On the relationship between morphological and semantic markedness

Transcription

1 Morphology (2011) 21: DOI /s ORIGINAL PAPER On th rlationship btwn morphological and smantic markdnss Th cas of plural morphology Alan Bal Æ Michaël Gagnon Æ Hrayr Khanjian Rcivd: 19 Jun 2008 / Accptd: 20 May 2009 / Publishd onlin: 1 July 2010 Ó Springr Scinc+Businss Mdia B.V Abstract This papr xplors two possibl connctions btwn th diagnostics for morphological and smantic markdnss. On possibility, a positiv corrlation, prdicts that if a grammatical fatur is diagnosd as bing morphologically markd thn it should also b smantically markd. This possibility follows from th assumption that faturs ar intrprtd as rstrictions on dnotations. Th scond possibility, a ngativ corrlation, prdicts that if a grammatical fatur is diagnosd as bing morphologically markd thn it should b smantically unmarkd. This systmatic inconsistncy follows from th assumption that faturs ar intrprtd as augmnting functions. In our xploration of numbr marking, w find that th ngativ corrlation is not only thortically consistnt with th smantic litratur (in particular Link, in: Bartsch t al. (ds.) Smantics and contxtual xprssions, 1983), but it is also mor consistnt with th mpirical landscap (as notd by Saurland, in: Young and Zhou (ds.) Procdings of Smantics and linguistic thory SALT XIII 2008). As a rsult, th morphological diagnostics lnd support to th viw that plural faturs ar intrprtd as augmnting functions. Kywords Smantic markdnss Morphological markdnss Plural Fatur intrprtations A. Bal (&) Linguistics Program, Concordia Univrsity, H663, 1455 d Maisonnuv Blvd., W. Montréal, QC H3G 1M8, Canada -mail: alancbal@gmail.com M. Gagnon Dpartmnt of Linguistics, Univrsity of Maryland, 1401 Mount Mary Hall, Collg Park, MD , USA H. Khanjian Dpartmnt of Linguistics and Philosophy, MIT, 77 Massachustts Avnu Bldg. 32-D808, Cambridg, MA 02139, USA

2 198 A. Bal t al. 1 Introduction Is thr a link btwn smantic and morphological markdnss? Linguists working on markdnss hav oftn implicitly assumd thr is. In fact, rarly is a clar distinction mad btwn thm. For xampl, Jakobson (1971) and Grnbrg (1966) trat smantic and morphological markdnss as symptoms of th sam undrlying proprty: markdnss in gnral. Idally, ths symptoms should b consistnt with ach othr. Howvr, as conflicts aris, th idalizd link btwn th two phnomna bcoms qustionabl. Som rsarchrs hav vn givn up on th ida that th smantic symptoms hav any rlation to traditional notions of markdnss (s Croft 2003). Th goal of this papr is to xplor and clarify th possibl links btwn smantic and morphological markdnss with a concntration on numbr marking (plural and singular marking). W discuss two ways thy might b connctd: (1) a positiv corrlation and (2) a ngativ corrlation. Both corrlations assum that markdnss facts rflct a particular thortical proprty: namly, markd faturs can b rfrncd by a grammatical rul and unmarkd faturs cannot (s, Noyr 1998; Nvins 2007a; among othrs). In a hypothsizd positiv corrlation, 1 th vidnc for a fatur bing morphologically markd would b consistnt with vidnc for it bing smantically markd. Idally, this corrlation would follow as a consqunc of markd faturs bing rfrncd by morphological ruls and intrprtation ruls. As w discuss in Sct. 2.1, this typ of corrlation is possibl as long as morphological faturs ar intrprtd as rstricting th dnotations of thir stms. Howvr, dspit its thortical plausibility, mpirical vidnc suggsts that a positiv corrlation is unlikly for numbr marking. In many languags, th diagnostics for smantic and morphological markdnss yild inconsistnt rsults. Th scond typ of corrlation, th ngativ corrlation, has not rcivd much attntion from thos who work on markdnss vn though this typ of connction is implicit in th work of many smanticists: in particular, thos who ar influncd by Link s (1983) tratmnt of th plural morphm as a closur opration. (A notabl xcption is Saurland 2008, who discusss th ngativ corrlation without adopting a Link-styl intrprtation of plurality.) Th ngativ corrlation prdicts that th morphological and smantic diagnostics should yild opposit rsults. This consistnt inconsistncy can b xplaind if th markd fatur is tratd smantically as an augmnting function: a function that applis to a st of individuals to crat a suprst containing groups formd from thos individuals in addition to th original st. Onc again, th hypothsis that only markd faturs can b rfrncd by grammatical ruls xplains this ngativ corrlation. Although this typ of corrlation is mor plausibl for numbr marking than th positiv on, thr ar still som mpirical difficultis involving plural marking on nouns such as pounds. In Sct. 4, w outlin ths problms and discuss how thy might b ovrcom by changing how masurmnts on lmnts in nominal dnotations ar calculatd. 1 Implicit in Jakobson (1971) and Grnbrg (1966).

3 Rlationship btwn morphological and smantic markdnss 199 Bfor discussing th dtails of positiv and ngativ corrlations, w should dscrib xactly what w man by morphological and smantic markdnss. In Sct. 1.1 and 1.2, w outlin th diffrncs btwn ths two phnomna. 1.1 Morphological markdnss For xpository purposs, w assum that th proprty of bing markd or unmarkd applis to grammatical faturs. Howvr, whthr particular typs of faturs ar ndd or how thy ar rprsntd (monovalnt vrsus bivalnt) is byond th scop of this papr. In th discussion that follows, w attmpt to us fatursymbols to rprsnt potntial formal morpho-syntactic proprtis in a thory nutral way. What thy rprsnt is potntial in that w ar only committd to th xistnc of th formal proprty in th markd cass. In unmarkd cass, w rmain agnostic about whthr thr is a formal proprty or not. Whthr or not unmarkd faturs ar part of th morpho-syntactic rprsntation dos not chang th potntial rlationships btwn th smantic and morphological diagnostics rviwd in this papr. Not howvr, for th sak of simplicity and uniformity, w will discuss unmarkd faturs as if thy ar a part of th morpho-syntactic rprsntation. To undrstand xactly what it mans for a formal proprty to b markd or unmarkd, it is bst to first outlin th diagnostics usd in dtrmining markdnss and thn rviw how ths diagnostics ar commonly intrprtd. Many of th diagnostics for markdnss ar basd on th form of crtain morphms and th (grammatical) nvironmnts in which thy appar. Som of th mor common ons ar listd in (1) (cf. Croft 2003; Grnbrg 1966). (1) Morphological Symptoms of Markdnss a. Morphms with unmarkd faturs oftn hav no phonological contnt. b. Morphms with unmarkd faturs oftn show mor paradigmatic distinctions than morphms with markd faturs. c. Forms associatd with markd faturs oftn appar in fwr grammatical nvironmnts. Th diagnostic in (1a) stats that unmarkd, grammatical proprtis ar oftn not associatd with any sound. For xampl, considr th subjct agrmnt morphms in Buriat. In this languag, first and scond prson, singular agrmnt on vrbs corrsponds with phonological contnt (.g., jaba-na-b (go-pres-1sg) I go, jabana-š (go-pres-2sg) you go ). In contrast, third prson, singular agrmnt corrsponds with no such contnt (.g., jaba-na-ø (go-pres-3sg) H/sh/it gos ). 2 Ths facts suggst that 3rd prson is likly unmarkd whras th othr prson faturs ar markd (s, Cysouw 2003, and Bnvnist 1966, for a mor dtaild discussion of null marking and prson agrmnt crosslinguistically). 2 W took ths xampls from Cysouw (2003, p. 61) who in turn took thm from Popp (1960, p. 57).

4 200 A. Bal t al. Th diagnostic in (1b) stats that unmarkd grammatical proprtis ar oftn associatd with mor paradigmatic distinctions. For xampl, singular pronouns in English dmonstrat mor distinctions in trms of gndr (.g., h, sh, it) than thir plural countrparts (.g., thy, thy, thy). Hnc, it is likly that singular is unmarkd whras plural is markd (s, Croft 2003, and Harly 2008, for a discussion of ths facts). Finally, th diagnostic in (1c) stats that th phonological forms mor commonly associatd with markd grammatical proprtis appar in fwr nvironmnts. For xampl, in North Sámi th sound associatd with th dual form of a vrb appars only with crtain dfinit subjcts. Vrbs with indfinit subjcts hav th sam sound as th plural form of th vrb. Hnc, it is likly that dual is markd (s Vinka 2001 for a discussion of th Sámi facts). Th diagnostics in (1) idally should corrlat with som undrlying grammatical proprty that xplains th morphological bhaviour of morphms with markd and unmarkd faturs. On possibility is that markd faturs ar th only faturs that can b rfrncd in grammatical ruls. 3 For xampl, th lack of phonological contnt dscribd in (1a) could b a consqunc of Vocabulary Insrtion Ruls (similar to Hall and Marantz 1993), whr morphms ar rprsntd by a bundl of faturs and phonological contnt is insrtd basd on ths faturs. 4 Givn this typ of charactrization, th ruls for th phonological insrtion of th prson agrmnt in Buriat could b rprsntd as follows: =b=,½1sgš ðinsrt=b=whn th morphm has th fatur ½1sgŠÞ =s=,½2ndš ðinsrt=s=whn th morphm has th fatur ½2sgŠÞ lswhr (othrwis insrt no phonological contnt) Unmarkd faturs cannot b rfrncd by such ruls and hnc ithr phonological contnt is not assignd or dfault forms ar insrtd. 5 Null marking is a common dfault form in many typs of paradigms. Similarly, th lack of paradigmatic distinctions among th morphms with markd faturs could b a consqunc of Impovrishmnt Ruls (as dscribd in Noyr 1998, and Nvins 2007a). Impovrishmnt Ruls dlt faturs on a morphm bfor th application of Vocabulary Insrtion Ruls. For xampl, to xplain th lack of gndr distinctions among plural pronouns in English on could hypothsiz an Impovrishmnt Rul that dlts gndr faturs in morphms 3 In th morphological litratur, this charactrization has mostly bn limitd to Impovrishmnt Ruls. In fact, both Noyr (1998) and Harbour (2003) hypothsiz th xistnc of rdundancy ruls that (only) insrt unmarkd faturs. Such ruls would ncssarily rfrnc unmarkd faturs and nvr markd faturs. Howvr, as Vinka (2001) suggsts, such rdundancy ruls might not b ndd if on chooss a fatur systm diffrnt from th on adoptd by Noyr (1998) and Harbour (2003). For now, w will put th issu of th xistnc of rdundancy ruls asid. 4 Som morphologists, such as Nvins (2007a), xplicitly allow Insrtion Ruls to rfrnc unmarkd faturs, although thy do not allow othr typs of grammatical ruls to do so. 5 Whthr th lack of phonological contnt is du to silnc (null contnt) bing a dfault insrtion or whthr th lack is du to th absnc of any application of an insrtion rul is of littl consqunc for this papr. Both ar consistnt with what w say about markdnss.

5 Rlationship btwn morphological and smantic markdnss 201 with th plural fatur, PL (as in Harly 2008). Th markd fatur bcoms a condition for th application of th Impovrishmnt Rul. Insrtion of lxical itms would not rsult in gndr distinctions sinc th faturs that provid such distinctions would not b prsnt at th tim of insrtion. Sinc unmarkd faturs cannot b rfrncd by a grammatical rul, thy cannot srv as a condition for th application of an Impovrishmnt Rul. As with lack of paradigmatic distinctions, th fact that th phonological forms associatd with th unmarkd faturs appar in mor grammatical nvironmnts could also follow as a consqunc of Impovrishmnt Ruls. For xampl, to xplain th fact that th phonological form associatd with dual marking on vrbs in North Sámi can only appar whn th vrb has a dfinit subjct, on could hypothsiz an Impovrishmnt Rul that dlts th dual faturs on th vrb whn th vrbal subjct is indfinit (as in Vinka 2001). Sinc th markd fatur is dltd, th vrb will not hav th phonological form associatd with it. Also, sinc unmarkd faturs cannot b rfrncd by a grammatical rul, thy cannot b a targt of an Impovrishmnt Rul. In summary, th diagnostics in (1) can b associatd with th thortical proprtis spcifid in (2). (2) Markd faturs ar th only faturs that can b rfrncd by grammatical ruls: a. Unmarkd faturs cannot b targtd by Lxical Insrtion Ruls. b. Unmarkd faturs cannot triggr Impovrishmnt Ruls. c. Unmarkd faturs cannot b th targt of Impovrishmnt Ruls. Th proprtis in (2) ar not th only ons that can account for morphological markdnss. Howvr with this typ of hypothsis, a clar connction can b stablishd btwn morphological and smantic markdnss. 1.2 Smantic markdnss Smantic markdnss, lik morphological markdnss, rlats to a crtain diagnostic. Basd on th discussions in Jakobson (1971), Grnbrg (1966) and Croft (2003), th diagnostic can b statd as follows: (3) A noun with an unmarkd fatur can oftn b usd to quantify ovr mor typs of ntitis than a noun with a markd fatur. (Jakobson 1971; Grnbrg 1966; Croft 2003; Silvrstin 1986) A classic illustration of th diagnostic in (3) involvs th diffrnc btwn lion and lionss (s Bobaljik and Zocca 2010). Th word lion can b usd to rfr to and quantify ovr lions of any sx. Thus, if thr ar two mal lions and two fmal lions in th univrsity hallways, on can (truthfully) say thr ar four lions roaming th univrsity hallways. In contrast, th word lionss can only b usd to rfr to and quantify ovr fmal lions. Thus, in th sam scnario as abov, on could only (truthfully) say thr ar two lionsss roaming th univrsity hallways.

6 202 A. Bal t al. Sinc th noun lion can b usd to quantify ovr mor typs of ntitis, th diagnostic suggsts that lion is mor likly to hav th unmarkd fatur (in this cas [+masc]) whras lionss is mor likly to hav th markd fatur (in this cas [+fm]). Anothr way of stating (3) is in trms of th subst rlation. Th gnralization in (3) could b du to th dnotational natur of nouns. Th dnotation of a noun with a markd fatur might b a subst of th dnotation of th sam noun with an unmarkd fatur. This proprty is rprsntd in (4) whr mf is th markd fatur, uf th unmarkd fatur and N th noun. (4) ½½N+mFŠŠ ½½N+uFŠ This rstatmnt of th diagnostic in st-thortical trms is a littl mor rstrictiv than th original statmnt in (3). In principl, th smantic diagnostic could also b charactrizd through prsuppositions inducd at th Dtrminr Phras (DP) lvl rathr than dnotations at th Noun Phras (NP) lvl: th markd faturs triggring a prsuppositional rstriction (such as ntity bing talkd about must b fmal) and th unmarkd faturs triggring no such rstriction. In fact, this has bn suggstd for numbr marking in Saurland (2003) and Saurland t al. (2005). Howvr, to simplify th prsnt discussion, w will pursu an approach to plurality at th NP lvl with th simplifid proprty in (4). For our purposs, adopting a dnotational approach as opposd to a prsuppositional on will mak vry littl diffrnc. W will try to b carful to mntion (in footnots) placs whr th diffrncs might b rlvant. In trms of numbr marking, th diagnostic spcifid in (3) and (4) oftn yilds rsults that ar consistnt with th hypothsis that plural is unmarkd (s Croft 2003; Krifka 1989; Saurland 2003, 2008; Saurland t al. 2005; Spctor 2003, 2007). For xampl, th singular noun child can only b usd to rfr to individual childrn (compar th cohrnt sntnc That individual is a child to th incohrnt #Thos individuals ar a child). In contrast, th plural noun childrn can oftn b usd to rfr to and quantify ovr singular individuals (a.k.a., singulars) as wll as groups of individuals (a.k.a., pluralitis). Th fact that it can b usd to quantify ovr singulars is dmonstratd by th sntncs in (5). (5) a. If you hav childrn, plas rais your hand. b. Evryon who has childrn, plas rais your hand. c. Do you hav childrn? d. Evry mothr who cam to th party brought hr childrn. Givn th commands in (5a) and (5b), on would rais thir hand vn if thy only had on child. Similarly, givn th qustion in (5c), on would answr ys vn whn thy only had on child. Furthrmor, th statmnt in (5d) ntails that vn th mothrs with only on child brought that child to th party. 6 Considring this 6 Th sntnc in (5d) also implis that at last on mothr has mor than on child. For dtails on how to driv this rading, s Saurland t al. (2005) and Spctor (2007).

7 Rlationship btwn morphological and smantic markdnss 203 typ of vidnc, many smanticists includ singulars in th dnotation of plural nouns such as childrn. It should b notd that not all nouns bhav th sam way in ths syntactic contxts. For xampl, many nouns usd to rfr to man-mad objcts (so-calld artifact nouns) do not asily prmit quantification ovr singulars, nouns such as amplifirs, brooms, forks, pncils, tlvisions, umbrllas and xylophons. 7 Yt this sub-class dos not yild systmatic rsults. For xampl, th nouns books and condoms asily prmit quantification ovr individuals vn though th nouns dictionaris and diaphragms do not. Also, contxt can influnc intuitions with rspct to ths nouns. For xampl, on would hsitat to answr ys to th qustion Do you hav umbrllas on your kitchn tabl? whn thr is only on umbrlla on th tabl, but on would not hsitat to answr ys to th qustion Do you hav umbrllas in your stor right now? whn thr is only on umbrlla on th shlf. In fact, in a stor contxt, or any othr contxt involving inquiris about currnt invntory, all th artifact nouns sm to prmit quantification ovr individuals. In contrast to artifact nouns, most natural-kind nouns asily prmit quantification ovr inividuals, including animal trms (cats, dogs, lizards, mic, zbras, tc.), plant trms (bushs, flowrs, trs, tc.), gological trms (rocks, stons, crystals, tc.), and mntal stat trms (motions, idas, fars, anxitis, tc.) just to nam a fw. Howvr, vn hr, contxt mattrs. Popl ar not likly to answr ys to th qustion Do you hav rocks in your gardn? whn thy only hav on tiny rock in thir gardn, howvr thy ar likly to answr ys to th qustion Do you hav rocks sitting on your kitchn tabl? whn thy only hav on such rock on th tabl. In contrast, popl ar likly to answr ys to th qustion Do you hav bouldrs in your gardn? whn thy hav only on bouldr in thir gardn. As an anonymous rviwr suggstd, what sms to b rlvant in ths contxts is an xpctation with rgards to numbr. In contxts whr th prsnc (or ownrship) of a singular objct is normally givn or assumd, it is difficult to gt spakrs to us th plural to quantify ovr individuals. Clarly much mor work nds to b don to figur out whthr thr is a systmatic pragmatic influnc on how nouns ar usd to talk about singularitis. Howvr, w will not attmpt to charactriz this influnc in this papr. For now, w will simply obsrv that vry noun, givn th propr contxt, can b usd to quantify ovr singularitis. Futhrmor, thr ar vn som plural nouns that prmit quantification ovr singularitis in any givn contxt, namly thos that do not hav singular countrparts such as scissors, pants, shorts and cloths. Givn ths facts, it sms rasonabl to hypothsiz that th dnotations of plural nouns contain singulars vn though pragmatic factors somtims obscur this proprty. 8 7 W would lik to thank an anonymous rviwr for pointing out this partial systmaticity. 8 In th litratur on plurality, thr hav bn many attmpts to xplain why in many syntactic contxts plurals do not always allow rfrnc to or quantification ovr singulars. Much of th discussion cntrs on a comptition btwn th singular noun and th plural noun (s Krifka 1989; Saurland t al. 2005; Spctor 2007). Such a story is bolstrd by th fact that plural nouns without any singular countrpart (so-calld pluralia tantum words such as scissors) ar always abl to quantify ovr individuals (.g. thos scissors ar blu can man that papr-cutting instrumnt is blu, although thos childrn ar blu cannot man that child is blu).

8 204 A. Bal t al. Assuming this charactrization is on th right track, th formal rlationship btwn plural and singular nouns can b rprsntd as in (6). 9 (6) ½½N+SGŠŠ ½½N+PLŠ Th diagnostic tlls us that singular is smantically markd in English whras plural is unmarkd. In Sct. 2.1 and 2.2 w will xplor whthr a connction can b mad btwn th rsult of th smantic diagnostic and th rsults of th othr tsts for morphological markdnss spcifid in Sct Corrlations 2.1 Positiv corrlations It is possibl that smantic markdnss has a dirct connction to morphological markdnss. Rcall that th grammatical hypothsis that (possibly) undrlis th morphological diagnostics involvs th conjctur that unmarkd faturs cannot b rfrncd by a grammatical rul. This can b xtndd straightforwardly to smantics. Sinc smantic intrprtation ruls ar grammatical ruls, it follows that unmarkd faturs cannot affct intrprtation whras markd faturs can. Furthrmor if th grammatical faturs adjoind to nouns ar tratd as modifying rstrictors (much lik adjctivs), thn thr would b a positiv corrlation btwn th smantic diagnostic spcifid in Sct. 1.2 and th morphological ons spcifid in Sct All diagnostics would b ways of accssing information about th sam undrlying grammatical proprty. For th sak of clarity, w provid som xampls blow of what this positiv corrlation would look lik. Two ways that a noun could b affctd by a fatur on a morphm ar rprsntd schmatically in (7). ð7þ In (7a), a noun is combind with a markd fatur, mf. Lik th noun itslf, this fatur is assignd a dnotation by th smantic intrprtation function. Th intrprtation of th markd fatur is thn intrsctd with th intrprtation of th noun, which yilds th dnotation for th ntir noun phras. As a rsult of 9 Altrnativly, on th prsuppositional account, w could charactriz th situation by assuming that singular faturs induc a prsupposition on th DP whras plural faturs do not. In fact, this is xactly how Saurland (2003) charactrizs th diffrncs btwn th plural and singular.

9 Rlationship btwn morphological and smantic markdnss 205 intrsctiv modification, th dnotation of th noun combind with th markd fatur will always b a subst of th dnotation of th noun bfor it combins with th markd fatur. In contrast to (7a), (7b) rprsnts th combination of a noun with an unmarkd fatur, uf. Sinc th unmarkd fatur cannot b rfrncd by grammatical ruls, th intrprtation function dos not assign it a dnotation. Givn th intrprtation rul in (8), th unmarkd fatur would not hav any ffct on th noun phras. (8) If a phras ZP immdiatly dominats nods X and Y whr X is assignd an intrprtation and Y is not assignd an intrprtation (or has bn markd for dltion), thn ½½ZPŠ = ½½XŠ. An intrprtation rul lik th on in (8) is commonly assumd for dltion rlatd to agrmnt and for many typs of prpositions. With this typ of intrprtation rul, th intrprtation of th noun combind with th unmarkd fatur is quivalnt to th intrprtation of th noun bfor it combins with th unmarkd fatur. Thus, it follows from both (7a) and (7b) that th intrprtation of a noun with a markd fatur is a subst of th intrprtation of th sam noun with an unmarkd fatur. 10 To put this in mor concrt trms, lt s considr th xampl givn in Sct. 1.2 of lion vrsus lionss. Lt s suppos that th intrprtation of th root noun p lion is simply th st of all lions in a givn contxt (mals and fmals). For th sak of th xampl, w assum that this st is fa; b; c; d; ; f g. Furthrmor, lt s suppos that th intrprtation of th markd fatur +fm, associatd with th morphm -ss, is simply th st of all fmal individuals in a givn contxt. For th sak of th xampl, w assum that this st is fa; b; c; g; h; ig. By hypothsis, th unmarkd fatur, +masc, is not assignd an intrprtation. Givn ths assumptions, th intrprtation of lionss and lion is rprsntd in (9). (9) ½½lion-ss Š ¼ ½½lion (+masc) Š ¼ ½½ p lionš \ ½½+fmŠ ¼ ½½ p lionš ¼ fa; b; cg fa; b; c; d; ; f g Th intrprtation of th noun with th markd fatur nds up bing a subst of th intrprtation of th noun with th unmarkd fatur Undr a prsuppositional account of smantic markdnss, a similar corrlation could xist btwn smantic and morphological markdnss. Rcall that in th prsuppositional account, morphological faturs combin with th DP and ithr hav no ffct (if thy ar smantically unmarkd) or thy induc prsuppositional rstrictions (if thy ar smantically markd). To stablish a corrlation with morphological markdnss, on could assum that th markd faturs ar intrprtd and, whn intrprtd, thy induc crtain prsuppositions. In contrast, on could assum that th unmarkd faturs ar not intrprtd and hnc hav no prsuppositional ffct. As a rsult, us of DPs with th morphologically and smantically markd faturs would b mor rstrictd than us of DPs with th unmarkd faturs. Th prsuppositional corrlation is basically isomorphic to th account in (7) whr markd faturs ar intrprtd as rstricting th noun s dnotation. 11 S Prcus (2010), for a mor indpth discussion of rstriction and gndr faturs.

10 206 A. Bal t al. It is possibl that th intrprtation of numbr faturs on nouns parallls th xampl givn in (9). For xampl, lt s suppos that th intrprtation of th root noun p child is th st of all individual childrn in a givn contxt combind with th st of all possibl groups consisting only of thos individual childrn. For th sak of argumnt, w assum that this st is fa; b; c; ab; ac; bc; abcg, whr a, b and c ar th individual childrn and ab, ac, bc and abc ar all th possibl groups. Furthrmor, lt s suppos that th intrprtation of th singular fatur, SG, is th st of all individuals in a givn contxt. For argumnt s sak, w assum this st is fa; b; c; d; ; f ; gg. Aswith+masc, th (smantically) unmarkd fatur PL is not assignd an intrprtation and hnc th intrprtation of childrn is quivalnt to th intrprtation of p child. (Rcall, th vidnc prsntd in Sct. 1.2 ld to th conclusion that PL was smantically unmarkd in English.) Givn ths assumptions, th intrprtation of singular and plural nouns can b rprsntd as in (10). (10) ½½child (SG)ŠŠ ¼ ½½child-rn (PL) Š ¼ ½½ p childš \ ½½SGŠ ¼ ½½ p childšš ¼ fa; b; cg fa; b; c; ab; ac; bc; abcg Th dnotation of th singular is a subst of th dnotation of th plural. W hav shown that smantic markdnss can b undrstood in a similar vin as morphological markdnss: th markdnss diagnostics, irrspctiv of whthr thy talk about rfrnc or morphological form, tll us which faturs can b rfrncd by a grammatical rul and which cannot. Th grat hop is that all th diagnostics yild consistnt rsults. If th smantic diagnostic tlls us that plural is unmarkd thn th morphological diagnostics should too. 2.2 Ngativ corrlations Although it is possibl that th smantic and morphological diagnostics for markdnss ar consistnt, such a consistncy is actually unxpctd whn on considrs th dtails of numbr marking. As discussd in Sct. 2.1, a positiv corrlation btwn th two typs of diagnostics is prdictd only if th following two conditions hold: (1) an unmarkd morphm cannot affct th intrprtation of a noun (sinc such faturs cannot b rfrncd by any grammatical rul) and (2) a noun phras is intrprtd as th intrsction of th intrprtation of th root noun and th intrprtation of th faturs adjoind to that root. Th ida that morphological faturs rstrict th dnotation of a root noun (similar to adjctivs) might b likly for somthing lik gndr faturs, howvr numbr faturs ar slightly diffrnt. Th standard viw in th smantic litratur is that plural faturs ar associatd with a function that taks a st of singular individuals (a singular dnotation) and crats a st of pluralitis basd on th individuals in th original st. (For argumnts against this standard viw, s Bal 2009; Krifka 1989; and Saurland 2003.) 12 This typ of 12 Bal (2009) rviws som problms for th standard viw involving plural morphology on masur nouns. Krifka (1989) discusss similar typs of issus with a focus on th us of plurals with numbrs that ar lss than on. Saurland (2003) outlins a sparat st of problms concrning rlational nouns, cumulativity and th syntactic position of th plural morphms.

11 Rlationship btwn morphological and smantic markdnss 207 intrprtation was promotd by Link (1983) who dmonstratd how such an intrprtation could hlp account for distributiv intrprtations of an NP subjct as wll as crtain prsuppositions introducd by dfinit dtrminrs. If on wr to adopt somthing lik Link s intrprtation for th plural morphm, thn on would no longr xpct a positiv corrlation btwn th two diagnostics. In fact, what would b xpctd is a ngativ corrlation. To spll out this ngativ corrlation, lt s considr som of th dtails of a Link-styl intrprtation. In Link (1983), a join or sum oprator was introducd that took two individuals and joind thm togthr to form a group. Although h usd th symbol for this oprator, w will stick to th convntion of using th rgular join symbol _. Also, as in Sct. 2.1, w will us singl lttrs to rprsnt individuals and a sris of lttrs to rprsnt groups. Thus if a and b ar individuals, thn a _ b ¼ ab. Furthrmor, this join oprator can combin two groups to form an vn largr group. For xampl, if ab and cd ar two groups, thn ab _ cd ¼ abcd. With this join oprator, on can dfin a closur opration on sts as in (11). (11) Dfinition of th group-closur function W : W is function from a st X to a st Y such that Y is th smallst st satisfying th following proprtis: 13 a. X Y b. If x; y ar mmbrs of Y, thn x _ y is a mmbr of Y. Th oprator W can tak a st of singular individuals as an argumnt and thn yild a st that contains all thos individuals and also any possibl group that can b formd from thos individuals. Altrnativly statd, th rsult of applying W to a st is an augmntd st that includs all th groups that can b formd from th individuals W in th original st. For xampl, givn W a st fa; b; cg, th application of to that st would b fa; b; c; ab; ac; bc; abcg: fa; b; cg ¼ fa; b; c; ab; ac; bc; abcg. Instad of intrprting th singular fatur SG as a rstriction of th root noun as in Sct. 2.1, on could intrprt th plural fatur PL as this augmnting function. 14 (12) ½½PLŠ ¼ W Furthrmor, th root noun could simply b intrprtd as a st of singular individuals. For xampl, th intrprtation of p child could simply b th st of all individuals who ar childrn. Thr would b no groups in th dnotation Link (1983) rprsntd this opration with th symbol, hnc somtims it is calld th staroprator. 14 This intrprtation is slightly diffrnt from Link (1983). Link did not allow for singulars to appar in th plural dnotation. Thus th plural fatur was actually intrprtd as th function kp W P P: 15 Not, unlik th cas with th positiv corrlation, it is difficult to draw a paralllism btwn th stthortical account of plural as an augmnting function on th NP and som kind of prsuppositional account that would apply to th DP. In othr words, it is not at all clar if a ngativ corrlation could b stablishd through a prsuppositional account lik in Saurland (2003) and Saurland t al. (2005).

12 208 A. Bal t al. Givn ths assumptions, lt s rconsidr what our prdictions would b for th smantic diagnostics prsntd in Sct As discussd in Sct. 1.1, th morphological diagnostics suggst that morphologically unmarkd faturs cannot b rfrncd by grammatical ruls. As mntiond bfor, this xtnds straight-forwardly to th smantic domain whr it was suggstd that unmarkd faturs cannot affct th intrprtation of a noun. With th possibility that faturs can b intrprtd as augmnting functions, it follows that a noun can b affctd by a markd fatur by having its dnotation xpandd. For xampl, th plural fatur can xpand th dnotation of th root noun as shown in (13). ð13þ As a consqunc, th intrprtation of th root noun will always b a subst of th intrprtation of th NP. In contrast to th plural fatur, th singular fatur would not affct th intrprtation of th root noun as shown in (14). ð14þ Lt s considr th intrprtation of th nouns childð p child þ SGÞ and childrn ð p child þ PLÞ in this typ of systm. For th sak of th xampl, w assum that ½ p childšš is th st fa; b; cg. ð15þ Clarly th dnotation of th singular noun child is a subst of th dnotation of childrn vn though it is th plural fatur that is rfrncd by th intrprtation rul. Hnc, prhaps th diagnostic in Sct. 1.2 has th wrong charactrization. At last whn it coms to numbr marking, it is possibl that th noun with th

13 Rlationship btwn morphological and smantic markdnss 209 markd fatur will b abl to quantify ovr mor typs of individuals (both singulars and pluralitis) than th noun with th unmarkd fatur. What is xpctd thn, at last with numbr marking, is that th smantic diagnostic and th morphological diagnostics should yild systmatically opposit rsults. 3 Empirical landscap Th grat hop for th thory of markdnss is that th smantic and morphological diagnostics yild consistnt rsults and thus support a positiv corrlation. Th lssr hop is that th smantic and morphological diagnostics ar in systmatic disagrmnt and thus support a ngativ corrlation. In this sction, w rviw numbr marking in Wstrn Armnian and English in som dtail. W thn conclud this sction with som commnts on univrsal trnds. 3.1 Wstrn Armnian Wstrn Armnian is slightly diffrnt from English in that th smantic diagnostic dos not support th hypothsis that plural is unmarkd. In Wstrn Armnian, plural is associatd with th morphm -r (or -nr dpnding on th syllabl structur of th stm). Singular is usually associatd with null marking. For xampl, th singular form of th noun Ð nk (building) appars in (16a) whras th plural form appars in (16b). Ð (16) a. nk- dsar} building-(df) saw (2,sg) You saw th building b. jrgu Ð nk-r- dsar two building-(df, pl) saw (2,sg) You saw th two buildings As shown in (16), thr is a clar singular and plural distinction in Wstrn Armnian. Unlik in English, whn a plural noun appars in an if-claus, in a ys-no qustion, or in th rstrictor of a univrsal quantifir, th noun is not abl to quantify ovr singular individuals. For xampl, considr th sntncs in (17). (17) a. b zdig-nr unis? child-(indf,pl) hav (2,sg) Do you hav (two or mor) childrn? b. jt b zdig-nr unis, dun k na. if child-(indf,pl) hav (2,sg), hom go (2, sg) If you hav (two or mor) childrn, thn go hom! c. amn mart vor b zdig-nr unr vodk-i gajn-tsav All prson that child-(indf,pl) had foot-(gn/dat) stand-up Evryon who had (two or mor) childrn stood up

14 210 A. Bal t al. Givn a contxt whr it is clarly rlvant whthr a prson has on or mor childrn vrsus no childrn and whr it is not rlvant whthr a prson has on child vrsus mor than on, Armnian spakrs find th qustion in (17a) awkward. In fact thy oftn suggst that on should us th singular form of th noun instad. Howvr, whn told that (17a) is th intndd qustion, spakrs will answr no if thy only hav on child but ys if thy hav mor than on. Also, givn th rqust in (17b), spakrs judg that in ordr to oby th command on nd not go hom if thy hav only on child. Similarly, th sntnc in (17c) is tru in a contxt whr th only ons who stood up wr popl who had two or mor childrn. Clarly, in ths typs of contxts, th plural noun dos not prmit quantification ovr individuals. Yt, if a plural noun can quantify ovr singular individuals at all, it would b prcisly ths nvironmnts (downward ntailing nvironmnts) that should allow for such quantification (s Krifka 1989; Saurland 2003, 2008; Saurland t al. 2005; Spctor 2003, 2007 for a discussion). Not that th Armnian spakrs w consultd, who wr all bilingual, had no difficulty intrprting plural nouns in Frnch and/or English as if thy quantifid ovr singular individual. Th bhaviour of th plurals in ths typs of contxt is spcific to Armnian. This vidnc suggsts that plural is not th smantically unmarkd form in Wstrn Armnian. 16 Although this conclusion is inconsistnt with th hypothsis that th plural form is smantically unmarkd univrsally, it is consistnt with th ida that th smantic diagnostic and th morphological diagnostics yild similar rsults within th sam languag. Th only morphological diagnostic that applis in Wstrn Armnian is th on involving null marking. As is clar from th data in (16) and (17), th plural fatur is associatd with phonological contnt whras th singular fatur is not, suggsting that singular is morphologically unmarkd whras plural is markd. Thus, th vidnc is consitnt with th plural fatur bing markd both smantically and morphologically. 3.2 English In English, vidnc from rgular prsnt tns agrmnt and from past tns agrmnt for th auxiliary to b could b rronously intrprtd as supporting an analysis involving a morphologically markd, singular fatur. For xampl, considr th paradigms in (18) along with th potntial vocabulary insrtion ruls for th agrmnt morphm and th auxiliary givn in (19). (18) To Run (prsnt tns) To B (past tns) SG PL SG PL 1 r n r n w z w r 2 r n r n w r w r 3 r nz r n w z w r v v v v v v v v 16 On downward ntailing contxt is lft out of this diagnostics and this involvs ngation. This has bn lft out for th sak of simplicity. Th rsults from ngation ar not at all clar and might vn spak in favour of th plural bing unmarkd. Howvr thr ar svral complications that must b controlld for. For a mor xtnsiv discussion of ngation in Wstrn Armnian s Bal and Khanjian (2009).

15 Rlationship btwn morphological and smantic markdnss 211 (19) Insrtion Ruls: a. /z/, [AGR, -participant, -spakr, prs, SG] b. ø, [AGR, prs]. /w z/, [ p b, -participant, past, SG] /w r/, [ p b, past] v In (18), th numbrs in th lft hand column rprsnt prson agrmnt, whras SG and PL in th scond row rprsnt numbr agrmnt. On th surfac, th singular forms rprsnt xcptions (3rd singular [z] and 1st/3rd singular [w z]) to a mor gnral dfault form (-ø and [w r]). Th ruls in (19) is on way that ths surfac forms could b drivd through Vocabulary Insrtion Ruls. Such ruls crucially involv th fatur SG. Howvr, as is oftn th cas with syncrtism in a singl paradigm, thr ar othr ways to intrprt th English data. Notic that in both paradigms in (18) th plural clls always shar th sam phonological ralization. As suggstd by Harly (2008) and Bobaljik (2001), such syncrtism within and across paradigms can b xplaind by Impovrishmnt Ruls that dlt morphological faturs bfor th Vocabulary Insrtion applis. For ths paradigms, th oprativ Impovrishmnt Rul would dlt all prson faturs in th nvironmnt of th plural fatur PL. Hnc, th following Impovrishmnt Rul and Vocabulary Insrtion Ruls would account for th paradigms in (18). (20) Impovrishmnt Rul: In vrbal (agrmnt) hads, prson faturs ar dltd in th nvironmnt of PL. (21) Insrtion Ruls: a. /z/, [AGR, -participant, -spakr, prs] b. ø, [AGR, prs]. /w z/, [ p b, -participant, past] /w r/, [ p b, past] v Th plural clls in th two paradigms ar all ralizd as th dfault form du to th fact that all prson faturs hav bn dltd bfor vocabulary insrtion: th rlvant dltd faturs bing th [-participant] fatur (not a participant in th convrsation) and th [-spakr] fatur (not th spakr in th convrsation). 17 Not, th only numbr fatur rfrncd in th morphological ruls in (21) is th PL fatur that triggrs th impovrishmnt. As thoroughly argud by Harly (2008) for English pronouns and in Bobaljik (2001) for Russian cas marking, th Impovrishmnt Rul in (21) has an advantag that th insrtion ruls in (19) do not. Although th insrtion ruls can account for within paradigm syncrtism, thy cannot xplain why othr paradigms would dmonstrat th sam kind of syncrtism vn though thy hav diffrnt dfault v 17 Things ar actually mor complicatd in English, spcially if third prson is morphologically unmarkd. S Nvins (2007a, 2007b) and Harly (2008) for a discussion. Sinc w ar concntrating on numbr in this papr, w will forgo a discussion of ths potntial complications.

16 212 A. Bal t al. phonological ralizations. Th Impovrishmnt Rul in (21) on th othr hand, prdicts that syncrtism of th plural forms should occur in paradigm aftr paradigm. Th dltion rul rmovs any potntial prson distinctions. In English, this is an mpirically wll-attstd fact. Th prson distinctions among othr auxiliaris also syncrtiz in th plural form, as shown in (22). (22) To Hav (prsnt tns) To B (prsnt tns) SG PL SG PL 1 hæv hæv æm ar 2 hæv hæv ar ar 3 hæz hæv Iz ar In fact, English nvr maks a prson distinction in any of its plural agrmnt forms dspit oftn having such distinctions in th singular. This cross-paradigm fact or mta-syncrtism can only b xplaind by th analysis with Impovrishmnt Ruls: an analysis that crucially involvs a morphologically markd plural fatur. In summary, dspit surfac apparancs, th vrbal paradigms in English support th hypothsis that plural faturs ar morphologically markd. Such vidnc is consistnt with othr diagnostics. For xampl, th singular is not associatd with any phonological contnt whras th plural is, namly /z/, suggsting that singular is morphologically unmarkd whras th plural is markd (although s Borr 2005, for argumnts to th contrary). Furthrmor, as discussd in Sct. 1.1, th plural pronouns in English, in contrast to singular pronouns, nvr dmonstrat any distinction in gndr, onc again suggsting that plural could b triggring Impovrishmnt Ruls. In contrast to th morphological vidnc, th smantic diagnostics for English, discussd in Sct. 1.2, clarly rval that th plural form is smantically unmarkd. Hnc, in English w hav a potntial contradiction btwn th smantic and morphological diagnostics. 3.3 Gnral trnds As is wll known, crosslinguistically most languags pattrn just lik English with rspct to morphological markdnss, xcpt prhaps without th surfac complications. As dscribd in Grnbrg s Univrsal 35 (Grnbrg 1963), thr ar many languags whr th singular fatur is not associatd with any ovrt phonological contnt but whr th plural is, but fw whr th opposit is tru. Such a pattrn supports th hypothsis that plural faturs ar oftn morphologically markd. Also, as discussd in Croft (2003), thr ar many languags whr th plural mmbrs of a paradigm syncrtiz in contrast to th singular mmbrs, but fw with th opposit pattrn. This kind of vidnc oftn supports th xistnc of mta-syncrtisms and thus suggsts that plural faturs triggr Impovrishmnt Ruls and hnc ar morphologically markd. In contrast to th morphological diagnostics, th smantic diagnostic oftn yilds th opposit rsult. In many languags (Frnch, Grman, Italian, Spanish, tc.), whn plural nouns appar in downward ntailing contxts (mbddd in qustions,

17 Rlationship btwn morphological and smantic markdnss 213 in th antcdnt of conditionals or in th rstriction of univrsal quantifirs) thy prmit quantification ovr individuals as wll as pluralitis (s, Saurland t al. 2005, for a discussion of ths facts and othrs). Just lik in English, thr ar usually complx intractions with pragmatic factors, but th trnd is th sam. W hsitat to labl this trnd a univrsal sinc so fw languags and languag familis (rlativly spaking) hav bn adquatly invstigatd using propr downward ntailing contxts. Also, at last on languag, Wstrn Armnian, sms to buck this trnd. Still, vidnc points in th dirction of a systmatic mismatch btwn th morphological and smantic diagnostics. Ovrall, th plural faturs sm to b morphologically markd but smantically unmarkd. 4 Problms for a ngativ corrlation Th lssr hop in stablishing a connction btwn th morphological diagnostics and th smantic on is that th inconsistncis btwn thm ar systmatic. As pointd out in Sct. 2.2, if numbr faturs can b intrprtd as augmnting functions and if thr is a rlationship btwn bing morphologically markd and bing rfrncd by grammatical ruls, thn on would xpct that languag aftr languag would hav th dnotation of a noun with th morphologically unmarkd numbr fatur bing a subst of th dnotation of th sam noun with th morphologically markd numbr fatur. As mntiond in Sct. 3.3, prliminary vidnc suggsts that many languags pattrn in this way. This connction btwn th smantic and morphological diagnostics is promising. Howvr, thr ar som problms. Rcntly, th ida that th plural fatur can b intrprtd as an augmnting function has com undr som scrutiny. For xampl, Bal (2009) mntions thr problms for this typ of intrprtation (Saurland 2003, also discusss problms for an augmnting function). In this sction, w will rviw on of ths problms and discuss a potntial solution. Our goal hr is to outlin a program of rsarch rathr than to offr complt solutions to th problms concrning th intrprtation of th plural fatur. In fact, this sction should rad mor lik a warning: If on thinks it is mpirically justifid to maintain a connction btwn th smantic diagnostic and th morphological diagnostics, thn thr is som thortical work to b don and som hard problms to solv. On problm that nds to b solvd cntrs around th us of th singular noun phras pound of potato and th plural noun phras pounds of potato. 18 As dmonstratd in Bal (2009), th way ths phrass ar usd is inconsistnt with th ida that th plural fatur is intrprtd as a Link-styl augmnting function. To undrstand th problm, lt s brifly st up a contxt in which to valuat ths typs of phrass. Considr a situation whr thr is a two-pound lump of mashd 18 In this sction, w will focus on masur phrass. Howvr, as mntiond by a rviwr, similar problms might xist for nouns that rfr to scattrd or dcomposabl objcts such as mals and manikins.

18 214 A. Bal t al. d c a b Fig. 1 A graphical rprsntation of th two pound lump of mashd potatos sitting on th tabl. Th vrtical strip in th cntr rprsnts th spilt food dy. Th brackts rprsnt th diffrnt placs pointd to in th ordr indicatd by th alphabtical ordr potatos sitting on a tabl. Suppos that whil cooking, food dy is spilt on th potatos putting a strip down th cntr of th lump (s Fig. 1). In this situation, dmonstrativs and fingr-pointing can b usd to talk about crtain portions of th lump. For xampl, on could point to th lft half of th lump and truthfully uttr th sntnc in (23a). On could also point to th right half and truthfully uttr th sntnc in (23b). Furthrmor, on could point to th top half and truthfully uttr th sntnc in (23c) and to th bottom half and truthfully uttr th sntnc in (23d). Finally, on could point to th cntr strip of th lump and truthfully uttr th sntnc in (23). (23) a. This pound of potato is partially rd. (lft-half, a) b. That pound of potato is also partially rd. (right-half, b) c. This othr pound of potato is partially rd. (top-half, c) d. That othr pound of potato is partially rd. (bottom-half, d). Howvr, this pound of potato is compltly rd. (cntr, ) For convninc, w hav labld th diffrnt pounds of potato with th lttrs a through. Th lttrs ar mant to indicat whr on is pointing whn uttring th sntncs in (23). Th fact that all fiv sntncs ar possibl in this situation has som consquncs for th dnotation of th phras pound of potato. It suggsts that a, b, c, d and ar all mmbrs of th singular dnotation. In othr words, th st fa; b; c; d; g is a subst of th dnotation of pound of potato. A problm ariss for a Link-styl plural function whn on considrs how it would combin with pound of potato. 19 If a, b, c, d and ar all mmbrs of th 19 For simplicity w trat pound of potato as th phras to which th plural combins. This is du to th fact that it is asir to rprsnt th dnotation of this phras on papr. Howvr this tratmnt of th plural morphm is not ncssary to mak our point. Th sam problms aris vn if th plural morphm applis only to th phras pound, th argumnt of potato somhow combining with th noun at som latr point.

19 Rlationship btwn morphological and smantic markdnss 215 singular dnotation, thn a Link-styl plural function will form lots of diffrnt groups. Spcifically, sinc a and b ar mmbrs of th singular dnotation, th group ab must b a mmbr of th plural dnotation. Sinc c and d ar mmbrs of th singular dnotation, th group cd must also b a mmbr of th plural dnotation. Furthrmor, sinc a, b and ar mmbrs of th singular dnotation, th group ab must b a mmbr of th plural dnotation. Ths groups, cratd as a consqunc of th augmnting function, lad to som intrsting and wrong mpirical prdictions. For xampl, if th numral modifirs two and thr simply rstrict th dnotation to groups that hav two mmbrs and thr mmbrs rspctivly (as is commonly assumd), thn th dnotation of two pounds of potato should contain th groups ab and cd (s (24b)) whil th dnotation of thr pounds of potato should contain th group ab (s (24c)). (24) a. ½pounds of potatoš ¼ f...; ab; cd...; ab...g b. ½two pounds of potatošš ¼ f...; ab; cd...g c. ½thr pounds of potatošš ¼ f...; ab...g Th problm with ths dnotations is that thy prdict that it would b possibl to point at th two pound lump of potato on th tabl and talk about it as thr pounds of potato. Thr is a group, namly ab, that has thr individual pounds in it. Hnc, th sntnc in (25a) is prdictd to b cohrnt in th contxt spcifid abov. Th dnotations in (24) also prdict that th phras th two pounds of potato could not b usd to rfr to th two pound lump of potato on th tabl. For xampl, th sntnc in (25b) should b unaccptabl. Th dfinit dtrminr rquirs thr to b a uniqu two pound group. Howvr, as shown in (24b) thr is no uniqu two pound group. (25) a. At last thr pounds of potato ar on th tabl./i put at last thr pounds of potato on th countr. 20 b. I pourd rd dy on th two pounds of potato. Both of ths prdictions ar incorrct. Th sntnc in (25a) is quit odd in a contxt whr thr is a two-pound lump of potato on th tabl, yt th sntnc in (25b) is prfctly accptabl. This problm can b solvd if on intrprts root nouns as bing inhrntly plural whil also intrprting th singular fatur (SG) as a rstrictor on th root noun (rstricting th noun to singularitis, s Bal 2009, for dtails). Howvr, such a solution rlis on allowing th singular fatur to influnc th intrprtation of th 20 Thr is an abstract concpt of pound that is not problmatic and can appar in sntncs lik Just fiv minuts ago I pointd to fiv diffrnt pounds of potato. Hr, th prdicat applis to ach possibl pound sparatly vn if th pounds ovrlap matrially. This rading is not problmatic for th joinclosur opration. Th problmatic rading only occurs whn on rfrs to a masurmnt of an aggrgat of matrial as in (25a) and (25b). A rviwr suggstd that such radings might b blockd whn th NP appars within th VP as in thr ar at last thr pounds of potato on th tabl. Spakrs that w talkd to did not agr with th rviwr s intuitions. Clarly mor rsarch nds to b don.

20 216 A. Bal t al. noun phras: somthing which should b avoidd if on wants to try to maintain a connction btwn smantic and morphological markdnss. An altrnativ solution involvs two parts: (1) a slight modification of th singular dnotation of pound of potato and (2) a mor intricat way of masuring groups. On of th implicit assumptions spcifid abov is that th dnotation of th singular noun phras pound of potato consists of atoms, ach atom bing on pound of potato. Atoms in th dnotations of singular nouns ar traditionally tratd as having no intrnal structur. Howvr, this assumption nd not hold. It is possibl that th singular dnotation of pound of potato is simply th st of all th aggrgats of potato matrial that wigh on pound. Furthrmor, th fact that this matrial is divisibl (that th pound of potato can b dividd into two clumps of potato, ach wighing lss than a pound) and th fact that som pounds shar matrial could all b rprsntd in th dnotation of th singular noun phras. To s how this could b don, lt s rconsidr th diagram of th two pound lump rprsntd in Fig. 1 with th divisions rprsntd in Fig. 2. In Fig. 2, w hav labld ths divisions with th lttrs m through t. With ths divisions, on can rprsnt th pound a as th group of aggrgats mnqr (a ¼ mnqr). Similarly, on can rprsnt th pound b as opst (b ¼ opst), c as mnop (c ¼ mnop), d as qrst (d ¼ qrst), and as nors ( ¼ nors). (Not, w ar no longr following th convntion that a group or complx aggrgat is always rprsntd by a sris of lttrs. W allow for th lttrs mnqr and a to b usd intrchangably. Both rprsnt th sam aggrgat.) With this kind of rprsntation of th intrnal structur of th pounds, som of our problms spcifid abov bgin to disappar. Rcall that on of th problms was that th augmnting function formd th group ab. Howvr, now th group ab is simply th join of mnqr and opst and nors : ab ¼ mnqr _ opst _ nors. Yt, th join of mnqr and opst and nors is quivalnt to th join of a and b : mnqr_ opst _ nors ¼ mnopqrst ¼ mnqr _ opst. Hnc, ab is quivalnt to ab. In othr words, in a contxt whr thr is only a two pound lump of potato, th join oprator is not crating groups that ar largr than groups formd by joining two individual pounds. Anothr problm spcifid abov was that thr wr at last two groups with two pounds in thm, namly ab and cd. Howvr, th group ab is simply th group m n o p q r s t d c a b Fig. 2 Two pound lump of potato with labld sctions