A large array of nominal measurement structures can give rise to proportional readings, i.e., readings which specify the proportional relation of two measurements. Two key questions in the analysis of such readings is (a) whether nominal measurement structures are (or can be) in some sense inherently proportional or whether proportionality comes to be part of the meaning of nominal measurement via some external factor, like the manipulation of a contextual standard, the choice of a proportional measure function, or the presence of a relative modifier, and (b) to what extent it is possible to attribute proportionality to a single source across different nominal measurement structures. This paper addresses these questions by investigating the proportional readings of three nominal measurement structures in Greek (comparatives, juxtaposed measurement structures, and partitive measurement structures) as they arise in the presence of precise proportions specified by percentages like

This paper investigates the distribution of proportional readings in nominal measurement structures in Greek. Proportional readings specify the proportional relation of two measurements. In the cases we are mostly interested in in this paper the relation is expressly specified by a percentage, i.e. a phrase of the form

(1)

Exthes

yesterday

proslavame

hired.1

peninta

fifty

tis

the.

ekato

hundred.

perisoterus

more.

fitites

student.

apo

from

oti

simera.

today

‘We hired fifty percent more students yesterday than we did today.’

Next, we will move to juxtaposed nominal measurement structures, as in (2), and partitive measurement structures, as in (3). The structures in (2) and (3) differ on the types of proportional readings they exhibit, a difference that is morpho-syntactically conditioned. As described first for the German equivalents of (2) and (3) in Ahn & Sauerland (

(2)

Exthes

yesterday

proslavame

hired.1

peninta

fifty

tis

the.

ekato

hundred.

fitites.

students.

‘Thirty percent of the people we hired yesterday were students.’

(3)

Exthes

yesterday

proslavame

hired.1

(to)

the

peninta

fifty

tis

the.

ekato

hundred.

ton

the.

fititon /

students.

apo

from

tus

the

fitites.

students.

‘We hired thirty percent of the students yesterday.’

This paper asks the question to what extent it is possible to unify the analyses of not only the data in (1)–(3), but also with structures that do not contain proportional modifiers like percentages. The crucial ingredient of the analyses we consider pertains to the locus of proportionality in the grammar of nominal measurement structures. An obvious candidate for the locus of proportionality in (1)–(3) is the percentage itself. Indeed, Ahn & Sauerland (

The paper is organized as follows. Section 2 presents an overview of existing literature on proportionality in the nominal domain. Section 3 presents the different readings of percentages in differential comparatives and proposes an analysis based on proportional measure functions. Section 4 presents Greek juxtaposed measurement structures and proposes an analysis in terms of proportional measure functions. Section 5 does the same for partitive measurement structures. Section 6 concludes.

This section presents a short excursion of the literature on proportionality in nominal measurement structures. We do not aim to provide an exhaustive overview of all relevant data and the analyses that have been proposed. Rather, we focus on the data that are more directly linked to the cases that are the main interest of the paper. In doing so, we present (a) the available analytical options as it pertains to the locus of proportionality in the grammar of nominal measurement, (b) the basic ingredients that any analysis must include, and (c) the existing alternatives that we pitch our own analysis against.

Proportional readings in the nominal domain have mainly been discussed in the literature on the basis of examples with

(4)

a.

b.

c.

There were few faculty children at the 1980 picnic.

Few egg-laying mammals suckle their young.

Few cooks applied.

The simplest way to capture the various uses of

(5)

a.

⟦ few_{CARD} ⟧ = λR_{et} λS_{et}. |

b.

⟦ few_{F_PROP} ⟧ = λR_{et} λS_{et}. |

c.

⟦ few_{R_PROP} ⟧ = λR_{et} λS_{et}. |

(6)

a.

⟦ many_{CARD} ⟧ = λR_{et} λS_{et}. |

b.

⟦ many_{F_PROP} ⟧ = λR_{et} λS_{et}. |

c.

⟦ many_{R_PROP} ⟧ = λR_{et} λS_{et}. |

Many attempts have been made to reduce the number of entries and avoid lexical ambiguity as much as possible. Such analyses have particularly focused on deriving reverse proportional readings on the basis of _{CARD}_{CARD}_{F_PROP}_{F_PROP}

(7)

a.

⟦ few ⟧ = λR_{et} λS_{et}. |

b.

⟦ few ⟧ = λR_{et} λS_{et}. |

(8)

a.

⟦ many ⟧ = λR_{et} λS_{et}. |

b.

⟦ many ⟧ = λR_{et} λS_{et}. |

(9)

a.

⟦ few ⟧^{c} = λd λR_{et} λS_{et}. ^{c}

b.

⟦ many ⟧^{c} = λd λR_{et} λS_{et}. ^{c}

(10)

To derive proportional readings, proportionality is built in the measure function itself (cf.

(11)

Given a non-proportional measure

Forward and reverse readings differ on what is measured in the denominator. The forward proportional reading of (4b) is derived by setting the degree

(12)

a.

b.

As Bale & Schwarz’s (

(13)

More cooks applied to our program than to yours.

Since the comparative obviously does not have a standard-related interpretation, an analysis along the lines of (7)/(8) is unavailable. Whereas (13) can be analyzed using both a lexical analysis along the lines of (5)/(6), or an analysis based on proportional measure functions, Bale & Schwarz (

(14)

There are more road signs on Rte 101 than on Rte 104.

Bale & Schwarz (

(15)

a.

_{1} = λx. |x|⁄|MILES.OF.RTE.101|

b.

_{2} = λx. |x|⁄|MILES.OF.RTE.104|

(16)

a.

_{1} = λx. |x|⁄|APPLICANTS.TO.OUR.PROGRAM|

b.

_{2} = λx. |x|⁄|APPLICANTS.TO.YOUR.PROGRAM|

As discussed initially in Solt (

(17)

a.

More of the cooks applied to our program than to yours.

b.

More of the road signs appear on Rte 101 than on Rte 104.

One might think that to derive the available readings of (17), it is enough that partitive

(18)

⟦ of ⟧ = λx λd λy. ^{c}

To solve this issue, Bale (

(19)

For all entities _{DIM;x}_{DIM;x}_{DIM}

The key step in eliminating the effects of proportional measure functions is to furthermore assume that partitive _{a}_{t}_{b}

(20)

As Bale (_{t}

(21)

The measure in the denominator is only defined if the cooks who applied to our program are a sub-aggregate of the applicants, which is true. By the definition of domain-restricted functions, this measure is equivalent to the non-restricted measure _{DIM}_{t}_{DIM;z}_{DIM;z}

(22)

By factoring out the denominator values, (22) is equivalent to (23), which is nothing more than a regular partitive proportional meaning based on a non-proportional measure. Bale (

(23)

What we have seen so far is that there exist, in principle, at least three possible analytical options when it comes to the grammar of proportionality and its interaction with the grammar of measurement. One possibility is to locate proportionality in the meaning of a certain functional element, the same one that also introduces measurement. We will refer to this as a

More recently proportional readings have also been discussed on the basis of nominal measurement structures with relative modifiers. Ahn & Sauerland (

(24)

Dreißig

thirty

Prozent

percent

Studierende

students.

arbeiten

work

hier.

here

‘Thirty percent of the workers here are students.’

(25)

Dreißig

thirty

Prozent

percent

der

the.

Studierenden

students.

arbeiten

work

hier.

here

‘Thirty percent of the students work here.’

Ahn & Sauerland provide an account of these cases that places proportionality solely in the meaning of the relative modifier, as in (26). The difference between (24) and (25) is driven by the different syntax of the relevant measurement constructions and independent properties of the relevant measurement constructions. In the most recent and more thorough investigation of these data, Pasternak & Sauerland (

(26)

(27)

Importantly for current purposes, the modifier is the only place where proportionality comes into place in these analyses. We will refer to this type of analysis as a ^{c}

(28)

(29)

⟦ DEG ⟧^{c} = λP_{et} λd λx. P(x) & ^{c}

(30)

⟦ NP_{2} ⟧^{c} = λd λx. STUDENTS(x) & ^{c}

(31)

(32)

⟦ ∃ ⟧^{c} = λP_{et} λQ_{et}. ∃x [P(x) & Q(x)]

To resolve the type-mismatch between the meanings of NP_{1} and NP_{2}, NP_{1} undergoes Quantifier Raising, as in (33). The percentage now composes with the degree predicate in (34). But this raises a different problem, since MAX(

(33)

(34)

⟦ vP_{2} ⟧^{c} = λd ∃x. STUDENTS.WHO.WORK.HERE(x) & ^{c}

This is where focus comes in. Assuming that _{1}_{1}_{F}_{3}

(35)

(36)

⟦ vP_{3} ⟧^{F} = { λd ∃x. P(x) & WORK.HERE(x) & ^{c}

(37)

⟦ FPRE X ⟧ is defined only if ⋁⟦ X ⟧^{F} is true.

Where defined, ⟦ FPRE X ⟧ = ⟦ X ⟧.

(38)

⟦ vP_{2} ⟧^{c} = λd: ∃x. INDIVIDUAL(x) & WORK.HERE(x) & ^{c}

d. ∃x. STUDENTS(x) & WORK.HERE(x) & ^{c}

Notice that in this analysis focus is necessary to generate the right reading. Pasternak & Sauerland (_{1}

(39)

Dreißig

thirty

Prozent

percent

[westfälische

westphalian.

Studierende]_{F}

students.

arbeiten

work

hier.

here

‘Thirty percent of the workers here are Westphalian students.’

(40)

Dreißig

thirty

Prozent

percent

[westfälische]_{F}

westphalian.

Studierende

students.

arbeiten

work

hier.

here

‘Thirty percent of the students who work here are Westphalian.’

We move next, briefly, to what Pasternak and Sauerland call the genitive structure in (25), which is assigned the syntactic structure in (41). The structure is essentially treated as a partitive, with the quirk that Pasternak & Sauerland prefer having the relevant partitive functional head shift the interpretation of

(41)

(42)

⟦ MEAS ⟧^{c}_{dt,t} λx λn λy.

where _{x}

(43)

⟦ Prozent MEAS ⟧^{c}

= λx λn λy. ^{c}^{c}

As we have just seen a key component of existing analyses is to explain differences in the distribution of available proportional readings to the properties of different nominal structures. Particularly, partitives are taken to restrict the range of available proportional readings by imposing some additional restrictions. At the same time, however, seemingly very similar readings (the reverse proportional reading of

For the remainder of this paper, we change the language of investigation from English and German to Greek. By focusing on the Greek facts, we are not only expanding the relevant empirical landscape, but we also motivate a revision of the analysis in Pasternak & Sauerland (

This section provides an analysis of percentages in comparatives, as in (44). Comparatives with percentages as differential measure phrases are three-way ambiguous, as they can be true in all the contexts in (44a–c). We will call the reading that makes (44) true in Context A, a

(44)

Exthes

yesterday

proslavame

hired.1

peninta

fifty

tis

the.

ekato

hundred.

perisoterus

more.

fitites

student.

apo

from

oti

simera.

today

‘We hired fifty percent more students yesterday than we did today.’

a.

Context A: We hired 75 students yesterday and 50 students today.

b.

Context B: We hired 75 students out of 100 hirees yesterday (i.e.75%) and 100 students out of 200 hirees today (i.e. 50%).

c.

Context C: We hired 75 students out of 100 hirees yesterday (i.e.75%) and 100 students out of 400 hirees today (i.e. 25%).

We argue that all three readings necessitate a revision of the entry for

Consider first a regular differential comparative as in (45).

(45)

Exthes

yesterday

proslavame

hired.1

tris

three

perisoterus

more.

fitites

student.

apo

from

oti

simera.

today

‘We hired three more students yesterday than we did today.’

Following Alexiadou et al. (

(46)

⟦ -ter- ⟧^{c} = λd λT_{dt} λM_{dt}. MAX(M) =

(47)

⟦ periso- ⟧^{c} = λd λR_{et} λS_{et}. ^{c}

The

(48)

[[[tris -ter-]

λd [ simera proslavame d-periso- fitites ]]

λd [ exthes proslavame d-periso- fitites ]]

The meaning of (45) comes out as in (49), i.e. it is true if the number of students we hired yesterday exceeds the number of students we hired today by three. The differential measure phrase then simply specifies the difference between two degrees.

(49)

⟦ (42) ⟧^{c} = MAX(λd. ∃_{#}

= 3 + MAX(λd. ∃_{#}

With this background we can now proceed to consider comparatives with percentages as differential measure phrases, repeated in (50). We observe that such examples are three-way ambiguous. In its first and most prominent reading, which we called the

(50)

Exthes

yesterday

proslavame

hired.1

peninta

fifty

tis

the.

ekato

hundred.

perisoterus

more.

fitites

student.

apo

from

oti

simera.

today

‘We hired fifty percent more students yesterday than we did today.’

(51)

a.

Context A: We hired 75 students yesterday and 50 students today.

b.

Context B: We hired 75 students out of 100 hirees yesterday (i.e.75%) and 100 students out of 200 hirees today (i.e. 50%).

c.

Context C: We hired 75 students out of 100 hirees yesterday (i.e.75%) and 100 students out of 400 hirees today (i.e. 25%).

We begin by considering an analysis that deviates minimally from the analysis of differential comparatives in the previous section; i.e. we assume that the percentage functions as a regular differential measure phrase and that the LF of (50) is identical to that of other differential comparatives, as in (52). Assuming a quantificational analysis of percentages as in Pasternak & Sauerland’s entry in (27), repeated here in (53), the percentage undergoes Quantifier Raising, interpreted here in the usual way.

(52)

[ [peninta tis ekato] [ λ_{1} [[ [t_{1} -ter-] [ λd [ simera proslavame d-periso- fitites ]] ]

[ λd [ exthes proslavame d-periso- fitites ]] ]] ]

(53)

Informally, the relative cardinal reading of (50) should represent the ratio in (54). But as is immediately obvious, whereas the degree predicate in the numerator correctly represents the difference between the two cardinalities, as required, the denominator is not the maximal degree in the domain of this degree predicate (there is no such degree), but the cardinality provided by the

(54)

As a first attempt (to be revised in section 4.3.2), we will assume the quantificational entry in (55). (55) replaces MAX(

(55)

The cardinal reading is generated when

(56)

(57)

The relative proportional reading can be accounted for by resolving the measure functions to proportional measure functions, as in (58). Crucially in this case, the variables over measure functions in the main clause and

(58)

a.

_{1} = λx. |

b.

_{2} =λx. |

(59)

(60)

Finally, we turn to the absolute proportional reading. In this case the percentage appears to act more like absolute measure phrases and simply specify the difference between two proportional degrees. The issue here is that, given the ingredients we have specified so far (the predicates of degrees provided by the main and the

(61)

_{1}(⊔ STUDENTS.WE.HIRED.YEST) – _{2} (⊔ STUDENTS.WE.HIRED.TOD)

To achieve this we claim that the measure functions relevant for the absolute (and relevant) proportional reading are not the ones in (58), but the domain-restricted versions of them in (62).

(62)

a.

_{1} = λx :x ⊑ ⊔ HIREES.YEST. |

b.

_{2} = λx :x ⊑ ⊔ HIREES.TOD. |

The crucial difference between the functions in (58) and the ones in (62) is that only the latter have a maximal degree in their range, the degree whose value is

(63)

λ_{1} (⊔ STUDENTS.WE.HIRED.YEST)-_{2} (⊔ STUDENTS.WE.HIRED.TOD)

Assuming, as in our Context C, that we hired 75% students yesterday and 25% students today, the predicate in (63) will contain the unique degree that corresponds to the difference between the two proportions, namely 0.5. Crucially, since we are dealing with degrees of domain-restricted proportionality, the maximal degree in the domain of the differential predicate is the maximal degree in a scale of domain-restricted proportionality, namely 1. If so, the result of applying the differential predicate to the percentage and resolving the variable

(64)

(65)

(66)

More generally, the analysis predicts that only domain-restricted proportional measure functions will give rise to absolute proportional readings. Solt (

(67)

For any measure function _{DIM%;x}

Importantly not all the proportional measures we have seen so far can be re-written as domain-restricted measures.

(68)

There are more road signs on Rte 101 than on Rte 104.

(69)

a.

_{1} = λx. |x|⁄|miles of Rte 101|

b.

_{2} = λx. |x|⁄|miles of Rte 101|

The analysis correctly predicts then that differential percentages will not give rise to absolute proportional readings in this case, since the functions in (69) do not have maximal degrees in their range (and the corresponding predicates of degrees have no maximal degrees in their domains). Indeed, (70) is felicitous in the contexts A and B in (71), but not in context C (or any other context).

(70)

Afti

this

i

the

leoforos

highway

exi

has.3

peninta

fifty

tis

the.

ekato

hundred.

perisotera

more.

simata

road.sign.

apo

from

ekini.

that

‘This highway has 50 percent more road signs than that one.’

(71)

a.

Context A: There are 75 road signs in this highway and 50 in that one.

b.

Context B: There are 75 road signs per mile in this highway and 50 road signs per mile in that one.

c.

Context C: There are 75 road signs per mile in this highway and 25 road signs per mile in that one.

Before moving on let us briefly discuss an alternative to our analysis of absolute proportional readings, based on the idea that percentages do not denote degree quantifiers, but rather individual degrees in the range of domain-restricted proportional measure functions, as in Solt (

(72)

⟦

If so, percentages can directly saturate the differential argument of -

We have argued that differential percentages provide further evidence for a

This section provides an analysis of reverse proportional readings that arise by use of percentages in juxtaposed measurement constructions, as in (73). As in the German example discussed briefly in section 2.2, (73) only gives rise to reverse proportional readings and is thus true in a context in which we hired 10 people half of which were students. We first argue that the phrase

(73)

Exthes

yesterday

proslavame

hired.1

peninta

fifty

tis

the.

ekato

hundred.

fitites.

students.

‘Thirty percent of the people we hired yesterday were students.’

(74)

Exthes

yesterday

faghame

ate.1

tria

three

kila

kilo.

mila.

apple.

‘We ate three kilos of apples yesterday.’

Juxtaposed measurement structures with absolute measures, as in (74), are comprised of a substance noun, a measure noun, and a numeral. The substance noun and the absolute measure noun, which inflect for case and number, bear the same case. Relative measures like

(75)

Exthes

yesterday

katanalothikan

consumed.

tria

three

kila

kilo.

mila.

apple.

‘Thirty percent of what was consumed yesterday was apples.’

(76)

Exthes

yesterday

etreksan

ran.

ston

in.the

marathonio

marathon

trianta

thirty

tis

the.

ekato

hundred.

fitites.

student.

‘Thirty percent of the people that ran the marathon yesterday were students.’

Notice that Greek allows a range of word-orders, usually conditioned by information structure. In (75) and (76) above, we used post-verbal subjects. Reverse proportional readings seem to require that the juxtaposed structure appears in post-verbal position. In the presence of multiple arguments, reverse proportional readings require the nominal construction to appear in sentence-final position, as in (77). There is significant controversy in the literature on the distribution and analysis of different word-orders in Greek, see Oikonomou & Alexiadou (

(77)

Exthes

yesterday

dhosame

gave.1

afksisi

raise

se

to

trianta

thirty

tis

the.

ekato

hundred.

fitites

student.

‘Thirty percent of the people we gave a raise to yesterday were students.’

Nominal constructions in adjunct positions also allow reverse proportional readings, as in (78).

(78)

Exthes

yesterday

taksidhepsame

travelled.1

me

with

trianta

thirty

tis

the.

ekato

hundred.

fitites.

student.

‘Thirty percent of the people we travelled with yesterday were students.’

The internal constituency of juxtaposed absolute measurement has been an issue of considerable debate in the literature (

(79)

(80)

The structure we adopt is mono-projectional in the sense that a single nominal is projected (see

(81)

a.

Fitites

student.

proslavame

hired.1

exthes

yesterday

trianta

thirty

tis

the.

ekato.

hundred.

‘Thirty percent of the people we hired yesterday were students.’

b.

Trianta

thirty

tis

the.

ekato

hundred.

proslavame

hired.1

exthes

yesterday

fitites.

student.

‘Thirty percent of the people we hired yesterday were students.’

(82)

a.

Mila

apple.

faghame

ate.1

exthes

yesterday

tria

three

kila.

kilo.

‘We ate three kilos of apples yesterday.’

b.

Tria

three

kila

kilo.

faghame

ate.1

exthes

yesterday

mila.

apple.

‘We ate three kilos of apples yesterday.’

One area where the absolute and relative measures differ in their behavior is verbal agreement. In the case of absolute measurement, verbal agreement in number depends on the number of the measurement construction, which itself depends on the number of the semi-lexical number, as shown in (83) and (84). In the case of relative measurement, however, number on the verb is always plural, as shown in (85). We will provide an analysis of these agreement patterns in section 4.4.

(83)

Exthes

yesterday

katanalothike

consumed.

ena

one

kilo

kilo.

mila.

apple.

‘One kilo of apples was consumed yesterday.’

(84)

Exthes

yesterday

katanalothikan

consumed.

tria

three

kila

kilo.

mila.

apple.

‘Three kilos of apples were consumed yesterday.’

(85)

Exthes

yesterday

*proslifthike/

hired.

proslifthisan

hired.

ena/

one

trianta

thirty

tis

the.

ekato

hundred.

fitites.

student.

‘One/Thirty percent of the people that were hired yesterday were students.’

Before moving on, we should mention that reverse proportional readings in Greek can also be generated with an adverbial strategy, as in (86), where the percentage appears as part of an adverbial PP, headed by

(86)

Exthes

yesterday

proslavame

hired.1

kata

by

trianta

thirty

tis

the.

ekato

hundred.

fitites.

student.

‘Thirty percent of the people we hired yesterday were students.’

The main reason to reject such an extension of the adverbial strategy has to do with the fact that PP percentages and bare percentages do not have the same distribution. Recall that juxtaposed relative measurement constructions can appear inside PPs, as we saw in (87) and (88) above, giving rise to a reverse proportional reading. PP-percentages, on the other hand, are ungrammatical in these positions.

(87)

*Exthes

yesterday

dhosame

gave.1

afksisi

raise

se

to

kata

by

trianta

thirty

tis

the.

ekato

hundred.

fitites.

student.

‘Thirty percent of the people we gave a raise to yesterday were students.’

(88)

*Exthes

yesterday

taksidhepsame

travelled.1

me

with

kata

by

trianta

thirty

tis

the.

ekato

hundred.

fitites.

student.

‘Thirty percent of the people we travelled with yesterday were students.’

Moreover, PP-percentages can appear in more positions within the clause than bare percentages. So, whereas PP-percentages can appear pre-verbally, as in (89), bare percentages cannot, as shown in (90). The same is true of the clause-final position in (91) and (92). We thus reject an adverbial analysis of percentages in juxtaposed measurement structures.

(89)

Exthes

yesterday

kata

by

trianta

thirty

tis

the.

ekato

hundred.

proslavame

hired.1

fitites.

student.

‘Thirty percent of the people we hired yesterday were students.’

(90)

*Exthes

yesterday

trianta

thirty

tis

the.

ekato

hundred.

proslavame

hired.1

fitites.

student.

‘Thirty percent of the people we hired yesterday were students.’

(91)

Exthes

yesterday

proslavame

hired.1

fitites

student.

kata

by

trianta

thirty

tis

the.

ekato.

hundred.

‘Thirty percent of the people we hired yesterday were students.’

(92)

*Exthes

yesterday

proslavame

hired.1

fitites

student.

trianta

thirty

tis

the.

ekato.

hundred.

‘Thirty percent of the people we hired yesterday were students.’

Before moving to our analysis, we present further motivation for seeking an alternative to a modifier-based analysis. We first observe a correlation between the availability of juxtaposed measurement structures with percentages and the absolute proportional readings of the corresponding comparatives. We then turn to the issue of focus-sensitivity.

We have seen that whereas readings based on domain-restricted measure functions, as in (93), give rise to absolute proportional readings of differential percentages, readings based on non-restricted measure functions, as in (94), do not.

(93)

Context C: We hired 75 students out of 100 hirees yesterday (i.e.75%) and 100 students out of 400 hirees today (i.e. 25%).

Exthes

yesterday

proslavame

hired.1

peninta

fifty

tis

the.

ekato

hundred.

perisoterus

more.

fitites

student.

apo

from

oti

simera.

today

‘We hired fifty percent more students yesterday than we did today.’

(94)

Context C: There are 75 road signs per mile in this highway and 25 road signs per mile in that one.

#Afti

this

i

the

leoforos

highway

exi

has.3

peninta

fifty

tis

the.

ekato

hundred.

perisotera

more.

simata

road.sign.

apo

from

ekini.

that

‘This highway has 50 percent more road signs than that one.’

We observe that this contrast carries over to the availability of proportional readings with percentages in juxtaposed measurement structures. Whereas, as we have seen, (95) is available, it is not possible for (96) to have a reading based on the density of road signs in the highway.

(95)

Exthes

yesterday

proslavame

hired.1

peninta

fifty

tis

the.

ekato

hundred.

fitites.

student.

‘Thirty percent of the people we hired yesterday were students.’

(96)

#Afti

this

i

the

leoforos

highway

exi

has.3

peninta

fifty

tis

the.

ekato

hundred.

simata.

road.sign.

‘This highway has fifty percent road signs.’

This pattern generalizes to all non-restricted proportional measures. To give one more example, consider the proportional reading of the comparative in (97) based on the proportional measures in (98). Such measures cannot support an absolute proportional reading, as shown in (99), and neither is it available in the juxtaposed measurement structure in (100). As in the case of absolute proportional readings in comparatives the intuition is that the percentage will only be felicitous in juxtaposed measurement if it can be taken to directly specify a degree in the dimension of the underlying proportional measure function.

(97)

I

the

Athina

Athens

exi

has.3

perisotera

more.

aftokinita

car.

apo

from

ti

the

Nea

New

Iorki.

York

‘Athens has more cars than New York.’

(98)

a.

_{1} = λx. |x|⁄|people in Athens|

b.

_{2} = λx. |x|⁄|people in New York|

(99)

#I

the

Athina

Athens

exi

has.3

peninta

fifty

tis

the.

ekato

hundred.

perisotera

more.

aftokinita

car.

apo

from

ti

the

Nea

New

Iorki.

York

‘Athens has fifty percent more cars than New York.’

(100)

#I

the

Athina

Athens

exi

has.3

peninta

fifty

tis

the.

ekato

hundred.

aftokinita.

car.

‘Athens has fifty percent cars.’

Our claim is not that modifier-based analyses cannot account for the unavailability of (96) and (100). For the reading of, e.g., (100), to be generated in such an account, the denominator of the percentage would have to measure the cardinality of the inhabitants of Athens. But recall that since in the account of Pasternak & Sauerland (

Consider next the issue of focus-sensitivity, which in the account of Pasternak & Sauerland (

(101)

??Exthes

yesterday

proslavame

hired.1

peninta

fifty

tis

the.

ekato

hundred.

ITALUS

Italian.

fitites.

student.

‘Intended: Fifty percent of the students we hired yesterday were Italian.’

The most natural way to convey the intended meaning is to use a hanging topic, as in (102). Hanging topics in Greek (

(102)

Oso

as

ja

for

fitites,

student.

exthes

yesterday

proslavame

hired.1

peninta

fifty

tis

the.

ekato

hundred.

ITALUS.

Italian.

‘Thirty percent of the students we hired yesterday were Italian.’

(103)

Oso

as

ja

for

servitorus,

waiter.

exthes

yesterday

proslavame

hired.1

peninta

fifty

tis

the.

ekato

hundred.

FITITES.

student.

‘Thirty percent of the waiters we hired yesterday were student.’

One cannot simply claim that the structures in (102) and (103) are necessary because F-marked constituents in Greek have to appear in sentence final position. For one thing, there is no such requirement in the language. For example,

(104)

Exthes

yesterday

proslavame

hired.1

mono

only

ITALUS

Italian.

fitites.

student.

‘We only hired ITALIAN students yesterday.’

Moreover, the analysis in Pasternak & Sauerland (

We can now proceed to present our analysis of proportional readings in juxtaposed measurement structures. As discussed above, the analysis should (a) explain the correlation between these readings and absolute proportional readings in comparatives, (b) allow enough context sensitivity to derive examples like (102) and (103) where the measures involved cannot be derived solely by grammatical means, (c) but not in a way that sneaks in unwanted readings, like the ones based on non-restricted proportional measure functions in (100). The key ingredient of the analysis that helps us derive objectives (a) and (b) are domain-restricted proportional measure functions. In section 4.3.1 we provide an analysis based on domain-restricted measure functions that also assumes the entry for percentages which we argued is necessary to derive all readings of percentages in differential comparatives. As we will see, however, the context sensitivity introduced in the meaning of percentages leads to an over-generation problem. To solve this issue and still achieve a unified treatment of percentages in both juxtaposed structures and differential comparatives, we will need to revise both the meaning of percentages and the meaning of differential comparatives. We make a concrete proposal to this end in section 4.3.2.

Recall the syntax we assume for juxtaposed measurement structures like (73) in (105). A head _{5}

(105)

(106)

⟦ Meas ⟧^{c} = λP_{et} λd λx. P(x) & ^{c}

(107)

⟦ ∃ ⟧^{c} = λP_{et} λQ_{et}. ∃x [P(x) & Q(x)]

(108)

⟦ DP ⟧^{c} = λQ_{et}. ∃x [STUDENT(x) & Q(x) & ^{c}_{1}]

(109)

⟦ vP_{5} ⟧_{c} = λd. ∃(x) [STUDENTS.WE.HIRED.YEST(x) & ^{c}

(110)

(111)

(112)

(113)

The derivation of reverse proportional readings is exactly parallel to that of absolute proportional readings in comparatives. The only difference is the measurement in the numerator of the percentage. The account predicts, then, that non-restricted measures (and non-proportional measures like cardinality) will not be licensed because their domain does not include a maximal degree.

Notice that there are two sources of context sensitivity in the proposed analysis; the contextually resolved measure function ^{c}^{c}^{c}^{c}

(114)

The second source of context sensitivity, however, raises a more serious challenge. Assume that ^{c}

(115)

_{#}(⊔

(116)

_{#}(⊔

More than that, in the case of examples like (73), nothing prevents

(117)

_{#}(⊔ MILES.OF.HIGHWAY) ≥ d}

One way to exclude the offending readings would be to assume that ^{c}

(118)

The issue that arises, however, is that contextual sensitivity in the meaning of the percentage was crucial in our analysis of the three readings of percentages in differential comparatives. The question, then, is whether we can come up with an entry for percentages that at the same time (a) does not include a variable over degree predicates and (b) generates all readings of differential percentages. We argue in the next section that this is possible, but only once we revise our analysis of differential comparatives.

Let us take the entry in (118) as our starting point and consider why it cannot account for all readings of percentages in differential comparatives under our current assumptions. Recall that in relative cardinal readings the percentage specified the relation of two cardinalities, the one representing the difference between the measurements in the main- and

To solve this problem in a unified way we need the differential degree predicate to simultaneously be able to provide (a) the difference between the two measurements (since this is what appear in the numerator in all readings), (b) the measurement associated with the

In that direction, we propose to revise the meaning of the differential comparative morpheme, as in (119).

(119)

⟦ -ter- ⟧^{c} = λ_{dt} λM_{dt}.

Crucially, we will also assume that all differential measure phrases (both absolute and relative ones) denote degree quantifiers and undergo QR. The LF of an example with an absolute measure phrase, like (120), will, thus, be as in (121).

(120)

Exthes

yesterday

proslavame

hired.1

tris

three

perisoterus

more.

fitites

student.

apo

from

oti

simera.

today

‘We hired three more students yesterday than we did today.’

(121)

[ [_{MP} tris] [_{vP} λ_{1} [[ [t_{1} -ter-] [ λd [ simera proslavame d-periso- fitites ]] ]

[ λd [ exthes proslavame d-periso- fitites ]] ]] ]

Since the function of the

(122)

⟦ vP ⟧^{c} = λd: _{#}(

_{#}(

(123)

{7, 8, 9, 10}

(124)

[7,10]

To get the intended interpretation we now relegate the job of extracting the difference between the two measurements to the differential measure phrase itself. There are different ways to achieve this._{#} is the set of degrees measuring cardinality and

(125)

⟦ tris ⟧^{c} = λD_{dt}: _{#}. LENGTH(

(126)

The LENGTH of an interval

The presupposition in (125) makes sure that the measure phrase and the predicate of degrees it takes as an argument deal in the same dimension. Since the maximal degree in (122) is the number of students we hired yesterday (i.e. the maximal degree of the predicate provided by the main clause) and the minimal degree is the number of students we hired today (i.e. the maximal degree of the predicate provided by the

(127)

LENGTH([7,10]) = 3

We can now revise the entry of

(128)

A problem persists, however. The entry in (128) will always pick out the maximal degree in the domain of the differential predicate as the value of the denominator. To account for the full range of readings of differential percentages (particularly the relative cardinal and proportional readings), we need to allow ourselves more leeway in the choice of denominator. Taking a hint from Bale’s (_{a}_{t}_{b}

(129)

With the entry in (129) and the revised entry for the differential comparative morpheme in (119) we have the ingredients to generate all the readings of differential percentages. We repeat our example in (130) and its LF in (131).

(130)

Exthes

yesterday

proslavame

hired.1

peninta

fifty

tis

the.

ekato

hundred.

perisoterus

more.

fitites

students.

apo

from

oti

simera.

today

‘We hired (thirty percent) more students yesterday than we did today.’

(131)

[ [peninta tis ekato] [_{vP} λ_{1} [[ [t_{1} -ter-] [ λd [ simera proslavame d-periso- fitites ]] ]

[ λd [ exthes proslavame d-periso- fitites ]] ]] ]

There are two points of choice in calculating the meaning of (131); the choice of measure function and the choice of ENDPOINT function. The type of measure function will determine whether we are dealing with a cardinal or a proportional reading. The choice of ENDPOINT function will determine whether we are dealing with a relative or an absolute reading. Consider first relative cardinal readings in the context in (132).

(132)

Context A: We hired 75 students yesterday and 50 students today.

To generate cardinal readings we assume, of course, that the measure function is resolved to the cardinality function. If so, the differential predicate is as in (133). In the context of (132), this predicate specifies the interval in (134). The length of this interval will be the value of the numerator in the meaning of the percentage.

(133)

⟦ vP ⟧^{c} = λd: _{#}(

_{#}(

(134)

[50, 75]

Consider next the ENDPOINT function. Since the measure in the differential predicate is cardinality, which has no maximal degree in its range, the domain of the degree predicate in (133) also contains no maximal degree. ENDPOINT_{t}_{b}_{b}

(135)

We move next to relative and absolute proportional readings, licensed in the contexts in (136a) and (136b) respectively.

(136)

a.

Context B: We hired 75 students out of 100 hirees yesterday (i.e.75%) and 100 students out of 200 hirees today (i.e. 50%).

b.

We assume that the measure functions in the main- and

(137)

a.

_{1} = λx :x ⊑ ⊔

b.

_{2} = λx :x ⊑ ⊔ HIREES.TOD.|x|⁄|⊔

(138)

⟦ ^{c}_{1}(

_{2}(

(139)

[.5, .75]

Consider next the ENDPOINT function. Since the measure in the degree predicate is domain-restricted, the differential predicate has both minimal and maximal degrees in its domain. Both ENDPOINT_{t}_{b}_{b}

(140)

ENDPOINT_{t}

(141)

Finally, we return to juxtaposed measurement structures, as in (142), and show that the revised entry for

(142)

Exthes

yesterday

proslavame

hired.1

peninta

fifty

tis

the.

ekato

hundred.

fitites.

student.

‘Thirty percent of the people we hired yesterday were students.’

In the case of juxtaposed measurement,

(143)

⟦ vP_{5} ⟧^{c} = λd. ∃_{1}(

(144)

_{1} = λx :x ⊑ ⊔ HIREES.YEST.|x|⁄|⊔

(145)

[0, .5]

The denominator will again depend on the choice of ENDPOINT function. Since ENDPOINT_{b}_{t}

(146)

More generally, the same reasoning leads us to conclude that only degree predicates with a maximal degree in their domain can be arguments of percentages. If there is no such maximal degree, ENDPOINT_{t}_{b}^{c}

To complete the analysis of juxtaposed measurement, we consider next juxtaposed structures with absolute measures, as in (147). Nothing special needs to be said. The head

(147)

Exthes

yesterday

faghame

ate.1

tria

three

kila

kilo.

mila.

apple.

‘We ate three kilos of apples yesterday.’

(148)

(149)

⟦ Meas ⟧^{c} = λP_{et} λd λx. P(x) & ^{c}

(150)

⟦ tria kila ⟧^{c} = λD_{dt}: _{kg}

(151)

⟦ vP_{5} ⟧^{c} = λd ∃(x) [APPLES.WE.ATE.YEST(x) & _{kg}

(152)

[0,3]

(153)

LENGTH([0,3]) = 3

Before moving to partitive measurement constructions, we show that our analysis can provide an explanation of the observed verbal agreement patterns in number. As we will see, the analysis of these patterns provides some additional evidence in favor of a quantificational analysis of

(154)

Exthes

yesterday

katanalothike

consumed.

ena

one

kilo

kilo.

mila.

apple.

‘One kilo of apples was consumed yesterday.’

(155)

Exthes

yesterday

katanalothikan

consumed.

tria

three

kila

kilo.

mila.

apple.

‘Three kilos of apples were consumed yesterday.’

(156)

Exthes

yesterday

*proslifthike/

hired.

proslifthisan

hired.

ena/

one

trianta

thirty

tis

the.

ekato

hundred.

fitites.

student.

‘One/Thirty percent of the people that were hired yesterday were students.’

We begin with the assumption that the number of the verb depends on the number of

(157)

(158)

To provide a concrete implementation, we adopt Scontras’ (

(159)

⟦ SG ⟧^{c} = λP_{et}: ∀x ∈P [

(160)

⟦ PL ⟧^{c} = λP_{et}. P

The singularity presupposition checks whether the degree of every member in the predicate denoted by

(161)

⟦ MeasP ⟧^{c} = λx. APPLE(x) & _{weight.kg}

(162)

⟦ MeasP ⟧^{c} = λx. APPLE(x) & _{weight.kg}

We move next to relative measurement, where number on the verb is always plural. We will see that both analyses with and without proportional measure functions make the right prediction. However, analyses that treat percentages as individual degrees do not. The crucial case is the one with the relative modifier

This section discusses the forward proportional readings that arise by use of percentages in partitive measurement structures, as in (163). We will first discuss some of the morpho-syntactic properties of partitive measurement. We show that cases like (163) are distinct from the juxtaposed structures we discussed previously and should be discussed on a par with absolute partitive measurement, as in (164). We will see, however, that some important differences between relative and absolute measurement do arise. We, then, present the range of proportional and non-proportional readings that partitives give rise to, discuss the analytical challenges that emerge from this picture, and present our current approach.

(163)

Exthes

yesterday

proslavame

hired.1

peninta

fifty

tis

the.

ekato

hundred.

ton

the.

fititon /

students.

apo

from

tus

the

fitites.

students.

(164)

a.

Exthes

yesterday

proslavame

hired.1

tris

three

apo

from

tus

the

fitites.

student.

‘We hired three of the students yesterday.’

b.

Exthes

yesterday

faghame

ate.1

tria

three

kila

kilo.

apo

from

ta

the

mila.

apple.

‘We ate three kilos of the apples yesterday.’

Partitives differ from juxtaposed measurement in some obvious ways. First of all, we are clearly dealing with two DP projections, since the inner nominal is definite and projects its own D layer. Moreover, the two nominals, the inner nominal and the measure noun, as seen in the absolute partitive in (164), do not share case. Whereas the case of the measure noun is determined by the syntactic position of the partitive, the inner nominal receives accusative case by the preposition

Unlike relative juxtaposed measurement, where a definite determiner can only appear under certain conditions and only in the case of absolute measurement, a definite determiner can readily head the partitive, as in (165) and (166), without any apparent difference in meaning. But whereas the number on the definite determiner is always SG with relative measures, in the case of absolute measures, its number value depends on the number of the measure noun.

(165)

Exthes

yesterday

proslavame

hired.1

to

the.

ena/trianta

one thirty

tis

the.

ekato

hundred.

ton

the.

fititon /

students.

apo

from

tus

the

fitites.

student.

‘We hired one/thirty percent of the students yesterday.’

(166)

a.

Exthes

yesterday

faghame

ate.1

to

the.

ena

three

kilo

kilo.

apo

from

ta

the

mila.

apples.

‘We ate one kilo of the apples yesterday.’

b.

Exthes

yesterday

faghame

ate.1

ta

the.

tria

three

kila

kilo.

apo

from

ta

the

mila.

apple.

‘We ate three kilos of the apples yesterday.’

As in juxtaposed measurement, an overt indefinite determiner is only possible with relative measures and functions as an approximator.

(167)

Exthes

yesterday

proslavame

hired.1

ena

one

trianta

thirty

tis

the.

ekato

hundred.

ton

the.

fititon /

students.

apo

from

tus

the

fitites.

students.

‘We hired approximately thirty percent of the students yesterday.’

(168)

*Exthes

yesterday

faghame

ate.1

ena

one

tria

three

kila

kilo.

apo

from

ta

the

mila.

apple.

‘Intended: We ate approximately three kilos of the apples yesterday.’

Partitives also differ from juxtaposed measurement with regard to verbal agreement patterns. Recall that in juxtaposed measurement, relative measures only licensed plural number on the verb, whereas absolute measures licensed both singular and plural, depending on the number of the measure noun. Partitives show the same pattern in the case of absolute measurement, as shown in (169) and (170). In the case of relative measurement, on the other hand, the pattern is reversed. Relative measures only license singular number, as shown in (171). Notice, however, that in positions where the partitive controls agreement on the verb the presence of an overt definite determiner (which, as we saw above, is always SG with relative measures) is strongly preferred.

(169)

Exthes

yesterday

katanalothike

consumed.

ena

one

kilo

kilo.

apo

from

ta

the

mila.

apple.

‘A kilo of the apples was consumed yesterday.’

(170)

Exthes

yesterday

katanalothikan

consumed.

tria

three

kila

kilo.

apo

from

ta

the

mila.

apple.

‘Three kilos of apples were consumed yesterday.’

(171)

Exthes

yesterday

proslifthike/

hired.

*proslifthisan

hired.

??(to)

the.

ena/trianta

one thirty

tis

the.

ekato

hundred.

ton

the.

fititon.

students.

‘One/Thirty percent of the people that were hired yesterday were students.’

Notice finally that partitives behave like juxtaposed structures in terms of left-dislocation. The PP/genitive DP can be left-dislocated, as shown in (172a) and (173a). Moreover, the numeral and the semi-lexical/measure noun form a constituent that can be left-dislocated, as shown in (173b) and (173b) for relative and absolute measures, respectively.

(172)

a.

Apo

from

tus

the

fitites

student.

proslavame

hired.1

exthes

yesterday

trianta

thirty

tis

the.

ekato.

hundred.

‘We hired thirty percent of the students yesterday.’

b.

?Trianta

thirty

tis

the.

ekato

hundred.

proslavame

hired.1

exthes

yesterday

apo

from

tus

the

fitites.

student.

‘We hired thirty percent of the students yesterday.’

(173)

a.

Apo

from

ta

the

mila

apple.

faghame

ate.1

exthes

yesterday

tria

three

kila.

kilo.

‘We ate three kilos of the apples yesterday.’

b.

?Tria

three

kila

kilo.

faghame

ate.1

exthes

yesterday

apo

from

ta

the

mila.

apple.

‘We ate three kilos of the apples yesterday.’

It goes beyond the scope of this paper to provide an analysis of partitives that captures all the properties we have observed. In the case of relative partitive structures, a particular challenge that arises is the analysis of structures with overt definite articles.

(174)

(175)

As in juxtaposed structures, the covert head _{part}_{Gen}

(176)

⟦ DP_{Gen} ⟧^{c} = σx [⟦ NP ⟧^{c} (x)]

Given the quantificational meaning of

(177)

(178)

Following Solt (_{part}_{part}_{part}

(179)

(180)

Let us start by considering the entry in (179). What readings does this entry license? Obviously, resolving ^{c}

(181)

⟦ vP_{5} ⟧^{c} = λd. ∃y [y ⊑ σx [STUDENT(x)] & WE.HIRED.YEST(y) & _{#};_{s}

(182)

LENGTH([0,3]) = 3

The same resolution of ^{c}_{t}_{b}

(183)

The entry in (179) also makes successful predictions in case ^{c}_{1};_{s}

(184)

⟦ vP_{5} ⟧^{c} = λd. ∃y [y ⊑ σx [STUDENT(x)] & WE.HIRED.YEST(y) & _{2};_{s}

(185)

_{2} = λx. |x|⁄|⊔ STUDENTS|

(186)

_{2};_{s}

(187)

Assume next that ^{c}_{part}_{t}_{part}

(188)

⟦ vP_{5} ⟧^{c} = λd. ∃y [y ⊑ σx [STUDENT(x)] & WE.HIRED.YEST(y) & _{1};_{s}

(189)

_{1} = λx. |x|⁄|⊔ HIREES.YEST|

(190)

_{1} = λx :x ⊑ ⊔

(191)

The account achieves, in the presence of percentages, the same result that Bale’s (

(192)

Exthes

yesterday

proslavame

hired.1

perisoterus

more.

apo

from

tus

the

fitites

student.

apo

from

oti

simera.

today

‘We hired more of the students yesterday than today.’

As we will see, however, there is an issue with simply adopting Bale’s entry instead of the one in (179). The issue does not have to do with the distribution of proportional readings, but with how the entry derives non-proportional readings of partitives.

(193)

Let us first reassure ourselves that we can unproblematically combine Bale’s entry in (193) with the proposed semantics of _{t}

(194)

(195)

Bale claims that the same entry can derive simple cardinal readings when _{b}_{DIM;x}_{5}

(196)

The same setting of

The first thing to note is that it is not possible to derive cardinal readings in this way under our own assumptions. Since we have been assuming that all the relevant measure functions (domain-restricted ones included) define ratio scales, all the functions discussed here will have a zero degree in their range (even if no individual in the domain of the function is mapped on zero.)_{b}

To summarize, the entry in (179) generates non-proportional readings, but it over-generates proportional readings in comparatives. Adopting Bale’s entry in (180), on the other hand, derives the right proportional readings across the board, but under-generates non-proportional readings. At this point we have not been able to solve this puzzle by defining a single entry for _{part}_{part}

This paper addressed a key issue in the grammar of nominal measurement, namely the source of proportionality in relative readings of nominal measurement structures. We identified four available analytical options employed in previous literature. A lexical analysis places proportionality in the meaning of a functional element that introduces measures. A standard-based analysis introduces proportionality via manipulating a contextual standard. A proportional

We investigated this question focusing in three non-standard-sensitive constructions with relative modifiers in Greek, namely comparatives with differential percentages, reverse proportional readings of juxtaposed nominal measurement structures, and forward proportional readings of percentages of partitives. We argued that the different readings of comparatives with differential percentages provide novel evidence in favor of proportional

As shown in Bale & Schwarz (

Like all the measure functions discussed in this paper, proportional measure functions are what in Measurement Theory are called ratio functions (or scales). As such, they have a non-arbitrary zero value in their range (even if no individual in their domain is mapped to zero) and operations like multiplication, division, addition, and subtraction are all meaningful. See Sassoon (

(i)

a.

Twice as many cooks applied this year as last year.

b.

Two times more cooks applied this year than last year.

Here and throughout, we use small capitals to abbreviate predicates of individuals.

Similar examples can be constructed with

_{t}_{b}

This captures the familiar constraint from the adjectival domain (see

(i)

a.

The glass is 75% full.

b.

#John is 75% tall.

Pasternak & Sauerland (

Our treatment of comparatives is based on that in Bale and Schwarz (

Next to the synthetic form of the comparative, an analytic form, as in (i), also exists. Like the synthetic form, the analytic form is also three-way ambiguous, and will not be discussed further here. See Makri (

(i)

Exthes

yesterday

proslavame

hired.1

peninta

fifty

tis

the.

ekato

hundred.

pio

COMP

polus

many.

fitites

students.

apo

from

oti

simera.

today

‘We hired fifty percent more students yesterday than we did today.’

Dan Lassiter (p.c.) points out that closed scale adjectives, as in (ii), also show the same type of ambiguity. Example (i) is true if the red glass is 75% full and the blue glass 50% full, but also if the red glass is 75% full and the blue glass 25% full. For another case of an absolute proportional reading see also (ii) from Klecha (

(i)

The red glass is 50% fuller than the blue glass.

(ii)

The odds increased 10%.

Just like the measure phrase

Domain-restricted proportional measure functions map their domain to the unit interval [0, 1].

This is exactly what motivates Bale & Schwarz (

See also the discussion in section 4.4.

In more colloquial speech the dative

We restrict our attention to absolute measure phrases with pure measure nouns, like

(i)

Ipia/

drank.1

Espasa

broke.1

dhio

two

potiria

glass.

krasi

wine.

‘I drank/broke two glasses wine.’

(ii)

Ipia

drank.1

dhio

two

potiria

glass.

perisotero

more.

krasi

wine.

apo

from

esena

you

‘I drank two glasses more wine than you did.’

A lot of the discussion centers around the proper treatment of the ‘semi-lexicality/-functionality’ of the measure and container nouns that appear in juxtaposed structures, i.e. the fact that they do not appear to project as full-fledged nominals. In the structure we propose, the measure nouns are part of the measure phrase and not part of the functional spine of the DP. Alternatively, semi-lexical nouns like unit nouns (or even

An overt indefinite determiner, which is homophonous with the numeral

(i)

Exthes

yesterday

proslavame

hired.1

ena /

one

*kapjo

some

trianta

thirty

tis

the.

ekato

hundred.

fitites.

student.

‘Approximately thirty percent of the people we hired yesterday were students.’

Notice that the examples with fronted MPs in (81b) and (81b) are somewhat more degraded if judged out of context. We believe this is because the fronted position is a topicalized position and MPs are harder to conceive as discourse topics. Both examples are perfectly felicitous if they are answers to questions like ‘What did you hire thirty percent of yesterday?’ and ‘What did you eat three kilos of yesterday?’.

The only (marginally) available reading of (96) is one in which the percentage specifies the proportional relation of the number of road signs to the total number of items that the highway has/is related to. This of course would be a reading based on a domain-restricted proportional measure.

To revise the account in a way that allows context sensitivity to determine the value of the denominator, one would minimally need to introduce a variable

The observed readings of examples (102) and (103), on the other hand, are predicted to be available if the measure function is resolved to the ones in (i) and (ii), respectively.

(i)

(ii)

This proposal has much in common with the analysis of comparatives in vector-based (

Alternatively, we can use a function, which returns the difference between two degrees, as in (i) (cf.

(i)

The denotation in (125) is a version of the quantificational approach to absolute MPs in von Stechow (

Other analyses of nominal number might also be suitable. A comparison between different analyses of nominal number lies beyond the scope of this paper.

Examples (172b) and (173b) are somewhat degraded out-of-the-blue since MPs are not the best candidates for discourse topics.

Falco & Zamparelli (

(i)

I

the.

elefantes

elephants.

exun

have.3

provoskides.

trunks

‘Elephants have trunks.’

Alternatively, _{part}

As Bale (

(i)

I removed more of the red paint that was on my left boot than the blue paint that was on my right boot.

One possible explanation for the discrepancy is that some speakers might take the definite descriptions

This work has been funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation), Grant AL554/12-1 (#387623969).

We are thankful to Stephanie Solt, Dan Lassiter, Rob Pasternak, and Uli Sauerland for helpful discussions, and to Stavroula Alexandropoulou, Nikos Angelopoulos, Maria Barouni, Margarita Makri, and Dimitris Michelioudakis for their judgements. We also wish to thank two anonymous reviewers for their valuable feedback.

The authors have no competing interests to declare.