenian,soitisthisdialectthatisdiscussedhere.AlldatafromLjubljanaSlovenianwasprovidedbyRokŽaucer,p.c.FormoreonSlovenianmoregenerally,seeDerganc(2003),Herrity(2016),MarušičandŽaucer(toappear)andToporišič(2000).

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(32) Dva stolatwo.NOM/ACC chair.MASC.NOM/ACC.DU‘Twochairs’

(33) Trije stoli, tri stole

Three.NOM chair.MASC.NOM.PL three.ACC chair.MASC.ACC.PL‘Threechairs’

(34) Pet stolov

Five.GEN chair.MASC.GEN.PL ‘Fivechairs’

(35) Dva-in-dvajsetimi bananami

Two-and-two.ten.INSTR banana.FEM.INSTR.PL‘Twenty-twobananas’

Thenounappearsinsingularwiththenumeralone,indualwiththenumeraltwo,andinpluralwithnumeralsthree,fiveandtwenty-two.19 If indeed Ljubljana Slovenian follows pattern 1, the noun should be morphologicallymarkedforpluralwithanynumeralgreaterthantwo.However,notallsuchnumeralscombinewith a plural noun: for numerals greater than one, the noun is marked for singular if thenumeralendsinone(101,201,301,…1001andsoon),anditismarkedfordualifthenumeralendsintwo(102,202,301,…1002andsoon),asillustratedin(36)(RokŽaucer,p.c.):20(36) a.Sto-dve banani

hundred-two.ACC banana.FEM.ACC.DUb.Sto-dvema bananamahundred-two.INSTR banana.FEM.INSTR.DU‘Onehundredandtwobananas’

In (36), thenounbananaappears in thedual formsbanani (Accusative case) orbananama(Instrumentalcase) following thenumeralstodve/dvema ‘onehundredand two’,not in thecorrespondingpluralforms.

Thus,thequestionweneedtoansweriswhynumeralsgreaterthanonebehaveinthisway—apart from these numerals, the rest of the Ljubljana Slovenian pattern conforms topredictions.TheinsightthatwilldrivetheanswerIproposebelowisthatinLjubjlanaSloveniancomplexnumeralssmallerthanone,asmallnumeralthatisaddedtoanothercomesfirstinthewordorder(en-ajst‘eleven,lit.one-on.ten’,dva-najst‘twelve,lit.two-on.ten’,tri-najst‘thirteen,lit.three-on.ten’,ena-in-dvajset ‘twenty-one,lit.one-and-two.ten’,etc.).Ontheotherhand,incomplexnumeralsgreaterthanone,thenumeralthatisaddedcomeslastinthewordorder(sto-en ‘a hundred and one, lit. hundred-one’, dva-sto-en ‘two hundred and one, lit. two-hundred-one’,dva-sto-dva‘twohundredandtwo,lit,two-hundred-two’,etc.).If,inbothcases,itisthelastnumeralinthewordorderthatdeterminesthenumbermarkingonthenounthat

19InwhatisnotanunusualpatterninSlaviclanguages(seeIoninandMatushanksy’s2018:ch.6),nounsinthenumeral+nounconstructionvarytheircasedependingonthenumeral.Forexample,whereasthenumeralsone,twoandthreecombinewithnounsinAccusativecasewhenthenounphraseappearsinsyntacticcontextsthatusuallycallforAccusativecase(e.g.,thedirectobjectpositionofmanytransitiveverbs),andinNominativecasewhenthenounphraseappearsinsyntacticcontextswhereusuallythatcaseiscalledfor(e.g.,thestandardsubjectposition),fivecombineswithnounsinGenitivecaseevenincanonicaldirectobjectandsubjectpositions.Moreonthisissueinsection4.1.3below.20ThisisagainacommonpatterninSlavic(seeIoninandMatushansky2018:ch.6andreferencescitedthere).

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accompaniesthenumeral,thepatternwehaveobservedabovefollowsinfull,whileallowingustomaintainthehypothesisthatLjubljanaSlovenianisalanguagethatexemplifiespattern1.

Intheremainderofthissection,IspelloutthedetailsofthesyntacticandsemanticaspectsofthisanalysisandcompareitwiththatinIoninandMatushansky(2006,2018).5.1.2 IoninandMatushansky(2006,2018)InIoninandMatushansky’sapproach,simplenumerals(liketwoorhundred)aresemanticallyoftype<et,et>,thatis,theyhavethesemanticsofmodifiers,andthenounstheycombinewithdenotesetsofatomicindividuals.Considerthedenotationsin(37),withauxiliarydefinitionsin(38)(forpartition)and(39)(forcover)(seeIoninandMatushanksy2018:13andreferencescitedthere):(37) ⟦two⟧=lP∈D<e,t>.lx∈De.∃S∈D<e,t>[P(S)(x)&|S|=2∧∀s∈SP(s)]

⟦hundred⟧=lP∈D<e,t>.lx∈De.∃S∈D<e,t>[P(S)(x)&|S|=100∧∀s∈SP(s)](38) P(S)(x)=1iffSisacoverofxand∀z,y∈S[z=y∨¬∃aa≤z∧a≤y](39) AsetofindividualsCisacoverofapluralindividualxiffxisthesumofallmembersof

CThenotionofpartitionin(38)ensuresthatthereisnooverlapofthecellsinthepartition,sothatindividualsarenotcountedtwice.Whenanumerallikehundredin(37)combineswithanounN,asetofatomicindividualsandthusoftype<e,t>,weobtainasetofpluralornon-atomicindividualsasin(40):(40) ⟦hundredN⟧=lx∈De.∃S∈D<e,t>[P(S)(x)&|S|=100∧∀s∈S⟦N⟧(s)]

=lx∈De.xisapluralindividualdivisibleinto100non-overlappingindividualsysuchthattheirsumisxandeachy∈⟦N⟧

Sincesimplenumeralshavethesemanticsofmodifiers,theyare,inprinciple,stackable.Thus,thesyntaxofanounphraseliketwohundredN,withthemultiplicativenumeraltwohundred,isasfollows:(41) 3

two3 hundred NWethenobtainthesemanticsin(42):(42) ⟦twohundredN⟧=lx∈De.∃S∈D<e,t>[P(S)(x)&|S|=2∧∀s∈S∃S’∈D<e,t>[P(S’)(s)&

|S’|=100∧∀s’∈S’⟦N⟧(s’)]]]=lx∈De.xisapluralindividualdivisibleinto2non-overlappingindividualsysuchthattheirsumisxandeachyisdivisibleinto100non-overlappingindividualszsuchthattheirsumisyandz∈⟦N⟧

That is,becauseof thesemanticsassumedforsimplexnumerals, thesemanticsofnumeralssuchastwohundredarisesstraightforwardlyfromthecompositionalprocess.

For additive numerals, such as twenty-two, Ionin and Matushansky assume thecoordination structure and analysis in (43) (inspired by Zweig 2006,who builds onKayne2003,2007):

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(43) wo 2ei

twentyNand2 twoNIoninandMatushanskyassumeastructurewithtwoNs,oneofwhichundergoesNPdeletion;thatis,thesyntaxandsemanticsoftwenty-twoNisjustlikethesyntaxandsemanticsoftwentyNandtwoN.Whetheraconjunctionlikeandispronouncedornotinagivenlanguage,itisthereforsyntacticandsemanticpurposes.Withtheset-productdenotationforand(asopposedtoanintersectiveone)in(44)(fromHeycockandZamparelli2005;seeIoninandMatushansky2018:149),thecorrectsemanticsispredictedfor(43)(for‘⨁’thesumoperator):(44) ⟦and⟧=lP<et>.lQ<et>.{x:x=y⨁z,fory∈Pandz∈Q}(44)takestwosetsPandQandcombinestheirmembersinsuchawaythatanewsetofpluralindividuals,allofthosethatareinParecombinedwithallofthosethatareinQ,iscreated.(43)thusdenotesasetofpluralindividualseachcombiningtwo-Npluralindividualwithatwenty-Nplural individual,which isasetofplural individualseachofwhichhasnumerosity22,asdesired21.Much empirical evidence, on thebasis of case, agreement andotherphenomena,across languages, is provided in Ionin and Matushansky in defense of this syntactic andsemantictreatmentofnumerals.5.1.3 MyproposalThesemanticsfornumeralsfromsections2and3isdifferentfromIoninandMatushansky’s;inparticular,we’vetakennumeralstodenotenumbersandtoappearinthespecifierpositionof a NumeralP. Whereas numeral stacking is possible in my approach, since CARD takesargumentsoftype<e,t>andthetypeofNumeralPisalso<e,t>,structuressuchas(45)(similarto (41), butwith oneNumeralP per numeral) yield thewrong semantics formultiplicativenumerals.ThecontributionofCARDisrepeatedas(46)foreaseofreference:(45) NumeralP1

eitwoei

CARD NumeralP2ei

hundredei CARD N(46) ⟦CARD⟧=lPlnlx.P(x)&#x=nThisisbecausethedenotationthat(45)isassignedisasfollows:(47) ⟦NumeralP1⟧=lx.⟦NumeralP2⟧(x)&#x=2

=lx.⟦N⟧(x)&#x=100&#x=2Thenumerosityofanindividualcannotbeboth100and2atthesametime.

21AsIoninandMatushansky(2018:151)note,setproductallowsforthepossibilityofoverlap,whichincorrectlyallows us to count the same individual twice, and thus include plural individuals of numerosity 101 in thedenotationof(43).IoninandMatushanskyproposethatthelackofoverlapispragmatic,motivatedbythefactthat“thewholepurposeofmeasuringandcounting is to achieve themaximalprecisiongiven the context and thespeaker’sknowledge.Treatingoverlapasapossibilityisexpresslycontrarytothispurpose”(p.151).

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Itis,however,possibletocombineadecompositionalapproachtocomplexnumeralswiththeapproachtonumeralsassumedinsections2and3.Startingwithmultiplicativenumerals,themostimportantassumptionisthemultiplicativeoperator∙in(48),oftype<n,<n,n>>(cf.Rothstein2013:184, Scha1981,Ouwayda2014,Zabbal2005),whichoperatesonnumeralwordsthemselves,i.e.,theonesthatappearinthespecifierpositionofNumeralP: (48) ⟦∙⟧=ln.lm.n∙m

(49) a.⟦two⟧=2

b.⟦hundred⟧=100Ifmorethanonenumeralwordcanappearinthatposition(cf.Giusti1991,1997,Ritter1991,Zamparelli1995,2002),wewouldhavethefollowingstructurefordva-stoN:(50) NumeralP qpNumeralei2CARD NumberP1dva2 qp ∙stoNumber0 NumberP2 [−minimal]qp Number0 nP [−atomic]The∙operatormultiplies100by2,resultingin(51):(51) ⟦dva∙sto⟧=200 Therestofthecomputationnowproceedsasnormal,producinganumeral+nouncombinationwherethenounismarkedforplural,correctly(recallTable5).Thus,wecanmaintainthatthemeaningoftwo isuniqueandconstantacrosstheboard(that is,as in(49)a),as longasthespecifierpositionofNumeralPcanbemorecomplex thanweassumedpreviously.Doingsoallows us tomaintain the attractive hypothesis, togetherwith Ionin andMatushansky, thatcomplexcardinalsarederivedfromsimpleones.22 I address a number of issues that arisewith this proposal formultiplicative complexnumeralsbeforemovingontomyproposalforadditiveones.First,anargumentagainstthemultiplicative operator in (48), based on Ionin and Matushansky’s (2018: 29) criticism ofRothstein(2013,2016,2017),wouldbethatpositingsuchanoperatorentailsthemasteringofthe arithmetic operation ofmultiplication—this could be a problematic assumption if, e.g.,childrencanusemultiplicativenumeralsbeforetheymastertheoperationofmultiplication.This argument, however, does not stand closer scrutiny: there’s plenty of operations andconceptsusedaspartof thedenotationof linguistic items(manyset theoryoperationsandconcepts,existentialanduniversalquantification,thenotionoffunction,etc.)whichpossiblynochildandonlyasubsetofadultshaveamasteryof.Thereisnoreasonwhythemultiplicativeoperatorin(48)shouldbeanydifferent. Second,whiletheproposalabovecomesclosetowhatIoninandMatushansky(2018:57)callthe“single-specifierstructure”(their(21)b),whichisnotinterpretableintheirsemantics,

22MuchlikeinIoninandMatushansky,thisproposalneedstoinvokeadditionalconstraints,e.g.,nothinginwhatIhavesaidherepreventsanumerallike,say,six-five,meaning‘thirty-five’,frombeinggenerated.Myhypothesisiscompatiblewiththekindsofadditional,possiblyextra-linguistic,constraintsthatIoninandMatushansky(2018:15-16)envisage.

20

interpretabilityisnotanissuehere,asstructuressuchas(50)areinterpretableaslongasthemultiplicativeoperatorin(48)isavailable. Third, and given much cross-linguistic evidence (see, e.g., Hurford 1975, Ionin andMatushansky2018:62-71andreferencescitedthere),itisdesirabletoallowthecategoryofnumeralwordstobeadjectival,nominalorverbal,asIoninandMatushanskydo.However,aScontras-compatibleviewofnumeralsneednotconsiderthemtobeaspecialcategoryNumeral(recall(13)andotherexamplesabove),oranycategoryinparticular,forthatmatter.Thatis,itis possible to think that the category of the items in the specifier position of NumeralP isnominal,adjectivalorverbal,asin,forexample,(52):(52) NumberP

4 Number0 NumeralP

4 N/NPNumeral’

4 Numeral0nP

CARDThefourthandfinalissueismoreproblematic.IoninandMatushansky(2018:3.1.1)alsoargueagainsttheideathatseveralnumeralwordscanformasyntacticunittotheexclusionofthenoun/restof theNP—suchconstituency isa fundamentalaspectofmyproposal (see (50)).They take case assignment to be a diagnostic for complementation and show that caseassignment can happen both within complex numerals in some languages (i.e., from onenumeraltoanother)andfromacomplexnumeraltoanouninothers.ThesepatternscanbeseeninRussian(wesawsomeevidenceforthisLjubljanaSlovenianabove,butIuseRussianhereasthatiswhatIononandMatushansky’sargumentisbasedon;seepp.51-52).InRussian,thenumeralstwo,threeandfourassignwhatIoninandMatushanskycall‘paucalcase’tothenoun/NP;numeralshigherthanfourassigngenitivecaseinstead:(53) Četyre šagá

four step.PAUCAL ‘Foursteps’

(54) Šest’ šagov

six step.GEN.PL ‘Sixsteps’

Withcomplexnumeralslikefourthousandorfivethousand,thousandappearsinthepaucalcaseintheformer,butinthegenitivecaseinthelatter:(55) Četyre tysjači šagov

four thousand.PAUCAL step.GEN.PL ‘Fourthousandsteps’(56) Pjat’ tysjač šagov

five thousand.GEN.PL step.GEN.PL ‘Fivethousandsteps’If heads,notphrases, are responsible for caseassignment, as is typically assumed, thebeststructureformultiplicativecomplexnumeralsis,theyargue,asin(57)(cf.(41)):

21

(57) NP 3

NNP četyre3

N NP tysjači @ šagovTheproposalthatnumeralwordsformaconstituentincomplexmultiplicativenumerals,asin(50),isproblematicinlightofthisdatainthatitwouldhavetobethewholecomplexnumeral(e.g.,četyretysjači)thatassignscasetotheaccompanyingnoun(phrase).That’sbecausetherewouldbenodirectrelationshipbetweentysjačiandšagov.Noticethatcaseassignmentwithinthecomplexnumeral(e.g.,fromčetyretotysjači)orcaseassignmentbyasimplexnumeral(asin(53)or(54))arenotnecessarilyproblematicinmyproposal,ascaseinthesecircumstancescanstillbeassignedbyahead.Butnotifexpressionssuchasčetyretysjačiareconstituents—inthatinstance,caseassignmentwouldhavetobecarriedoutbyaphrase. However, itmayactuallybenecessary toallowphrases toassigncase.That’sbecausethereissuggestiveevidencefortheconstituencyofnumeralslikečetyretysjači.Russianiswell-knownforthephenomenonofapproximativeinversion(seeIoninandMatushansky2018:118-9andreferencescitedthere),23illustratedin(58)and(59)(cf.(55)):24,25(58) Tysjači četyre šagov

thousand.PAUCAL four step.GEN.PL ‘Somefourthousandsteps’(59) Šagov četyre tysjači

step.GEN.PL four thousand.PAUCAL ‘Somefourthousandsteps’The linearorderofčetyre and tysjači canbe reversed,and thenouncanprecede thewholenumeral. Inbothcases,anapproximativemeaningarises. Inadditionto inversion,however,Russian also allows the insertion of an approximative word, such as primerno ‘about’,illustratedin(60):(60) Primerno četyretysjači šagov

About four thousand.PAUCAL step.GEN.PL ‘Aboutfourthousandsteps’Interestingly,inversionofthewholecomplexnumeralcanbecombinedwithprimerno,butnotallpossiblepermutationsareallowed.Consider(61)-(63):(61) Šagov primerno četyretysjači step.GEN.PL about four thousand.PAUCAL

23IoninandMatushanskyuseapproximative inversiontoargueforadifferentstructureformultiplicativeandadditivenumerals,anargumentwhichIembrace.Formoreonadditivenumerals,seebelow.24DataonapproximativeinversioninRussianisfromMashaEsipovaandNatashaKorotkova,p.c.25Example(i)isdeemedungrammaticalbyIoninandMatushansky(2018:199,their(8)c):(i) *Mašin sorok tysjač

car.GEN.PL forty thousand.GEN.PLMyinformants,however,found(59)tobegrammatical,or,atmost,slightlyodd.Theyalsofound(59)tobeworsethan(i),butnotungrammatical.Whileitisatpresentunclearwhat’sresponsibleforthiscontrast,theargumentinthetextstillstands,asitpertainstothestarkcontrastbetween(59)and(63).

22

‘Aboutfourthousandsteps’(62) Šagov četyretysjači primerno step.GEN.PL four thousand.PAUCAL about ‘Aboutfourthousandsteps’(63) ??Primerno šagov četyre tysjači

about step.GEN.PL four thousand.PAUCALThepatternweobservehereisthat, if thenounprecedesthecomplexnumeral,primerno ispossibleaslongasitaccompaniesthenumeral,butimpossibleifitbecomesstrandedfromit,asin(63).Thisissuggestiveofaconstituentstructurewherebyprimernočetyretysjačiformsasyntacticunit,asin(64)andassumedabove:(64) NumeralP

qpNumeralwo

eiCARD NumberPprimernoei ei četyreei nP ∙ tysjačiIfprimernočetyre tysjačiwasnotaconstituentbuthad insteadthecascadingstructurethatIoninandMatushanskyenvisageformultiplicativenumerals,we’dhave(65):26(65) wo

primernowo četyrewo tysjači NButonly(64)providesastraightforwardexplanationfortheungrammaticalityof(63):inordertoallow(59), IoninandMatushanskyhavetoallowthemovementorrotationofčetyreandtysjači, but then nothing prevents (63) from being generated. With a structure like (64),however, if approximative inversion involves movement of whatever is in Numeral (or ofNumberP/nP),thefactsabovefollowstraightforwardly. Crucially,ifthisisthecase,thencaseassignmenttonounsbynumeralshavetobeeffected,at least sometimes,byphrases,not justheads—e.g., šagovwillneed tobeassignedcaseby(primerno) četyre tysjači. This means that the only remaining argument of Ionin andMatushanskyagainsttheconstituencyofmultiplicativenumeralsdoesnotstand.27 Movingonnowtoadditivenumerals,anenrichedversionofstructuressuchasthosein(43)isnecessary.Consider(66),for(36)a,followingIoninandMatushanskyquiteclosely:(66) qpNumeralP1qp 2 and NumeralP2 sto2 woCARDNumberPdvewo 3 CARD NumberP [−min]NumberP wo

26It’sclearfromthesemanticsthatprimernocannotattachjusttočetyre:theapproximationisto4,000,notto4.27Anissuethatremainstobeaddressedisthegrammaticalnumberofthenouninexamplessuchas(53).ThespecialcaseweseeinthisexampleraisescomplexquestionsthatIamnotpreparedtoaddresshere(formoreonthisissue,see,e.g.,Franks1994).

23

3 [+min] NumberP[−at] nP1 wo

[−at] nP2In this structure, two NumeralPs are generated, one for each of sto and dve. Ionin andMatushansky’sandin(44)isused.BothnumeralwordsprojectaNumeralPherebecausetheellipsis envisagedby Ionin andMatushansky is nounellipsis (recall (43)), so space for twonounsisneeded.EllipsisthenproceedstodeletenP1andthetwoNumberPsaboveit,producing(36)a,withdualmarkingonthenounbecausethatisthenumbermarkingofthesurvivingnounin(66).Suchananalysisrequiresnounellipsistooccurevenwhentheelidedmaterialisnotfullyidenticaltoitsantecedent,obviatingthedifferentNumberfeaturesofnP1andnP2.28Ifthisisnotdesired,onemayassumethealternative in(67),wherenP1 isgeneratedwithoutanyNumberP,andwherenounellipsisoccursinthecontextofafullyidenticalantecedent:(67) qpNumeralP1qp 2 and NumeralP2 sto2 woCARDnP1dvewo CARD NumberP wo

[+min] NumberP wo

[−at] nP2It is easy to account for complex numerals that mix the multiplicative and the additivestrategies,suchasdva-sto-en‘twohundredandone’,asin(68)(ifwechoose(66)forsto-dve):(68) qp NumeralP1qp 4 and NumeralP2 2 3 wodva2CARDNumberPenwo ∙sto3 CARD NumberP [−min]NumberP wo

3 [+min] NumberP [−at]nP1 wo

[+at] nP2(68)correctlypredicts(69):(69) Dva-sto-en banana

two-hundred-one.NOM banana.FEM.NOM.SG‘Twohundredandonebananas’

ComplexnumeralssmallerthanonearealladditiveinLjubljanaSlovenian.(35)receivestheanalysisin(70).(70)correctlypredictsthatthenounin(35)withtakethepluralform:(70) qpNumeralP1qp 2 in NumeralP2 dva2 woCARDNumberPdvajsetimi wo 3 CARD NumberP

28Elidingnounswhicharenotfullyidenticaltotheirantecedentsisn’tinitselfaproblem,asitisverycommoncross-linguistically,e.g.,Ihaveonecatandyouhavetwocats.ThankstoKlausAbelsfordiscussionofthispoint.

24

[+min]NumberP wo 3 [−min] NumberP

[−at] nP1 wo [−at] nP2TheanalysisofLjubljanaSloveniancomplexnumeralsproposedheremaintainsthespiritofthedecompositionalapproachtonumeralsfromIoninandMatushansky’sworkwhileatthesametime integrating theapproach tonumeralsandgrammaticalnumber fromsections2and3.LjubljanaSlovenianisindeedanexampleofpredictedpattern1,butthesyntaxandsemanticsofitscomplexnumeralsissuchthatthoseabove100thatendin1or2takethesingularordualformofthenoun,respectively. AfinalquestionbeforeclosingthissectionpertainsnotsomuchtoSlovenian,buttosomeoftheotherlanguageswesawearlier:iftheanalysisof(69)isasin(68),whyare*twohundredandonebananaor*twentyonebananaungrammaticalinEnglish—thatis,whymustthenountherebeinitspluralform?Likewise,whyisthenounintheYimasexamplein(26),repeatedhere, not in the dual form if the complex numeral namarawt muntakn prpal ‘twenty-two’containsthenumeralprpal‘two’?(71) Yimas

Tan-pat namarawt munta-k-n p-rpal Bone-VII.PL person whole-IRR-I.SG VB-two‘Twenty-twobones’

AndwhyisthenounintheHopiexamplein(30),alsorepeatedhere,notinthedualformifthecomplexnumeralpakwt lööqsìikya‘ytaqam‘twelve’containsthenumerallööq‘two’?(72) Hopi

Pakwt lööq sìikya‘ytaqam pahaana-m (Hilletal.1998:382)Ten two.ACC plus Anglo-NOM.PL‘TwelveAnglos’

Tounderstandwhycombinationssuchas*twohundredandonebananaor*twentyonebananaareungrammaticalinEnglish,considerthestructureofEnglishtwentyoneNin(73)(cf.(43)):(73) NumberP qp [−atomic]wo

NumeralP1ei 2andNumeralP2 twenty2 2 CARDnP one2 CARDnPRecallthatMartíhypothesizesthatEnglishisa[±atomic]languagewithNumberP≫NumeralP(Table 2). Importantly, with additive numerals this means that NumberP is above thecoordinationstructurehypothesizedbyIoninandMatushansky.Crucially,[−atomic],butnot[+atomic], yields a grammatical result in (73), since the denotation of the constituent thenumberfeatureoperatesonisasetofindividualseachofwhichisofnumerosity21—thatis,asetofnon-atoms.And[−atomic]givesrisetoaplural-markednoun,whichcorrectlypredictsthenumbermarkingonthenounwiththisandanyothercomplexnumeralinEnglish.ThatinEnglishadditivenumeralsalwaystakeplural-markednounsmightbetakenasevidencethat(73),and,thus,thesysteminTable2,isthecorrectanalysisforEnglish(asopposedtothatinTable6,whereNumeralPdominatesNumberP).Inotherwords,numbermarkingofnounswithcomplexnumerals isapotential sourceof independentevidence for therelationship that is

25

takentoholdbetweenNumeralPandNumberPinaparticularlanguage,arelationshipthatistakenbythetheoryproposedheretopotentiallyvaryfromonelanguagetoanotherandforwhichthereisaneedoflanguage-particularevidence.

In other cases, such as Yimas and Hopi, it is possible that complex numerals aresyntactically decomposed in a way not too dissimilar to the way they are decomposed inLjubljanaSlovenian,butnounellipsistargetsadifferentsite;thatis,thecorrectanalysisof(71)mightbetanpatnamarawtmuntakntanplprpal,whereitisthedualmarkednounthatiselided.Andtherewillmostlikelybeotherparticularitiesinagivenlanguagethatmightinterferehere. Thus, all in all, it is possible to maintain the Ljubljana Slovenian indeed instantiatespredictedpattern1.Ithasbeenpossibletodothatandincorporateimportantaspectsoftheanalysis of complex numerals in Ionin and Matushansky (2006, 2018). While the nounsnumeralscombinewitharenottakenbydefaulttobesetsofatomicindividualsinmyapproach,theonlyaspectoftheiranalysisthatrequiredmodificationwastheanalysisofmultiplicativenumerals,wherea∙operatorandadifferentconstituentstructurewasfoundtobenecessary.295.2 Imere30

InImere,dualmarkingonnounsdoesn’tappearatallinthenumeral+nounconstruction:allnumeralsgreaterthanone,includingthenumeraltwo,combinewithnounsmarkedforplural.Thisisneitherpattern1norpattern2.InthissectionIarguethatinImerethedualmarkerisnotjustthespelloutofthenumberfeaturecombination[+minimal,−atomic],thatmarkeralsospellsoutD.Assuch,wedonotexpectittobeabletocombinewithnumerals.Thus,Imereis,despiteappearances,arguedtoinstantiatepattern1inwhatfollows.

Imereisalanguagethatdisplaysasingular-dual-pluralsystemonitsnon-pronominals,asshowninTable11(Clark1975,1998,2002/2011,Martí2019):singular dual plural translationte-sea ruu-sea a-sea chairte-manu ruu-manu a-manu birdte-soa ruu-soa a-soa friendte-ngata ruu-ngata a-ngata snakeTable11SomeImerenounsandtheirnumberImereusesprefixesonnounstoexpressgrammaticalnumber.Theseprefixesattachtonounsthatbelongtothenativevocabulary,thoughnotallnativenounscantakethem.Verbsdisplaysubjectagreementprefixesthataresensitivetothegrammaticalnumberonthenouninsubjectposition.31

Regardingthenumeral+nounconstruction,thefactsinImereareasfollows(datafrommyownfieldwork):(74) Te-sea ee-tasi

29InseveralArabicdialects,uptothenumeraltenthepatternisasinPredictedPattern1,butnumeralselevenandhighercombinewithsingular-markednouns(seeHurford2001:10757,Ouwayda2014,Zabbal2005).Moreworkisneededtounderstandwhetherthispatternisproblematicforthetheorypresentedhere.30Imere isaPolynesian languagespoken inVanuatu.Earlyworkon the language includesClark (1975,1998,2002/2011).AllImeredatanotattributedtoasourceisfrommyownfieldwork.SpellingfollowsClark(1975,1998,2002/2011),withsomemodificationsfromvanUrk(2018).Theletter jcorrespondsto[tʃ],k isvariablyrealizedas[k]or[ɣ]intervocalically,mandparelabio-velars.31Clark(1975,1998,2002/2011)proposesthatImeremakesmorenumberdistinctions,includingwhatlooklikepaucalsorgreaterplurals.However,IhavenotbeenabletoattestthepresenceofpaucalsorgreaterpluralsinImere.Speculatively,itmaybethatinapreviousstageofthelanguagethegrammaticalnumbersystemwasmorecomplexthanasingular-dual-pluralsystem.

26

SG-chair 3SG.NFUT-one‘Onechair’

(75) a.Ruu-sea (??ee-rua)

DU-chair 3SG.NFUT-two b.A-sea ee-rua

PL-chair 3SG.NFUT-two‘Twochairs’

(76) A-sea ee-toru

PL-chair 3SG.NFUT-three‘Threechairs’

All other numerals use the plural prefix on the noun. 32 That is, the numeral eetasi ‘one’combines with nouns that necessarily bear the prefix te- ((74)), which indicates singularnumber;numeralsgreaterthanonenecessarilycombinewithnounsthatbearthepluralprefixa-((76));curiously,thenumeraleerua‘two’isincompatiblewithdualnumbermarkingonthenoun((75)a)andpluralmarkingmustbeusedtheretoo((75)b).Thisisanunexpectedpatternfromtheperspectiveofthetheoryinsection3. Before proceeding with the argument, it’s important to notice that (non-borrowed)numeralsinImere,asshownin(74)-(75),isthattheytakeverbalmorphology(compareee-tasiwithroo-tasi‘one’,withthefuturemarkerroo-;Clark2002/2011:684).Thisstateofaffairsisnotunheardofcross-linguistically,asdiscussedearlierinsection4.1(IoninandMatushansky2018: 69-71). Iwill follow Ionin andMatushansky in assuming that Imere (non-borrowed)numeralsprojectreducedrelativeclauses/participles,ananalysisthatissupportedbythefactthatregularrelativeclauses in Imerearepostnominal (Clark2002/2011:686).Thus, te-seaeetasi ‘onechair, lit.SG-chairbe.one’wouldbeanalyzedaswhatinEnglishcouldperhapsberenderedwith‘chair[whichisone]’.Itsstructurewouldbeasfollows(‘rRC’standsfor‘reducedrelativeclause’;Idonotexploreherewhattheinternalstructureofthatrelativeclausewouldbe):(77) NumeralP

ei ru Numeral/rRCNumberPCARD@ru eetasi[+min]ru [+at]nP

te- -seaProceedingnowwiththeargumentthatImereisnotacounterexampletothetheorypresentedinsection3,thestatusofthedualprefixruu-andofthepluralorsingularprefixesisnotequalinthislanguage.Whileitisfeasibletoanalyzete-anda-asthespelloutofnumberfeaturesonly, as Martí (2019) does, there is evidence that ruu- spells out not only dual numbermorphology, but is also a determiner. Its status as determiner, I suggest, prevents it fromcombiningwiththenumeraleerua‘two’((75)a).Afirstindicationthatruu-issetapartfromte-anda-inImereisthat,whereasthereare(morphophonological)constraintsonwhichnouns

32Fornumeralsgreaterthan9or10,EnglishborrowingsareusedandtheEnglishpatternforthenoun,thatis,pluralnumbermarking,isfollowed.

27

can take te- anda-,withsomenouns takingneither,othernouns takingoneprefix,andyetotherstakingboth,all(native)nounscantakeruu-.Table12illustratesthisphenomenon(datafrommyownfieldwork):singular dual plural translationte-fine ruu-fafine fafine womantangata ruu-taangata taangata manfunumui ruu-funumui funumui girllooto ruu-looto looto carte-kori ruu-kori kori dogTable12SomeImerenounsandtheirnumberAnargumentthat, inaddition,ruu- isactuallyadeterminer,andnotjustanumberprefix, isthat, whereas te- and a- are compatible with demonstratives and quantifiers, ruu- isn’t.Considertheexamplesin(78)-(82)(datafrommyownfieldwork):(78) Te-fare poulapa-raa

SG-house big-DEM‘Thatbighouse’

(79) A-fare pwoulapa-raaPL-house big-DEM

‘Thosebighouses’(80) a.A-ngata toope

PL-snake many‘Manysnakes’b.*Ruu-ngata toopeDU-snake many

(81) a.A-ngata eewji PL-snake all/every ‘All(the)snakes’b.*Ruu-ngata eewejiDU-snake all/every

(82) a.A-ngata afaruPL-snake some ‘Somesnakes’b.*Ruu-ngata afaru

DU-snake someConsiderthatthereisnothinginprinciplewrongwithquantifyingovertwosomes:itispossibletotalkaboutmany,all,orsomepairsofsnakes—thatis,theimpossibilityof(80)b,(81)b,and(82)bcannotbeblamedonasemanticill-formedness.Theungrammaticalityoftheseexamplescan be understood if ruu- sits inD, in addition to spelling out numbermorphology, on theassumptionthatdemonstrative-raaandquantifierssuchastoope‘many’,eeweji‘all/every’orafaru ‘some’ also occupy this position.33The syntax thatwe can thus assume for ruu- is asfollows:

33 Demonstratives and quantifiers are incompatible with the definite article in other languages:*this/that/these/thosethe,*thethis/that/these/those,*every/manythe,*theevery/many.Many/all/someoftheispossibleinEnglish,butthepresenceofofisindicativeofamorecomplexstructure(allmightnotbeaquantifier

28

(83) DP

3 DNumberP3 [+min]3ruu-[−at]nP -seaTheexplanationIproposefor??ruu-seaeerua((75)a)isthat,ifitistruethatruu-isadeterminerandalsospellsoutnumberfeaturesinNumberP,DandNumberPmustbecloseenoughtoeachother inthestructure; that is,an intervening(c-commanding)NumeralPwoulddisrupt thatcloserelationship,asshownin(84):34(84) D

ei DNumeralP ei

ru Numeral/rRC✖NumberPCARD@ru eeruaruu-[+min]ru [−at]nP -seaAquestionthatarisesinthisanalysisishowthenumeraltwocancombinewithaplural-markednouninasingular-dual-pluralsystem.IwouldliketoconsiderherethepossibilitythatpluralformsinImereareambiguousbetweenanexclusivesemantics(theonewe’vebeenassumingallalong)andaninclusivesemantics,whichcanbeobservedin(85)and(86)(datafrommyownfieldwork):(85) Au seia kee a-ngata.

I see not PL-snake ‘Ididn’tseeanysnakes’/’Ididn’tseethesnakes’(86) A:Lekina a-tama?

exist PL-child‘Doyouhavechildren?’B:Ai, eetasiyes 3SG.NFUT-one‘Yes,one’

Ifangata‘snakes’oratama‘children’couldn’tbeunderstoodinclusively,thatis,pertainingtooneormoresnakes/children,(85)wouldbetrueifIhadseenonesnake,and(86)Awouldbeaquestionaboutpluralitiesofchildren,andthusnotanswerableasin(86)B,contrarytofact.InMartí (2020b), I analyse inclusive plurals as lacking NumberP altogether—the absence of

inEnglishanyway,seeBrisson2003,amongothers).InlanguagessuchasSpanish,nounphrasessuchaselchicoese‘thatboy(pejorative),lit.theboythat’arepossible,butonlyifthedemonstrativeappearsphrase-finally,whichisplausiblyindicativeofadifferentstructure(cf.Brugè2002).34Analternativeanalysismightbethatruu- isactuallythespelloutofboththenumeraleeruaand[+minimal,−atomic].Iwillnotpursuethispossibilityfurtherhere.

29

NumberPtranslatesintopluralmorphologyinlanguagesthathaveinclusiveplurals(seealsofootnote 5). That is, the analysis of inclusive and exclusive plurality is one of ambiguity:exclusivepluralsareanalysedjustaswehavedonesofar(seesection2),andinclusivepluralshave an inclusive semantics and lack NumberP35 . If the latter possibility is available in alanguage, as it is in Imere, thenplural-markednouns cancombinewith thenumeral two, apossibilitythatisexploitedbyImereeeruabecause,asI’vearguedabove,nounsmarkedwithruu-cannotcombinewithitforsyntacticreasons(eetasi‘one’isnotallowedtomakeuseofthispossibility,*angataeetasi,becausete-isavailable,soa-isblocked).6 ConclusionInthispaperIhaveexploredsomeoftheimplicationsforthecombinationofHarbour’snumberfeaturetheorywithScontras’approachtonumeralsinlanguagesthatdistinguishsingular,dualandpluralnumberonnouns.IhavehypothesizedthatthesyntacticrelationbetweenNumberP,wherenumber featuresreside,andNumeralP,wherenumeralsreside,mightvary fromonelanguagetoanother.Thetheorythatresultsfromtheseassumptionsleadstoaveryrestrictedsetofpredictionsregardingthenumbermarkingonnounsinthenumeral+nounconstruction.

IarguedthatbothYimasandHopiconstitutestraightforwardconfirmationthatpredictedpattern1 is attested. I alsoargued thatLjubljanaSlovenianand Imere instantiate the samepattern,butadditionalgrammaticalpropertiesoftheircomplexnumeralsandthegrammarofDmakethatconfirmationmoredifficulttoestablish.

IshowedthatLjubljanaSlovenianconformstopredictedpattern1,evenwhencomplexnumeralsgreaterthanonearetakenintoaccount,oncetheircomplexsyntaxandsemanticsareproperly understood, something that became possible once certain ideas in Ionin andMatushansky(2006,2018)aboutthesemanticsandcompositionofnumeralswereadaptedforourpurposes.ImeredualsalsoseemedtoposeaprobleminitiallybutIarguedthatthedualprefixruu-canreasonablybetakentobethespelloutofanarticleinadditiontospellingoutnumbermorphology, whichwould prevent it from combinationwith the numeral two, forwhichcaseplural-markednounsareused. Muchremainstobeexplored.Tobeginwith,itisatpresentunknowntomewhetherthereare any languages in which dual-marked nouns combine with numerals greater than two(predictedpattern2),but thispossibility ispredictedbythetheorypresentedhere.Certainassumptions thatwere necessary tomake, such as the variable syntactic relation betweenNumberPandNumeralP,remaintobejustifiedempirically.Butthemostimportantunderlyingissuehereisthat,descriptively,weknowlittleaboutwhatispossibleandwhatisimpossibleinthenumeral+nounconstructioninlanguageswithduals,despitetheeffortsofPlank(1995).IhopethatthemostlytheoreticalexplorationIhaveundertakeninthispaperwillatleastservetomotivateustofillthisimportantempiricalgapinourknowledge.ReferencesAlexiadou,Artemis.2019.MorphologicalandSemanticMarkednessRevisited:theRealizationofPluralityacrossLanguages.ZeitschriftfürSprachwissenschaft38.123–154.https://doi.org/10.1515/zfs-2019-0004.

Bale, Alan, Michaël Gagnon and Hrayr Khanjian. 2011. Cross-linguistic Representations ofNumeralsandNumberMarking.SALT20,582-598

Bylinina, Lisa, andRickNouwen.2018.OnZero andSemanticPlurality.Glossa: a JournalofGeneralLinguistics3(1):98,1-23.

Borer,Hagit.2005.StructuringSense:InNameOnly.OxfordUniversityPress.

35Recallfootnote5.

30

Brisson,Christine.Plurals,‘all’,andtheNonuniformityofCollectivePredication.LinguisticsandPhilosophy26:129-184.

Brugè,Laura.2002.ThePositionsofDemonstrativesintheExtendedNominalProjection.InGuglielmo Cinque (ed.) Functional Structure of DP and IP. The Cartography of SyntacticStructures,vol.1,15-54,OxfordUniversityPress,Oxford,UK

Clark, Ross. 1975. Mele notes. Auckland University Working Papers in Anthropology,Archaeology,Linguistics,andMaoriStudies40.

Clark,Ross.1998.AdictionaryoftheMelelanguage(AtaraImere),Vanuatu.PacificLinguistics,TheAustralianNationalUniversity.DOI:10.15144/PL-C149.

Clark,Ross.2002/2011.Ifira-Mele.InJohnLynch,MalcolmRossandTerryCrowley(eds.)TheOceanicLanguages,Routledge,681-693.

Corbett,Greville.2000.Number.Cambridge,CambridgeUniversityPress,Cambridge,UK.Derganc,Aleksandra.2003.ThedualinSlovenian.InSlovenianfromatypologicalperspective,ed.byJanezOrešnikandDonaldD.Reindl,165-181.Berlin:AkademieVerlag.

Dvorak,BostjanandUliSauerland.2006.ThesemanticsoftheSloveniandual.InProceedingsofFASL14,ed.byJamesLavine,StevenFranks,MilaTasseva-KurktchievaandHanaFilip,98–112.MichiganSlavicPublications.

Farkas, Donka and Henriëtte de Swart. 2010. The Semantics and Pragmatics of Plurals.SemanticsandPragmatics3:1–54.

Foley,William.1991.TheYimasLanguageofNewGuinea.StanfordUniversityPress.Stanford,California.

Franks,Stephen.1994.ParametricPropertiesofNumeralPhrasesinSlavic.NaturalLanguageandLinguisticTheory12:597–674

Giusti,Giuliana.1991.TheCategorialStatusofQuantifiedNominals.LinguistischeBerichte136:438–452.

Giusti, Giuliana. 1997. The Categorial Status of Determiners. TheNew Comparative Syntax,LilianeHaegeman(ed.),94–113.Cambridge:CambridgeUniversityPress.

Grimm,Scott.2012.PluralityisDistinctfromNumber-Neutrality.ProceedingsofNELS41Harbour,Daniel.2011.DescriptiveandExplanatoryMarkedness.Morphology21:223-245Harbour,Daniel.2014.Paucity,AbundanceandtheTheoryofNumber.Language90,158-229.Herrity,Peter.2015.Slovene:acomprehensivegrammar.Abingdon:Routledge.Heycock, Caroline and Roberto Zamparelli. 2005. Friends and Colleagues: Plurality,Coordination,andtheStructureofDP.NaturalLanguageSemantics13:201-270.

Hill, Kenneth, Emory Sekaquaptewa, Mary E. Black, Ekkehart Malotki, and MichaelLomatuway'ma.1998.HopìikwaLavàytutuveni:AHopiDictionaryoftheThirdMesaDialectwithanEnglish-HopiFinderListandaSketchofHopiGrammar.TheHopiDictionaryProject,BureauofAppliedResearchinAnthropology,UniversityofArizona,Tucson,Arizona

Hurford,Jim.1975.TheLinguisticTheoryofNumerals.Cambridge:CambridgeUniversityPress.Hurford, Jim.2001. “Numeral systems.” InN. J. SmelserandP.B.Baltes (eds.) InternationalEncyclopediaoftheSocialandBehavioralSciences,10756–10761,Pergamon,Amsterdam

Ionin,TaniaandOraMatushansky.2006.TheCompositionofComplexCardinals. JournalofSemantics23:315-360

Ionin, Tania and Ora Matushansky. 2018. Cardinals. The Syntax and Semantics of Cardinal-containingExpressions,theMITPress

Ivlieva,Natalia.2013.Scalarimplicaturesandthegrammarofpluralityanddisjunction,PhDdissertation,MIT.

Kayne,RichardS.2003.Silentyears,silenthours.InGrammarinFocus:FestschriftforChristerPlatzack, ed. Lars-OlofDelsing, Cecilia Falk, Gunlog Josefsson, andHalldorA� . Sigurðsson,209–226.Lund,Sweden:WallinandDalholm

31

Kayne,R.S.2007.OntheSyntaxofQuantityinEnglish.InLinguisticTheoryandSouthAsianLanguages:EssaysinhonourofK.A.Jayaseelan,ed.JosefBayer,TanmoyBhattacharyaandM.T.HanyBabu.LinguistikAktuell/LinguisticsToday102,73–105.

Kiparsky,PaulandJudithTonhauser.2012.SemanticsofInflection.InClaudiaMaienborn,Klausvon Heusinger and Paul Portner (eds.), Handbook of Semantics, 2070–2097. Berlin: deGruyter.

Krifka,Manfred.1989.NominalReference,TemporalConstitutionandQuantificationinEventSemantics.InRenateBartsch,JohanvanBenthem&PetervanEmdeBoas(eds.),SemanticsandContextualExpression,Dordrecht

Krifka,Manfred.1995.CommonNouns:aContrastiveAnalysisofChineseandEnglish.InGregCarlsonandJeffreyPelletier(eds.)TheGenericBook,Chicago:ChicagoUniversityPress,398-411

Lasersohn, Peter. 1998. Plurality, Conjunction, and Events. Studies in Linguistics andPhilosophy55,Springer

Lasersohn,Peter.2011.MassNounsandPlurals.InKlausvonHeusinger,ClaudiaMaienbornand Paul Portner (eds.), Semantics: An International Handbook of Natural LanguageMeaning,vol.2,1131-1153.DeGruyter.

Link,Godehard. 1983.TheLogicalAnalysis ofPlural andMassTerms: a Lattice-TheoreticalApproach.InRainerBäuerle,ChristophSchwarze&ArnimvonStechow(eds.),Meaning,UseandInterpretationofLanguage,302-323.Berlin:deGruyter.

Martí, Luisa.2019. “TheSemanticsofNounPrefixes in Imere”, talkgivenatTripleA6,MIT,Cambridge,Massachussets.

Martí, Luisa. 2020a. Numerals and the Theory of Number, Semantics and Pragmatics 13.3,https://semprag.org/index.php/sp/article/view/sp.13.3

Martí, Luisa. 2020b. Inclusive Plurals and the Theory of Number, Linguistic Inquiry 51.1,doi.org/10.1162/ling_a_00330

Martí, Luisa. Under review. Zero N: number features and ⊥,https://ling.auf.net/lingbuzz/003627

Marušič, Lanko and Rok Žaucer. To appear. Case study: Slovenian dual. In Handbook ofgrammatical number, ed. by Patricia CabredoHofherr and JennyDoetjes, Oxford:OxfordUniversityPress.

Nelson,DianeandIdaToivonen.2000.CountingandtheGrammar:CaseandNumeralsinInariSami.InDianeNelsonandP.Foulkes(eds)LeedsWorkingPapersinLinguistics8,179-192.

Nevskaya,Irina.2005.InclusiveandexclusiveinTurkiclanguages,inElenaFilimonova(ed.)Clusivity: Typology and case studies of the inclusive–exclusive distinction, 341–358, JohnBenjamins,Amsterdam/Philadelphia

Nevins,Andrew.2011.Marked targetsvs.marked triggersand impoverishmentof thedual.LinguisticInquiry42:413-444.

Noyer,Rolf.1992.Features,positionsandaffixesinautonomousmorphologicalstructure.PhDdissertation,MIT.

Ouwayda, Sarah. 2014.Where Number Lies: Plural Marking, Numerals, and the Collective-DistributiveDistinction.PhDdissertation,UniversityofSouthernCalifornia.

Plank,Frans.1995.Domainsofthedual,inMalteseandingeneral.RivistadiLinguistica8:123-140.

Ritter,Elisabeth.1991.Twofunctionalcategoriesinnounphrases:EvidencefromModernHebrew.PerspectivesonPhraseStructure,SyntaxandSemantics,37–62.NewYork:AcademicPress.

Rothstein, Susan. 2013. A Fregean semantics for number words. Proceedings of the 19thAmsterdamColloquium, ed.MariaAloni,Michael Franke, and FlorisRoelofsen, 179–186.Amsterdam:InstituteforLogic,Language,andComputation.

32

Rothstein, Susan. 2016. Counting andmeasuring: A theoretical and crosslinguistic account.BalticInternationalYearbookofCognition,Logic,andCommunication11:1–49.

Rothstein, Susan. 2017. The Semantics of Counting and Measuring. Cambridge: CambridgeUniversityPress.

Rubino,Carl.1997.AReferenceGrammarofIlocano.PhDDissertation,UniversityofCaliforniaatSantaBarbara

Sauerland, Uli. 2003. A New Semantics for Number. In Rob Young & Yuping Zhou (eds.),Proceedingsofthe13thSemanticsandLinguisticTheoryConference,258–275.Ithaca,N.Y:CornellUniversityCLC-Publications.

Sauerland, Uli, Jan Anderssen and Kazuko Yatsushiro. 2005. The Plural is SemanticallyUnmarked.InStefanKepserandMargaReis(eds.),LinguisticEvidence,409–30.deGruyter.

Scha, Remko. 1981. Distributive, Collective and Cumulative Quantification. Jeroen A. G.Groenendijk, TheoM. V. Janssen,Martin B. J. Stokhof,Martin J. B. Stokhof (eds.), Formalmethodsinthestudyoflanguage(part2).483-512.Amsterdam:MathematischCentrum

Scontras,Greg.2014.TheSemanticsofMeasurement.PhDdissertation,HarvardUniversitySigler, Michele. 1997. Specificity and Agreement in Standard Western Armenian, PhDdissertation,MIT.

Spector, Benjamin. 2007. Aspects of the Pragmatics of PluralMorphology: onHigher-OrderImplicatures.InUliSauerland&PenkaStateva(eds.),PresuppositionsandImplicaturesinCompositionalSemantics,243–281.

Toporišič,Jože.2000.Slovenskaslovnica.Maribor:Obzorja.Yatsushiro,Kazuko,Uli Sauerland&ArtemisAlexiadou.2017.TheUnmarkednessofPlural:CrosslinguisticData.InMariaLaMendola&JenniferScott,BUCLD41:Proceedingsofthe41stannualBostonUniversityConferenceonLanguageDevelopment,753-765.Somerville,USA:Cascadilla.

Zabbal, Youri. 2005. The Syntax of Numeral Expressions, Manuscript, University ofMassachusettsAmherst.

Zamparelli,Roberto.1995.Layers in theDeterminerPhrase.PhDdissertation,UniversityofRochester.

Zamparelli,Roberto.2002.Definiteandbarekind-denotingnounphrases.RomanceLanguagesand Linguistic Theory 2000: Selected Papers from Going Ro- mance 2000, ed. ClaireBeyssade, Reineke Bok-Bennema, Frank Drijkoningen, and Paola Monachesi, 305–342.Amsterdam:JohnBenjamins.

Zweig,Eytan.2006.NounsandAdjectivesinNumeralNPs.InL.BatemanandC.Ussery(eds.)ProceedingsofNELS35.GLSAPublications,Amherst,MA.663-675.

Zweig,Eytan.2009.Number-NeutralBarePluralsandtheMultiplicityImplicature.LinguisticsandPhilosophy32:353-407.