Event and degree numerals:
Evidence from Czech
Mojmír Dočekal
Masaryk University in Brno
Marcin Wągiel
Masaryk University in Brno
In this paper, we bring in novel data concerning distribution and semantic properties
of two classes of adverbs of quantification in Czech, i.e., event numerals such
as dvakrát (‘twice/two times’) as opposed to degree numerals such as dvojnásobně
(‘doubly/twofold’). We explore the contrasts between the expressions in question
including the interaction with comparatives and equatives as well as scope asymmetries.
We propose that degree numerals target values on a provided scale and
are, hence, best analyzed as predicates of degrees whereas event numerals have a
more general semantics which primarily allows for quantification over individuated
events, but also enables to operate on degrees.
1 Introduction
Lexicons of many natural languages distinguish between two types of adverbs
involving quantification which correspond to English adverbs of quantification
such as twice and doubly, see (1).1 Surprisingly, though cardinal numerals have
received a lot of attention in the semantic literature on quantification (Landman
2004, Ionin & Matushansky 2006, Hofweber 2005, and Rothstein 2012 among
many others), expressions such as those in (1) remain strikingly understudied
both from a descriptive and theoretical perspective (with notable exceptions of
1
We would like to thank two anonymous reviewers, the audience at the FDSL 12 conference,
especially Berit Gehrke, Manfred Krifka, and Barbara Tomaszewicz, as well as Manfred Bierwisch,
Daniel Büring, Pavel Caha, Kim Hoangová, Stephanie Solt, Viola Schmitt, and Markéta
Ziková for their insightful remarks and inspiring comments. All errors are, of course, our own.
\lsCollectionPaperCitationText.
Mojmír Dočekal, Marcin Wągiel
Bhatt & Pancheva 2007, Donazzan 2013 and Landman 2006).2
(1) a. twice/doubly (English)
b. deux fois/doublement (French)
c. dvaždy/vdvojne (Russian)
d. kétszer/kétszeresen (Hungarian)
e. hai-lần/gấp-đôi (Vietnamese)
The aim of this paper is to present novel data concerning the distribution and semantic
properties of such expressions in Czech, exemplified in the text by (2). In
recent years the meaning of different types of Slavic derived numerals attracted
considerable attention (see Dočekal 2012, 2013 for Czech, Wągiel 2014, 2015 for
Polish, and Khrizman 2015 for Russian), and thus the analysis of the presented
data regards a broader enterprise intended to examine numeral quantification
from the perspective of morphologically complex languages.
(2) a. dvakrát
twice/two-times
(Czech)
b. dvojnásobně
doubly/twofold
(Czech)
In the paper, we refer to Czech adverbs of quantification such as (2-a) as event
numerals, whereas we will address expressions like (2-b) as degree numerals.
Our goal is primarily empirical, hence we aim our attention on discussing novel
data. The main focus of the article lies on constructions in which the degree argument
is being manipulated, specifically on the interaction with comparatives
and equatives. We claim that event numerals are best analyzed as adverbs of
quantification whose semantics is general enough to allow for counting distinctive
events in terms of iteration as well as operations on degree intervals. On
the other hand, degree numerals are in fact degree predicates which makes their
distribution more restricted.
The article is outlined in the following way. In Section 2, we discuss the distribution
of Czech event and degree numerals based on the corpus study we have
conducted. In Section 3, we examine the key environments in which such expressions
occur. In Section 4, we focus on categorial and typal differences and
we bring in additional contrasts involving event and degree numerals whereas
2
Wągiel (to appear) proposes an analysis of Slavic adjectival multipliers similar to English double,
however, we are not aware of any semantic treatment of adverbial expressions corresponding
to English doubly.
2
Event and degree numerals:
Evidence from Czech
Section 5 discusses properties of adjectival and nominal degree numerals. Section
6 summarizes the data and in Section 7, we propose a predicative semantics
for degree numerals as well as suggest an analysis of event numerals. Section 8
concludes the paper.
2 Distribution
At first blush, in some contexts Czech numerals such as dvakrát (‘twice/two
times’) and dvojnásobně (‘doubly/twofold’) appear to be synonymous:
(3) a. Petrovi
for-Petr
se
REFL
to
this
vyplatilo
paid-off
dvakrát/dvojnásobně.
twice/doubly
‘For Petr it paid off twice.’
b. Ceny
Prices
tady
here
jsou
are
dvakrát/dvojnásobně
twice/doubly
vyšší
higher
než
than
tam.
there
‘The prices here are two times higher than there.’
However, a more careful investigation reveals that there are multiple environments
in which they are not. To determine the distribution of event and degree
numerals and define properties of contexts in which they occur we have conducted
a corpus study based on the Czech National Corpus (CNC).3 The selected
corpus samples contained 100 random occurrences of the event numeral dvakrát
and the degree numeral dvojnásobně, which were reduced to 98 and 99 occurrences,
respectively, after filtering. Figures 1 and 2 present the preferred environments
in which the numerals in question appear in the samples.
The results show a significant difference in the distribution of event and degree
numerals that, in our opinion, unveils the real nature of these expressions.
Whereas dvakrát in 77% of occurrences targets event-denoting VPs as well as
temporal AdvPs and PPs,4 dvojnásobně tends to modify comparatives, APs, and
secondary predicates as well as degree-related VPs.5 In total, in 90% of the stud-
3
The CNC is a representative corpus of contemporary Czech. We have selected the SYN2015
subcorpus which is the largest reference corpus of contemporary written Czech consisting of
more than 100 million tokens. We searched for the lemmas: dvakrát and dvojnásobně.
4
Following Doetjes (2007), we assume that adverbials such as dvakrát denně (‘twice a day’) and
dvakrát za týden (‘twice a week’) are similar to frequency expressions in the sense that their
interpretation is dependent on the time interval they introduce.
5
Out of 30 VPs modified by dvojnásobně 9 were headed by deadjectival verbs, e.g., zvětšit (‘enlarge’)
and zvýšit (‘raise’), whereas 11 involved predicates inherently associated with scales
including verbs operating on degrees such as zvednout and vzrůst (both ‘increase’). The remaining
10 examples involved predicates such as platit (‘pay’), trestat (‘punish’), and jásat
3
Mojmír Dočekal, Marcin Wągiel
Figure 1: Distribution of dvakrát
Figure 2: Distribution of dvojnásobně
4
Event and degree numerals:
Evidence from Czech
ied cases it targets scales. The observed contrast suggests that dvakrát naturally
favors event-denoting environments (though it can appear in comparatives and
equatives) whereas dvojnásobně exhibits a very strong tendency to select for degree
expressions.
In the following sections, we will examine two contexts we assume to be crucial
for understanding the character of the event/degree numerals alternation as
well as further contrasts and differences between those expressions.
3 Key contexts
3.1 Degrees and differentials
The first environment to be discussed is constituted by degree constructions involving
comparison. Both event and degree numerals can appear in comparatives
as differentials, as attested by the examples from the CNC corpus in (4).
(4) a. …je
is
dnes
today
až
even
dvojnásobně
doubly
větší
bigger
nebezpečí
danger
ničivých
destructive
povodní
floods
než
than
před
before
20
20
lety.
years
‘…today, the danger of destructive floods is two times bigger than 20
years ago.’ (CNC)
b. …a
and
tak
thus
se
REFL
dokážou
manage
dvakrát
twice
rychleji
faster
ohřát
heat
nebo
or
zchladit
cool-down
než
than
běžné
ordinary
žehličky.
irons
‘…and thus they can heat or cool down two times faster than ordinary
irons.’ (CNC)
Furthermore, both event and degree numerals are unacceptable in superlatives,
as (5) demonstrates.6
(‘rejoice’) which arguably at least to some extent also pertain to the notion of gradability.
6
Event numerals may appear as superlative modifiers, e.g., in the past tense. However, a sentence
such as (i) has only an event reading which states that there were two occasions on
which Petr was the tallest one among the compared individuals. Therefore, it seems that in
such cases the event numeral modifies the whole phrase, i.e., the copula and the superlative,
rather than the superlative alone.
(i) Petr
Petr
byl
was
dvakrát
twice
nejvyšší.
tallest
5
Mojmír Dočekal, Marcin Wągiel
(5) a. *Petr
Petr
je
is
dvakrát
twice
nejvyšší.
tallest
b. *Petr
Petr
je
is
dvojnásobně
doubly
nejvyšší.
tallest
Nevertheless, an interesting contrast arises when we consider differentials in
equatives. Though Czech event numerals are perfectly fine in such an environment,
see (6), degree numerals are significantly less acceptable in equatives than
in comparatives, as witnessed by the oddity of (7-b).7 In addition, there are no
attested occurrences of equatives with degree numerals in CNC.
(6) a. Petr
Petr
je
is
dvakrát
twice
vyšší
taller
než
than
Marie.
Marie
‘Petr is two times taller than Marie.’
b. Petr
Petr
je
is
dvakrát
twice
tak
so
vysoký
tall
jako
as
Marie.
Marie
‘Petr is twice as tall as Marie.’
(7) a. Petr
Petr
je
is
dvojnásobně
doubly
vyšší
taller
než
than
Marie.
Marie
‘Petr is two times taller than Marie.’
b. *Petr
Petr
je
is
dvojnásobně
doubly
tak
so
vysoký
tall
jako
as
Marie.
Marie
This property of degree numerals corresponds to the behavior of standard differentials
which, as indicated in (8), although frequently attested in comparatives,
are not possible in equatives.8
(8) a. Petr
Petr
je
is
o
by
10
10
cm
cm
vyšší
taller
než
than
Marie.
Marie
‘Petr is 10 cm taller than Marie.’
b. *Petr
Petr
je
is
o
by
10
10
cm
cm
tak
so
vysoký
tall
jako
as
Marie.
Marie
These data seem to suggest that though both event and degree numerals can
‘Petr was the tallest twice.’
7
A similar contrast between twice and two times in English has been observed in Gobeski (2011).
8
As an anonymous reviewer points out it seems that (8-b) is out because equatives need to
apply AP internally, before the degree variable d is bound, for instance by pos (e.g., Kennedy
& McNally 2005).
6
Event and degree numerals:
Evidence from Czech
operate on scales, they differ in that they employ distinct strategies to modify
the degree they target. On the basis of the presented evidence, we assume it
is plausible to hypothesize that degree numerals share core semantic properties
with differentials. On the other hand, the compatibility of event numerals with
equatives seems to imply that they are expressions of a very distinct type.
3.2 Count events
The second key environment to be discussed here involves VPs referring to individuated
count events. Multiple examples attested in the CNC corroborate the
well-known fact that event numerals can combine with VPs in order to quantify
over eventualities. Interestingly, as witnessed by the ungrammaticality of (9-b),
degree numerals cannot be used to count events.
(9) a. Dvakrát
twice
se
REFL
přesvědčím,
I-will-ensure
že
that
jsou
are
dvířka
door
zavřená.
closed
‘I will make sure twice that the door is closed.’ (CNC)
b. *Dvojnásobně
doubly
se
REFL
přesvědčím,
I-will-ensure
že
that
jsou
are
dvířka
door
zavřená.
closed
Not surprisingly, neither event nor degree numerals modify VPs denoting homogeneous
eventualities such as static states, as demonstrated in (10). As expected,
no such examples were found in the CNC samples.
(10) a. *Petr
Petr
dvakrát
twice
zná
knows
Marii.
Marie
b. *Petr
Petr
dvojnásobně
doubly
zná
knows
Marii.
Marie
Another observation concerns VPs referring to values on scales. While both
event and degree numerals can modify verbs such as vzrůst (‘increase’), there
is an asymmetry with respect to possible readings of sentences containing such
phrases. Let us consider the contrast between (11-b) from the CNC and the corresponding
example in (11-a). As indicated in the translation, (11-a) is ambiguous
between the quantified-degree and the quantified-event interpretation, i.e., it is
either true of a scenario when the demand increased by two times irrespective
of the number of times it increased, or of a situation when there were two events
of increasing the demand irrespective of the value by which the demand was increased.
Crucially, (11-b) lacks the quantified-event interpretation and can only
be true of a scenario in which the degree of increase was multiplied by two.
7
Mojmír Dočekal, Marcin Wągiel
(11) a. Poptávka
demand
po
after
dotacích
subsidies
vzrostla
increased
dvakrát.
twice
‘The demand for subsidies increased (by) twice.’
b. Poptávka
demand
po
after
dotacích
subsidies
vzrostla
increased
dvojnásobně.
doubly
‘The demand for subsidies increased doubly.’ (CNC)
The discussed observations further support the semantic nature of the event/degree
numerals alternation. At this point, it seems innocuous to state that the distinction
relies on the strategy the expressions in question make use of in terms of
quantification. Whereas degree numerals are unable to count events and are restricted
to operations on degrees, event numerals seem to employ a more general
semantics which allows for quantification over both events and degrees. Further
differences will be examined in the next section.
4 More contrasts
4.1 Categorial differences
Another difference between Czech event and degree numerals concerns their
derivational potential. Both classes involve morphologically complex expressions
derived from a numeral root, e.g., dv- (corresponding to English tw-), by
different suffixes, i.e., -krát and -násobn-.9 However, the contrast between (12)
and (13) indicates an apparent categorial asymmetry. Unlike degree numerals
which employ distinct morphology to display a broad range of syntactic categories
including adverbial, adjectival, and nominal forms (all derived from the
same stem), event numerals are defective in the sense that they have only adverbial
forms and cannot appear in syntactic contexts which are sensitive for
adjectives and nominals.10
(12) dvakrát:
9
In fact, -násobn- can be further decomposed at lest to -násob-, as attested in násobit (‘multiply’),
and -n-. For the sake of simplicity, we will ignore the morphological complexity here.
10
It should be noted that the inability of event numerals to take adjectival and nominal morphology
seems to be a Czech idiosyncrasy since, for instance, Polish allows for forms such
as dwukrotny (‘twice.A’) and dwukrotność (‘twice.N’). Similar, there is adjectival dvukratnyj in
Russian and dvakratni in Slovenian. However, a detailed cross-linguistic comparison of event
and degree numerals is beyond the scope of this paper and constitutes a challenge for further
research.
8
Event and degree numerals:
Evidence from Czech
a. Adv: pršelo
rained
dvakrát
twice
‘it rained twice’
b. *A: [dvakrát(ní)
twice.A
objem
capacity
nádrže]
tank
c. *N: [dvakrát(ek)
twice.N
rychlosti]
speed
(13) dvojnásob-:
a. Adv: dvojnásobně
doubly
dlouhý
long
‘two times longer’
b. A: dvojnásobný
double
objem
capacity
nádrže
tank
‘double the capacity of a tank’
c. N: dvojnásobek
double.N
ceny
price
‘double the price’
Although the categorial asymmetry provided in (12) and (13) may suggest that
event and degree numerals are exponents of distinct semantic objects, as such it
is, of course, insufficient to draw a typal distinction between the two. In the next
section, we investigate such a possibility in more detail.
4.2 Typal compatibility
A further observation concerns the fact that event and degree numerals in Czech
can be stacked, as witnessed by the grammaticality of examples such as (14-a).
This suggests that Czech expressions of those kinds are compatible in terms of
their semantic types. Moreover, the reversed order of numerals, as provided in
(14-b), is not possible which further suggests different input requirements.
(14) a. Petrovi
for-Petr
se
REFL
to
this
třikrát
thrice
dvojnásobně
doubly
vyplatilo.
paid-off
‘For Petr it paid off doubly three times.’
b. *Petrovi
for-Petr
se
REFL
to
this
dvojnásobně
doubly
třikrát
thrice
vyplatilo.
paid-off
Furthermore, there is solid evidence that unlike event numerals, degree numerals
are anchored to a particular event. Let us consider possible interpretations of
9
Mojmír Dočekal, Marcin Wągiel
a sentence such as (15) in which the conjoined NP in subject position denotes a
plurality of entities whereas the modified VP refers to a plurality of events. As
indicated in (15-a) and (15-b), the sentence can either have a distributive reading
where the events of paying off doubly are distributed equally onto each of the
individuals, i.e., Petr and Honza, or a collective reading in which it payed off
doubly three times for Petr and Honza as a group. Moreover, a cumulative interpretation
as in (15-c) is also possible. In such a scenario there was a total of three
events of paying off doubly and Petr and Honza share the total gain disproportionately.
Nevertheless, (15) cannot have a meaning such as the one in (15-d) or
in (15-e). It is impossible to understand the sentence in such a way that the total
gain corresponds to six units, similar to (15-b) or (15-c), but the total number of
events is lesser or greater than three. Such cumulations are simply unaccessible
which implies that degree numerals cannot outscope the event quantifier and are
forced to operate on degrees within a particular event.
(15) Petrovi
for-Petr
a
and
Honzovi
for-Honza
se
REFL
to
this
třikrát
thrice
dvojnásobně
doubly
vyplatilo.
paid-off
‘For Petr and Honza it paid off doubly three times.’
a. for
for
Petr:
Honza:
3
3
x
x
(it-paid-off
(it-paid-off
x
x
2)
2)
b. for Petr⊕Honza: 3 x (it-paid-off x 2)
c. for
for
Petr:
Honza:
2
1
x
x
(it-paid-off
(it-paid-off
x
x
2)
2)
d. *for Petr⊕Honza: 2 x (it-paid-off x 3)
e. *for
for
Petr:
Honza:
4
1
x
x
(it-paid-off
(it-paid-off
x
x
1)
2)
The data clearly demonstrate that adverbial event and degree numerals differ
with respect to their semantic type and scopal properties. The following sections
explore some additional semantic phenomena related to adjectival and nominal
forms of degree numerals.
5 Adjectival and nominal degree numerals
5.1 Quantification over amounts and values
Let us now consider Czech adjectival degree numerals such as dvojnásobný (‘double/twotime’).
The CNC data confirm the intuition that such expressions often modify
10
Event and degree numerals:
Evidence from Czech
amount nominals and nouns implicitly associated with scales like those in (16).11
In those contexts, the degree numeral appears to multiply a contextually provided
value on a particular scale. As a result, the predicates in (16) are true of a
twice as high volume and a twice as high salary, respectively.
(16) a. dvojnásobný
double
objem
volume
‘double the volume’
b. dvojnásobný
double
plat
salary
‘double the salary’
Interestingly, adjectival degree numerals are not compatible with container nouns,
as the contrast between (17-a) and (17-b) shows. This property differentiates them
from basic cardinal numerals since in order to quantify over amounts determined
by container nominals Czech requires cardinals to do the job, see (17-c). Czech
cardinals, however, are unable to combine with amount nouns to count quantities,
as witnessed by the ungrammaticality of (17-d).
(17) a. dvojnásobné
double
množství
amount
čaje
tea
‘double the amount of tea’
b. *dvojnásobný
double
hrnek
cup
čaje
tea
c. dva
two
hrnky
cups
čaje
tea
‘two cups of tea’
d. *dvě
two
množství
amount
čaje
tea
The data discussed above show that degree numerals and cardinals are in complementary
distribution with respect to container and amount nouns. This fact
suggests that the two types of expressions in question make use of distinct quantificational
strategies and should be analyzed differently.
11
In the CNC, among the 15 most frequent collocation candidates for the lemma dvojnásobný
(1,567 occurrences in SYN2015) one can find the followings nouns: počet (‘number’), množství
(‘amount’), cena (‘price’), and rychlost (‘speed’).
11
Mojmír Dočekal, Marcin Wągiel
5.2 Events and social roles
Amount nouns do not exhaust the combinatorial potential of adjectival degree
numerals since they can also modify two other classes of expressions, specifically
nominals referring to events, as exemplified in (18-a), as well as nominals denoting
social functions such as, e.g., family roles and public capacities, see (18-b).12
Nevertheless, the interpretation of such phrases differs from the meaning of, e.g.,
(16) in which the degree numeral seems to merely multiply the value indicated by
the implicit degree argument of the amount nominal. For instance, (18-a) refers
to a set of murdering events involving two victims in each such an event, i.e., the
degree numeral seems to access an internal argument of the deverbal nominal.
On the other hand, similar to what was observed in Wągiel (2015b) examples
such as (18-b) denote a set of individuals that have gained a particular property
two times – in this case, the property of becoming a champion.13
(18) a. dvojnásobná
double
vražda
murder
‘double murder’
b. dvojnásobný
double
mistr
champion
‘two-time champion’
Further evidence that amount noun phrases and nominals implicitly associated
with scales substantially differ from nominals denoting events or social roles
modified by adjectival degree numerals comes from the distribution of nominal
degree numerals such as dvojnásobek (‘double.N’). As demonstrated in (19), such
nominalizations cannot take expressions referring to events or social roles as
their complements though they frequently combine with amount nominals.14
(19) a. dvojnásobek
double.N
rychlosti
speed
‘double the speed’
12
The CNC collocation candidates list includes, among others, the following examples for the
first class: vražda (‘murder’), přesilovka (‘power play’), and radost (‘joy’), as well as vítěz (‘winner’),
matka (‘mother’), and účastník (‘participant’) for the latter.
13
Notice that such behavior seems to be a Czech idiosyncrasy since many other languages make
use of a different adjective to express such a meaning, e.g., see the English translation in (18-b).
14
For instance, the CNC lists the following among the 15 most frequent collocation candidates
for the lemma dvojnásobek (845 hits in SYN2015): cena (‘price’), částka (‘sum of money’), počet
(‘number’), and velikost (‘quantity’).
12
Event and degree numerals:
Evidence from Czech
b. *dvojnásobek
double.N
mistra
champion
c. *dvojnásobek
double.N
vraždy
murder
Moreover, the asymmetry is further supported by the contrast in (20). In such
examples, je (‘is’) is not used as a copula of predication, but rather it seems to
establish the identity relation between the denotation of its complement and that
of the subject noun phrase.15 In (20-a), the definiendum, i.e., the modified degree
noun, is associated with the definiens comprising the comparative construction.
On the other hand, (20-b) and (20-c) are odd since neither mistr (‘champion’),
nor sebevražda (‘suicide’) provides a degree argument to be accessed by the degree
numeral, and thus the subject NPs are not equivalent to the corresponding
comparatives. In other words, since the subjects and the nominals within the
matrix predicates in (20-b) and (20-c) refer to different entities, establishing of
the identity relation is impossible.16
(20) a. Dvojnásobná
double
rychlost
speed
je
is
dvakrát
twice
větší
bigger
rychlost.
speed
‘Double the speed means two times higher speed.’
b. #Dvojnásobný
double
mistr
champion
je
is
dvakrát
twice
větší
bigger
mistr.
champion
c. #Dvojnásobná
double
sebevražda
suicide
je
is
dvakrát
twice
větší
bigger
sebevražda.
suicide
The contrasts described above indicate that adjectival and nominal degree numerals
display heterogeneous behavior in interaction with nouns implicitly associated
with scales on the one hand and with event and social role nominals on
the other. Possibly, the relationship between the two types of phrases is much
less straightforward than it might initially seem. In this paper, however, we are
primarily concerned with examples such as (16-a) and we assume that use of
15
Note that (20-a) is ungrammatical with the Instrumental, see (i), which is commonly associated
with predication.
(i) *Dvojnásobná
double
rychlost
speed
je
is
dvakrát
twice
větší
bigger
rychlostí.
speed.instr
16
This property seems to resemble some sort of a monotonicity constraint, as discussed in
Schwarzschild (2002). However, the exact nature of this phenomenon requires further
investigation.
13
Mojmír Dočekal, Marcin Wągiel
adjectival degree numerals to be the basic one.
5.3 Predicate position
Finally, the last observation concerns the attributive and predicative use of adjectival
degree numerals. In all the examples provided in the previous sections,
dvojnásobný appears as a nominal modifier which seems to be the most natural
syntactic context for such an expression. Nevertheless, it is not unusual to find
dvojnásobný in predicate position as well, as attested in the CNC sentences in (21).
In both examples, the degree numeral serves as a main predicate of a sentence
and attributes a property to an amount denoting subject, i.e., údaj (‘number’) and
hodnota (‘value’) respectively. For instance, in (21-a) it is predicated of the value
corresponding to the body fat percentage in men in their seventies that it is twice
as high relative to value for men in their twenties, i.e., it amounts to 29%. Similar,
in (21-b) dvojnásobný functions as a predicate assigning a property to the value
of saved property such that it is two times higher than the value corresponding
to the damages.
(21) a. …podíl
proportion
tuku
fat
v
in
těle
body
[…]
[…]
průměrný
average
dvacátník
twenty-year-old-man
jej
it
má
has
14,5 %,
14,5%
údaj
number
pro
for
sedmdesátníky
seventy-year-old-men
je
is
dvojnásobný.
double
‘…the body fat percentage […] for an average man in his twenties it
is 14,5% whereas for men in their seventies the number is twice as
high.’ (CNC)
b. …škoda
damage
dosahuje
reaches
asi
approximately
50
50
tisíc
thousand
korun.
crowns
Hodnota
value
uchráněného
saved
majetku
property
je
is
dvojnásobná.
double
‘…the damages reach approximately 50 000 CZK. The value of saved
property is twice as high.’ (CNC)
Sentences such those in (21) are far less frequent in the CNC than examples with
adjectival degree numerals in attributive position. However, we regard their existence
as an important piece of evidence revealing the predicative nature of
degree numerals.
14
Event and degree numerals:
Evidence from Czech
6 Data summary
Before we move on to the semantic analysis of the event/degree numerals distinction,
let us briefly recapitulate our empirical findings. Table 1 summarizes
the observed contrasts.17
Property Event numerals Degree numerals
Morphology Adv Adv/A/N
Degree yes yes
Diff. in comparatives yes yes
Diff. in superlatives no no
Diff. in equatives yes no
Modify count events yes no
Modify degree events yes yes
Events (N) no yes
Roles (N) no yes
Table 1: Properties of event and degree numerals
In brief, event numerals are able to target both events and degrees. They have
only adverbial forms and tend to appear in eventive environments though they
can also modify degree constructions including comparatives and equatives. On
the other hand, degree numerals cannot scope over events and they heavily favor
scalar contexts excluding equatives. Not only can they take adverbial and nominal,
but also adjectival morphology and as such they can quantify over amounts,
arguments of events, as well as time intervals associated with social roles specified
by nominals they modify. In the next sections, we attempt to account for at
least some of the puzzling differences between the two classes of expressions in
question. We will propose an analysis of adverbial degree numerals and suggest
possible directions of development to account for the meaning of event numerals
as well as adjectival degree numerals.
17
In bold we have emphasized the most frequent environments based on the CNC corpus study.
15
Mojmír Dočekal, Marcin Wągiel
7 Proposal
7.1 Degree numerals
On the basis of the distributional evidence, we argue that the comparative examples
introduced in Section 3.1 reveal the true nature of degree numerals. Let us
now consider more closely the example in (7-a), repeated here as (22). The truth
conditions of the sentence are specified informally in (22-a) and (22-b) gives an
exemplary situation of which the sentence would be true.
(22) Petr je dvojnásobně vyšší než Marie.
Petr is doubly higher than Marie
‘Petr is two times taller than Marie.’
a. True in all situations where the gap between Petr’s and Marie’s height
is equal to the height of Marie
b. µheight(Petr) = 180 ∧ µheight(Marie) = 90
Building on the observations discussed in Section 3.1, we acknowledge that degree
numerals seem to behave similar to differentials in that they define the
difference between compared values on a scale provided by the comparative.
Nonetheless, we argue that the underlying mechanism which yields such a result
is distinct. Degree numerals differ from typical differentials in that they do
not determine the gap in terms of some absolute value, e.g., 10 cm as in (8-a).
Instead, they provide information about the degree corresponding to a correlate
in terms of the value related to a standard of comparison. For instance, in (22)
the degree numeral specifies the height of the correlate, i.e., Petr, in terms of the
multiplied height of the standard of comparison, i.e., Marie.
We are now ready for the first approximation. Based on the observation discussed
in Section 5.3, namely that dvojnásobný can occur in predicate position,
see (21), we propose that the primary interpretation degree numerals have is the
predicative one. Furthermore, based on the morphological evidence examined in
Section 4.1, we assume that Czech degree numerals are compositional. We posit
that numeral roots simply refer to numbers modeled as abstract entities and as
such are expressions of type n. On the other hand, the suffix -násobn- introduces
an operation involving multiplication of a degree by a number denoted by the
root. Therefore, we model degree numerals as degree predicates, i.e., expressions
denoting a characteristic function of degrees (type ⟨d, t⟩). We posit that such a
function yields the truth value True iff a selected degree d is two times higher
than some contextually determined value g. The semantics for dvojnásobný is pro-
16
Event and degree numerals:
Evidence from Czech
posed in (23-a) whereas (23-b) gives the abstracted meaning of degree numerals
in general.
(23) a. dvojnásobně = λd[d = 2 × g] type ⟨d, t⟩
b. Degree Numeral = λnλd[d = n × g] type ⟨n, ⟨d, t⟩⟩
Let us now consider how (23-a) accounts for the meaning of (21-a). The denotation
of the subject NP (an expression of type d), i.e., the body fat percentage for
seventy year old men, has the property of being equal to the body fat percentage
for men in their twenties multiplied by two. The logical type of the degree
numeral is ⟨d, t⟩, hence the composition of (21-a) is trivial and proceeds via the
standard rule of Function Application. The predicate of degrees (type ⟨d, t⟩) is
applied to the degree denoting subject (type d) and after the degree variable is
saturated a truth value is obtained.
7.1.1 Comparatives
Before we demonstrate how the proposed semantics fits into the big picture involving
comparatives and equatives, let us introduce several assumptions concerning
gradability and comparison we make. First of all, we adopt the standard
view and assume an ontology including degrees, i.e., objects of a primitive type
d, which are ordered into scales. A scale is modeled as a triple ⟨D, >, DIM⟩
where D is a set of degrees, > is an ordering relation on D, and DIM represents
a dimension of measurement such as height or weight. Notice, however,
that we embrace the interval-based approach to degrees (e.g., Kennedy 2001 and
Schwarzschild & Wilkinson 2002).
Second, following Solt (2014) we assume that individuals are associated with
scales via measure functions that map an entity to the unique degree on the scale
corresponding to the particular dimension. For instance, the measure function
µheight yields the measure of an individual with respect to the dimension of
height. Thus, the semantics of a gradable adjective such as tall looks like (24).
(24) tall = λdλx[µheight(x) ≥ d]
However, we slightly diverge from the standard semantics for the comparative
(e.g., Von Stechow 1984, Heim 2000, and Schwarzschild 2008) in that we model
the comparative marker in constructions such as (22) as involving the ≥ (rather
than >) relation between maximal degrees corresponding to compared entities
on a provided scale, as in (25) (see Gobeski & Morzycki 2017 for a similar treatment
of -er in English percentage differential comparatives). What is important
17
Mojmír Dočekal, Marcin Wągiel
is that the ≥ relation may be pragmatically strengthened to = unless a suitable
context prevents strengthening. We will discuss this issue in more detail below.
(25) −erfactor = λD′λD[max(D) ≥ max(D′)] type ⟨⟨d, t⟩, ⟨⟨d, t⟩, t⟩⟩
Furthermore, we assume the standard syntactic analysis of comparatives. In particular,
we adopt the so-called small DegP view on which the comparative marker
-er and the than-clause form a constituent at LF and the entire DegP serves as an
argument of the gradable predicate (e.g., Heim 2000), as illustrated in (26).
(26) AP
DegP
Deg
-er
PP
[than…]
A
tall
Finally, following Pancheva (2006) we assume that Slavic comparatives such as
(22) involve an elided clause introducing the maximal interval corresponding to
a standard of comparison on a proper scale. Within such an approach, Czech
clausal comparatives such as (27-a) are analyzed as in (27-b).
(27) a. Petr
Petr
je
is
vyšší
taller
než
than
Marie.
Marie
‘Petr is taller than Marie.’
b. LF: [IP [IP Petr is d1-tall] [ DegP -er1 [PP than [CP Marie is d-tall]]]]
In the assumed structure, the comparative morpheme is interpreted as an operation
that takes a set of degrees and returns a function from a set of degrees to
a truth value (type ⟨⟨d, t⟩, ⟨⟨d, t⟩, t⟩⟩). As discussed in detail in Pancheva (2006),
such typing is incompatible with the denotation of the than-clause since as a free
relative it is interpreted as a definite description, i.e., a degree denoting expression
of type d (Heim 2000). To remedy such a type clash, some approaches (e.g.,
Von Stechow (1984) and Rullmann (1995)) attribute a non-trivial semantics to
than.18 We follow this line of analysis. In particular, we adopt Pancheva (2006)’s
treatment of than as a partitive preposition in the domain of degrees which in
clausal comparatives gets the semantics in (28).
18
This contrasts with the standard view assuming that than is semantically vacuous (e.g., Heim
2000, Kennedy 2001, and Schwarzschild & Wilkinson 2002).
18
Event and degree numerals:
Evidence from Czech
(28) than = λd′λd[d is part of d′] type ⟨d, ⟨d, t⟩⟩
In prose, than takes a denotation of a free relative clause, i.e., a degree d, and
yields a set of degrees which d is member of. For instance, if the standard of
comparison in (27-a), i.e., Marie, corresponded to, e.g., 170 cm, then the entire
than-clause would denote a set of degrees in the interval between 0 and 170 on
the scale of height calibrated in centimeters. In terms of semantic types, the result
of than being applied to the standard of comparison is an expression of type ⟨d, t⟩
which can serve as the first argument of the comparative morpheme. We assume
that the same mechanism applies to the Czech preposition než (‘than’).
With all the ingredients in place, let us now consider how the pieces fit together.
Assuming that Heim & Kratzer (1998)’s rule of Predicate Modification
applies also to degree predicates, the adopted analysis creates a plausible attachment
site for degree numerals. Since they are expressions of type ⟨d, t⟩, we propose
that they can modify the PP node resulting in a syntactically more complex
argument for Deg, as illustrated in the tree in (29). Crucially, the derived
expression is also of type ⟨d, t⟩ which is suitable for the interpretation by the
comparative morpheme.
(29) DegP
⟨⟨d, t⟩, t⟩
Deg
⟨⟨d, t⟩, ⟨⟨d, t⟩, t⟩⟩
-ší
PP
⟨d, t⟩
Degree Numeral
⟨d, t⟩
dvojnásobně
PP
⟨d, t⟩
P
⟨d, ⟨d, t⟩⟩
než
CP
d
Marie is d1-tall
The composition proceeds as follows. The proposition než takes the maximal interval
to which Marie is tall as its input and yields a set of degrees which are
part of that interval. Subsequently, the degree numeral combines with the PP
19
Mojmír Dočekal, Marcin Wągiel
via Predicate Modification, and thus multiplies each member of the set by two.
The output is a set of intervals that are two times bigger than the intervals corresponding
to Marie’s height and can serve as the first argument of the comparative
morpheme -ší. The comparative morpheme applies the maximization operation
max which picks the degree, i.e., the maximal interval, to which Marie is tall
multiplied by two. As a result, the whole sentence is true iff the degree on a
scale of height corresponding to the correlate, i.e., Petr, is equal or exceeds the
value corresponding to Marie, as stated in the truth-conditions in (30-a). However,
this is not the way one would normally understand a sentence such as (22).
In order to account for that deficiency, we propose that (30-a) gets strengthened
to (30-b), i.e., the ≥ relation is replaced by =, which finally gives rise to an expedient
result. We assume that the pragmatic enrichment results from a scalar
implicature, a consequence of the competition between dvojnásobně and higher
degree numerals similar to what has been proposed in the neo-Gricean theories
of cardinals (e.g., Horn 1972).
(30) a. (22) = max(λd.µheight(Petr) ≥ d) ≥ max(λd′.d′ = 2×µheight(Marie))
b. ⇝ (22) = max(λd.µheight(Petr) ≥ d) = max(λd′.d′ = 2 ×
µheight(Marie))
On the other hand, in a sentence such as (31-a) where aspoň (‘at least’) prevents
from the pragmatic inference the unstrengthened meaning unearths and we obtain
the at least interpretation given in (30-a). The lack of pragmatic enrichment
in examples such as those in (31) is parallel to well-studied cases like more than
three boys where the modified numeral never gives rise to a scalar implicature
(see, e.g., Krifka 1999 and Schulz & Van Rooij 2006). Another observation concerns
the disappearance of scalar implicatures in downward-entailing contexts
as in (31-b). Unlike (22), (31-b) deos not suggest that Petr’s height cannot correspond
to Marie’s height multiplied by three or more. We regard it as an argument
for the competition account resulting in the strengthening of (30-a) to (30-b).
(31) a. Petr
Petr
je
is
aspoň
at-least
dvojnásobně
doubly
vyšší
taller
než
than
Marie.
Marie
‘Petr is at least two times taller than Marie.’
b. Petr
Petr
není
isn’t
dvojnásobně
doubly
vyšší
taller
než
than
Marie.
Marie
‘Petr is not two times taller than Marie.’
The developed account seems to deliver desirable results. Not only have we provided
an explanation of the semantic composition of degree numerals within the
20
Event and degree numerals:
Evidence from Czech
structure of the DegP but also we have proposed a plausible analysis of how
comparatives modified by factor phrases involving degree numerals are being
interpreted.
7.1.2 Equatives
So far we have demonstrated how our proposal accounts for the interaction between
degree numerals and comparatives. Let us now turn to one of the main
puzzles of the paper, namely the incompatibility of degree numerals with equatives,
as witnessed by the ungrammaticality of (7-b) repeated here as (32).
(32) *Petr
Petr
je
is
dvojnásobně
doubly
tak
so
vysoký
tall
jako
as
Marie.
Marie
We assume that similar to comparatives equative sentences involve a CP with
elided material. However, unlike comparatives equatives lack an element such
as than which would shift the type of a free relative of degrees to ⟨d, t⟩. Therefore,
are at LF an equative sentences such as (33-a) gets the structure in (33-b) where
the DegP takes the CP as its argument directly (see Gobeski & Morzycki 2017 for
a similar analysis of equatives).
(33) a. Petr
Petr
je
is
tak
so
vysoký
tall
jako
as
Marie.
Marie
‘Petr is as tall as Marie.’
b. LF: [IP [IP Petr is d1-tall] [DegP as… as1 [CP Marie is d-tall]]]
Additional evidence suggesting that the proposed analysis is on the right track
comes from the morpho-syntax of Slavic equatives. In Czech, the equative contains
only the wh-element jako (‘as; literally: how’) and the non-obligatory demonstrative
pronoun tak (‘so; literally: like this’) which precedes the adjective. Unlike
in the comparative, there is no preposition or complementizer.
The final assumption concerns the denotation of the equative marker. We follow
the standard view that the meaning of as… as differs from the semantics
of the comparative morpheme. However, we argue that it is not the case that
the only difference between the two lies in employing the = or ≥ relation instead
of >, as often assumed (e.g., Rett 2014a). On contrary, we propose that
unlike -er which requires a set of degrees as its first argument, see (25), as… as
yields a function from sets of degrees to truth values for a particular degree (type
⟨d, ⟨⟨d, t⟩, t⟩⟩), see (34). In other words, the equative operates on the maximal interval
associated with a standard of comparison rather than on a set of degrees.
21
Mojmír Dočekal, Marcin Wągiel
This seems intuitively correct since equative constructions appear to evaluate
values with respect to a particular degree rather than to a set of intervals. We
assume the same applies to Czech tak… jako.
(34) as… as = λdλD[max(D) ≥ d] type ⟨d, ⟨⟨d, t⟩, t⟩⟩
Given the components discussed above, the reason why degree numerals are
incompatible with equatives is simply because of type mismatch. Consider the
structure of the DegP illustrated in (35). Since the equative does not involve the
node of type ⟨d, t⟩ but rather the CP of type d, the degree numeral cannot combine
with any expression within the DegP via Predicate Modification. In principle,
Function Application would still be applicable. Nevertheless, if a definite
description denoted by the CP saturated the degree variable, the resulting expression
could not combine with the equative marker. In any case, the derivation of
(7-b) would necessarily crash.
(35) DegP
⟨⟨d, t⟩, t⟩
Deg
⟨d, ⟨⟨d, t⟩, t⟩⟩
tak… jako
CP
d
Marie is d1-tall
At this point, we consider the main puzzle of the paper solved. The (in)compatibility
of degree numerals with comparatives and equatives is essentially type-driven.
Degree numerals are of type ⟨d, t⟩, and thus in comparatives they modify the
than-clause of the same type. On the other hand, since there is no such node
available in equatives, degree numerals cannot find a plausible attachment site
which leads to type mismatch and unacceptability of sentences such as (7-b). In
Section 7.2.2, we will demonstrate that event numerals, unlike degree numerals,
can appear in both comparatives and equatives due to the fact that they are of
a different semantic type. However, before we move to dvakrát, let us briefly
discuss adjectival degree numerals such as dvojnásobný.
7.1.3 Adjectival degree numerals
So far, the proposed semantics for degree numerals seems to work well. However,
it is insufficient to account for the data which involve adjectival dvojnásobný
22
Event and degree numerals:
Evidence from Czech
modifying event and social role nominals, as discussed in Section 5.2. Inspired
by Rett (2014b)’s M-Ope and M-Opd operators, we propose that the analysis of
degree numerals can be extended by adopting operations which introduce mappings
between entities, events, degrees, and time intervals.
In general, quantified noun phrases exhibit an individual/degree polysemy
(Rett 2014b). This is also true for Czech NPs modified by cardinal numerals. (36-a)
has an individual reading on which five individuated portions (or sorts) of beer
were such that they were top-fermented. On the other hand, (36-b) refers to the
amount of beer rather than to particular entities (or sorts).
(36) a. Pět
five
piv
beers
bylo
was
svrchně
top
kvašených.
fermented
‘Five beers were top-fermented.’
b. Pět
five
piv
beers
bylo
was
pro
for
Karla
Karel
dost/Karlovi
enough/for-Karel
stačilo.
was-enough
‘For Karel, five beers were enough.’
For degree numerals, we assume that the degree interpretation is the basic one, as
in (37) where adjectival dvojnásobný modifies the amount nominal plat (‘salary’)
in order to multiply the relevant degree.19 Apart from the data already introduced
in favor of such a claim, further evidence comes from the fact that degree numerals
can target gradable nouns such as idiot (see Morzycki 2009), as indicated
in (38) which is an attested example from the CNC. The second clausal conjunct
means that the speaker attributes to themselves the level of idiocy which is twice
as high as the contextually relevant value. It is the internal degree argument of
the predicate idiot that is targeted by the degree numeral.
(37) Dvojnásobný
double
plat
salary
Karlovi
for-Karel
stačil.
was-enough
‘For Karel, double salary was enough.’
(38) Bratr
brother
Čuchraj
Čuchraj
je
is
idiot
idiot
a
and
lhář
liar
a
and
já
I
dvojnásobný
double
idiot…
idiot
‘Frater Čuchraj is an idiot and a liar and I am a double idiot…’ (CNC)
Similar, in the case of modified measure nouns such as dvojnásobný objem (‘double
volume’), see (16-a), we assume that the degree numeral quantifies over the
19
We assume that the composition involves at least the following steps: (i) modification of the
amount noun (type ⟨d, t⟩) by the degree numeral via Predicate Modification and then (ii) typeshifting
of the entire phrase to the type d via the ι operation.
23
Mojmír Dočekal, Marcin Wągiel
degree though it does not supply the dimension µ. The relevant dimension seems
to be always provided by the modified predicate. For instance, in (39-a) it is the
adjective that feeds the adverbial degree numeral with the dimension of size.
Likewise, in (39-b) and (39-c) the measure noun and the gradable noun supply
the dimensions of length and idiocy, respectively.
(39) a. dvojnásobně
doubly
velký
big
‘twice as big’
b. dvojnásobná
double
délka
length
‘double the length’
c. dvojnásobný
double
idiot
idiot
‘double idiot’
In the discussed examples, the degree numeral simply multiplies values on a
proper scale, hence it seems that the proposed degree semantics can be extended
straightforwardly to capture such cases. We assume that the core of the analysis
of dvojnásobně given in (23) would carry over to examples such as (39). In such
examples, the degree numeral predicates of a degree supplied by the adjective,
measure noun, or gradable noun, compared to a contextually supplied value in
comparatives. However, due to lack of space we have to postpone a thorough
implementation. Instead, in the next section we will try to suggest a way of
dealing with the data that pose a more serious challenge.
7.1.4 Events and social role interpretations
In order to account for examples such dvojnásobná vražda (‘double murder’) and
dvojnásobný mistr (‘two-time champion’), see (18), we assume mappings between
events and entities on the one hand and entities and times on the other. Let us
start with proposing a treatment for the social role interpretation. In such cases
there is no internal degree argument the degree numeral could target. Therefore,
in order to approach, e.g., (18-b), we adopt the notion of time trace function (e.g.,
Krifka 1989 and Lasersohn 1995). A standard time trace function is an operation
which maps an event to its running time, i.e., the smallest time at which it occurs.
For our purposes, however, this is insufficient since in order to explain the behavior
of phrases such as (18-b) we need to relate events with entities. Therefore, we
assume a mapping of a property P, in this case: the property of being a champion,
24
Event and degree numerals:
Evidence from Czech
to its running time, i.e., the time of being a champion. Consequently, the degree
numeral counts the introduced running times which results in the predicate true
of entities that repetitively gained the property of being a champion.
The proposed approach predicts that the time reading can only be obtained for
nominals denoting properties which are constrained in time, i.e., either lowerbound,
as in the case of champion, or bilaterally bound in the case of, e.g., president.
In other words, adjectival degree numerals are only possible with nominals
denoting a property which can be felicitously associated with fluctuation within
the dimension of time (see Wągiel 2015b). For this reason, the phrases in (40-b)
constitute weird expressions.
(40) a. dvojnásobný
double
mistr
champion
‘two-time champion’
b. #dvojnásobný
two-time
Čech/člověk/pes
Czech-person/human/dog
However, the interpretation of modified deverbal nominals such as dvojnásobná
vražda (‘double murder’), see (18-a), cannot be explained in terms of time trace
function. In this case, we assume a mapping between properties of events and
entities related to those events as themes, i.e., such a function for a particular
event would return its themes. As a result, in (18-a) the two victims reading is
obtained.
7.2 Event numerals
Our proposal concerning event numerals builds on the classification developed
by Doetjes (2007) who on the basis of French data draws a distinction between
two classes of adverbs of quantification, namely degree expressions such as a
lot and frequency adverbs such as often. According to that proposal, the division
follows from the fact that the first involve degree modification whereas the latter
quantify over times.
7.2.1 Frequency and scope
Prima facie, event numerals seem to be similar to frequency adverbs since they
both imply iteration and, unlike degree expressions, can scope over indefinites.
The data in (41) illustrate the distinction between frequency and degree adverbs
in Czech. Since a similar contrast regards event and degree numerals, as demon-
25
Mojmír Dočekal, Marcin Wągiel
strated in (42), it might seem appealing to simply claim that they are representatives
of the corresponding classes.
(41) a. Petr
Petr
často
twice
kupoval
bought.ipfv
nějaké
some
pivo.
beer
‘Petr often bought some beer.’
b. *Petr
Petr
hodně
a-lot
kupoval
bought.ipfv
nějaké
some
pivo.
beer
(42) a. Petr
Petr
dvakrát
twice
koupil
bought.pfv
nějaké
some
pivo.
beer
‘Petr bought some beer twice.’
b. *Petr
Petr
dvojnásobně
doubly
koupil
bought.pfv
nějaké
some
pivo.
beer
According to Von Fintel (1994), frequency adverbs including event numerals can
be analyzed as expressions which quantify over situations and contain a hidden
domain anaphor. Following Doetjes (2007) in assuming an abstract restrictor
times, it is possible to analyze event numerals as in (43). The example in (42-a)
would then be interpreted as (44) which is true of two buying events in which
Petr is the agent and beer is the theme of that event.
(43) dvakrát: 2 [restriction times][nuclear scope VP/IP]
(44) ∃ex[µ(e) = 2 ∧ Buy(e) ∧ θ1(e) = Petr ∧ θ2(e) = x ∧ Beer(x)]
However, as Doetjes (2007) herself observes, there is a scopal asymmetry between
expressions such as often and event numerals, specifically frequency adverbs
can have a relational reading whereas event numerals cannot. For instance,
in (45) the frequency adverb často (‘often’) can be interpreted either as having a
wide or a narrow scope relative to když (‘when’). The relational reading in (45-a)
could be paraphrased as Often when he was in Budapest, Karel visited Gellért. On
the other hand, the non-relational reading in (45-b) would be interpreted along
the lines Whenever he was in Budapest, Karel often visited Gellért. Crucially, (46)
has only the interpretation in (46-b) and cannot mean something like Twice when
he was in Budapest, Karel visited Gellért.
(45) Když
when
byl
was
Karel
Karel
v
in
Budapešti,
Budapest
tak
then
byl
he-was
často
often
v
in
Gellértu.
Gellért
‘When Karel was in Budapest, he often visited Gellért.’
a. often > when
26
Event and degree numerals:
Evidence from Czech
b. when > often
(46) Když
when
byl
was
Karel
Karel
v
in
Budapešti,
Budapest
tak
then
byl
he-was
dvakrát
twice
v
in
Gellértu.
Gellért
‘When Karel was in Budapest, he visited Gellért twice.’
a. #twice > when
b. when > twice
Doetjes (2007) attributes the lack of relational reading to the incompatibility of
event numerals with the stative interpretation. However, event numerals differ
significantly from frequency adverbs in yet another respect, i.e., they are compatible
with comparatives and equatives and can access internal arguments of
degree verbs, as discussed in Section 3.1 and 3.2. On the other hand, frequency
adverbs cannot target scales of degrees. Neither (47-a), nor (47-b) can mean that
the height of Petr exceeds the height of Marie multiple times. The only possible
reading would be that there are many happenings in which Petr is taller or as
tall as Marie which is a very strange interpretation. Similar, (48) can only mean
that there were multiple events leading to increase of the demand, i.e., the degree
reading is unavailable.
(47) a. #Petr
Petr
je
is
často
often
vyšší
taller
než
than
Marie.
Marie
b. #Petr
Petr
je
is
často
often
tak
so
vysoký
tall
jako
as
Marie.
Marie.
(48) Poptávka
demand
po
after
dotacích
subsidies
rostla
increased.ipfv
často.
often
‘The demand for subsidies increased often.’
In light of the discussed data, we argue that the assumption that event numerals
simply quantify over times (which implies iteration) is insufficient to explain
all the observed contrasts. Instead, we propose that there is a scale of adverbs
of quantification with respect to how wide scope they can take, see Table 2. In
particular, degree adverbs including degree numerals have the narrowest scope,
event numerals rank in the middle since they can scope over indefinites, and
finally frequency adverbs can have the widest scope resulting in the possibility
of relational readings but cannot access internal arguments of degree predicates.
There starts to appear a promising correlation, specifically the scope of an expression
seems to correspond to its sortal polymorphicity. At this point, we can only
speculate on what the cause and what the consequence is, and hence we remain
27
Mojmír Dočekal, Marcin Wągiel
agnostic with respect to the nature of the relationship in question. Nevertheless,
we intend to investigate this issue in a future work.
Property Degree adverbs Event numerals Frequency adverbs
Access degrees yes yes no
Scope over indefinites no yes yes
Relational readings no no yes
Table 2: Properties of event and degree numerals
We propose that the semantics of event numerals is more general than that of
frequency and degree adverbs. Essentially, we assume that they are basically able
to target totally ordered sets of an unspecified type. Since non-stative eventualities
comprise time scales which share core properties with degree scales, event
numerals are, thus, able to modify both events involving duration and degree
expressions such as comparatives and equatives. On the other hand, frequency
expressions such as often can operate only on a specified scale, i.e., a time scale,
whereas degree adverbs including degree numerals target a scale of degrees.
7.2.2 Comparatives and equatives
Finally, let us discuss how event numerals differ from degree numerals in equatives.
Consider the examples in (49), repeated here as (49). We propose that in
equatives event numerals do not measure the gap between the degrees associated
with the standard of comparison and the correlate as standard differentials.
Instead, they multiply the degree associated with the standard.
(49) a. Petr
Petr
je
is
dvakrát
twice
vyšší
taller
než
than
Marie.
Marie
‘Petr is two times taller than Marie.’
b. Petr
Petr
je
is
dvakrát
twice
tak
so
vysoký
tall
jako
as
Marie.
Marie
‘Petr is twice as tall as Marie.’
We assume that in comparatives and equatives event numerals are simple operators
of type ⟨d, d⟩. They take a degree and return a value multiplied by the number
corresponding to the numeral root, see (50-a) for the semantics of dvakrát
and (50-b) for the generalized meaning of event numerals. As a result, they are
28
Event and degree numerals:
Evidence from Czech
less sensitive to a particular structure of a phrase of comparison in which they
can appear. We propose that within the DegP event numerals pick CPs as their
arguments. We hypothesize that their wider scope follows from that fact.
(50) a. dvakrát = λd[2 × d] type ⟨d, d⟩
b. Event Numeral = λnλd[n × d] type ⟨n, ⟨d, d⟩⟩
Such a semantics fits nicely both with comparatives and equatives. In (51), the
event numeral adjoins to the CP denoting the maximal interval corresponding
to the standard of comparison, i.e., Marie’s maximal height, before the partitive
preposition applies. The event numeral returns the maximal degree to which
Marie is tall multiplied by two and it is not until then that než yields a set of
degrees the maximal degree corresponding to Marie is part of. The resulting
⟨d, t⟩ expression is compatible with the input requirement of the comparative
marker -ší.
(51) DegP
⟨⟨d, t⟩, t⟩
Deg
⟨⟨d, t⟩, ⟨⟨d, t⟩, t⟩⟩
-ší
PP
⟨d, t⟩
P
⟨d, ⟨d, t⟩⟩
než
CP
d
Event Numeral
⟨d, d⟩
dvakrát
CP
d
Marie is d1-tall
In the case of equatives, see (52), the composition proceeds in a parallel manner
the only difference being that there is no partitive preposition to shift the denotation
of the CP to ⟨d, t⟩. As a result, the equative marker selects the degree
provided by the outcome of the multiplication operation introduced by the event
numeral.
29
Mojmír Dočekal, Marcin Wągiel
(52) DegP
⟨⟨d, t⟩, t⟩
Deg
⟨d, ⟨⟨d, t⟩, t⟩⟩
tak… jako
CP
d
Event Numeral
⟨d, d⟩
dvakrát
CP
d
Marie is d1-tall
Assuming pragmatic enrichment, as discussed in Section 7.1.1, in both cases we
obtain the same truth conditions, as specified in (53). This corresponds to an
intuition that both sentences are actually equivalent and would be judged true
iff the maximal interval to which Petr is tall is equal to the maximal interval to
which Marie is tall multiplied by two.
(53) a. (49) = max(λd.µheight(Petr) ≥ d) ≥ 2 × µheight(Marie)
b. ⇝ (49) = max(λd.µheight(Petr) ≥ d) = 2 × µheight(Marie)
Similar to (31-a), the strengthening does not take place in the presence of aspoň
(‘at least’). Therefore, both (54-a) and (54-b) get the ≥ interpretation in (53-a).
(54) a. Petr
Petr
je
is
aspoň
at-least
dvakrát
twice
vyšší
taller
než
than
Marie.
Marie
‘Petr is at least two times taller than Marie.’
b. Petr
Petr
je
is
aspoň
at-least
dvakrát
twice
tak
so
vysoký
tall
jako
as
Marie.
Marie
‘Petr is at least twice as tall as Marie.’
The proposed analysis seems to derive the desirable truth conditions and explains
different behavior of event and degree numerals in constructions of comparison.
Though, our approach does not answer the question why event numerals can be
used to both modify degrees and to count eventualities, we would like to speculate
that a possible explanation lies in their type requirement. Event numerals
seem to be polymorphic operators whose both domain and range consists of expressions
of a primitive type d or v which allows then to target degree-denoting
free relatives of degrees as well as event-denoting clauses. However, this hypoth-
30
Event and degree numerals:
Evidence from Czech
esis requires careful consideration and we leave this issue for further investiga-
tion.
8 Conclusion
In this paper, we have presented novel evidence from Czech concerning the distinction
between two classes of adverbs of quantification, i.e., event numerals
such as dvakrát (‘twice/two times’) and degree numerals such as dvojnásobně
(‘doubly/twofold’). We have discussed their distribution and examined multiple
contrasts in various environments including equatives and modification of count
events. According to our proposal degree numerals denote properties of degrees
which explains their occurrence in predicate position as well as their ungrammaticality
in equatives. On the other hand, event numerals have a more general
semantics which results in wider scope as well as the possibility to target both
events and degrees. We have hypothesized that event numerals in comparatives
and equatives behave as simple operators that yield a multiplied value of an input
degree which allows for the compatibility with both comparatives and equatives.
Furthermore, we have suggested a treatment for adjectival degree numerals such
as dvojnásobný (‘double/two-time’). Nevertheless, many questions remain open.
The exact and systematic representation of the meaning of event and degree numerals
poses a challenge for further research. It would be also exciting to pursue
a cross-linguistic investigation to explore even more properties of the discussed
alternation.
Abbreviations
Syntactic categories: A – adjective, AP – adjectival phrase, Adv – adverb, AdvP
– adverbial phrase, COMP – comparative, CP – complementizer phrase, Deg –
degree, DegP – degree phrase, Diff – differential, EQ – equative, IP – inflectional
phrase, N – noun, NP – noun phrase, P – preposition, PP – prepositional phrase,
REFL – reflexive pronoun, VP – verb phrase. Cases: INSTR – Instrumental. Aspect:
IPFV – imperfective, PFV – perfective. Others: CNC – Czech National
Corpus, LF – Logical Form.
31
Mojmír Dočekal, Marcin Wągiel
Acknowledgements
We gratefully acknowledge that the research was supported by a Czech Science
Foundation (GAČR) grant to the Department of Linguistics and Baltic Languages
at the Masaryk University in Brno (GA17-16111S) as well as an Aktion ÖsterreichTschechien
scholarship awarded to Marcin Wągiel and financed by the Austrian
Federal Ministry of Science, Research and Economy (ICM-2016-05748).
References
Bhatt, Rajesh & Roumyana Pancheva. 2007. Degree quantifiers, position of merger
effects with their restrictors, and conservativity. In Chris Barker & Pauline Jacobson
(eds.), Direct Compositionality, 306–335. Oxford University Press.
Dočekal, Mojmír. 2012. Atoms, groups and kinds in Czech. Acta Linguistica Hungarica:
An International Journal of Linguistics 59(1–2). 109–126.
Dočekal, Mojmír. 2013. What do we count with numerals? Semantic analysis of
Czech group-denoting and kind-denoting NPs. In Uwe Junghanns, Dorothee
Fehrmann, Denisa Lenertová & Hagen Pitsch (eds.), Formal Description of Slavic
Languages: The Ninth Conference. Proceedings of FDSL 9, Göttingen 2011, 87–105.
Frankfurt am Main: Peter Lang.
Doetjes, Jenny. 2007. Adverbs and quantification: Degrees versus frequency. Lingua
117(4). 685–720.
Donazzan, Marta. 2013. On counting and measuring events. In Emmanuel Chemla,
Vincent Homer & Grégoire Winterstein (eds.), Proceedings of Sinn und Bedeutung
17, 219–236.
Gobeski, Adam. 2011. Twice versus Two times in Phrases of Comparison. Michigan
State University, East Lansing MA thesis.
Gobeski, Adam & Marcin Morzycki. 2017. Percentages, relational degrees, and
degree constructions. Paper presented at Semantics and Linguistic Theory 27.
12th–14th May 2017. University of Maryland, Baltimore.
Heim, Irene. 2000. Degree operators and scope. In Brendan Jackson & Tanya
T. Matthews (eds.), Proceedings of Semantics and Linguistic Theory 10, 40–64.
Ithaca, NY: Cornell Linguistics Club.
Heim, Irene & Angelika Kratzer. 1998. Semantics in Generative Grammar. Oxford:
Blackwell Publishers.
Hofweber, Thomas. 2005. Number determiners, numbers, and arithmetic. The
Philosophical Review 114(2). 179–225.
32
Event and degree numerals:
Evidence from Czech
Horn, Laurence. 1972. On the Semantic Properties of the Logical Operators in English.
University of California, Los Angeles PhD thesis.
Ionin, Tania & Ora Matushansky. 2006. The composition of complex cardinals.
Journal of Semantics 23(4). 315–360.
Kennedy, Chris. 2001. Polar opposition and the ontology of ‘degrees’. Linguistics
and Philosophy 24(1). 33–70.
Kennedy, Christopher & Louise McNally. 2005. Scale structure, degree modification,
and the semantics of gradable predicates. Language. 345–381.
Khrizman, Keren. 2015. Cardinal/collective alternation in Russian numerals. Paper
presented at Formal Description of Slavic Languages 11. 2nd–4th December
2015. University of Potsdam.
Krifka, Manfred. 1989. Nominal reference, temporal constitution and quantification
in event semantics. In Renate Bartsch, Johan van Bentham & Peter van
Emde Boas (eds.), Semantics and Contextual Expressions, 75–155. Foris: Dor-
drecht.
Krifka, Manfred. 1999. At least some determiners aren’t determiners. In Ken Turner
(ed.), The Semantics/Pragmatics Interface from Different Points of View, 257–291.
Oxford: Elsevier.
Landman, Fred. 2004. Indefinites and the Type of Sets. Oxford: Blackwell.
Landman, Fred. 2006. Indefinite time-phrases, in situ-scope, and dual-perspective
intensionality. Non-definiteness and Plurality 95. 237.
Lasersohn, Peter. 1995. Plurality, Conjunction and Events. Boston: Kluwer Academic
Publishers.
Morzycki, Marcin. 2009. Degree modification of gradable nouns: Size adjectives
and adnominal degree morphemes. Natural Language Semantics 17(2). 175–203.
Pancheva, Roumyana. 2006. Phrasal and clausal comparatives in Slavic. In James
Lavine, Steven Franks, Mila Tasseva-Kurktchieva & Hana Filip (eds.), Formal
Approaches to Slavic Linguistics 14: The Princeton Meeting 2005, 236–257. Ann
Arbor: Michigan Slavic Publications.
Rett, Jessica. 2014a. Measure phrase equatives and modified numerals. Journal of
Semantics. ffu004.
Rett, Jessica. 2014b. The polysemy of measurement. Lingua 143. 242–266.
Rothstein, Susan. 2012. Numericals: Counting, measuring and classifying. In Ana
Aguilar Guevara, Anna Chernilovskaya & Rick Nouwen (eds.), Proceedings of
Sinn und Bedeutung 16, 527–543. Cambridge, MA: MIT Working Papers in Lin-
guistics.
Rullmann, Hotze. 1995. Maximality in the Semantics of wh-constructions. University
of Massachusetts, Amherst PhD thesis.
33
Mojmír Dočekal, Marcin Wągiel
Schulz, Katrin & Robert Van Rooij. 2006. Pragmatic meaning and non-monotonic
reasoning: The case of exhaustive interpretation. Linguistics and Philosophy
29(2). 205–250.
Schwarzschild, Roger. 2002. The grammar of measurement. In Brendan Jackson
(ed.), Proceedings of Semantics and Linguistic Theory 12, 225–245. Ithaca, NY:
CLC Publications.
Schwarzschild, Roger. 2008. The semantics of comparatives and other degree constructions.
Language and Linguistics Compass 2(2). 308–331.
Schwarzschild, Roger & Karina Wilkinson. 2002. Quantifiers in comparatives: A
semantics of degree based on intervals. Natural Language Semantics 10(1). 1–
41.
Solt, Stephanie. 2014. Q-adjectives and the semantics of quantity. Journal of Semantics
32(2). 221–273.
Von Fintel, Kai. 1994. Restrictions on Quantifier Domains. University of Massachusetts,
Amherst PhD thesis.
Von Stechow, Arnim. 1984. Comparing semantic theories of comparison. Journal
of Semantics 3(1). 1–77.
Wągiel, Marcin. 2014. Boys, girls, and scissors: A semantic analysis of Polish
NPs headed by the numeral dwoje. In Ludmila Veselovská & Markéta Janebová
(eds.), Nominal Structures: All in Complex DPs, 69–84. Olomouc: Palacký Uni-
versity.
Wągiel, Marcin. 2015a. Sums, groups, genders, and Polish numerals. In Gerhild
Zybatow, Petr Biskup, Marcel Guhl, Claudia Hurtig, Olav Mueller-Reichau &
Maria Yastrebova (eds.), Slavic Grammar from a Formal Perspective. The 10th
Anniversary FDSL Conference, Leipzig 2013, 495–513. Frankfurt am Main: Peter
Lang.
Wągiel, Marcin. 2015b. What do we count with multiplicative adjectives? Paper
presented at Event Semantics 12. 20th-21st November 2015. University of
Stuttgart.
Wągiel, Marcin. to appear. Entities, events, and their parts: The semantics of multipliers
in Slavic. In Peter Kosta & Teodora Radeva-Bork (eds.), Current Developments
in Slavic Linguistics. Twenty Years After. Frankfurt am Main: Peter
Lang.
34