Keywords

Below we classify examples of quantificational expressions. To the extent possible provide semantically comparable expressions in the language (L) you’re presenting. If L has many translations of a given expression, identify these differences (both syntactic and semantic) if you can.

We take the basic semantic type of quantifiers to be a relation between two properties – extensionally, two sets, and we say they have type (1,1). No barber shaves himself relates the set of barbers and the set of people who shave themselves. NO says their intersection is empty. Ann always takes the bus to work expresses the ALWAYS relation between the set of events in which Ann goes to work and the set in which she is riding a bus – the former is a subset of the latter. Our classification is semantic – logically equivalent expressions are typically not syntactically isomorphic: some students in Malagasy translates as ny mpianatra sasantsasany (lit: the student some-some). (See Baker (1995), Lee (2008), Matthewson (2001) for extensive discussion.)

We distinguish (Partee 1995) D-quantifiers and A-quantifiers. The former build expressions which are (or bind) arguments of predicates. A-quantifiers directly build predicates – verbal affixes, pre-verbs, auxiliary verbs, or predicate modifiers (adverbs, PPs). They are mathematically less well understood and morpho-syntactically and semantically more variable than D-quantifiers.

I Core Quantifiers: Three Basic Semantic Classes

Exhibit from your L D- and A-Quantifiers in each class below if possible (Jelinek 1995 and Vieira 1995 claim that Straits Salish and Asurini Do Trocara (Tupi-Guarani) lack D-quantifiers. No one claims that any languages lack A-quantifiers). We begin with count quantifiers.

1.1 Generalized Existential (Intersective) Quantifiers

Here, for Q a quantifier and A,B sets, Q(A)(B) is determined by A∩B, the set of As that are Bs. So NO is existential as NO(A)(B) = true iff (if and only if) A∩B is empty regardless of which As are not Bs and which Bs are not As.

1.1.1 D-Quantifiers

D-Quantifiers in English include: a/an, some, several, no, zero, one, two, …, many, few, a few, a couple, a dozen, which?, how many?, finitely many. Cardinal quantifiers are the most productive subclass. Here QAB just depends on |A∩B|, the number of As that are Bs.

(1)

a. I saw a / one picture of Churchill above the fireplace

 

b. Some / Two sailors are singing in the street

Interrogative How many? is cardinal, but Which? is merely intersective. Which As are Bs? requires identifying the members of A∩B, not just their number.

(2)

a. How many students passed the exam?

 

b. Which students passed the exam?

Semantically more difficult are value judgment Qs: many, few and enough. Sometimes they refer to a cardinality (not a proportion) comparing it to an expected value (Moltmann 1996).

(3)

a. Many students attended the lecture, few understood it

 

b. Enough members attended to constitute a quorum

1.1.2 A-Quantifiers

A-Quantifiers include: once, twice, sometimes, three times, occasionally, often, frequently, rarely, seldom, never, a lot. (4c) from Passamaquoddy (Algonkian) illustrates a cardinality preverb. (4d) shows an A-quantifier within verbal morphology (Kalaallisut; Eskimo-Aleut).

(4)

a. John failed the exam twice before passing it the third time

 

b. He often / occasionally / never visits museums on weekends

 

c. Kehsi=koti+pson-uk

sikiliyem-ok

Passamaquoddy

 

X.many-Fut-catch-1Conj

cricket-3proximate plural

 
 

I’m going to catch a lot of crickets

(Bruening 2008:97)

 

d. …Skakki+r+llattaar+tar+pu+gut (Skakkirlattaartarugut) Kalaallisut

 

…chess+do+sometimes+habit+IND.IV+1pl

 
 

…Sometimes we play chess.

(Bittner and Trondhjem 2008:42)

1.2 Generalized Universal (Co-intersective) Quantifiers

Here QAB depends on the property A – B, the set of As that are not Bs.

1.2.1 D-Quantifiers

D-Quantifiers in English include all, every, and each. Note: All As are Bs is true iff A is a subset of B, which is equivalent to A – B is empty. In addition any sometimes has a universal interpretation, as do the -ever pronominals:

(5)

a. Every / Each child won a prize

 

b. Any linguist can answer that question

 

(≈ Every linguist can answer that question)

 

c. Whoever finishes the exam gets a prize

 

(≈ Each person who finishes …)

1.2.2 A-Quantifiers

A-Quantifiers Simplex ones are always and, perhaps, whenever. Here are a few cases from languages where A-quantification is a prominent or the only type (6c,d,e).

(6)

a. John always takes the bus to school

 
 

b. John sings whenever he is in the shower

 
 

c. yas = sən ʹəwʹ čey

Straits Salish

 

always = 1.s.nom link work

(Jelinek 1995:515)

 

I always work

 

d. məkʹw = Ø ʹəwʹ pʹəq tsə spʹeqəŋ

Straits Salish

 

all = 3abs link white Det sprout

(Jelinek 1995:514)

 

They are all/completely white, the flowers

 

e. aoseoho sekwehe i-tow-i ŋoa

Asurini do Trocara

 

all evidential 3agt-lay.down-obl men

(Tupi-Guarani)

 

All men lay down

(Vieira 1995:706)

 

f. Pesq skitap nokka=psehl-n kiwhosu

Passamaquoddy

 

one man (3)-all=skin-3Subj.ObvP muskrat.ObvP

(Bruening

 

One man skinned all the muskrats

2008:99)

 

g. barri-djarrk-dulubom gunj

Mayali (Australian)

 

3plPast-all-shoot.past.perf kangaroo

(Evans 1995:209)

 

They all shot the kangaroo

 
 

h. Gunj barri-bebbe-yame-ng

Mayali

 

kangaroo 3aP-dist-spear-Past.Perf

(Evans 1995:221)

 

They each speared a kangaroo

 

1.3 Proportional Quantification

QAB depends on the proportion of As that are Bs: |A∩B|/|A|.

1.3.1 D-Quantifiers

Simplex ones include most, half, and some uses of many / few. Often most translates as a / the majority of, which is syntactically complex.

(7)

a. Most students read the Times

 

b. Half the students got an A in the course

 

c. Many Nobel Prize winners have been Scandinavian (Westerståhl)

1.3.2 A-Quantifiers

A-Quantifiers usually, mostly, often, always, frequently, rarely. It is often not easy to decide when these adverbs pick out a number or a proportion.

(8)

a. Sue usually / occasionally takes the bus to work

(de Swart 1996)

 

b. John often fills out his own income tax forms

 

1.4 Morpho-Syntactically Complex Quantifiers

Work in generative grammar often treats quantifier as a functional category, implying that its members are not productively formed. But work on English (Keenan 1996), Malagasy (Keenan 2008) and Finnish (Suihkonen 2007) suggests that this is not the case. Many of the articles in Matthewson (2008) exhibit richer quantifier inventories than in earlier work in generative grammar. Primary means of forming complex quantifiers are (1) Modification (more than ten, almost all) and (2) Boolean Compounding (and, or, neither…nor…, and not) (3) Exception Phrases (all but ten students) and (4) Bounding Phrases (He exercised twice a day, six days a week for one year). Proportional Qs and partitive constructions (some / all / most of the students) are typically complex.

1.4.1 Complex D-Quantifiers

1.4.1.1 Cardinal Quantifiers

Most productive here are modified cardinal Qs, (9). In (9c) many functions as a +count carrier of adverbs building complex quantifiers:

(9)

a. (More than) five / Just five / About ten women are in the class

 

b. Quite a few / Hardly any / Almost all linguists are musicians

 

c. There are uncountably many / surprisingly many blue dwarfs

 

more than two, exactly/only/just ten, less/fewer than a hundred, at

 

least/at most five, about/approximately ten, nearly/almost two

 

hundred, between five and ten, just finitely many, infinitely many,

 

hardly any, practically/almost no, fifty give or take a few

1.4.1.2 Value Judgment Cardinals

Value judgment cardinals also allow some novel modification. many and, less freely, few function to host adverbial modifiers productively forming intensional quantifiers.

(10)

a. Too many / Not enough students came to the lecture

 

b. Surprisingly many / few administrators came to the party

1.4.1.3 Exception Modifiers

Exception modifiers (Moltmann 1995, 1996, von Fintel 1993) seem most natural with no (intersective) and every (co-intersective), but (11c) from Garcia-Alvarez 2003, cited in Peters and Westerståhl 2006, finds some cases with most (proportional) using the more permissive except.

(11)

a. No student but John / Every student but John came to the lecture

 

b. All but two students passed the course

 

c. Almost/Nearly every student signed the petition

 

d. Most dishwashers except very low-end models have a water-saving feature

1.4.1.4 Proportional Quantifiers

Proportional quantifiers are usually syntactically complex in English:

(12)

More than / Exactly / Nearly /About / Less than half the students passed

There are several dedicated structures in proportionality quantifiers:

(13)

a. (More than) seven out of ten sailors smoke Players

 

b. Only / Just / Not one student in ten can answer that question

(14)

a. Sixty percent of American teenagers are overweight

 

b. Less than a third of Americans are bilingual

 

c. (Only) Every second car off the production line was inspected

 

ten percent of, two thirds of, a (large) majority of, a (small) minority of,

 

more than twenty percent of, less than a quarter of, between twenty

 

and thirty percent of, all but a tenth of, (just) a small percentage of,

 

What percentage / fraction of?, more/less than / exactly half (of), all of

1.4.1.5 Boolean Compounds

(15)

a. Not all poets daydream

 

b. At least two but not more than ten students got scholarships last year

 

c. Most but not all students are liberal

 

d. Either very few or else very many students will pass that exam

 

e. Neither every teacher nor every student came to the party

 

f. Not more than one teacher in ten knows the answer to that question

1.4.1.6 Partitives

Partitives in English = [(Q N) of NPdef], Q any of the quantifiers presented so far and NPdef a definite plural NP determining a non-empty domain.

(16)

a. (All / None / Both / Neither / Just two / Each) of those thieves fled

 

b. Some/Most but not all of John’s dogs were inoculated

 

c. Not more than a third of the prisoners escaped

 

d. John didn’t see any of those films

1.4.2 Complex A-Quantifiers

1.4.2.1 A-Quantifiers

A-quantifiers are modifiable as above, often with bounding phrases, as in (17f,g):

(17)

a. Sean has been to Dublin {exactly twice / more than five times}

 

b. He jogs to work on most if not all weekends / almost every Friday

 

c. Ann {almost never / only occasionally} takes the bus to school

 

d. Ann jogs to school twice as often as you do

(Comparative +count)

 

e. Ann smokes twice as much as you do

(Comparative –count)

 

f. Ed worked 50 weeks a year for 30 years

(Bounding)

 

g. John does twenty push-ups twice a day, five days a week.

  

(Pratt and Francez 2001)

1.4.2.2 Boolean Compounds

(18)

a. In local elections Ann has usually but not always voted Democrat

 

b. Ed has taken the exam at least twice but not more than five times

 

c. Ann sleeps late on weekends and on holidays except for Easter

II Selected Topics

Consider the expression of the phenomena in 1.5–1.17 in your L

1.5 Comparative Quantifiers

In (19a,b,c) the italicized expressions denote quantifiers mapping two properties to a quantified NP (QNP) denotation. See Keenan and Moss (1984), Keenan (1987) and Beghelli (1994).

(19)

a. More students than teachers are vegans

 

b. The reporter interviewed twice as many students as teachers

 

c. We talked to the same number of students as teachers

 

d. How many more students than teachers signed the petition?

 

e. Just as many students as teachers’ bicycles were stolen

 

f. Proportionately more students than teachers signed the petition

That more students than teachers is an argument expression is supported by the diversity of ordinary NP positions in which it occurs in (19a–e). The quantifiers in (20a–e) are cardinal, but now depend on two numbers – in (19a) the number of students who are vegans and the number of teachers who are. Proportionately more…than… in (19f) is Proportional.

1.6 Type (2) Quantifiers

Type (2) Quantifiers (Keenan 1992, 1996, Szabolcsi 1997, Peters and Westerståhl 2006) express a property of binary relations. We seek ones provably not reducible to the iterated application of two ordinary QNPs. Useful here are adjectives implying ‘different’, e.g. rival, mutually antagonistic, opposing, etc., but also ‘same’, e.g. similar, same color, etc.

(20)

a. Different people like different things

 

b. Each student answered a different / the same question on the exam

 

c. Which pupils answered which questions (on the exam)?

 

(= Identify the pairs (x,y), x a pupil, y a question and x answered y).

 

d. Sy and Jim live in neighboring towns / support rival political parties

 

e. John danced with Mary but no one else danced with anyone else

  

(Moltmann 1996)

 

f. Ann often/never sees the same movie more than once

 

g. The paintings should be hung in separate rooms or on opposite walls of the same room

 

h. Different jurors drew different conclusions from the same arguments

  

(Tyhurst 1989)

(21)

Men are usually taller than women (Proportional).

 

(Compares man-woman pairs <x,y> with x taller than y) to man-

 

woman pairs in general)

1.7 Distributive Numerals and Binominal Each

Binominal each in (22a), like apiece, forces a distributive reading of the subject NP the assistants. See Safir and Stowell (1988) and Zimmermann (2002). By contrast between them in (22b) forces a collective reading on the subject.

(22)

a. The assistants graded sixty exams each / apiece

 

b. The assistants graded sixty exams between them

Binominal each shares readings with distributive numerals found in Latin, Tagalog, Japanese, Georgian, Rumanian and Basque among others. See Gil (1982, 1988, 2005).

(23)

a. Bina hastilia ferunt

Latin. Betts (1986)

 

Two-each spears carry+3pl

 
 

They carry two spears each

 
 

b. Legiones singulas posuit Brundisi, Tarenti, Siponti

 

Legions one-each station+at Brundisium, Tarentum, Sipontum

 

He stationed one legion each at Brundisium, Tarentum, and Sipontum

 

c. Doi oameni au cărat cîte trei valise Romanian

 

two men have carry.pastpart dist. three suitcases

 

Two men carried three suitcases each

(Gil 1993)

 

*Three suitcases are such that each of two men carried them

 

d. Ikasle-ek irakasle-a-ri azapi-na lan aurkeztu  zizkioten

 

student-pl.erg teacher-sg-dat seven-each work present aux.pl

 

The students presented seven works each to the teacher

    

(Basque, Etxeberria 2008)

Sometimes distributive numerals are more naturally translated as ‘in threes’:

(24)

a. Romanma da Zurabma sam-sami čanta caiɣo

 

Roman.erg and Zurab.erg 3-each.abs suitcase.abs carry.pst.3sg

 

Roman and Zurab carried three suitcases each, or (Georgian)

 

Roman and Zurab carried the suitcases three by three (Gil 2005)

 

b. Nilahatra tsiroaroa ny mpianatra Malagasy

 

lined+up tsi-2-2 the student

 

The students lined up two by two / in twos

1.8 Mass Quantifiers and Noun Classifiers

Count Nouns denote properties of individuated objects. They combine directly with quantifiers: two books, most cats, etc. Mass nouns like sand and hydrogen do not: *most hydrogens, *two sands. To quantify over mass N denotations we pair them with numeral classifiers (Gil 2005:226–230), themselves often count Ns, usually illustrated with cardinal quantifiers, (25a), but other Qs occasionally license them, (25b).

(25)

a. Five ears of corn, two sticks of gum, several sheets of paper, a loaf

 

of bread, ten pieces of candy, no bars of soap, a hundred head of

 

cattle, a head of lettuce

 

b. every piece of gum, most grains of sand

In English such classifiers are of limited utility as typically object denoting nouns are quantifiable without them. But in some Ls two books would gloss as two volume book, two cats as two tail cat, etc. Indicate the prominence of classifiers in your L. Mass Ns may also be quantified using container nouns, (26a) and measure phrases, (26b), (Higginbotham 1994).

(26)

a. two bottles of wine, a carton of milk, many boxes of candy,

 

every keg of beer

 

b. a kilogram of salt, two pounds of cheese, a ton of fertilizer

Some D-quantifiers, including some comparatives, combine just with +count nouns:

ten houses / *ten hydrogens, How many houses? / *How many

hydrogens? few students / *few butter, ten per cent of U.S. teenagers /

*ten per cent of gold, Fewer students than teachers / *fewer rice than corn

Occasionally such quantifiers combine with a mass N yielding a ‘kind’ interpretation: two fine wines, an excellent cheese.

Some D-quantifiers combine with both mass and count nouns: All (the) houses / all (the) beer, a lot of cats / a lot of wine, (some/no) car(s) / (some/no) rubber, not enough students / not enough water, hardly any students / hardly any wine, more boys than girls / more rice than corn

Some D-quantifiers (fewer, we think) combine just with mass nouns:

much oatmeal / *much hamburgers, How much soup? / *How much soups?,

very little wine / *very little houses, as much rice as corn / *as much boys as

girls, less flour than buttermilk / *less cats than dogs, the whole/entire day /

*the whole/entire days

Lastly the Qs in (27a,b) form partitives in English with a grammatically singular head noun.

(27)

a. all/some/most/a lot/hardly any of the house was damaged in the

 

flood

 

b. much/(very) little/How much of the house was damaged in the flood

 

c. *no/*both/*many/*every/*each/*one of the house was damaged in

 

the flood

1.9 Existential Constructions

Existential Constructions (ECs) assert, deny, or query the existence of objects or stuff with a certain property. A language may lack a distinctive EC (Passamaquoddy; Bruening 2008:85). If a language has one they accept as pivots cardinal NPs, including comparatives (28d), and value judgement NPs, both count, (28a), and mass (28e).

(28)

a. There are too many students in the class now

 

b. Are there any women / more than two women in the class?

 

c. There aren’t any students on the committee

 

d. There aren’t more cats than dogs / as many cats as dogs in the pen

 

e. There is too much / not enough salt in the soup

Query 1 Definiteness effect

Which quantifiers are acceptable as pivots in your L?

(29)

a. *Aren’t there most men in the army?

 

(Intended: Aren’t most men in the army?)

 

b. *Aren’t there all men in the army?

 

(Intended: Aren’t all men in the army?)

Query 2

Is negation in Existentials, (28c), the same or different than negation in non-existential Ss? They are the same in English and Malagasy but different in Hebrew and Tagalog.

Query 3

Is the EC construction used for inalienable possession, as in (30) from Malagasy?

(30)

a. Misy zazakely ao an-trano

b. Misy rihana roa io trano io

 

Exist children there in-house

Exist storey two that house that

 

There are children in the house

That house has two storeys

1.10 ‘Floating’ Quantifiers

‘Floating’ quantifiers are ones that occur both within the predicate and as D-quantifiers yielding rough paraphrases. In English only all and both float, anteceded by the subject:

(31)

a. All (of) the girls came to the party

The girls all came to the party

 

b. Both Jack and Jill fell down the hill

Jack and Jill both fell down …

 

c. The two students laughed out loud

*The students two laughed …

But in Hebrew and Japanese (Gil 1993) numerals may float. And in Pima (Munro 1984) Qs that float include vees ‘all’, ha ʹi ‘some’, mu ʹi ‘many’, ʹal ha ʹas ‘a little’, and ʹal ha ʹakia ‘a few’. They may be anteceded by Subjects, Direct Objects, Indirect Objects/PPs, and Possessors:

(32)

a. Vees hegam ceceoj ′o ñeid heg Alice

 

all those men 3.aux see art Alice

 

All those men saw Alice

 

b. Hegam ceceoj ′o vees ñeid heg Alice

 

those men 3.aux all see art Alice

 

Those men all saw Alice

 

c. Gook ceceoj ′o voopo

d. Ceceoj ′o gook voopo

 

two men 3.aux run:pl

men 3.aux two run:pl

 

Two boys are running

 

Two boys are running

 

e. Vaik ceceoj ′añ ha-ñeid

f. M ′añ vaik ha-ñeid heg ceceoj

 

three men 1 s.aux them-see

1 s.aux three them-see art men

 

I see three boys

 

I see three boys

 
 

g. Nei ′ant heg vees heñ-navpuj ha-maakaika

 

see 1 s.aux art all my-friends their-doctor

 

I saw the doctor of all my friends

 

h. Vees nei ′ant heg heñ-navpuj ha-maakaika

 

all see 1 s.aux art my-friends their-doctor

 

I saw the doctor of all my friends

Curiously non-subjects trump subjects for antecedence when both are possible:

(33)

Heñ-navpuj ′at ha′i ha-maa hegam ceceoj heg ′e-o′′ohan

 

my-friends 3.aux some them-give those men art 3refl-books

 

My friends gave some of their books to the men

 

*Some of my friends gave their books to the men

 

*My friends gave their books to some of the men

Moreover two quantifiers may float simultaneously, in which case antecedence is determined by linear order (even if it leads to crossing dependencies, as below):

(34)

a. Rina ′at gook ha′i ha-maa heg ′e-o′′ohgan hegam mamakai

 

Rina 3.aux two some them-give art 3refl-books those doctors

 

Rina gave two of her books to some of the doctors

 

b. Rina ′at gook ha′i ha-maa hegam mamakai heg ′e-o′′ohgan

 

Rina 3.aux two some them-give those doctors art 3refl-books

 

Rina gave some of her books to two of the doctors

1.11 Distribution of Quantifiers

1.11.1 Bare Qs as Predicates

In English a limited usage, (35), but well attested elsewhere, (36):

(35)

The students in the course were ?few / *twelve / *all

(36)

a. Maro / Vitsy / Folo ny mpianatra afa-panadinana Malagasy

 

Many Few Ten the student free-exam

 

The students who passed the exam were many / few / ten

 

b. *Rehetra / *Sasany ny mpianatra nanatrika ny lanonana

 

All / Some the student attended the celebration

 

The students who attended the celebration were all / some

 

c. Sami pilce ktanaqsu-pon-ik motewolonu-wok

 

because long.ago be.many-Pret-3 motewolon-3

 

Because there used to be many motewolonu Passamaquoddy

     

(Bruening 2008:72)

 

d. ŋənʹ = Ø cə sčeenəx

 

Big/many = 3abs Det fish

Straits Salish

 

They are many, the fish

(Jelinek 1995:519)

 

e. *məkʹw = Ø cə sčeenəc

“

 

All = 3abs Det fish

 

They are all, the fish

Are Predicate Quantifiers limited to cardinal numerals and value judgment cardinals?

1.11.2 Can Bare Qs Function as Arguments?

If so, which ones?

(37)

a. The ties were cheap so I bought three, several, a few, many, *most,

 

*all, *each

 

b. Here are the cars I have available. Most / All / Only a few are in good condition.

1.12 Relations Between Lexical Universal, Existential and Interrogative Pronouns

Can your L form quantifiers from interrogative or indefinite pronouns?

1.

English: whoever, whatever, whenever, wherever, however, *whyever

 

Malagasy: iza = who?, na iza na iza ‘or who or who’ = whoever, na inona na inona ‘whatever’, na aiza na aiza ‘wherever, etc.

2.

Are (negative) existential and interrogative pronouns morphologically

 

related?

 

Russian kto? ‘Who?’, nikto ‘no one’, kogda? ‘when’, nikogda ‘never’.

 

Passamaquaddy (Bruening 2008:75) keq ‘What[inan]’?, wen

 

‘[what[animate]?’ and tama ‘where?’ are also used as indefinites:

 

something, someone, and somewhere respectively.

1.13 Decreasing D-Quantifiers

Q is decreasing (on its second argument) iff QAB implies QABʹ whenever Bʹ is a subset of B (Dually Q is increasing if QAB implies QABʹ if B ⊆ Bʹ). No is decreasing since No boys are laughing implies No boys are laughing loudly.

1.13.1 Does Your L Have Quantifiers Which Build Decreasing NPs?

(38)

No students came to the lecture

(Intersective)

 

Fewer than five students attended

“

 

Not all children cry a lot

(Co-intersective)

 

Less than a quarter of the students passed the exam

(Proportional)

 

Not more than seven out of ten sailors smoke Players

“

1.13.2 If Your L Has Decreasing NPs Do They License Negative Polarity Items?

(39)

Neither John nor Bill have ever been to Moscow

 

Not more than two students saw any birds on the walk

 

Less than half the students here have ever been to Pinsk

1.14 Distribution

1.14.1 Grammatical Roles

Do QNPs occur in all major grammatical roles – subject, object, object of adposition, possessor? Does your L have possessive quantifiers, (40d)?

(40)

a. John answered just two / all but two questions on the exam

 

b. Ruth answered most / three quarters of the questions

 

c. The library sent a notice to several students / all the students / about

 

half the students

 

d. Two students’ doctors were arrested

1.14.2 Special Positions

Do QNPs occupy special positions not allowed or unusual for definite NPs? For example in English overtly negated NPs occur better in subject than object position:

(41)

a. Not every student answered every question

 

b. *Every student answered not every question

In San Lucas Quiavini Zapotec, normally VSO, quantified subjects appear preverbally, while quantified objects occur in situ (Lee 2008):

(42)

a. B-daʹuh

Carlos

chòonn

gueht

 

perf-eat

Carlos

three

tortilla

 

Carlos ate three tortillas

 
 

b. Yraʹtaʹ

gyllaʹ

nàa

neyets

 

Every/all

flower

neut.be

white

 

All the flowers are white

 

Chamorro (mostly VSO; Chung 2008) forbids quantified external arguments to the right of the predicate. But such QNPs can be topicalized to the left of the predicate, and quantified NPs can occur as subjects of passive and unaccusative predicates, (43f):

(43)

a. Ha-na’säagi’ i semnak i atadok-ku

 

Agr-make.painful.prog the sun the eye-agr

 

The sun hurts my eyes

 

b. *Man-aitai käda patgun lepblu.

c. *Man-aitai lepblu käda patgun.

 

agr.AP-read each child book

agr.AP-read book each child

 

Each child read a book

Each child read a book

 

d. Käda patgun man-aitai lepblu.

 

each child agr.AP-read book

 

Each child read a book

 

e. käda saina guäha diretcho-nña… pära u-fam-a’tinas areklu

 

each parent agr.exist right-agr… Fut agr-AP-make rule

 

Every parent has the right to make rules (Chung 1998:263)

 

f. Ma-na’sinmagagu käda patgun

 

agr.Pass-make.be.without.clothes each child

 

Each child was made to undress

Finally, we do find Ss with more than one QNP binding arguments of the same predicate:

(44)

Todu i taotao gi ha:lum kuattu mang-ue.kuentus dos na lingguahi.

 

All the person Loc inside room agr-speak.Prog two Lnk language

 

Every person in the room speaks two languages. (‘every’ wide scope)

1.15 Scope Ambiguities

Can two or more arguments of a given predicate be bound simultaneously by QNPs? If so do you get scope ambiguities?

(45)

a. Some editor read every manuscript (Scope ambiguous in English)

 

Subject Wide Scope (SWS): There is one editor x who read all the ms

 

Object Wide Scope (OWS): Each manuscript is such that at least one

 

editor read it (possibly different editors read different manuscripts)

 

b. Three teachers graded 100 exams

 
 

?? SWS: There are 3 teachers each of whom graded 100 exams

 

?? OWS: There are 100 exams such that each teacher graded them

 

Group: There is a group of 3 teachers and a group of 100 exams

 

and the group of teachers graded the group of exams

(Natural)

In (22) we saw that apiece and binominal each force a distributive (SWS) reading, whereas the adverbial between them forces group (collective) readings,

In English, modified numerals in object position tend to force narrow scope, but an appropriate existential S will force object wide-scope:

c. Each student read one Shakespeare play over the vacation

(Scope

 

ambiguous)

d. Each student read at least one Shakespeare play

(Just SWS)

e. There was one Shakespeare play that each student read

(Just OWS).

f. In English, NPs which are not increasing tend to be interpreted in situ

No politician kissed every baby at the fair

(Just SWS)

Every politician kissed no baby at the fair

(Just SWS)

Just one pupil answered every question on the exam

(Just SWS)

All but one pupil answered at least one question

(Just SWS)

In English different lexical choices of quantifier may trigger different judgments of scope (non-)ambiguity even when the Qs are near synonyms.

g. Some editor read all the manuscripts

(Just SWS)

Some editor read every/each manuscript (Scope Ambiguous)

A picture of all the students

[Maybe one picture, many students]

A picture of each student

[As many pictures as students]

some friend of every senator

(Scope ambiguous)

some x such that x is a friend of every senator (Some wide scope)

for every senator y, some friend of y (Every senator wide scope)

h. Scope ambiguity asymmetries in wh-questions.

1. Which student answered the most / all the questions? (Just SWS)

2. a. Which question did each student answer? (Scope Ambiguous)

SWS: For each student x, identify the question x answered

OWS: Identify a unique question y such that each student

answered y.

 

b. Which question did all the students answer? (Just OWS)

(46)

Ambiguity between nominal and verbal quantifiers (Gil 1993)

 

Two boys sang three times

 

SWS: There are two boys who sang three times each

 

OWS: On three occasions there were two boys who sang

(47)

Quantifier-Negation scope. In preference in English quantified subjects scope semantically over negation, as in (48a,b). (48aʹ,bʹ) forces negation to scope over the subject:

(48)

a. Every student in my class doesn’t smoke

(Every > not)

 

aʹ. Not every student in my class smokes

(Not > every)

 

b. More than four teachers didn’t sign the petition

(Four > not)

 

bʹ. Not more than four teachers signed the petition

(Not > four)

(Short universal subjects are ambiguous. Everyone doesn’t know that might be used to mean that no one knows that or simply that not everyone knows that.) In contrast, objects in English naturally scope under negation: Ed hasn’t read more than 30 Shakespeare plays may be true and is not used to mean that there are 30 such plays he hasn’t read, which may be false.

1.16 One to One Dependency

(49)

a. For every drop of rain a flower grows

(Boolos 1981)

 

b. Every acorn we planted grew into a big oak tree

 
 

(Lee et al. 1999, see Jackendoff 1983, Gruber 1965)

1.17 Rate Phrases

(50)

a. John washes his face three times a day

 

b. I run twenty kilometers a day

1.18 Some Concluding Spot Checks

(51)

Does your L

 

a. have at least one monomorphemic all?

 

b. have at least one monomorphimic one?

 

c. have at least one monomorphemic value judgment many?

 

d. have a monomorphemic Det translating no?

 

e. make a lexical or phrasal distinction between a distributive and a collective universal quantifier? E.g. English distinguishes all (the) from each / every. Mohawk (Baker 1995 distinguishes akwéku ‘all’ and skátshu ‘each’; Malagasy (Keenan 2008) has 7 or 8 universal type quantifiers.

(52)

In your L are A-quantifiers morphosyntactically more complex than D-ones (Gil 1993)?

 

frequently, occasionally are built from frequent, occasional. Three times, many times even have the internal structure of an NP. But often and seldom are not more complex than many and few. And we appear to have some semantic back-formation, with the adjective interpreted as a function of the adverb:

(53)

a. He is a frequent visitor at the zoo = He visits the zoo frequently

 

b. An occasional sailor walked by = Occasionally a sailor walked by

   

(Stump 1981)

Note that in (53b) the right hand S is scope ambiguous, the left one only has occasionally with wide scope – so the sailors may vary with the occasions.

(54)

Does your L have a simple translation of only? If so does it apply in the same form in the following three contexts?

 

a. Only John came to the party

 

b. Only five students came to the lecture

 

c. John only sang, he didn’t also dance