Markers of distributivity in Czech
16-04-2019, Humboldt-Universität zu Berlin
Mojmír Dočekal
Mojmír Dočekal Markers of distributivity in Czech 1 / 91
Outline
1) distributivity
2) four distributive markers in Czech
3) typology of distributive markers: Zimmermann (2002)
4) Czech binominal each
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Semantics preliminaries
distributive readings: quantification over atoms
distributive markers are incompatible with cumulative interpretation
(1) Two singers performed ten songs.
a. cumulative: singer 1 – 6 songs, singer 2 – 4 songs
b. distributive: ∃𝑋[𝑠𝑖𝑛𝑔𝑒𝑟𝑠(𝑋) ∧ #(𝑋) = 2 ∧ ∀𝑦 ∈
𝑋[𝑝𝑒𝑟𝑓𝑜𝑟𝑚𝑒𝑑(𝑦, 𝑇 𝑒𝑛𝑆𝑜𝑛𝑔𝑠)]]
Mojmír Dočekal Markers of distributivity in Czech 3 / 91
English distributive markers:
(2) a. Each of the two singers performed ten songs. determiner
b. The two singers performed each ten songs. binominal
Mojmír Dočekal Markers of distributivity in Czech 4 / 91
Czech much more expressive
sentence with Czech “and” and cardinal numeral:
(3) a. Petr
Petr
a
and
Karel
Karel
zazpívali
sang
deset
ten
písní.
songs
‘cumulative/distrbitutive/collective/…’
1) the conjunction strategy:
(4) a. Petr
Petr
i
and
Karel
Karel
zazpívali
sang
deset
ten
písní.
songs
‘distributive’
Mojmír Dočekal Markers of distributivity in Czech 5 / 91
Three sub-types of i
1) focus particle with:
scalar (least-likely) presupposition: (5-a)
additive presupposition: (5-b)
(5) Petr
Petr
přečetl
read
i
even
třetí
third
díl
volume
Pána-prstenů.
LOTR.GEN
‘Petr read even the third volume of LOTR.’
a. scalarity: ?? Petr read i first volume LOTR
b. additivity: ?? Petr read i third volume LOTR but not the first
two
Mojmír Dočekal Markers of distributivity in Czech 6 / 91
2) obligatory distributive conjunction (boolean ∧)
(6) V
in
Praze
Prague
se
SE
sešli
gathered
anarchisti
anarchists
i
i
skinheadi.
skinheads
‘Anarchists gathered in Prague ∧ skinheads gathered in Prague.’
a. #𝐺𝑎𝑡ℎ𝑒𝑟𝑒𝑑(𝐴𝑛𝑎𝑟𝑐ℎ𝑖𝑠𝑡𝑠 ⊔ 𝑆𝑘𝑖𝑛ℎ𝑒𝑎𝑑𝑠)
Mojmír Dočekal Markers of distributivity in Czech 7 / 91
3) additive particle (without scalar presupp.)
(7) Na
to
náměstí
square
přišli
arrived
anarchisti.
anarchists
A
and
pak
then
přišli
arrived
i
i
skinheadi.
skinheads
‘Anarchists arrived to the square and then skinheads arrived too.’
(8) ??The square was empty and then arrived i skinheads.
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Czech National Corpus (CNK) survey (Šafratová 2018)
1) scalar i (47%)
2) additive i (41%)
3) conjunction i (12%)
Mojmír Dočekal Markers of distributivity in Czech 9 / 91
Second strategy: “po Num N”
the dependent indefinites strategy
(9) a. Petr
Petr
a
and
Karel
Karel
zazpívali
sang
po
P
deseti
ten
písních.
songs
‘distrbitutive’
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similar to adverbial German jeweils (vs. English each):
(10) Die Mädchen haben jeweils zwei Hunde gesehen.
a. #cumulative
b. individual distributivity (each girl … two dogs)
c. occasional distributity (each time … two dogs)
(11) The girsl saw two dogs each.
a. #cumulative
b. individual distributivity
c. #occasional distributivity
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in many languages (sign languages, Hungarian, Telugu) is the
dependent indefinites strategy grammaticalized via reduplication
participant, temporal and spatial keys are grammatical with
reduplication (Telugu)
(12) prati
every
pilla-vaaDu
kid
renDu
two
renDu
two
kootu-lu-ni
monkey.pl.acc
cuus-ee-ru
see.past.3pl
lit. ‘every kid saw two two monkeys’
(13) a. Every kid saw two monkeys each. Participant-key
b. Every kid saw two monkeys in each interval. Temporal-key
c. Every kid saw two monkeys in each location. Spatial-key
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but also languges which allow only participant-key readings with
reduplication (Hungarian):
(14) A
the
gyerekek
children
két-két
two-two
majmot
monkey.acc
láttak.
saw.3pl
‘The children saw two monkeys each’
Mojmír Dočekal Markers of distributivity in Czech 13 / 91
Zimmermann (2002)
(15) Zimmermann’s Generalization: If a distance distributivity item can
also be used as a distributive determiner, it lacks the occasion
reading.
reported data from Dutch, Norwegian, Italian, Russian, French,
Turkish, Czech, Bulgarian, and Korean
Czech seems to fit
Mojmír Dočekal Markers of distributivity in Czech 14 / 91
Sidenote
very dubious data reported in Zimmermann (2002)
(16) Chlapci
boys
koupili
bought
po
Dist
dvou
two
párcích/párkách.
sausages.loc
‘The boys bought two sausages each.’
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“po” cannot be used as a determiner:
(17) Každý/*Po
Dist
chlapec
boy
koupil
bought
dva
two
párky.
sausages
‘Each boy bought two sausages.’
totally unaceptable in Czech:
(18) Po
Dist
třech
three.loc
ženách
women.loc
vstupovalo
entered.3sg
do
into
místnosti.
room
‘Three women entered the room [i.e., one triplet after another]’
Mojmír Dočekal Markers of distributivity in Czech 16 / 91
individual distribution vs. (possible) occasion distribution with Czech
dependent indefinites is possible though:
(19) Mojmírek
Mojmírek
a
and
Mariánka
Mariánka
si
SE
dali
consumed
po
po
dvou
two
zmrzlinách.
ice-creams
‘Mojmírek and Mariánka consumed two ice creams each/each time’
a. each of two children …2 ice creams
(i) Ma … 1 ice cream + 1 ice cream
(ii) Moj … 1 ice cream + 1 ice cream
b. each time …2 ice creams
(i) Ma … 1 ice cream
(ii) Moj … 1 ice cream
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Contrast with binominal každý ‘each’:
(20) Mojmírek
Mojmírek
a
and
Mariánka
Mariánka
si
SE
dali
consumed
každý
each
tři
three
zmrzliny.
ice-creams
‘Mojmírek and Mariánka consumed each three ice-creams.’
a. *cumulative reading: Mo …1, Ma …2+3
b. distributive: Mo 1+2+3, Ma 1+2+3
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with singular NPs only the occasion reading: (21)
singular NP + adnominal DD → doubling of distributivity
…ungrammaticality
can be used as a test: adverbial distributivity with proper name in sg.
should be acceptable
(21)???Mojmírek
Mojmírek
si
SE
každý
each
dal
consumed
dvě
two
zmrzliny.
ice-creams
‘???Mojmírek consumed each two ice-creams.’
(22) Mojmírek
Mojmírek
si
SE
dal
consumed
po
po
dvou
two
zmrzlinách.
ice-creams
‘Mojmírek consumed two ice creams each time.’
Mojmír Dočekal Markers of distributivity in Czech 19 / 91
i behaves more like dependent indefinites allowing occasional distributivity:
(23) Petr
Petr
zamíchal
mixed
červenou
red
i
i
zelenou
green
barvu.
color
‘𝑀 𝑖𝑥𝑒𝑑(𝐺𝑟𝑒𝑒𝑛) ∧ 𝑀 𝑖𝑥𝑒𝑑(𝑅𝑒𝑑)’
(24) Mariánka
Mariánka
i
i
Mojmírek
Mojmírek
si
SE
dávali
consumed
dvě
two
zmrzliny.
ice-creams
‘individual distributive/occasional reading’
Mojmír Dočekal Markers of distributivity in Czech 20 / 91
3) binominal/determiner strategy
(25) Každý
each
z
of
těch
the
dvou
two
zazpíval
sang
deset
ten
písní.
songs
‘distrbitutive’
(26) Petr
Petr
a
and
Karel
Karel
zazpívali
sang
každý
each
deset
ten
písní.
songs
‘distributive’
Mojmír Dočekal Markers of distributivity in Czech 21 / 91
Terminology
data: binominal each vs. distributive each
diagnosis of the distributive reading: lack of the cumulative reading
(27) Two boys bought three books.
(28) a. Each of the two boys bought three books. determiner
b. Two boys bought [three beers each]. binominal
(28-a): determiner each, two boys restriction, VP nuclear scope
(28-b): binominal each, two boys key, three books share
syntactic structure: Safir and Stowell (1988)
joint work with Radek Šimík
Mojmír Dočekal Markers of distributivity in Czech 22 / 91
4) Pluractional strategy
plurality of events
Upriver Halkomelem: the verb yáleq’ is the pluractional form
many trees fell down at the same time/the same tree fell down
multiple times
but not one tree once
(29) yáleq’
fall.pl
-et
-tr.
-es
-3S
te
det.
theqát
tree
‘He/they felled the tree(s).’
Mojmír Dočekal Markers of distributivity in Czech 23 / 91
Kuhn’s typology:
1) Pluralizing operators sum together the objects in a set {a, b, c} →
{a, b, c, a ⊔ b, a ⊔ c, b ⊔ c, a ⊔ b ⊔ c}
2) Plural filters restrict a set to only its plural objects {a, b, c, a ⊔ b, a
⊔ c, b ⊔ c, a ⊔ b ⊔ c} → {a ⊔ b, a ⊔ c, b ⊔ c, a ⊔ b ⊔ c}
dependent indefinites and pluractional markers: plural filters
Mojmír Dočekal Markers of distributivity in Czech 24 / 91
Diagnostics
1) No variation of plain indefinites
French Sign Language:
(30) EVERY-DAY JEAN ONE WORD FORGET. ✓many words✓ one
word
‘Every day, Jean forgot one word.’
(31) JEAN ONE WORD FORGET-rep. *many words✓ one word
‘Jean forgot one word repeatedly.’
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2) Innocent redundancy
pluralizing operators: double distributivity (3 dogs x 7 evenings)
(32) John walked each of his dogs every evening.
two filters (pluractional marker and dependent indefinite) don’t
multiply: vary with respect to a single key
Kaqchikel: pluractional marker (-ala’) and an dependent indefinite
(33) Xinkan-ala’
I-search-LA’
ju-jun
one-one
wuj.
book
‘I looked for a book on each occasion.’
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distributive operators license pluractionals and distributive numerals:
Kaqchikel
(34) Chikijujunal
each
ri
the
tijoxela’
students
xkiq’etej
hugged
ju-jun
one-one
tz’i’.
dog
‘Each of the students hugged a dog.’
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Czech pluractional -(o)va seems to fit:
no variation:
(35) Každý student po-líbil maminku. ✓ 1 ✓ many
‘Every student kissed a mother.’
(36) Petr líb-áva-l maminku. ✓ 1 * many
‘Petr kissed a mother (on many occasions).’
Mojmír Dočekal Markers of distributivity in Czech 28 / 91
can be licensed by distributivity operator and doesn’t multiply distr.
(37) Petr každý den vyčistil každé kolo.
‘Petr cleaned each of his bikes every day.’
(38) Petr každý den čistíval kola.
‘Petr cleaned his bikes every day.’
(39) Každý student líbával maminku.
‘Every student kissed the mother.’
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Basic properties of Czech binominal each I
Expected properties of Czech binominal each
seminal discussion (English binominal each): Safir and Stowell (1988),
recently Dotlačil (2012), Zimmermann (2002), a.o.
Both pre- and post-position wrt share NP (jednu čepici) possible:
(40) Chlapci
boys.nom.pl
si
refl
koupili
bought.pl
každý
each.nom.sg
jednu
one
čepici.
cap.acc
‘The boys bought each one cap.’
(41) Chlapci
boys.nom.pl
si
refl
koupili
bought.pl
jednu
one
čepici
cap.acc
každý.
each.nom.sg
‘The boys bought one cap each.’
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Basic properties II
Bare (non-determined) share NP not allowed; cf. VP-related each
(44):
(42) ??Chlapci
boys.nom.pl
si
refl
koupili
bought.pl
každý
each.nom.sg
čepici.
cap.acc
Intended: ‘The boys bought each one cap.’
(43) ??Chlapci
boys.nom.pl
si
refl
koupili
bought.pl
čepici
cap.acc
každý.
each.nom.sg
Intended: ‘The boys bought one cap each.’
(44) Chlapci
boys.nom.pl
si
refl
každý
each.nom.sg
koupili
bought.pl
čepici.
cap.acc
‘The boys each bought a cap.’
Mojmír Dočekal Markers of distributivity in Czech 31 / 91
Clause-mate restriction
(45) *Chlapci
boys.pl
říkali,
said
že
that
Marie
Marie
koupila
bought
každý
each.sg.m
jednu
one
čepici.
cap.acc
Intended: ‘Each of the boys said that Mary bought one cap.’
Key can be any argument, not just subject.
(46) Marie
Marie
přinesla
brought
chlapcům
boys.dat.pl
každému
each.dat.sg
jednu
one
čepici.
cap.acc
‘Marie bought each of the boys one cap.’
(47) Marie
Marie
přinesla
brought
ty
the
čepice
caps.acc.pl
každou
each.acc.sg
jednomu
one
chlapci.
boy.dat
‘Marie brought each of caps to one boy.’
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Share can be non-accusative
(48) Těm
the
chlapcům
boys.dat.pl
se
refl
líbila
liked
každému
each.dat.sg
jedna
one
dívka.
girl.nom
‘The boys liked one girl each.’
Mojmír Dočekal Markers of distributivity in Czech 33 / 91
Underlying structure of Czech binominal each I
Language specific properties: agreement with the key
Idea: Czech binominal each contains a covert singular definite description
referring back to / bound by a plural antecedent.
Example with discourse anaphora:
(49) Přišli
came
nějací
some
muži𝑖.
men.pl
Každý
each
/ Jeden
one
( ten
the
muž𝑖)
man.sg
měl
had.sg
zbraň.
weapon
‘Some men came. (Each) one of them (lit. each/one the man) had
a weapon.’
Mojmír Dočekal Markers of distributivity in Czech 34 / 91
Hypothesized structure of binominal each, where <ten muž> is
obligatorily deleted under (partial) identity with its antecedent;
cf. Sauerland (1998), Fox (2003), Johnson (2012), a.o., for a similar
treatment of traces
(50) Ti
the
muži𝑖
men.pl
měli
had.pl
každý
each
< ten
the
muž𝑖>
man.sg
jednu zbraň.
‘The men had one weapon each.’
Mojmír Dočekal Markers of distributivity in Czech 35 / 91
Proposed constituent structure
S
DP
key
the men.nom.pl𝑖
VP
V
had.pl
DP
Det
each.nom.sg
DP
<the man.nom.sg𝑖 >
DP
share
one weapon.acc
Mojmír Dočekal Markers of distributivity in Czech 36 / 91
Argument: Movement
Binominal each vs. floating all: Binominal each forms a constituent
together with the share.
(51) [ Každý
each.sg.masc
/*Všichni
all.pl.masc
3
3
medaile]
medals
jsme
be.1pl
vyhráli
won.pl
jen
only
my.
we
(Intended:) ‘We were the only ones to win three medals each.’
Mojmír Dočekal Markers of distributivity in Czech 37 / 91
Semantic properties
distributivity over atoms in key’s denotation
→ prevents (usually) cumulative and collective interpretation
pseudoCzech
(52) two professors examined three students.
a. cumulative: 2 professors … 3 students
b. distributive: 2 professors … 6 students
c. collective: 2 professors (cooperating) … 3 students
(53) two professors examined [each three students].
a. #cumulative: 2 professors … 3 students
b. distributive: 2 professors … 6 students
c. #collective: 2 professors (cooperating) … 3 students
Mojmír Dočekal Markers of distributivity in Czech 38 / 91
Collectives
predicates like gather, be a good team, be a group (of NP)
usually enforce collective reading
(54) The group of two authors wrote three books.
a. *distributive: 2-6
b. *cumulative: 2-3
c. ✓ collective: 2(together)-3
usually collectives and distributivity markers clash:
(55) *The group of two authors wrote three books each.
Dowty (1987), Brisson (2003), Winter (2002), Dočekal (2012)
Mojmír Dočekal Markers of distributivity in Czech 39 / 91
Two types of collectives
two types of collective predicates (Dowty (1987), Winter (2002),
Brisson (2003), …):
1 gather, meet, sing together, … set predicates
2 be a good team, outnumber NP, … atom predicates
▶ the criterion (compatibility with all – Dowty, sg/pl Winter):
(56) a. all the boys gathered
b. *all the boys are a good team
Mojmír Dočekal Markers of distributivity in Czech 40 / 91
collective Czech numerals like dvojice ‘twosome’ (parallel data in other
Slavic langauges: Polish, Russian, …) enforce the collective reading
(57) a. Dva
two
sportovci
athletes
vyhráli
won.pl
2
2
medaile,
medals
✓první
first
zlato
gold
a
&
stříbro,
silver
druhý
second
stříbro
silver
a
&
bronz.
bronze
‘Two athletes won 2 medals, the first one G & S, the second
one S & B.’
b. Dvojice sportovců vyhrála 2 medaile, #první zlato a stříbro,
druhý stříbro…twosome athletes.gen won.sg.fem 2 medals
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collective set predicates allow limited distributivity (Dotlačil (2012))
collective Czech numerals can distribute over reciprocals like set
collectives
(58) [Bill and Peter, together],/#[the team of students] carried the
piano across each other’s lawns.
(59) Dvojice
twosome
/# Skupina
group
podezřelých
suspects.gen
zradila
betrayed
jeden
one
druhého.
other.
(Intended:) ‘The people within the twosome / group of suspects
betrayed one another.’
provisional assumption: collective numerals are set collectives
Mojmír Dočekal Markers of distributivity in Czech 42 / 91
The contrast
binominal each + set collectives
(60) Dvojici
twosome.dat
detektivů
detectives.gen
byly
were
předány
given
[každému
[each.dat
tři
three.nom
ceny].
prizes.nom]
‘Three prizes each were given to twosome detectives.’
a. only distr.: 2 detectives … 6 prizes (3 each)
binominal each can distribute ‘into’ set collectives
Mojmír Dočekal Markers of distributivity in Czech 43 / 91
determiner each + set collectives
(61) [Každé
[each.dat
dvojici
twosome.dat
detektivů]
detectives.gen]
byly
were
předány
given
tři
three.nom
ceny.
prizes.nom
‘Three prizes were given to each twosome of detectives.’
a. only distr. over twosome: (each) 2 detectives … 3 prizes
determiner each can distribute only over groups, not ‘into’
Mojmír Dočekal Markers of distributivity in Czech 44 / 91
binominal each + atom collective predicate
(62)???Týmu
team.dat
detektivů
detectives.gen
byly
were
předány
given
každému
each.dat
tři
three
ceny.
prizes
‘???Three prizes each were given to the team of detectives.’
binominal each clashes with atom collectives
Mojmír Dočekal Markers of distributivity in Czech 45 / 91
determiner each + atom collective predicates
(63) [Každému
each.dat
týmu
team.dat
detektivů]
detectives.gen
byly
were
předány
given
tři
three.nom
ceny.
prizes.nom
‘Three prizes were given to each team of detectives.’
a. only distr. over teams (each 2 prizes)
determiner each can distribute only over group atoms
Mojmír Dočekal Markers of distributivity in Czech 46 / 91
Cumulative readings with binominal každý ‘each’
distributivity can survive with operators normally contradicting it
(collective or cumulative) if the distributivity and the other operator
don’t compete for the same argument
(64) Dva
two
zelináři
greengrocers
prodali
sold
deseti
ten.dat
zákazníkům
customers.dat
tři
three.acc
řepy
beets.acc
každému.
each.dat
‘Two greengrocers sold to ten customers three beets each.’
Mojmír Dočekal Markers of distributivity in Czech 47 / 91
(65) Dva
two
zelináři
greengrocers
prodali
sold
deseti
ten.dat
zákazníkům
customers.dat
tři
three.acc
řepy
beets.acc
každému.
each.dat
‘Two greengrocers sold to ten customers three beets each.’
(65): subject (dva zelináři ‘two greengrocers’) and the indirect object
(deseti zákazníkům ‘ten customers’) allow a cumulative interpretation
direct object (tři řepy ‘three beets’) is interpreted obligatorily
distributively w.r.t indirect object
Mojmír Dočekal Markers of distributivity in Czech 48 / 91
Agreement confound
subject vs. non-subject assymetries
(66) a. Dva
two.nom
detektivové
detectives.nom
dostali
received
[každý
[each.nom
3
3
ceny].
prizes.acc]
‘Two detectives received [each three prizes].’
b. Deset
ten.nom
detektivů
detectives.gen
dostalo
received.sg
[*každý/*každého
[*each.nom/*each.gen
3
3
ceny].
prizes.acc]
Mojmír Dočekal Markers of distributivity in Czech 49 / 91
provisional generalization
(67) Czech (Slavic?) binominal each cannot take as its antecedent
genitive complement of a numeral.
(68) Generál
general.nom
dal
gave.sg
deseti
three.dat
detektivům
detectives.dat
[dvě
[two.acc
ceny
prizes.acc
každému].
each.dat]
‘The general gave ten detectives [three prizes each].’
Mojmír Dočekal Markers of distributivity in Czech 50 / 91
similarly for collective numerals:
(69) Dvojice
twosome.nom
detektivů
detectives.gen
chytla
caught.sg
[*každý/*každého
[*each.nom/*each.gen
tři
three.acc
zloděje.]
thieves.acc]
‘Twosome of detectives caught [trhee thieves each].’
Mojmír Dočekal Markers of distributivity in Czech 51 / 91
binominal + set collectives perfectly fine in dativ
(70) Dvojici
twosome.dat
detektivů
detectives.gen
byly
were
předány
given
[každému
[each.dat
tři
three.nom
ceny].
prizes.nom]
‘Three prizes each were given to twosome detectives.’
a. only distr.: 2 detectives … 6 prizes (3 each)
Mojmír Dočekal Markers of distributivity in Czech 52 / 91
PCDRT
Dotlačil (2012), Dotlačil (2012), Brasoveanu (2008)
(71) Prediction: expected difference between binominal and determiner
each. Both supply distributivity but binominal distributes locally
over the share (it is anaphoric to key but don’t scope over it).
Determiner each scopes over the whole nuclear scope. Predicted
innertia of binominal each w.r.t. colectivity (and cumulativity)
outside of its share.
main point: illustrate the prediction (Czech data)
byproduct: semantic and syntactic description of Slavic binominal
each
and interaction of determiner/binominal each with collectives
Mojmír Dočekal Markers of distributivity in Czech 53 / 91
Cumulative readings in PCDRT
(72) Two boys bought three books.
essentials: PCDRT works with sets of assignments
Info state J u1 u2
j1 boy1 book1
j2 boy1 book2
j3 boy2 book3
columns: values of discourse referents, rows: assignments to drefs
cumulative reading, fully compositional
Mojmír Dočekal Markers of distributivity in Czech 54 / 91
E(existential) C(losure): shifts predicates into arguments
S
DP 𝑟𝑡,𝑡
D
EC 𝑢1
NP 𝑟𝑡
two boys
VP 𝑟𝑡
V
buy
DP 𝑟𝑡,𝑡
D
EC 𝑢2
NP 𝑟𝑡
three books
(73) [𝑢1, 𝑢2|#(𝑢1) = 2 ∧ boys{𝑢1} ∧ #(𝑢2) =
3 ∧ books{𝑢2} ∧ buy{𝑢1, 𝑢2}]
Mojmír Dočekal Markers of distributivity in Czech 55 / 91
Determiner and binominal each in PCDRT
(74) a. det-každý 𝑢 𝑛 = 𝜆𝑃 𝑟𝑡 𝜆𝑄 𝑟𝑡.𝛿 𝑢 𝑛
(𝑃(𝑢 𝑛)) ∧ 𝑄(𝑢 𝑛)
b. binom-každý 𝑢 𝑚 = 𝜆𝑣 𝑟 𝜆𝑃 𝑟𝑡 𝜆𝑄 𝑟𝑡.[𝑢 𝑚 ∣]∧𝛿 𝑣(𝑃(𝑢 𝑚))∧𝑄(𝑢 𝑚)
distributivity operator 𝛿 in both
but binominal each introduces discourse referents
binominal: anaphoric to the key but scopes locally over the share
determiner: distributes over the nuclear scope
Types in PCDRT: r … drefs, t … truth value
Mojmír Dočekal Markers of distributivity in Czech 56 / 91
Determiner each
(75) Each of the two boys bought three books.
Info state J u1 u2
j1 boy1 book1
j2 boy1 book2
j3 boy1 book3
j4 boy2 book4
j5 boy2 book5
j6 boy2 book6
Mojmír Dočekal Markers of distributivity in Czech 57 / 91
Determiner each
S
DP 𝑢1
𝛿 𝑢1
NP
VP
V DP
NP EC
existential closure of the subject (predicative semantics: ⟨𝑟, 𝑡⟩)
distributes over the nuclear scope
𝛿 𝑢1([𝑢2] ∧ [|#(𝑢2) = 3 ∧ books{𝑢2}] ∧ [|buy{𝑢1, 𝑢2}])
(76) [𝑢1|#(𝑢1) = 2 ∧ boys{𝑢1} ∧ 𝛿 𝑢1([𝑢2] ∧ [|#(𝑢2) =
3 ∧ books{𝑢2}] ∧ [|buy{𝑢1, 𝑢2}])]
Mojmír Dočekal Markers of distributivity in Czech 58 / 91
Binominal each
(77) Dva
two
sportovci
athletes
vyhráli
won.pl.masc
každý
each.sg.masc
3
3
medaile.
medals
✓distributive
Mojmír Dočekal Markers of distributivity in Czech 59 / 91
the same info state as for (93)
Info state J u1 u2
j1 athlete1 medal1
j2 athlete1 medal2
j3 athlete1 medal3
j4 athlete2 medal4
j5 athlete2 medal5
j6 athlete2 medal6
Mojmír Dočekal Markers of distributivity in Czech 60 / 91
S
DP1
key.pl
VP1
V
won.pl
DP2
Det
each.sg
NP3
𝑢1
the athlete.sg
NP2
share
Mojmír Dočekal Markers of distributivity in Czech 61 / 91
(78) [𝑢1|#(𝑢1) = 2 ∧ athletes{𝑢1} ∧ [𝑢2|𝛿 𝑢1
([#(𝑢2) =
3 ∧ prizes{𝑢2}])] ∧ win{𝑢1, 𝑢2}]
distributivity percolates through the semantic computation
the same info state but:
1 determiner each: distributes over the nuclear scope + closes the
predicative meaning of the subject (⟨𝑟, 𝑡⟩)
2 binominal each: scopes only over share
(𝛿 𝑢1
([#(𝑢2) = 3 ∧ prizes{𝑢2}])) and is anaphoric to the key (𝑢1)
predicted difference: local (binominal) vs. global (determiner)
distributivity
Mojmír Dočekal Markers of distributivity in Czech 62 / 91
Main data puzzle
binominal vs. determiner each vs. set and atom collectives
pseudoCzech:
(79) a. binominal each + set collective
[Three prizes each] were given twosome detectives.
b. *binominal each + atom collective
#[Three prizes each] were given team detectives.
c. determiner each + set/atom collective
Three prizes were given [each twosome/team detectives] only
distribution over groups
Mojmír Dočekal Markers of distributivity in Czech 63 / 91
The set collective formalization
(80) Dvojice
twosome
sportovců
athletes.gen
vyhrála
won.sg.fem
3
3
medaile.
medals. *distributive
S
DP1
EC 𝑢1 two-ice athletes
VP1
V
won
DP2
EC 𝑢2 3 medals
Mojmír Dočekal Markers of distributivity in Czech 64 / 91
(81) a. S = [𝑢1, 𝑢2|#(𝑢1) = 2 ∧ athletes{𝑢1} ∧ #(𝑢2) =
3 ∧ medals{𝑢2} ∧ win{⋃ 𝑢1, 𝑢2}]
b. DP1 = 𝜆𝑄 𝑟𝑡.[𝑢1|#(𝑢1) = 2 ∧ athletes{𝑢1}] ∧ 𝑄(⋃ 𝑢1)
c. VP1 = 𝜆𝑣 𝑟[𝑢2|#(𝑢2) = 2 ∧ medals{𝑢2} ∧ win{𝑣, 𝑢2}]
d. DP2 = 𝜆𝑄 𝑟𝑡.[𝑢2|#(𝑢2) = 3 ∧ medals{𝑢2}] ∧ 𝑄(𝑢2)
our addition to PCDRT: treatment of numeral collectives as imposing
the collectivity on its argument (gets propagated into the verb
external argument slot)
technically (81-b)
Mojmír Dočekal Markers of distributivity in Czech 65 / 91
(82) [𝑢1, 𝑢2|#(𝑢1) = 2 ∧ athletes{𝑢1} ∧ #(𝑢2) =
3 ∧ medals{𝑢2} ∧ win{⋃ 𝑢1, 𝑢2}]
one verifying info state:
collective on the subject
all the athletes won together the three medals (technically
win{⋃ 𝑢1, 𝑢2})
Info state J u1 u2
j1 athlete1 medal1
j2 athlete2 medal2
j3 athlete1 medal3
Mojmír Dočekal Markers of distributivity in Czech 66 / 91
Binominal each + set collective
(83) [Three prizes each] were given twosome detectives.
S
DP 𝑢2
NP
three prizes
𝛿 𝑢1
VP
V
were given
DP 𝑢2
EC NP
twosome detectives
Mojmír Dočekal Markers of distributivity in Czech 67 / 91
(84) [Three prizes each] were given twosome detectives.
Info state J u1 u2
j1 detective1 prize1
j2 detective1 prize2
j3 detective1 prize3
j4 detective2 prize4
j5 detective2 prize5
j6 detective2 prize6
collective set numeral checks ⋃ (cardinality) of u1 + imposes
collectivity on the predicate
▶ binominal each distributivity is local: scopes over the share (u2)
Mojmír Dočekal Markers of distributivity in Czech 68 / 91
PCDRT formalization
(85) [Three prizes each] were given twosome detectives.
a. [𝑢1|#(𝑢1) = 2 ∧ 𝑑𝑒𝑡𝑒𝑐𝑡𝑖𝑣𝑒𝑠{𝑢1} ∧ [𝑢2]|𝛿 𝑢1
([#(𝑢2) =
3 ∧ 𝑝𝑟𝑖𝑧𝑒𝑠{𝑢2}]) ∧ 𝑔𝑖𝑣𝑒𝑛{⋃ 𝑢1, 𝑢2}]
the detectives were given collectively (local collectivity: key plus
predicate) prizes
each of them received two prizes (local distributivity over the share)
Mojmír Dočekal Markers of distributivity in Czech 69 / 91
Binominal each plus atom collective
(86) #[Three prizes each] were given team detectives.
Info state J u1 u2
j1 detective1 + detective2 prize1
j2 detective1 + detective2 prize2
j3 detective1 + detective2 prize3
atom collectivity is horizontal, set collectivity is vertical
probably bad for the same reason as:
(87) Petr drank *[two beers each].
Mojmír Dočekal Markers of distributivity in Czech 70 / 91
Determiner each + set/atom collective
(88) Three prizes were given [each twosome/team detectives]
Info state J u1 u2
j1 detective1 + detective2 prize1
j2 detective1 + detective2 prize2
j3 detective1 + detective2 prize3
j4 detective3 + detective4 prize4
j5 detective3 + detective4 prize5
j6 detective3 + detective4 prize6
with the determiner each the distributivity scopes over collectives and
cannot decompose them
Mojmír Dočekal Markers of distributivity in Czech 71 / 91
Summary
both determiner and binominal each contribute distributivity
determiner each scopes globally (nuclear scope) and interferes with a
collectivity (and cumulativity) of other arguments
binominal each distributes locally over the share and allows set
collectivity (and cumulativity) outside of its share
Mojmír Dočekal Markers of distributivity in Czech 72 / 91
Thanks!
Mojmír Dočekal Markers of distributivity in Czech 73 / 91
Mojmír Dočekal Markers of distributivity in Czech 74 / 91
Appendix
Mojmír Dočekal Markers of distributivity in Czech 75 / 91
Main data puzzle
pseudoCzech:
binominal each and collective numerals
(89) a. Each from twosome athletes won three medals. coll+distr ok
b. *Twosome from athletes won each three medals. col+bin-each
(90) Two from athletes won three medals each. num+bin ok
Mojmír Dočekal Markers of distributivity in Czech 76 / 91
Repeating the pattern
pseudoCzech:
binominal each and collective numerals
(91) a. Each from twosome athletes won three medals. coll+distr ok
b. *Twosome from athletes won each three medals. col+bin-each
(92) Two from athletes won three medals each. num+bin ok
Mojmír Dočekal Markers of distributivity in Czech 77 / 91
The determiner distributive sentence
(93) Každý
each
z
of
dvojice
twosome.gen
sportovců
athletes.gen
vyhrál
won.sg.masc
3
3
medaile.
medals
✓distributive
Mojmír Dočekal Markers of distributivity in Czech 78 / 91
verifying info state:
Info state J u1 u2
j1 athlete1 medal1
j2 athlete1 medal2
j3 athlete1 medal3
j4 athlete2 medal4
j5 athlete2 medal5
j6 athlete2 medal6
Mojmír Dočekal Markers of distributivity in Czech 79 / 91
needed ingredients:
(94) a. det-každý 𝑢 𝑛 = 𝜆𝑃 𝑟𝑡 𝜆𝑄 𝑟𝑡.𝛿 𝑢 𝑛
(𝑃(𝑢 𝑛)) ∧ 𝑄(𝑢 𝑛)
b. z ‘from/of’ predicates of groups → predicates of their parts –
𝜆𝑃 𝑟𝑡 𝜆𝑣 𝑟.[|𝑣 ⊆ 𝑃]
c. predicative meaning of CN:
𝜆𝑤 𝑟[|#(𝑤) = 2 ∧ athletes{⋃ 𝑤}]
d. whole subject: 𝜆𝑄 𝑟𝑡.[𝑣|𝛿 𝑣([|𝜆𝑣 𝑟.[𝑣 ⊆ 𝜆𝑤 𝑟[|#(𝑤) =
2 ∧ athletes{⋃ 𝑤}]]]) ∧ 𝑄(𝑣)
determiner each quantifies over parts (partitioning z ‘from’) of the
group denotation
predicative meaning results in:
(95) [𝑣, 𝑢2|athlete{𝑣} ∧ 𝛿 𝑣([|𝜆𝑣 𝑟.[𝑣 ⊆ 𝜆𝑤 𝑟[|#(𝑤) =
2∧athletes{⋃ 𝑤}]]])∧#(𝑢2) = 3∧medals{𝑢2}∧win{𝑣, 𝑢2}])]
Mojmír Dočekal Markers of distributivity in Czech 80 / 91
Clash of CN with binominal each
(96) *Z dvojice
twosome
sportovců
athletes.gen
vyhrál
won.sg.masc
každý
each.sg.masc
3
3
medaile.
medals
star for the binominal each
can be floated each but not the binominal each
the problem is that the percolated distributivity cannot be applied to
the subject’s argument meaning
plus argument subject imposes collectivity ↔ clash:
(97) a. DP1 of
(96) = 𝜆𝑄 𝑟𝑡.[𝑢1|#(𝑢1) = 2 ∧ athletes{𝑢1}] ∧ 𝑄(⋃ 𝑢1)
b. VP1 of
(96) = 𝜆𝑣 𝑟[𝑢2|𝛿 𝑢1
([#(𝑢2) = 3 ∧ medals{𝑢2}]) ∧ win{𝑣, 𝑢2}]
Mojmír Dočekal Markers of distributivity in Czech 81 / 91
Each can “float” in both cases, even in a position that apparently
points to a binominal each. Note two differences though: NP (being
obligatorily plural) triggers plural verb agreement vs. PP antecedent
does not trigger agreement → agreement with the postverbal sg
každý.
(98) [NP Ti
the
chlapci]
boys.nom.pl
vyhráli
won.pl
{ každý}
each.nom
jednu
one
cenu
prize.acc
{
každý}.
each.nom
‘The boys won one prize each.’
(99) [PP Z
from
těch
the
chlapců]
boys.gen.pl
vyhrál
won.sg
{ každý}
each.nom
jednu
one
cenu
prize.acc
{ každý}.
each.nom
‘Each of the boys won one prize.’
Mojmír Dočekal Markers of distributivity in Czech 82 / 91
Derived collective numerals
Czech: group nouns/numerals derived from cardinal numerals with
the suffix -ice: tr-oj-ice námořníků
properties:
1 both singular and plural: s troj-icí 𝐼𝑁𝑆𝑇.𝑆𝐺 námořníků, s
troj-ice-mi 𝐼𝑁𝑆𝑇.𝑃 𝐿 námořníků
2 incompatible with the singular universal quantifier všechno ‘all’:
*všechna troj-ice námořníků (not mass)
3 obligatorily non-cumulative: troj-ice + troj-ice = 2 troj-ice
4 obligatorily non-divisive: parts of troj-ice are not troj-ice
Mojmír Dočekal Markers of distributivity in Czech 83 / 91
5 can be counted with cardinal numerals: dvě troj-ice námořníků
6 usualy enforce the collective interpretation:
Mojmír Dočekal Markers of distributivity in Czech 84 / 91
Two arguments that PP antecedents cannot antecede binominal each,
despite the initial appearance:
Agreement with the each-phrase rather than with the antecedent (see
above).
No constituent:
(100) *[ Každý
each.nom
jednu
one
cenu]
prize.acc
vyhrál(i)
won.sg(pl)
jenom
only
[PP z
from
těch
the
chlapců].
boys.gen.pl
Intended: Only the boys were such that each of them won one
prize.’
Mojmír Dočekal Markers of distributivity in Czech 85 / 91
NP ellipsis of the each-restrictor not obligatory:
(101) [PP Z
from
těch
the
chlapců]
boys.gen.pl
vyhrál
won.sg
[NP každý
each
chlapec]
boy.nom.sg
jednu
one
cenu.
prize.acc
‘From the (group of) boys, each boy won one prize.’
Mojmír Dočekal Markers of distributivity in Czech 86 / 91
Possibility to combine binominal each with distributive po:
(102) Ty
the
slepice
hens.nom.pl
snesly
layed
po
po
třech
three
vajíčkách.
eggs.loc
‘The hens layed three eggs each.’
(103) Ty
the
slepice
hens.nom.pl
snesly
layed
každá
each.nom
tři
three
vajíčka.
eggs.acc
‘The hens layed three eggs each.’
(104) Ty
the
slepice
hens.nom.pl
snesly
layed
každá
each.nom.sg
po
po
třech
three
vajíčkách.
eggs.loc
‘The hens layed three eggs each.’
Mojmír Dočekal Markers of distributivity in Czech 87 / 91
Comparison with prepositional restrictors
The following two have identical truth-conditions in Czech → the
singular nominative NP ten chlapec can have the same use as a
prepositional PP containing a (partitive?) plural genitive těch
chlapců.
(105) Každý
each.nom
[NP ten
the
chlapec]
boy.nom.sg
vyhrál
won.sg
jednu
one
cenu.
prize.acc
‘Each of the boys won one prize.’
(106) Každý
each.nom
[PP z
from
těch
the
chlapců]
boys.gen.pl
vyhrál
won.sg
jednu
one
cenu.
prize.acc
‘Each of the boys won one prize.’
Mojmír Dočekal Markers of distributivity in Czech 88 / 91
každý v vs. každý z
the distinction seems to be between non-distinguishing každý z
vs. plurality non-accepting každý v
partially based on ČNK:
case distinction: LOC vs. GEN
(107) Každý z
a. pronouns: nich, nás, …
b. plural count: manželů, partnerů, účastníků
c. -ice: trojice
d. numerals (indefinite?): pěti, …
e. collective nouns: týmu, rodiny
Mojmír Dočekal Markers of distributivity in Czech 89 / 91
(108) Každý v
a. collective nouns: týmu, říši, rodině, nemocnici
b. entity denoting: Praze, ČR,
c. *plural count: # každý v účastnících, #každý v manželích, …
d. *pronouns: # [každý v nich], …
e. *numerals: # [každý v pěti], …
f. -ice: každý ve dvojici (dostane do ruky …)
Mojmír Dočekal Markers of distributivity in Czech 90 / 91
References I
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Philosophy 31 (2): 129–209.
Brisson, Christine. 2003. “Plurals, All, and the Nonuniformity of Collective Predication.” Linguistics and Philosophy 26 (2):
129–84.
Dočekal, Mojmı́r. 2012. “Atoms, Groups and Kinds in Czech.” Acta Linguistica Hungarica 59 (1-2): 109–26.
Dotlačil, Jakub. 2012. “Binominal Each as an Anaphoric Determiner: Compositional Analysis.” In Sinn Und Bedeutung,
16:211–24.
Dotlačil, Jakub. 2012. “Reciprocals Distribute over Information States.” Journal of Semantics 30 (4): 423–77.
Dowty, David. 1987. “Collective Predicates, Distributive Predicates and All.” In Proceedings of the 3rd Escol, 97–115. (Eastern
States Conference on Linguistics), Ohio State University Ohio.
Fox, Danny. 2003. “On Logical Form.” In Minimalist Syntax, edited by Randall Hendrick, 82–123. Oxford: Blackwell.
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Winter, Yoad. 2002. Flexibility Principles in Boolean Semantics: The Interpretation of Coordination, Plurality, and Scope in
Natural Language. Vol. 37. MIT press.
Zimmermann, Malte. 2002. Boys Buying Two Sausages Each: On the Syntax and Semantics of Distance-Distributivity.
Netherlands Graduate School of Linguistics.
Mojmír Dočekal Markers of distributivity in Czech 91 / 91