Proportional numerals like

Research on the formal properties of natural language determiners has shown that not every possible determiner is a natural language determiner (

(1)

Most students are anarchists.

Roughly speaking, (1) is true just in case the cardinality of students who are anarchists exceeds the cardinality of students who are not anarchists. To decide whether (1) is true of a group of people, we would first pick out the students in this group and then find out if the number of anarchists exceeds the number of non-anarchists among the students. Crucially, the question of whether there are any anarchist non-students (or non-anarchist non-students) in this group is irrelevant to the truth value of (1).

We could imagine another determiner, call it

(2)

Tsom students are anarchists.

Meaning: ‘Most anarchists are students.’

The absence of

(3)

Conservativity (definition)

A determiner Det denotes a conservative function if and only if

Det(P)(Q) ⇔ Det(P)(P∩Q) for any P_{et} and Q_{et}.

CONS: Natural language determiners denote conservative functions.

The truth value of a sentence of the form

(4)

a.

tsom(P)(Q) ⇔ |P∩Q| > |Q – P|

b.

tsom(P)(Q) ⇎ tsom(P)(P∩Q)

since |P∩Q| > |Q – P| ⇎ |P∩(P∩Q)| > |(P∩Q) – P|

since |P∩Q| > |Q – P| ⇎ |(P∩Q)| > |∅|

There are some putative counter-examples to CONS (see

(5)

a.

There were many students outside.

b.

(There were few students in the exam but…)

Many (of the few) students did well in the exam

c.

Many Scandinavians have won the Nobel prize in literature.

d.

Many winners of the Nobel Prize in literature are Scandinavians.

The determiner

(6)

⟦many_{CARD} ⟧(P)(Q) ⇔ |P ∩ Q| > k, k a large number

(7)

⟦many_{PROP} ⟧(P)(Q) ⇔ |P ∩ Q|/ |P| > k, k a large proportion

(8)

a.

⟦many_{R.PROP}⟧(P)(Q) ⇔ |P ∩ Q|/ |Q| > k, k a large proportion

b.

⟦many_{R.PROP}⟧(P)(Q) ⇎ ⟦many_{R.PROP}⟧(P)(P ∩ Q)

since |P ∩ Q|/|Q| > k ⇎ |P ∩ (P ∩ Q)|/|P ∩ Q| > k

Herburger (_{R.PROP}

(9)

Few cooks applied

‘Few of the applicants were cooks.’

(10)

⟦few_{R.PROP}⟧(P)(Q) ⇔|P ∩ Q|/ |Q| < k, k a small proportion

Ahn & Sauerland (

(11)

a.

The company hired 75% of the women (proportional)

‘75% of the women were hired by the company.’

b.

The company hired 75% women. (reverse proportional)

‘75% of those hired by the company were women.’

To know whether (11a) is true of a group of people, we would only need information about the recruitment status of the women in this group. As far as the non-women in this group are concerned, whether they are hired or not is irrelevant to the truth value of (11a). This reading can be captured with a conservative denotation for proportional numerals.

(12)

⟦n%_{PROP} ⟧(P)(Q) ⇔ |P ∩ Q|/ |P| = n / 100

To know whether (11b) is true, we would have to know not only how many women are hired but also how many non-women are hired. This non-conservative interpretation can be expressed with the denotation in (13a).

(13)

a.

⟦n%_{R.PROP}⟧(P)(Q)⇔ |P ∩ Q|/ |Q| = n / 100

b.

⟦n%_{R.PROP}⟧(P)(Q) ⇎ ⟦n%_{R.PROP}⟧(P)(P ∩ Q)

since |P ∩ Q|/ |Q| = n / 100 ⇎ |P ∩ (P ∩ Q)|/|P ∩ Q| = n / 100

The presence of non-conservative readings of a determiner does not entail that this determiner has a non-conservative denotation. There might be other factors involved in non-conservativity effects associated with a determiner. Herburger (

(14)

Few

‘Few of the applicants were cooks.’

Moreover, when focus is on a subconstituent of the subject we obtain a reading that is not predicted by _{R.PROP}_{R.PROP}

(15)

Few

‘Few of the cooks that applied were incompetent cooks.’

Ahn & Sauerland (_{R.PROP}

(16)

30%

30%

Studenten

students

aus

from

Italien_{F}

Italy

arbeiten

work

hier

here

‘30% of the students that work here are from Italy.’

Following Herburger (

(a) DP-movement of a quantificational element blocks non-conservativity effects due to the NP-copy in the tail of this movement chain (

(b) non-conservativity effects associated with determiners of proportionality arise only when the nominal expression modified by these determiners remains in its vP-internal position (

In the next section, we shall examine the syntax of proportional and reverse proportional measurement constructions in Turkish and note some key differences between these constructions that play a crucial role in explaining their semantic properties. In

In this section, we take a closer look at the syntactic representation of proportional and reverse proportional measurement constructions in Turkish. We focus on the differences between these two constructions in terms of the presence of genitive marking on the noun as well as in the order of the proportional numeral with respect to the noun. These two constructions also differ in the obligatory presence of the accusative marker when they are in the object position as well as in their ability to control verb agreement in the subject position. We shall see in

Proportional numerals in Turkish appear in two different types of constructions with two distinct interpretations.

(17)

Şirket

company

öğrenci-ler-in

student-

yüz-de

hundred-

yetmiş-in-i

seventy-

istihdam.et-ti

hire-

‘The company hired seventy percent of the students’

In (18), however, we are given information about the ratio of the students that the company hired to all the individuals hired by the company. This interpretation is made available by the presence of the reverse proportional measurement construction

(18)

Şirket

company

yüz-de

hundred-

yetmiş

seventy

öğrenci

student

istihdam.et-ti

hire-

‘Seventy percent of those hired by the company were students.’

In this paper, we shall claim that proportional numerals in Turkish form a nominal constituent with the noun they modify. Before we delve into the details of the syntactic representation of these constructions, it is important to rule out an alternative analysis in which a proportional numeral like

(19)

*Şirket

company

öğrenci-ler-in

student-

çoğunlukla-sın-ı/sadece-sin-i

mostly-

istihdam.et-ti

hire-

Arguments against an adverbial analysis for proportional numerals inside reverse-proportional expressions as in (18) need to be more nuanced since replacing the proportional numeral in (18) with an adverb does not lead to unacceptability.

(20)

Şirket

company

çoğunlukla/sadece

mostly/only

öğrenci

student

istihdam.et-ti

hire-

‘The company hired mostly/only students’

We now show that proportional numerals inside reverse-proportional expressions are not adverbial elements. Let us first observe that the adverbs

(21)

a.

Şirket

company

çoğunlukla/sadece

mostly/only

öğrenci-ler-i

student-

istihdam.et-ti

hire-

‘The company hired mostly/only the students’

b.

*Şirket

company

yüz-de

hundred-

yetmiş

seventy

öğrenci-ler-i

student-

istihdam.et-ti

hire-

Secondly, adverbs in Turkish can be displaced to the post-verbal domain as in (22a). However, proportional numerals inside reverse-proportional expressions cannot occupy this position (22b). They must immediately precede the noun they modify.

(22)

a.

[Şirket

company

_{1}

öğrenci

student

istihdam.et-ti]

hire-

çoğunlukla_{1}/sadece_{1}

mostly/only

‘The company hired mostly/only students’

b.

*[Şirket

company

_{1}

öğrenci

student

istihdam.et-ti]

hire-

yüz-de

hundred-

yetmiş_{1}

seventy

The discussion above indicates that proportional numerals in Turkish should not be given an adverbial analysis. Rather, they seem to form a nominal constituent with the noun they modify. Given this finding, we can now focus on the internal syntax of proportional and reverse proportional measurement constructions in Turkish. These expressions differ in the presence of number and case marking on the substance noun as well as in the order of the proportional numeral with respect to the noun.

(23)

a.

yüz-de

hundred-

yetmiş

seventy

öğrenci

student

(reverse-proportional)

‘70% students’

b.

öğrenci-ler-in

student-

yüz-de

hundred-

yetmiş-i

seventy-

(proportional)

‘70% of the students’

In this section, we shall explicate, and to some extent defend, our assumptions about the internal syntax of (23a) and (23b). Let us start with reverse proportional measurement constructions (rPMCs). Research on nominal syntax of Turkish suggests that the extended projection of a noun includes

(24)

Turning now to proportional measurement constructions (PMCs), we see that they differ from rPMCs in the obligatory presence of the plural morpheme and the genitive case marker on the substance noun. The obligatoriness of genitive case suggests that the substance noun is dominated by DP

(25)

a.

o

that

öğrenci-ler-in

student-

yüz-de

hundred-

yetmiş-i

seventy-

‘seventy percent of those students’

b.

*yüz-de

‘hundred-

yetmiş

seventy

o

that

öğrenci(-ler)

student(-

Finally, word order in PMCs can be explained on the assumption that there is DP-internal DP movement in Turkish (

(26)

Under this analysis of PMCs in Turkish, the genitive-marked DP starts out as an argument of the Num head and moves to Spec DP, which is the position where DP is assigned genitive case. We might, of course, imagine an alternative analysis in which the genitive DP is base-generated at Spec DP. In what follows, we shall provide some syntactic evidence suggesting that the genitive DP, indeed, starts out as a lower argument in the tree.

Genitive-marked DPs can be used both with relational nouns and with non-relational nouns and this distinction plays a role in the acceptability of a genitive DP in the predicate position (

(27)

a.

John’s brother (relational)

b.

#That brother is John’s.

(28)

a.

John’s team (non-relational)

b.

That team is John’s.

Partee & Borschev (

(29)

b.

ubijica

murderer.

Peti

Petja.

(argument)

‘murderer of Petja’

b.

Petin

Petja.

ubijica

murderer.

(modifier)

#’murderer of Petja’ [ok as a murderer Petja hired.]

Öztürk & Taylan (

(30)

Ali-nin araba-(sı)

Ali-

‘Ali’s car’ (the car that Ali owns/likes/chose etc.)

However, the victim-murderer relation that we find in (29a) can only be expressed if the genitive constuction contains the POSS suffix on the associate noun. In the absence of the POSS suffix (‘naked genitives’), this reading is not available.

(31)

a.

kadın-ın

woman-

katil-i

murderer-

‘the murderer of the woman’

b.

kadın-ın

woman-

katil

murderer

# ‘The murderer of the woman’

‘the murderer the woman hired/chose/liked etc.’

Öztürk & Taylan observe that inherently relational nouns (kinship terms, verb-related nouns and nouns that denote various types of part-whole relations) are unacceptable in naked genitive constructions.

(32)

a.

öğretmen-in

teacher-

hala*(-sı)

aunt-

b.

bina-nın

building-

yıkım*(-ı)

demolition-

c.

masa-nın

table-

kenar*(-ı)

edge-

Under their analysis, the absence of the POSS suffix implies that the genitive-marked DP does not participate in DP-internal DP movement. Rather, it is directly merged at DP as an adjunct. ((33) is the representation of (30) in the absence of the POSS suffix).

(33)

Inherently relational nouns, however, require the presence of a syntactically represented argument in a lower position, which then moves to the specifier of DP presumably for case reasons.

Going back to PMCs in Turkish, we observe that the POSS suffix is obligatory in these constructions.

(34)

*öğrenci-ler-in

student-

yüz-de

hundred-

yetmiş

seventy

‘70% of the students’

This observation provides independent evidence for the lower position of the genitive DP in the analysis of PMCs. The genitive-marked DP starts out as the syntactic sister of Num and moves to Spec DP as we have shown in (26).

Another difference between PMCs and rPMCs in Turkish is the obligatoriness of case-marking. When used in the object position, PMCs must be in the accusative case. rPMCs, on the other hand, need not be case-marked. In fact, the presence of the accusative case marker on an rPMC is highly marked, if not unacceptable.

(35)

a.

Şirket

company

kadın-lar-ın

woman

yüzde

hundred-

yetmiş-in^{*}(-i)

seventy-

işe

job.

aldı

take.

‘The company hired 70% of the women.’

b.

Şirket

company

(işe)

job.

yüz-de

hundred-

yetmiş

seventy

kadın(^{*}/^{??}-ı)

woman-

aldı

take.

‘The company hired 70% women.’

Unlike non-case-marked objects, which remain in their VP-internal position, case-marked objects in Turkish undergo DP-movement (

(36)

a.

Ali (*güzel)

Ali beautiful.

şarkıyı

song-

güzel

beautiful.

söyledi

say.

‘Ali sang the song beautifully’

b.

Ali

Ali

güzel

beautiful.

şarkı

song

(*güzel)

beautiful.

söyledi

say.

‘Ali sang (a song) beautifully.’

PMCs in the object position are similar to other case-marked objects in that they must precede low adverbs.

(37)

Ahmet (*tamamen)

Ahmet completely

kitap-lar-ın

book-

yüz-de

hundred-

yetmiş-in-i

seventy-

tamamen

completely

okudu.

read

‘Ahmet read seventy percent of the books completely.’

As expected, rPMCs in the object position must immediately precede the verb.

(38)

Şirket

company

hemen

immediately

(işe)

job.

yüz-de

hundred-

yetmiş

seventy

kadın

woman

(*hemen)

immediately

aldı.

take.

‘The company hired seventy percent women immediately.’

We shall assume that ACC-marked objects in Turkish move to the specifier of vP (

(39)

rPMCs, on the other hand, remain in their VP-internal position.

(40)

PMCs and rPMCs in Turkish also differ in their ability to control subject agreement. In Turkish, finite verbs agree with the subject in number and person. For third person plural DP-subjects, agreement with the finite verb is optional:

(41)

Çocuk-lar

child-

çok

a.lot

çalış-tı(-lar)

work-

‘The children worked hard.’

Similar to simple DP subjects, PMCs also participate in (optional) plural agreement with the verb.

(42)

Öğrenci-ler-in

student-

yüz-de

hundred-

yetmiş-i

seventy-

bu

this

şirket-te

company-

çalış-ıyor(-lar)

work-

‘Seventy percent of the students work in this company.’

In the context of an rPMC in the subject position, however, plural agreement is not possible.

(43)

Bu

this

şirket-te

company-

yüz-de

hundred-

yetmiş

seventy

öğrenci

student

çalış-ıyor(*-lar)

work-

‘In this company, seventy percent of the workers are students.’

Note that (42) and (43) also differ in the relative position of the subject with respect to the adjunct PP. Similar to rPMCs in the object position, rPMCs in the subject position must remain adjacent to the verb. Forcing movement of a rPMC to the canonical subject position leads to a sentence that is highly marked (possibly unacceptable).

(44)

*/??Yüz-de

hundred-

yetmiş

seventy

öğrenci

student

bu

this

şirket-te

company-

çalış-yor

work-

These observations about proportional numerals in the subject position can be explained within the

(45)

The optional presence of the plural agreement in the context of a PMC in the subject position can be expressed with the help of the optional rule in (46):

(46)

[3, PL] → lAr (optional)

An rPMC in the subject position lacks the D layer. This means that the T head cannot find a DP that contains valued instances of its unvalued features. In this case, the uninterpretable features on the T head get the default value (which is third person singular in Turkish, see

(47)

This concludes our discussion of the syntactic analysis of constructions involving proportional numerals in Turkish. In the next section, we shall take a closer look at how the form of rPMCs is related to their semantic properties. We show that the analysis proposed in Ahn & Sauerland (

In this section, we focus on the semantic analysis of reverse proportional measurement constructions (rPMCs) in Turkish. Adopting largely the analysis by Ahn & Sauerland (

In this section, our focus is the semantic analysis of rPMCs in Turkish, an example of which is given below.

(48)

(Bu şirkette)

(This company-

yüz-de

hundred-

70

70

öğrenci

student

çalışıyor

work.

‘%70 of the workers (in this company) are students’

(48) is true just in case the student workers constitute seventy percent of all the workers in the company. In other words, the ratio of the student workers to the non-student workers is claimed to 7 to 3. Let us pretend, for the moment, that the truth conditions of (48) is obtained as a result of the denotation of

(49)

⟦yüzde 70⟧(P)(Q) ⇔ |P ∩ Q|/ |Q| = 70 / 100

What is striking about the entry in (49) is that it makes the determiner

(50)

Conservativity (definition)

A determiner Det denotes a conservative function if and only if

Det(P)(Q) ⇔ Det(P)(P∩Q) for any P_{et} and Q_{et}.

CONS: NL-determiners denote conservative functions.

The denotation assigned to

(51)

⟦70 %⟧(P)(Q) ⇎ ⟦70⟧(P)(P ∩ Q)

since |P ∩ Q|/|Q| = 70 / 100 ⇎ |P ∩

Intuitively, CONS implies that the truth value of an expression of the form

The fact that (48) has a non-conservative reading does not entail that the determiner

(52)

30 Prozent

30 percent.

[StuDIERende]_{F}

students.

arbeiten hier

work here

‘30 percent of workers here are students.’

In (48), too, there is a pitch accent on

(53)

a.

Bu

this

şirket-te

company-

yüz-de

hundred-

70

70

[Türk

Turkish

öğren_{F}

student

çalışıyor.

work.

‘%70 of the workers in the company are students from Turkey.’

b.

Bu

this

şirket-te

company-

yüz-de

hundred-

70

70

[_{F}

Turkish

öğrenci

student

çalışıyor

work.

‘%70 of the student workers in the company are from Turkey.

The denotation we have assumed for the determiner

In order to model focus-sensitivity of rPMCs, we follow Ahn & Sauerland (_{F}_{F}_{f}_{<et>}, as in (54b). Contextual restrictions determine which subset of the domain of entities of type <e,t>, i.e. which subset of D_{<et>}, is chosen to be the focus value of _{F}

(54)

a.

⟦ Turkish_{F} ⟧ = λx.x is Turkish

b.

⟦ Turkish_{F} ⟧_{f}

The focus semantic value of a node

(55)

a.

⟦ student ⟧ = λx.x is a student

b.

⟦ student ⟧_{f}

Since both the adjective

(56)

⟦ Turkish_{F} student ⟧ = λx.x is Turkish and x is a student

The focus denotation of this merger is obtained via the pointwise application of the rule of

(57)

Pointwise Predicate Modification

If

Then

φ has two daughters, α and β, of type <e,t>

⟦ φ ⟧_{f}_{f}_{f}

The rule of _{F}_{F} student

(58)

⟦ Turkish_{F} student ⟧_{f}

λx.x is Russian and x is a student,

λx.x is German and x is a student …}

Assuming that _{F} student_{F} students

(59)

a.

⟦ some⟧ = λP. λQ. ∃x: P(x) ∧ Q(x)

b.

⟦ some Turkish_{F} student⟧ = λQ. ∃x:Turkish(x) ∧ student(x) ∧ Q(x)

c.

⟦ some Turkish_{F} student⟧_{f}

λQ. ∃x:Russian(x) ∧ student(x) ∧ Q(x),

λQ. ∃x:German(x) ∧ student(x) ∧ Q(x) … }

We are now ready to explicate our assumptions about the semantic analysis of rPMCs in Turkish. The sensitivity of proportional numerals to the placement of the focus feature in an LF-tree is modelled with the help of a free variable

(60)

A node with the squiggle operator,

(61)

The regular denotation of _{1}_{1}

(62)

a.

⟦ VP_{1} ⟧ = λx. x is a student and x works here

b.

⟦ V’ ⟧_{f}

c.

⟦ NumP ⟧_{f}

d.

⟦ VP_{1} ⟧_{f}

λx. x is a teacher and x works here,

λx. x works here and x works here ≈ λx. x works here…}

Since both the predicate _{F}_{1}_{1}_{f}

The denotation of a consituent obtained by adjoining _{β} ∼ C α]_{1}_{f}

(63)

Given a structure [_{β} ∼ C α], ⟦ β ⟧ is defined only if C = ⟦ α ⟧_{f}

If defined, ⟦ α ⟧ = ⟦ β ⟧

We suggest that

(64)

⟦ yüzde ⟧ = ⟦ % ⟧ = λn.λP.λQ.|P ∩ Q | / |P| = n / 100

The result of combining a numeral

(65)

⟦ 70% ⟧ = λP.λQ.|P∩Q| / |P| = 70 / 100

Such a determiner is conservative, as can be seen from the equivalence in (66).

(66)

⟦ 70% ⟧(P)(Q) ⇔ ⟦ 70% ⟧(P)(P∩Q)

since |P∩Q| / |P| = 70 / 100 ⇔ |P∩(P∩Q)| / |P| = 70 / 100

In fact, more generally, we can say that any determiner of the form

(67)

⟦ n% ⟧(P)(Q) ⇔ ⟦ n% ⟧(P)(P∩Q)

since |P∩Q| / |P| = n / 100 ⇔ |P∩(P∩Q)| / |P| = n / 100

Going back to the interpretation of (61), we realize that the free variable

(68)

EXIS(C) = λx.∃f ∈ C such that f(x) = 1

We have noted earlier that ⟦

(69)

⟦ 70 % ⟧(EXIS(C))(S∩W) ⇔ |EXIS(C)∩(S∩W)|/|EXIS(C)|=70/100

⇔ |W∩(S∩W)|/|W|=70/100

⇔ |S∩W|/|W|=70/100

This is the reverse proportional interpretation that arises in the context of rPMCs. As expected, we are comparing the cardinality of student workers to all workers. It should be noted that, for any

At this point, a question arises as to why proportional measurement constructions (PMCs) do not give rise to non-conservative readings in the way that rPMCs do. In Section 2, we have shown that, unlike rPMCs, PMCs undergo obligatory DP-movement, which is evidenced by the obligatory presence of the accusative marker when they are used in the object position. In the next section, we show that it is this movement operation that makes it impossible for PMCs to have non-conservative readings (

In Section 3, we have seen that non-conservative readings of reverse proportional measurement constructions (rPMCs) can be analyzed as arising from the interaction of focus with a conservative denotation for proportional numerals. We now take a look at the absence of non-conservative readings for proportional measurement constructions (PMCs) in Turkish. In Section 2, we have shown that, unlike rPMCs, PMCs undergo obligatory DP-movement (presumably for case reasons). Following Fox (

Ahn & Sauerland (

(70)

Under such an analysis, focus does not play any role in the interpretation of PMCs. There is, however, reason to believe that the placement of the focus feature has truth conditional consequences for sentences containing PMCs. Consider (71a) and (71b), which minimally differ in the constituents that are focused.

(71)

a.

Öğrenci-ler-in

student-

yüz-de

hundred-

yetmiş-i

seventy-

suşi-yi

sushi-

fork

ile

with

yedi.

eat.

‘70% of the students who ate sushi ate it with a fork.’

b.

Öğrenci-ler-in

student-

yüz-de

hundred-

yetmiş-i

seventy-

sushi-

çatal

fork

ile

with

yedi.

eat.

‘70% of the students who ate something with a fork ate sushi with a fork.’

In (71a), we are interested in the proportion of the students who ate sushi with a fork to the students who ate sushi. In (71b), we are interested in the proportion of the students who ate sushi with a fork to the students who used a fork to eat something (sushi, pasta, cake etc). An analysis of PMCs must reflect focus-sensitivity of these constructions.

Note also that partitive syntax might be a sufficent condition to block non-conservativity effects but it is not, strictly speaking, necessary. Westerståhl (

(72)

a.

Many Scandinavians have won the Nobel prize in literature.

b.

Many Scandinavians are Nobel prize winners in literature.

Similarly, Herburger (

(73)

a.

Few cooks applied. (stage-level)

‘Few of the applicants are cooks’

‘Few of the cooks applied.’

b.

Few cooks know how to make a soufflé. (individual-level)

#‘Few of those who know how to make a soufflé are cooks.’

‘Few of the cooks know how to make a soufflé.’

The presence of an individual-level predicate seems to be sufficent to block non-conservativity effects.

We have noted earlier that one syntactic difference between rPMCs and PMCs in Turkish is that PMCs undergo syntactic movement operation, which accounts for the position of PMCs with respect to vP-level adverbs.

(74)

Ahmet

Ahmet

(*tamamen)

completely

kitap-lar-ın

book-

yüz-de

hundred-

yetmiş-in-i

seventy-

tamamen

completely

okudu.

read

‘Ahmet read seventy percent of the books completely.’

When a quantificational DP undergoes movement, the tail of the movement chain is usually assumed to be a trace. An alternative approach, inspired by the Copy Theory of movement (

(75)

Every student came to the party

(76)

Fox (

(77)

a.

every’(P)(Q) ⇔ P ⊂ Q (non-conservative)

b.

every’’(P)(Q) ⇔ Q ⊆ P (non-conservative,

Replacing the determiner

(78)

a.

every’(S)(S ∩ C) ⇔ S ⊂ S ∩ C (Contradiction)

b.

every’’(S)(S ∩ C) ⇔ S ∩ C ⊆ C (Tautology)

Assuming that semantic grammar does not tolerate trivialities of this sort (

We claim that the absence of non-conservativity effects in PMCs can be accounted for under similar assumptions. More precisely, we assume that DP movement in Turkish leaves a subconstituent, i.e. NP, in the tail of the movement chain. As far as DP movement

(79)

DP in (79) moves to Spec TP, leaving an NP-copy in the tail of the chain:

(80)

Similar to what we have seen in rPMCs, the node containing

(81)

Let us consider the interpretation of (81).

(82)

a.

⟦VP⟧ = λx. x is a student and x works here

b.

⟦TP_{1}⟧ = λx. x is a student and x works here

c.

⟦TP_{1}⟧_{f}

…}

Observe that the set characterized by _{1}_{f}_{1}

(83)

⟦%70⟧(EXIS(C))(⟦TP_{1}⟧) ⇔ ⟦%70⟧(S∩W)(S∩W) (Contradiction)

For any n, 0 < n < 100, replacing

Let us show that the analysis we have for PMCs can account for the focus-sensitivity of such consturctions ((71a) and (71b)). Observe that, given the assumptions we have made, the tree representation of (71a) is as in (84):

(84)

(85)

C = ⟦TP_{1}⟧_{f}

λx. x is a student and x ate sushi with chopsticks

λx. x is a student and x ate sushi with a spoon, … }

We assume the equivalence in (86) holds:

(86)

EXIS(C) = λx. x is a student and x ate sushi somehow

λx. x is a student and x ate sushi somehow ≈ λx. x is a student and x ate sushi

EXIS(C) = λx. x is a student and x ate sushi

The overall interpretation for (84) is shown in (87), where _{u}_{u}_{u}

(87)

⟦%70⟧(EXIS(C))(⟦TP_{1}⟧) ⇔ ⟦%70⟧(S∩S_{u})(S∩S_{u}∩F)

⇔ |S∩S_{u}∩F| / |S∩S_{u}| = 70/100

This interpretation captures the intuitions reported in (71a) accurately.

Before closing this section, we must mention an issue about the placement of focus inside a PMC in the subject position. In (81), we have assumed that the tail of a movement chain cannot be focus-marked. This is a crucial assumption for the sentence to be trivial. To see why, consider a variant of (81) in which there is also a focus feature on the noun dominated by VP as in (88):

(88)

Replacing each focus marked constituent in (88) with

Beaver & Clark (

(89)

a.

Fishsticks, I believe Kim only buys. (Topicalization)

*‘I believe that Kim buys fishsticks and nothing else.’

b.

On Sunday, I thought you only went to the store (Adverb Preposing)

*‘I thought that you only went to the store on Sunday and no other day.’

c.

Guinness is what I think Kim only wants to drink. (Inverted wh-cleft)

*‘I think Kim wants to drink Guinness and nothing else.’

Interestingly, this behavior of

(90)

a.

Mary_{F}, John even met at the party.

b.

*Mary_{F}, John only met at the party.

Moreover,

(91)

a.

A professor_{F} is even at the party.

b.

*A professor_{F} is only at the party

Erlewine argues that a successful account of why (90a) and (91a) are grammatical relies on the presence of an F-marked constituent in the tail of the movement chains as in:

(92)

a.

[Mary_{F} [John even [met Mary_{F} at the party]]]

b.

[A professor_{F} [is even [_{VP} [a professor_{F}] at the party]]]

For Erlewine, the unacceptability of (90b) and (91b) is related to the fact that

All in all, the assumption that the tail of a movement chain cannot be focus-marked is not uncontroversial. Let us pretend, for the sake of argument, that the tail of a movement chain can be focus-marked. That is, a tree representation like (88) is possible, at least in principle. Looking at (88), one cannot help but notice that one of the focus-marked constituents is redundant. In the absence of a genuine understading of why this tree should be ruled out, we shall blame the ungrammaticality of (88) on this redundancy.

(93)

Economy Constraint on Focused-Constituents

An F-marked constituent α in a tree T is focus-redundant if by eliminating α we obtain the tree T’ such that ⟦ T ⟧ ⇔ ⟦ T’ ⟧

Claim: An LF-tree with a focus-redundant constituent is ungrammatical.

Erlewine (

In this section, we have claimed that the movement of PMCs blocks non-conservative interpretations due to the semantic contribution of the NP-copy in the tail of the movement chain. In the next section, following Herburger (

In the previous section, we have argued that proportional measurement constructions (PMCs) lack non-conservative readings as a consequence of the movement operation they participate in. The NP-copy that is left behind in the tail of this movement chain makes a non-conservative interpretation impossible. In this section, we show that the distribution of conservative and non-conservative readings associated with context-sensitive proportional determiners

(94)

a.

Many

‘Many winners of the Nobel Prize in literature are Scandinavians.’

b.

Few

‘Few of the applicants were cooks.’

Similar to rPMCs, the exact placement of focus within the subject has truth conditional effects (

(95)

Few

‘Few of the cooks that applied were incompetent.’

Interestingly, there are contexts in which

(96)

Many Scandinavians are Nobel prize winners in literature.

#‘Many winners of the Nobel Prize in literature are Scandinavians.’

Many of the Scandinanians have won the Nobel prize in literature.

Following Diesing (

(97)

#Yüz-de yetmiş kadın

hundred-

siyah saçlı-Ø

black haired-

Int. ‘Seventy percent of the people who have black hair are women.’

Let us first explicate our assumptions about the nature of conservative and non-conservative readings in the case of context-sensitive determiners. Romero (_{PROP}

(98)

⟦many_{PROP}⟧ = λd.λP.λQ.|P∩Q | / |P| ≥ d

_{PROP}

(99)

John has solved many questions in the exam.

Whether (99) is true or false depends, at least partially, on what percentage of the questions other students have solved. Suppose the exam is also taken by Bill and Sue. Then in order to decide whether (99) is true we need to take into consideration the percentage of questions solved by Bill and Sue, too. That is, we need to consider the comparison class given in (100).

(100)

C = { λd. Sue has solved (at least) d-many questions in the exam,

λd. Bill has solved (at least) d-many questions in the exam,

λd. John has solved (at least) d-many questions in the exam}

Suppose that Sue has solved 12% of the questions and Bill has solved 8% of them. Then it seems fair to say that that John has solved many questions in the exam (compared to others). However, if Sue has solved 96% of the questions and Bill has solved 88% of them, then (99) seems to be an overstatement. If the average is 42%, then we can perhaps say that John has solved neither few nor many questions.

Following earlier work on adjectives (_{PROP}

(101)

(102)

⟦ POS C ⟧ = λD_{dt}. Neutral.Segment(C) ⊆ D

Under these assumptions, we have the representation in (103) for the subject of (94a).

(103)

While _{PROP}

(104)

The comparison class is obtained by replacing the predicate

(105)

C = { λd. |Scandinavian ∩ NPinLit| / |Scandinavian| ≥ d,

λd. |N.American ∩ NPinLit| / |N.American| ≥ d,

λd. |Mid.Eastern ∩ NPinLit| / |Mid.Eastern| ≥ d, … }

(106)

Neutral.Segment((105)) ⊆ λd. |Scandinavian ∩ NPinLit| / |Scandinavian| ≥ d

That is, comparing population of various regions with respect to their Nobel Prize winners in literature, we find that the Scandinavian people have done well (by some measure _{PROP}

We now show that the movement of the quantificational subject blocks the non-conservative reading of _{PROP}

(107)

Replacing the focus marked constituent

(108)

C = { λd. |Scandinavian ∩ Scandinavian ∩ NPinLit| / |Scandinavian| ≥ d,

λd. |Scandinavian ∩ N. American ∩ NPinLit| / |N.American| ≥ d,

λd. |Scandinavian ∩ Mid.Eastern ∩ NPinLit| / |Mid.Eastern| ≥ d,

… }

Assuming each Nobel Prize winner belongs to one and only one region, all the alternatives in C that is distinct from the prejacent would denote

(109)

C = { λd. |Scandinavian ∩ Scandinavian ∩ NPinLit| / |Scandinavian| ≥ d,

λd. d = 0}

Since no comparison is being made between Scandinavian Nobel Prize winners and Nobel Prizer winners in other regions of the world, we conclude that the reverse-proportional readings of _{PROP}_{PROP}

We have already seen that reverse proportional readings of

(110)

a.

Many Scandinavians are Nobel prize winners in literature.

#‘Many winners of the Nobel Prize in literature are Scandinavians.’

Many of the Scandinanians have won the Nobel prize in literature.

b.

Few cooks know how to make a soufflé.

#‘Few of those who know how to make a soufflé are cooks.’

‘Few of the cooks know how to make a soufflé.’

Diesing (

The substance noun of a reverse proportional measurement construction (rPMC) in Turkish must remain in its base position. However, individual-level predicates require Quantifier Raising of the quantificational subject, as we have just seen. What this means is that an rPMC in the subject position cannot be used with individual-level predicates. In (111a), (111b) and (111c), we have an rPMC subject

(111)

a.

#Yüz-de

hundred-

yetmiş

seventy

kadın

woman

siyah

black

saçlı-Ø

haired-

Int. ‘Seventy percent of the people who have black hair are women.’

b.

#Yüz-de

hundred-

yetmiş

seventy

kadın

woman

160

160

santim-den

cm-

uzun-Ø

tall-

Int. ‘Seventy percent of the people who are taller than 160 cm are women.’

c.

#Yüz-de

hundred-

yetmiş

seventy

kadın

woman

sufle

soufflé

yapmayı

make.

biliyor.

know.

Int. ‘Seventy percent of those who can make a soufflé are women.’

The unacceptability of rPMCs with individual-level predicates is in line with the proposal developed in this paper.

Milsark (

(112)

a.

There are {three, some, few, many, no} cooks in the kitchen. (weak)

b.

*There is/are {every, each, most, all} cook(s) in the kitchen. (strong)

Enç (

(113)

a.

Hasan üç /pek.çok/çok.az/birkaç

Hasan three /many/few/some

kitap

book

okudu.

read.

‘Hasan read three/many/few/some books.’

b.

Hasan

Hasan

çoğu/her

most/every

kitap*(-ı)

book-

okudu

read.

‘Hasan read most/every book(s).’

Recall that PMCs in the object position must be marked for accusative while rPMCs in the same position cannot be case-marked (unless modified by a relative clause).

(114)

a.

Şirket

company

kadın-lar-ın

woman-

yüz-de

hundred-

yetmiş-in^{*}(-i)

seventy-

işe.aldı

hire.

‘The company hired %70 of the women.’

b.

Şirket

company

(işe)

job.

yüz-de yetmiş

hundred-

kadın(^{*}/^{??}-ı)

woman-

aldı

take.

‘The company hired %70 women.’

This means that proportional numerals inside PMCs behave as strong determiners while those inside rPMCs behave as weak determiners. In the context of this paper, the main distinction between a weak and strong determiner is the position(s) in which the substance noun is interpreted. The substance noun modified by a weak determiner is interpreted only inside vP while the substance noun modified by a strong determiner is interpreted both inside vP and in the head of the movement chain. We have alrady noted that the presence of the substance noun in both positions blocks non-conservativity effects. This means that the following generalization, which comes from Herburger (

(115)

Strong determiners do not exhibit non-conservativity effects.

One difference between the analysis developed here and that of Herburger’s (

1/2/3 = first/second/third person, ABL = ablative, ACC = accusative, ADV = adverb, CONS = the Conservativity Constraint, COP = copula, DAT = dative, Det = Determiner, EPP = Extended Projection Principle, GEN = genitive, IMPF = imperfective, LOC = locative, NMZ = nominalizer, NOM = nominative, Num = Number, M = masculine gender, NL = natural language, SG = singular, P = Person, PL = plural, PMC = proportional measurement construction PST = past, POSS = Possessive, REL = relativizer, rPMC = reverse proportional measurement construction

In our terminology, determiners like

All the Turkish judgments reported in this paper belong to the author.

The obligatoriness of the plural morpheme on the substance noun would follow from the assumption that the D head in Turkish selects for NumP (

(i)

Adam

man

kitabı

book-

çocuğa

child-

verdi.

give.

‘The man gave the book to the child.’

The obligatory presence of NumP might be playing a role in blocking number-neutral interpretations for case-marked nouns. Note also that the substance noun inside an rPMC cannot be marked with plural.

(ii)

yüz-de

hundred-LOC

yetmiş

seventy

öğrenci-(*ler)

student-PL

‘seventy percent students’

In Turkish, nouns must remain unmarked for number when they are used with numerals (see (iii)). Then, the absence of plural marking in (ii) can be thought as an instance of a more general ban in Turkish on plural-marked nouns in the context of numerals. This is in line with the analysis of

(iii)

üç

three

öğrenci-(*ler)

student-PL

‘three students’

In the semantic analysis of these constructions, we will ignore the head of this movement chain; see

The acceptability of a case-marked rPMC somewhat improves when there is a relative clause modifying the rPMC.

(i)

?Ayşe

Ayşe

Merve-nin

Merve-

işe.aldığı

hire.

yüz-de

hundred-

yetmiş

seventy

kadın-ı

woman-

kovdu.

fire.

‘Ayşe fired the seventy percent women that Merve hired.’

# ‘Ayşe fired seventy percent of the women that Merve hired.’

Following Solt (

(ii)

[DP [CP Merve hired seventy percent women]_{Presup} [DP the

The pro-form

If

Then

φ has two daughters, α and β, of type <e,t>

⟦ φ ⟧ = λx. ⟦ α ⟧ (x) ∧ ⟦ β ⟧(x)

If

Then

φ has two daughters, α and β, where α is of type <σ,τ> and β is of type σ

⟦ φ ⟧_{f}_{f}_{f}

This assumption raises the question of what happens with rPMCs in the object position. In such constructions, the noun and the verb do not have the right type for

The silent

See Pasternak & Sauerland (

rPMCs in Turkish are not acceptable in the subject position when they are used with individual-level predicates:

(i)

??/*

Yüz-de

hundred-

70

70

kadın

woman

siyah

black

saçlı-Ø

haired-

‘70% of the people who have dark hair are women.’

We shall discuss this unacceptability in

Fox (

(i)

[TP [every student] λx [_{VP} [the student x] [came to the party]]]

In (76), we are exploiting the fact that ⟦NP⟧ and ⟦V’⟧ can compose via

The implicit assumption being made here is that the tail of a movement chain cannot be focus-marked (

For n = 100, (83) becomes a tautology, another type of triviality. Presumably n cannot be equal to 0 and 100 for independent reasons.

To see how, observe that, in Erlewine’s (

(i)

[A [professor]_{F} is [_{VP2} only [_{VP} [a [professor]_{F}] [at the party]]]]

(ii)

[[A [professor]_{F} λx [_{VP2} only [_{VP} [the professor_{F} x] [at the party]]]]

The assertion of VP_{2} is obtained by negating alternative sentences that are obtained with the replacement of the predicate _{2} for now, we have (iii) for the denotation of VP_{2}. Consequently, (ii) has the denotation in (iv)

(iii)

⟦ VP_{2} ⟧ ⇔ it is not the case that the student x is at the party.

(iv)

⟦(ii)⟧ ⇔ ∃x. x is a professor and it is not the case that the student x is at the party.

This means that, in every context where students and professors are disjoint, (91b) is not interpretable.

There is reason to believe that semantic grammar does not tolerate certain types of redundancies. It has been noted that the focus-sensitive covert operator

(i)

Economy constraint on Exh: An occurrence of exh in a given sentence S is not licensed if eliminating this occurence leads to sentence S’ such that S’ entails S.

This condition has been made use of in the explanation of the Positive Polarity behavior of French complex disjunction

The tree in (88) has a contingent meaning. When we eliminate one of the focus features in (88), we obtain a representation that is interpreted as contradiction (81). Formally a contradictory sentence is stronger than a contingent sentence. Making use of this fact, we may state (93) as a constraint on focus features as in:

(i)

Economy Constraint on the Focus feature: An occurence of the Focus feature in a sentence is not licensed if eliminating this occurence leads to sentence S’ such that S’ entail S

What is somewhat strange about (i) is that even though grammar does not tolerate some types of contradictory sentences (

It is likely that sentences with a structure like (107) have trivial meanings. Suppose that the

Ahn & Sauerland (

(i)

YOLISA-ka

cook-

90-puhlo

90-percent

swuphulley-lul

souffle-

mantul-cwul-anta

know-how.to-make

‘%90 of those who know how to make a souffle are cooks.’

In Ahn & Sauerland’s analysis, (i) is derived by first moving [90% C] from within the vP-internal subject, followed by the remnant movement of [yolisa t_{90% C}] to the canonical subject position. That is, the derivation of (i) takes place as in (ii):

(ii)

a.

[[yolisa 90 puhlo C] [swuphulley-lul mantul-cwul-anta]]

b.

[[90 puhlo EXIS C]_{1} [[yolisa t_{1}] [swuphulley-lul mantul-cwul-anta]]]

c.

[[[yolisa t_{1}]-ka] [[90 puhlo EXIS C]_{1} [~~[yolisa t1]~~ [swuphulley-lul mantul-cwul-anta]]]]

One way to explain the acceptability of (i) would be to assume that

The author has no competing interests to declare.