Counting degrees and events: A
cross-linguistic perspective
Mojmír Dočekal & Marcin Wągiel
28.06.2017, Heinrich-Heine-University Duesseldorf
1 / 74
Introduction I
▶ lexicons of many natural languages distinguish between
two types of adverbs of quantification
(1) a. twice/doubly (English)
b. deux fois/doublement (French)
c. dvaždy/vdvojne (Russian)
d. kétszer/kétszeresen (Hungarian)
▶ puzzling contrasts
▶ cross-linguistic semantic investigation
2 / 74
▶ aim: an analysis of such expressions in two typologically
distinct languages
(2) a. dvakrát/dvojnásobně (Czech)
b. hai-lần/gấp-đôi (Vietnamese)
▶ more data from other languages
▶ focus on: constructions where degree argument is
manipulated – comparatives and equatives + factor
phrases
▶ terminology:
1. twice-type adverbs → event numerals (EN)
2. doubly-type adverbs → degree numerals (DN)
3 / 74
▶ main puzzle: contrasts concerning acceptability of
event/degree numerals in COMP/EQ
▶ claim:
1. Czech twice-type adverbs → degree/event multiplier
2. Czech doubly-type adverbs → predicative degree
multiplier
▶ 2 distinct strategies of degree multiplication
▶ particular expressions differ wrt to which strategy they
employ
4 / 74
▶ variation wrt what is (in)compatible with COMP and/or
EQ (cf. Gobeski 2011)
English
(3) a. John is two times taller than Mary.
b. John is two times as tall as Mary.
c. *John is twice taller than Mary.
d. John is twice as tall as Mary.
e. *John is doubly taller than Mary.
f. *John is doubly as tall as Mary.
5 / 74
Macedonian
(4) a. Jon
Jon
je
is
dva
two
puti
times
po
more
visok
tall
od
from
Mari.
Mari
‘John is two times as tall as/taller than Mary.’
b. *Jon
Jon
je
is
dva
two
puti
times
visok
tall
kolku
as
Mari.
Mari
6 / 74
German
(5) a. Hans
Hans
ist
is
zweimal
twice
größer
taller
als
than
Maria.
Maria
‘Hans is two times taller than Maria.’
b. Hans
Hans
ist
is
zweimal
twice
so
so
groß
tall
wie
as
Maria.
Maria
‘Hans is twice as tall as Maria.’
c. *Hans
Hans
ist
is
doppelt
twice
größer
doubly
als
than
Maria.
Maria
d. Hans
Hans
ist
is
doppelt
doubly
so
so
groß
tall
wie
as
Maria.
Maria
‘Hans is twice as tall as Maria.’
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Data I
▶ in some contexts Czech dvakrát ‘twice/two times’ and
dvojnásobně ‘doubly/twofold’ are synonymous:
(6) a. Petrovi
for-Petr
se
REFL
to
this
vyplatilo
payed-off
dvakrát/dvojnásobně.
twice/doubly
‘For Petr it payed 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, there are multiple contexts in which they are not
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▶ Czech and Vietnamese: contrastive analysis
▶ Czech: study based on National Czech Corpus (SYN2015)
▶ Advs dvakrát and dvojnásobně in SYN2015
▶ 100 random examples + filtering: 98, 99
▶ Vietnamese: introspective data (informants)
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VP 62%
COMP/EQ 12%
AdvP 8%
PP 8%
AP 7%
Clause 3%
98 sentences; 77% − events: VPs or AdvPs/PPs
Figure 1: Distribution of dvakrát
10 / 74
COMP 32%
VP 30%
AP 22%
sec. pred. 14%
AdvP 2%
99 sentences; 90% − scales: APs, deadjectival Vs, COMPs, and secondary pred.
Figure 2: Distribution of dvojnásobně
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Czech: dvakrát ~ dvojnásobně
Property Event numerals Degree numerals
Morphology Adv Adv/A/N
Degree yes yes
Diff. in comparatives yes yes
Diff. in equatives yes no
Diff. in superlatives no no
Modify count events yes no
Modify homog. events yes yes
Events (N) no yes
Roles (N) no yes
In bold the most frequent cases based on the corpus study
(SYN2015)
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Vietnamese: hai-lần ~ gấp-đôi (very partial)
Property Event numerals Degree numerals
Morphology absent absent
Degree yes yes (comparative)
Diff. in comparatives yes yes
Diff. in equatives yes yes
Adjectival no postnominal
Adverbial postverbal/postadjectival no
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Key contexts I: degree and differential
▶ Czech: both event and degree numerals: ✓
(7) a. 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’
b. 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.’
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Key contexts I: degree and differential
▶ Vietnamese: both event and degree numerals: ✓
(8) a. Nam
year
nay
this
giá
price
xăng
petrol
đắt
expensive
hơn
than
năm
year
ngoái
previous
hai-lần
twice
‘This year, the price of petrol is twice higher than
the last year.’ comparative
b. Năm
year
nay
this
giá
price
xăng
petrol
dắt
expensive
gấp-đôi
doubly
năm
year
ngoái.
previous
‘This year, the price of petrol is twice as high as
last year.’ equative
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Key contexts II: count events
▶ Czech: event numerals: ✓, degree numerals: *
(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.’
b. *Dvojnásobně
doubly
se
REFL
přesvědčím,
I-will-ensure
že
that
jsou
are
dvířka
door
zavřená.
closed
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Key contexts II: count events
▶ Vietnamese: event numerals: ✓, degree numerals: *
(10) a. Petr
Petr
đã
already
viết
write
thư
letter
cho
for
mẹ
mother
hai-lần
twice
‘Petr wrote the letter to his mother twice.’
b. *Petr
Petr
đã
already
viết
write
thư
letter
gấp-đôi
doubly
cho
for
mẹ.
mother
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Categorial differences I:
▶ Czech
(11) dvakrát:
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
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(12) 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’
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Categorial differences II:
▶ Vietnamese
(13) hai-lần: ✓ with VPs/ ✓ with APs
a. Anh-ấy
he
đã
already
gõ
knock
cửa
door
hai-lần.
twice
‘He knocked on the door twice.’
b. Giá
price
gạo
rice
đắt
expensive
hơn
than
giá
price
bột-mỳ
flour
hai-lần.
twice
‘The price of rice is two times higher than the
price of flour.’
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(14) gấp đôi: * with VPs/ ✓ with APs
a. *Anh-ấy
he
đã
already
gấp-đôi
doubly
gõ
knock
cửa.
door
b. Giá
price
gạo
rice
đắt
expensive
gấp-đôi
doubly
giá
price
bột-mỳ.
flour
‘The price of rice is double the price of flour.’
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Typal compatibility
▶ Czech
(15) Petrovi
for-Petr
se
REFL
to
this
třikrát
thrice
dvojnásobně
doubly
vyplatilo.
payed-off
‘For Petr it payed off doubly three times.’
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Crucial contrast
▶ Czech degree numerals are less acceptable in equatives
than in comparatives
(16) 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
how
Marie.
Marie
‘Petr is twice as tall as Marie.’
(17) 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
how
Marie.
Marie
▶ SYN2015: no occurrences of EQ with degree numerals 23 / 74
▶ but Vietnamese equatives are acceptable with degree
numerals:
(18) a. Petr
Petr
cao
tall
hơn
than
Marie
Marie
hai-lần.
twice
‘Petr is two times taller than Marie.’
b. Petr
Petr
cao
tall
Marie
Marie
hai-lần.
twice
‘Petr is two times as tall as Marie.’
(19) a. Petr
Petr
cao
tall
hơn
than
gắp-đôi
doubly
Marie.
Marie
‘Petr is two times taller than Marie.’
b. Petr
Petr
cao
tall
gắp-đôi
doubly
Marie.
Marie
‘Petr is two times as tall as Marie.’
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Attested patterns of EN/DN ~ COMP/EQ
▶ Czech
EN DN
COMP yes yes
EQ yes no
▶ German
EN DN
COMP yes no
EQ yes yes
25 / 74
▶ Vietnamese
EN DN
COMP yes yes
EQ yes yes
▶ Macedonian
EN DN
COMP yes no
EQ no no
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▶ English
EN1 EN2 DN
COMP yes no no
EQ no yes no
▶ possibly more patterns to be observed
▶ it seems though that ENs are always compatible with
COMP/EQ
27 / 74
▶ degree numerals are anchored to particular events (no
cumulative readings):
(20) Petrovi
for-Petr
a
and
Honzovi
for-Honza
se
REFL
to
this
třikrát
thrice
dvojnásobně
doubly
vyplatilo.
paid-off
‘For Petr and Honza it payed off doubly three times.’
a. for
for
Petr:
Honza:
3
3
x
x
(paid-off
(paid-off
x
x
2)
2)
b. for Petr⊕Honza: 3 x (paid-off x 2)
c. #for
for
Petr:
Honza:
4
1
x
x
(paid-off
(paid-off
x
x
1)
2)
28 / 74
Scopal properties of event/degree numerals
▶ frequency vs. degree adverbs (Doetjes (2007))
(21) a. Petr
Petr
často
often
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
(22) 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
29 / 74
▶ but frequency adverbs can have a relation reading,
whereas event numerals cannot
(23) 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
b. when > often
(24) 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
30 / 74
▶ furthermore, frequency adverbs cannot target scales of
degrees → incompatible with comparatives and equatives
(25) 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
how
Marie.
Marie
31 / 74
Property Degree Advs Event numerals Frequency Advs
Access degrees yes yes no
Scope over indef. no yes yes
Relational reading no no yes
32 / 74
Theory
▶ following Kennedy (1999) and Kennedy and McNally
(2005)
▶ adjectives are relations between individuals and degrees –
(26-a) (⟨d, ⟨e, t⟩⟩)
▶ degree morphemes, measure phrases and other degree
modifiers are of the type ⟨⟨d, ⟨e, t⟩⟩, ⟨e, t⟩⟩
(26) a. long = λdλx.µA(x) ≥ d
b. 2 meters = λdλgλx.max(g)(x) ≥ 2 meters
c. John is [λx.max(long)(x) ≥ 2 meters]
33 / 74
▶ standard comparative and equative in Kennedy style of
degree analysis:
(27) a. −er/more than = λdλgλx.max(g)(x) > d
b. as as = λdλgλx.max(g)(x) ≥ d
▶ we assume DegP (functional layer of AP) part of the tree
loosely corresponding to (27):
(28) DegP
diff Deg’
Deg
er/as
AP
34 / 74
▶ adding the differential slot requires more “active”
semantics of the differential
▶ evidence for this comes from many types of differential
semantics like in (30) (compare Solt (2014))
(29) −er/more D(iff) than = λdλgλDλx.[max(g)(x) >
d ∧ max(g)(x) = D]
(30) John is [[about 3 years] older than Mary.]
a. about 3 years ≈ λd.d = dM + 3
(31) a. John is about three years older than Mary.
…> dM + 3
b. John is about three years younger than Mary.
…< dM − 3
c. John is two times older than Mary. …= dM ∗ 2
35 / 74
Hypothesis (typological)
▶ generally we assume two strategies of multiplication:
1. predicative – in Czech case degree numerals
2. multiplicative – in Czech case event numerals
▶ different expressions in different languages can employ
strategy 1) or strategy 2)
36 / 74
Czech degree numerals (dvojnásobně) I
▶ the comparative examples reveal the true nature of
degree numerals
(32) Petr je dvojnásobně vyšší než Marie.
Petr is doubly higher than Marie
a. 1 in all situations where the gap between Petr’s
and Marie’s height is equal to the height of Mary
b. µHEIGHT(Petr) = 180 ∧ µHEIGHT(Marie) = 90, …
▶ the degree numeral specifies an interval of the gap
between the correlate (Petr) and the standard (Marie) by
multiplication the standard value on an appropriate scale
37 / 74
▶ first approximation: a characteristic function of degrees
equal to a contextually salient degree dc multiplied by n
▶ dc = the MAX value of standard on the appropriate scale
(33) Degree Numeral : λnλd.d = n ∗ dc type ⟨n, ⟨d, t⟩⟩
a. dvojnásobně : λd.d = 2 ∗ dc
▶ Rett (2014a) and Rett (2014b): quantity words such as
many, much, … → degree modifiers denoting relations
between sets of degrees (D) and their measure (d)
▶ Czech degree numerals differ in: (i) explicitly specifying d,
(ii) determining d via multiplication
38 / 74
▶ denotations of degree numerals:
(34) Petr is doubly higher than Marie. (cs)
a. doubly = λd.d = 2 ∗ dM
b. −er/more D(iff) than =
λdλgλDλx.[max(g)(x) > d ∧ max(g)(x) = D]
c. Petr is [λx.[max(tall)(x) > dM ∧ max(tall)(x) =
max(λd.d = 2 ∗ dM)]]
39 / 74
▶ equative is ungrammatical with degree numerals since it
doesn’t have a differential version:
(35)???Petr is doubly as high as Marie. (cs)
a. doubly = λd.d = 2 ∗ dM
b. as as = λdλgλx.max(g)(x) ≥ d
c. (35-a) + (35-b) semantic/syntactic(?)
incompatibility
40 / 74
Czech event numerals (dvakrát) I
▶ Czech event-numerals are different, they can combine
even with EQ without differential
▶ and maybe with COMP with differential too (ambiguity?)
▶ they are degree/event/time(?) multipliers:
(36) Petr is twice as high as Mary. (cs)
a. twice = λd.2 ∗ d
b. as as = λdλgλx.max(g)(x) ≥ d
c. Petr is [ λx.[max(g)(x) ≥ dM ∗ 2]]
41 / 74
▶ analysis based on the classification of Doetjes (2007)
Scopal properties of adverbs of quantification
Property Degree Advs Event numerals Frequency Advs
Access degrees yes yes no
Scope over indef. no yes yes
Relational reading no no yes
42 / 74
▶ frequency adverbs (often)
▶ → quantification over times, scope over indefinites
▶ degree adverbs (a lot)
▶ → degree modification, do not scope over indefinites
▶ event numerals ≈ frequency adverbs
▶ degree numerals ≈ degree adverbs
43 / 74
▶ quantification over situations and a hidden domain
anaphor (von Fintel 1994)
▶ abstract restrictor times (Doetjes 2007)
(37) dvakrát: 2 [restriction times][nuclear scope VP/IP]
▶ → unary quantification and wide scope
(38) a. Petr
Petr
dvakrát
twice
koupil
bought.perf
nějaké
some
pivo.
beer
‘Petr bought five beers twice’
b. ∃ex[µ(e) = 2 ∧ Buy(e) ∧ Θ1(e) = Petr ∧ Θ2(e) =
x ∧ Beer(x)]
44 / 74
▶ quantification over events is wide scope reading ↔
cumulative scopelless reading is not possible:
(39)???Dvakrát Petr koupil nějaké pivo dvakrát.
Twice Petr bought some beer twice
a. cumulative reading: ∃ex[µ(e) = 2 ∧ µ(e) =
2 ∧ Buy(e) ∧ Θ1(e) = Petr ∧ Θ2(e) = x ∧ Beer(x)]
45 / 74
Our contribution
▶ event numerals denote a function which yields a
multiplied value of a degree/time
▶ the common property of degrees and times …totally
ordered scale
(40) a. event numeral = λnλd.n ∗ d
b. dvakrát = λd.2 ∗ d
▶ type ⟨⟨n, d⟩, d⟩
▶ event numerals are operators which can QR (similar to
cardinals)
▶ → multiplication via variable binding (λ-abstraction) →
wide scope
46 / 74
(41) Petr
Petr
je
is
dvakrát
twice
tak
so
vysoký
high
jako
how
Marie.
Marie
‘Petr is twice as high as Marie.’
(42) Petr is twice as high as Mary. (cs)
a. twice = λd.2 ∗ d
b. as as = λdλgλx.max(g)(x) ≥ d
c. Petr is [ λx.[max(g)(x) ≥ dM ∗ 2]]
▶ on the other hand, degree numerals are predicative
47 / 74
Vietnamese equatives
▶ recall: Vietnamese equatives are acceptable with degree
numerals:
(43) Petr
Petr
cao
tall
gắp-đôi
doubly
Marie.
Marie
‘Petr is doubly as tall as Marie.’
▶ sidenote: Vietnamese comparative is built on the equative
and allows regular differentials:
48 / 74
(44) Petr
Petr
cao
tall
hơn
than
Marie
Marie
10
10
cm
cm
‘Petr is 10 cm taller than Marie.’
(45) Petr
Petr
cao
tall
hơn
than
gấp-đôi
doubly
Marie
Marie
‘Petr is doubly taller than Marie.’
49 / 74
▶ why Vietnamese and Czech equatives differ w.r.t. the
degree numerals acceptability?
▶ reasonable hypothesis: Vietnamese equatives use the
implicit comparison strategy (Kennedy (2007))
▶ implicit comparison: equative ordering by manipulating
the context that the positive form (A) is true both of x
and y
▶ no degree operator in equatives unlike in degree questions
e.g.:
(46) Anh-ấy
he
thông-minh
smart
thế-nào?
much-how
‘How smart is he?’
50 / 74
▶ Czech equatives use the explicit comparison strategy:
the equative ordering is achieved by the degree argument
binding ↔ the same free relative wh-word as in degree
questions:
(47) Jak
how
chytrý
smart
je
is
ten
that
kocour?
tomcat
‘How smart is the tomcat?’
(48) Ten
that
kocour
cat
je
is
chytrý
smart
jak
how
ten
that
pes.
dog
‘The cat is as smart as the dog.’
51 / 74
▶ explicit strategy: the degree standard
▶ implicit strategy: the individual serves as a standard
▶ formally:
(49) a. −erD = λdλgλx.max(g)(x) ≥ d
b. −erI = λyλgλx.max(g)(x) ≥ max(g)(y)
52 / 74
▶ pseudo-Czech explicit (degree) equative plus degree
numerals → incompatibility in types
▶ pseudo-Vietnamese implicit (context) equative plus
degree numeral → restrictive modification … set of
individuals of Mary’s height
▶ similar to Kennedy’s analysis of Japanese clausal standard
as relative clauses
(50)???Petr is doubly as high as Marie. (cs)
a. doubly = λd.d = 2 ∗ dM
b. as as = λdλgλx.max(g)(x) ≥ d
c. (50-a) + (50-b) semantic/syntactic(?)
incompatibility
(51) a. Petr tall doubly Marie.
b. Petr
is[λx.max(tall)(x) ≥ max(tall)(y | µA(y) ≥ 2∗dM)]
53 / 74
▶ similar to the style of cross-linguistic analysis initiated by
Kennedy (2007) and Beck et al. (2009)
▶ but the data look more complex – Vietnamese allows
subcomparatives (52), degree questions (53) + negative
islands are ungrammatical in VN (54):
(52) Xe-ô-tô
CL-car
to
big
hơn
than
đường
road
hẹp
narrow
này.
this
‘The car is bigger than the road is narrow.’
(53) Anh-ấy
he
thông-minh
smart
thế-nào?
much-how
‘How smart is he?’
54 / 74
(54) *Petr
Petr
thông-minh
smart
hơn
than
không-ai-cả
nobody
ở
AUX
trong
inside
lớp.
class
‘*Petr is smarter than nobody in his class.’
▶ unexpected in Beck et al. (2009)’s framework ↔
languages allowing sumcomparatives, degree questions
and exhibiting negative islands use explicit comparison
strategy (do allow syntactic binding of a degree variable
in Beck’s terms)
▶ empirically: VN is very different from the Mandarin
Chinese and Japanese data
55 / 74
▶ the data seems to indicate that the implicit/explicit mode
of comparison is construction specific rather than
language parametrized
(55) Petr
Petr
cao
tall
bằng
equal
Marie
Marie
*gấp-đôi
*doubly
‘Petr equals with Marie in height doubly’
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Summary
Observations:
▶ factor phrases target comparatives and equatives
▶ factor phrases involve event numerals and degree
numerals
▶ in different languages event/degree numerals differ wrt
acceptability in COMP and EQ
57 / 74
Proposal:
▶ 2 strategies of multiplication: predicative ⟨d, t⟩ and
multiplicative ⟨d, d⟩
▶ event/degree numerals differ wrt to which strategy they
employ
▶ the implicit/explicit comparison strategy also plays a role
▶ event numerals cannot be reduced to quantifiers over
events
58 / 74
Thanks!
59 / 74
Appendices
Appendix I: comparative
▶ strictly speaking (56) requires scenarios like dM=100,
dP>200, …: pragmatic hallo?
(56) Petr is twice higher than Mary. (cs)
a. twice = λd.2 ∗ d
b. −er/more than = λdλgλx.max(g)(x) > d
c. Petr is [ λx.[max(g)(x) > dM ∗ 2]]
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Appendix 2: Theory 2
▶ application to the comparative example:
▶ standard semantics for the comparative (Von Stechow
(1984); Heim (2000); Schwarzschild (2008)):
−er = λD′
λD.MAX(D) > MAX(D′
)
▶ comparative and degree numerals are both degree
modifiers → ∧
(57) Petr je dvojnásobně vyšší než Marie.
Petr is doubly higher than Marie
a. comparative = MAX1(λd′′
.µHEIGHT(Petr)) >
MAX2(λd′′′
.µHEIGHT(Marie))∧
b. dvojnásobně : MAX1 = 2 ∗ MAX2
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▶ the proposed semantics is predicative (⟨n, ⟨d, t⟩⟩):
explains the predicative usage, ungrammatical for event
numerals:
▶ plus acceptable conjunction with measure phrases
(58) a. Petrův plat je letos dvojnásobný.
Petr’s salary is this year double.
b.???Petrův plat je letos dvakrát.
Petr’s salary is this year twice.
(59) Letošní finálový zápas byl 240 minut dlouhý a
dvojnásobný proti loňsku.
This year final match was 240 minutes long and double
against last year.
▶ degree numerals do not (at least semantically) fill the
differential slot of the comparative
▶ the formalization can explain the observed oddity of
equative constructions with degree numerals
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▶ again standard semantics for the equative:
as = λD′
λD.MAX(D) ≥ MAX(D′
)
(60)???Petr je dvojnásobně tak vysoký jako Marie.
a. equative = MAX1(λd.µHEIGHT(Petr)) ≥
MAX2(λd′
.µHEIGHT(Marie))∧
b. … pragmatically strengthened to
equative = MAX1(λd.µHEIGHT(Petr)) =
MAX2(λd′
.µHEIGHT(Marie))∧
c. dvojnásobně : MAX1 = 2 ∗ MAX2
d. (60-b) + (60-c) … ⊥
63 / 74
Back to Czech
▶ the contradiction can be avoided if the equative isn’t
strengthened analogically to examples such as:
(61) a. The kids dove as deep as their parents (did).
(i) … Each parent dove 10m deep and their
children dove 15m deep.
(ii) #. . .Each child dove 10m deep and their
parents dove 15m deep.
(62) Petr a Marie chodí spolu, ale je to bláznivá dvojice,
protože jsou úplně rozdílně vysocí. Je to skoro tak, že
Petr je dvojnásobně tak vysoký jako Marie.
‘Petr and Marie are together, but they are a weird
couple, because they are of totally different heights.
It’s almost as if Petr is twice as tall as Marie.’
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Quantification over amounts (N)
▶ adjectival degree numerals modify degree nominals
(63) a. dvojnásobný
double
objem
volume
‘double volume’
b. dvojnásobný
double
plat
salary
‘double salary’
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Events (N) and Social roles (N)
▶ adjectival degree numerals modify nominals denoting
events
(64) dvojnásobná
double
vražda
murder
‘double murder’
▶ adjectival degree numerals modify nominals denoting
social roles
(65) dvojnásobný
double
mistr
champion
‘two-time champion’
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Contrasts
▶ contrast 1:
(66) a. dvojnásobné
double
množství
amount
čaje
tea
‘double the amount of tea’
b. *dvojnásobný
double
hrnek
cup
čaje
tea
(67) a. dva
two
hrnky
cups
čaje
tea
‘two cups of tea’
b. *dvě
two
množství
amount
čaje
tea
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▶ contrast 2:
(68) a. dvojnásobek
double.N
rychlosti
speed
‘double the speed’
b. *dvojnásobek
double.N
mistra
champion
c. *dvojnásobek
double.N
sebevraždy
suicide
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▶ contrast 3 (≈ monotonicity constraint as in Schwarzschild
2002):
(69) a. Dvojnásobná
double
rychlost
speed
je
is
dvakrát
twice
větší
bigger
rychlost.
speed
‘Double speed is 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
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▶ the social role and event readings are mappings – via
Rett’s Ope or Opd which maps entities into degrees (see
Rett (2014b) & Rett (2014a)) but the other way round:
(70) 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’
(71) Dvojnásobný
double
plat
salary
Karlovi
for-Karel
stačil.
was-enough
‘For Karel, double salary was enough’
70 / 74
▶ for degree numerals, the degree use is the basic one
(unlike for cardinal numerals)
(72) 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. . .’
▶ measure nouns (‘double volume’) map entities to degrees
which the degree numeral quantifies over (≈ Rett’s
M-OP)
(73) a. M-OP → λPλdλx.P(x) ∧ µ(x) = d attributive
b. M-OP → λdλx.µ(x) = d
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Social role interpretation:
▶ time trace function (Krifka (1989), Lasersohn (1995)):
maps an event to its running time (= the smallest time at
which it occurs)
▶ dvojnásobný mistr ‘two-time champion’: we map a
property P (being a champion) to its running time (the
time of being a champion) and the degree numeral
quantifies over these running times
72 / 74
▶ dvojnásobně velký – the dimension (µ) ← the adjective
▶ dvojnásobná délka lana – the dimension ← the measure
noun (µ)
▶ event interpretation: dvojnásobná vražda ‘double murder’
← mapping between events and entities, the two victims
reading is obtained
▶ the root quantifies over degrees but doesn’t supply the
dimension:
▶ the time reading is obtained only for nouns denoting
properties which constrained in time (lower-bound) –
champion or bilaterally bound (president)
(74) a. dvojnásobný mistr (two-time champion) …
dimension of time (µ … time)
b. #dvojnásobný Čech, člověk, pes ‘two-time Czech,
human, dog’
73 / 74
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