distributive numerals, dependent indefinites and event...
TRANSCRIPT
Distributive numerals, dependent indefinites andevent plurality
Patricia Cabredo Hofherr1 Lucia Tovena2
1UMR 7023CNRS & Université Paris 8
2Université Sorbonne Paris Cité - Paris 7
ESSLLI 2015 Barcelona
Outline
1 Marking the distributive share
2 D-indefinites vs. d-numerals: Hungarian (Farkas 1997)
3 Cross-linguistic variationTelugu (Balusu 2006)Pereltsvaig 2012Tlingit (Cable 2014)D-numerals cross-linguistically: temporal/locative keyD-numerals cross-linguistically: subjectsD-numerals cross-linguistically: adverbials
Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities: d-numerals & d-indefinites ESSLLI 2015 2 / 64
Marking the distributive share
Marking the distributive share
We have seen the general schema of distribution (day 2):
(1) Every childDist.key
ate a peachDist.share
The distributive key is marked by a quantifier everyThe distributed share can also be marked: binominal each
(2) The childrenDist.key
ate a peach each
Dist.share
IKey: the children
IKey unit: 1 child
IShare sum: as many peaches as will be handed to the children
IShare unit: 1 peach
Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities: d-numerals & d-indefinites ESSLLI 2015 3 / 64
Marking the distributive share
Marking the distributive share
In distributive configurations each unit of the key is attributed aunit of the share:
(3) The childrenDist.key
ate a peach each
Dist.share1 child �!1 peach
Distributive configurations look like the pairs resulting from auniversal quantifier taking scope over an existential quantifier.8 x child(x) 9 y peach (y): eats(x,y)However, these pairs need not be the result of quantificationThese pairs do not need to be asserted.
Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities: d-numerals & d-indefinites ESSLLI 2015 4 / 64
Marking the distributive share
Marking the distributive share
Day 4: pluractional adverbials:I pairing is the result of the existence of the cover with certain
properties, imposed by [[Pl]]I the pluractional adverbial imposes a felicity condition that a cover
yielding pair-wise association has to be possible (plus otherrestrictions, e.g. temporal sequence)
(4) a. John ate the peach (*one by one).b. The children ate a peach (one by one).
Cover: child 1 eats peach 1, child 2 eats peach 2,...
Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities: d-numerals & d-indefinites ESSLLI 2015 5 / 64
Marking the distributive share
Marking the distributive share
Choe (1987) calls markers of the distributive shareanti-quantifiers.Quantifiers provide multiplication of the events.
Markers of the distributive share / anti-quantifiers
I require multiple events for licensingI do not provide the event plurality themselves
(5) a. *The child ate a lolly each.b. Every child ate a lolly each.
Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities: d-numerals & d-indefinites ESSLLI 2015 6 / 64
Marking the distributive share
Marking the distributive share: dependent indefinites
D-indefinitesI need to be part of a distributive shareI need to be distributed over a plurality (depend on a plurality)
Following Farkas (2015) call dependent indefinites d-indefinites
D-indefinites include distributive numerals (Gil, 1982, 1988)
Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities: d-numerals & d-indefinites ESSLLI 2015 7 / 64
Marking the distributive share
Marking the distributive share: dependent indefinites
Distinguish two types of d-indefinites (Farkas, 2015)d-existentials: d-indefinites whose D is a specially markedindefinite article
d-numerals: d-indefinites whose D is a specially marked cardinal
numeral
Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities: d-numerals & d-indefinites ESSLLI 2015 8 / 64
Marking the distributive share
D-indefinites and narrow scope
D-definites cannot be reduced to narrow scope indefinites.There are contexts that license d-existentials but in whichunmarked indefinites can only have ‘wide’ scope, i.e., fixedreference readings. (Henderson 2014 for Kaqchikel)This also holds for Hungarian Farkas (2015)
Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities: d-numerals & d-indefinites ESSLLI 2015 9 / 64
Marking the distributive share
D-indefinites and narrow scope
Caveat: Scope here is understood semantically
An NP1 is in the semantic scope of NP2 ifthe reference of NP1 co-varies with the reference of NP2Being in the syntactic scope of a quantifier is one way to co-vary,but not the only one.Fixed reference of an NP can be the result of (at least)
I wide syntactic scope of the NP with respect to another quantifierI lack of distributive dependencies with another plurality
Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities: d-numerals & d-indefinites ESSLLI 2015 10 / 64
Marking the distributive share
D-indefinites and narrow scope: Kaqchikel
With pluractional suffix -Vla’ on the verb in Kaqchikel Henderson(2012)
I reduplicated numerals are licensedI narrow scope of simple numerals impossible
Caveat: Narrow scope is understood as co-varying reading wrt toanother expressionSee discussion of scope wrt to habitual iteration (Day 1& 3):
I narrow syntactic scopeI no co-variation of the sg indefinite with different events
(no multiplication of the sg indef)
Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities: d-numerals & d-indefinites ESSLLI 2015 11 / 64
Marking the distributive share
D-indefinites and narrow scope: Kaqchikel
With pluractional suffix -Vla’ on the verb in KaqchikelI reduplicated numerals are licensedI multiplication of simple numeral indefinites impossible
(6) X-e’-in-chap-ala’
COM-A3p-E1s-handle-Vla’ox-ox
three-REDwäy.tortilla
‘I touched tortillas in threes.’ FALSE if there are three tortillas in total(or only one touching event)�!co-varying three tortillas
(7) X-e’-in-chap-ala’COM-A3p-E1s-handle-Vla’
oxi’
threewäy.tortilla
‘I touched three tortillas individually (many times).’FALSE if there are more than three tortillas involved�!no multiplication of three tortillasHenderson (2012, exs 403/404)
Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities: d-numerals & d-indefinites ESSLLI 2015 12 / 64
Marking the distributive share
D-indefinites
Question 1: what are the licensing environments for d-indefinitesQuestion 2: what are the parameters of variation
Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities: d-numerals & d-indefinites ESSLLI 2015 13 / 64
D-indefinites vs. d-numerals: Hungarian (Farkas 1997)
D-indefinites vs. d-numerals: Hungarian (Farkas 1997)
Common contexts for d-existential egy-egy and d-numeralsFarkas (2015): both can be licensed by
I Quantified argumentI Distributive predication (plural subject and distributive predicate)I Quantificational adjuncts
Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities: d-numerals & d-indefinites ESSLLI 2015 14 / 64
D-indefinites vs. d-numerals: Hungarian (Farkas 1997)
D-indefinites vs. d-numerals: Hungarian (Farkas 1997)
(8) Quantified argument
Minden‘Every
gyerekchild
hozottbrought
egy-egy/a-a
két-két/two-two
könyvet.book.’ (Farkas, 2015, ex1-2)
(9) Distributive predication
A‘The
gyerekekchildren
hoztakbrought
egy-egy/két-kéta-a/two-two
könyvet.book.’
The children brought a book each. (Farkas, 2015, ex6)(10) Quantificational adjuncts
Minden‘Every
utcasarokracorner
egy-egy/két-kéta-a/two-two
rendörtpoliceman
állitottak.placed.III.Pl’
Only interpretation: policemen co-vary with corners (Farkas, 2015,ex14)
Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities: d-numerals & d-indefinites ESSLLI 2015 15 / 64
D-indefinites vs. d-numerals: Hungarian (Farkas 1997)
D-indefinites vs. d-numerals: Hungarian (Farkas 1997)
Common contexts for d-existential egy-egy and d-numeralsFarkas (2015): both cannot be licensed by
I out of the blueI modalsI generic contexts
Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities: d-numerals & d-indefinites ESSLLI 2015 16 / 64
D-indefinites vs. d-numerals: Hungarian (Farkas 1997)
D-indefinites: Hungarian (Farkas 1997)
(11) no licensor
*Egy-egy/két-két‘A-a/two-two
gyerekchild
(épp)right.now
szalad.runs.’
(Hungarian)
(12) Modals
*Mari‘Mari
kellmust
találkozzonmeet.with
egy-egy/két-kéta-a/two-two
párizsi tanárral.professor from Paris.’
(13) Gen operator
*Egya
sirályseagull
szeretlikes
egy-egy/két-kéta-a/two-two
halat.fish
Attempted reading: A seagull likes a/two fish(d-nominal under the scope of Gen binding the Su)(Farkas, 2015, exs 3,8,9)
Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities: d-numerals & d-indefinites ESSLLI 2015 17 / 64
D-indefinites vs. d-numerals: Hungarian (Farkas 1997)
D-existentials vs. d-numerals in Hungarian
HomophonyI indefinite article egyI numeral egy "one"
egy-egy : d-indefinite or d-numeral?Farkas: the d-indefinite egy-egy differs from other d-numerals
Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities: d-numerals & d-indefinites ESSLLI 2015 18 / 64
D-indefinites vs. d-numerals: Hungarian (Farkas 1997)
D-existentials vs. d-numerals in Hungarian
Licensor sensitivityI d-existentials in Hungarian can co-vary with a
situation/event/temporal variable;I d-numerals cannot (Farkas, 1997)
Situation/event/temporal variables:I implicit multiple event licensingI licensing by pluractionalsI licensing by overt adverbs of quantification
Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities: d-numerals & d-indefinites ESSLLI 2015 19 / 64
D-indefinites vs. d-numerals: Hungarian (Farkas 1997)
D-existentials vs. d-numerals: implicit multiple events
Implicit multiple event licensing: contexts that make clear thatseveral events are involved
I egy-egy possibleI d-numeral impossible
(14) Context: We are discussing how things are in the departmentgenerally:A diákok általában jól haladnak.‘The students usually well advance.’
Egy-egy/*két-két‘A-a/*two-two
diákstudent
megbukikfails
debut
ezthis
ritkánrarely
fordulcomes
elö.up.’
Only interpretation: The students usually do well. From time to time,a student fails but this happens rarely – students co-vary with timesFarkas (2015, ex16)
Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities: d-numerals & d-indefinites ESSLLI 2015 20 / 64
D-indefinites vs. d-numerals: Hungarian (Farkas 1997)
D-existentials vs. d-numerals: pluractional morphology
Licensing by pluractional morphology on the verbI egy-egy possibleI d-numeral impossible
(15) Context:Nurses are talking about how the night went in a children’sward:
Egy-egy/*két-két‘A-A/*two-two
gyerekchild
fel-felébredt
up-up wokedebut
másother
bajtrouble
nemwas
volt.not.’
Only interpretation: From time to time a child woke up but otherthan that there was no trouble – child co-varies with times(Farkas, 2015, ex19)
Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities: d-numerals & d-indefinites ESSLLI 2015 21 / 64
D-indefinites vs. d-numerals: Hungarian (Farkas 1997)
D-indefinites/d-numerals: adverbs of quantification 1
Licensing by overt adverb of quantification
I egy-egy possibleI distributive numeral impossible
(16) Frequency adverbial
A‘The
politikuspolitician
néha/sometimes/
mindig
always
megtapsoltapplauded
egy-egy/*két-kéta-a/*two-two
ellenzékiopposition
hozzászólást.comment.’
(17) Adverbial distributive suffixe -enként
Helyenként‘In several places
egy-egy/*két-kéta-a/*two-two
rendörpolicemen
leállított.stopped me.’
In several places a policeman stopped me – policemen co-vary withplaces. Farkas (2015, exs 12-13)
Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities: d-numerals & d-indefinites ESSLLI 2015 22 / 64
D-indefinites vs. d-numerals: Hungarian (Farkas 1997)
D-indefinites/d-numerals: adverbs of quantification 2
Licensing by overt adverb of quantificationI egy-egy possibleI distributive numeral impossible
(18) Generic whenever
Ahányszor‘Whenever
egy-egy/*két-kéta-a/*two-two
híresfamous
személyperson
meglátogattavisited
athe
várost,town
elvittékthey took him
a kastélyba.to the castle.’
(Farkas, 2015, exs 11)
Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities: d-numerals & d-indefinites ESSLLI 2015 23 / 64
D-indefinites vs. d-numerals: Hungarian (Farkas 1997)
D-indefinites and intensiontal / extensional worldvariables in Hungarian
Modals/ generic operator range over intensional world variables.D-indefinites possible with extensional world variables.
(19) Factual conditionals (extensional world variable)Ha egy-egy tanár megbetegedik helyettesiti egy szülöIf a-a teacher gets-sick replaces-him a parent.If a teacher gets sick a parent replaces him. (ex 44 Farkas1997)
D-numerals not possible with world variables.
Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities: d-numerals & d-indefinites ESSLLI 2015 24 / 64
D-indefinites vs. d-numerals: Hungarian (Farkas 1997)
D-indefinites and scope in Hungarian
D-indefinites cannot be reduced to obligatory narrow scope.With pluractional morphology on the verb and implicit multiple
events in Hungarian (Farkas 2015)I egy-egy possibleI narrow scope of egy impossible
Caveat: Narrow scope is understood as co-varying reading wrt toanother expression
Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities: d-numerals & d-indefinites ESSLLI 2015 25 / 64
D-indefinites vs. d-numerals: Hungarian (Farkas 1997)
D-indefinites and scope in Hungarian
No multiplication of sg indefinitesI with implicit events (26)I with pluractional morphology (21)
(20) Egy
‘Adiák
studentpananszkodikcomplains
debut
ezthis
ritkánhappens
fordulrarely.’
elö.
Only interpretation: From time to time, a student (the same)complains but this happens rarely. 6= (14)
(21) Egy
‘Agyerek
childfel-felébredtup-up
dewoke
másbut
bajother
nemtrouble
volt.was not.’
Only interpretation: From time to time a child (the same every
time) woke up but other than that there was no trouble. 6= (15)(Farkas, 2015, ex23-24)
Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities: d-numerals & d-indefinites ESSLLI 2015 26 / 64
D-indefinites vs. d-numerals: Hungarian (Farkas 1997)
D-indefinites in Hungarian: Analysis
D-indefinites are subject to a co-variation condition: the variablethey introduce must receive multiple values (variation) and mustbe referentially dependent on another varying variable(co-variation) Farkas (2015, 13)Dependent Variable Condition (See Farkas (1997), ex. (39))D-indefinites must introduce dependent variables.A variable y is dependent on a variable x iff values for y co-varywith values assigned to x. (See Farkas (1997), ex. (27))
Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities: d-numerals & d-indefinites ESSLLI 2015 27 / 64
D-indefinites vs. d-numerals: Hungarian (Farkas 1997)
D-indefinites in Hungarian: Analysis
The dependent variable y is co-varies with a variable x, itsdomain variable Farkas (2015, 13)The domain variable is evaluated by a set of functions G x thatrange exhaustively over x’s non-singleton domain (Domain x).
I for the functions in G x the value at x is in the domain of x8 g 2 G x, g(x) 2 Domain x
I each element in the domain of x is assigned a value by some g 2G x
8 z 2 Domain x 9 g: g(z) = xI the functions in G x differ with respect to their value for x8 g, g’ 2 G x, g(x) 6= g’(x)
Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities: d-numerals & d-indefinites ESSLLI 2015 28 / 64
D-indefinites vs. d-numerals: Hungarian (Farkas 1997)
D-indefinites in Hungarian: Analysis
The dependent variable y is evaluated by a set of functions H thatdepends on the set G x chosen to evaluate x (Farkas, 2015, 14)
I for each h 2 H, there is a g 2 G x such that h differs from g at mostwith respect to the value assigned to y.
I For each g 2 G x, there is an h 2 H such that h differs from g atmost with respect to the value assigned to y.
I Variation condition:there are at least two functions h, h’ 2 H such thath(y) 6= h’(y)
Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities: d-numerals & d-indefinites ESSLLI 2015 29 / 64
D-indefinites vs. d-numerals: Hungarian (Farkas 1997)
D-indefinites in Hungarian: Analysis
Variation condition:there are at least two functions h, h’ 2 H such thath(y) 6= h’(y)The functions in H differ wrt to the value they assign to x
I the functions in G x differ wrt to their values on x,I the functions in H are identical to the functions in G x except
possibly on yThe variation condition imposes co-variation of y wrt to x:
I h and h’ differ on their value for x by inheritance from G xI h and h’ differ on their value for y by the Variation condition
Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities: d-numerals & d-indefinites ESSLLI 2015 30 / 64
D-indefinites vs. d-numerals: Hungarian (Farkas 1997)
D-indefinites in Hungarian: Analysis
The variation condition for the dependent indefinite is a constrainton the output context: post-supposition (following Henderson2014)Post-suppositions are checked after calculation of thetruth-conditions.
Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities: d-numerals & d-indefinites ESSLLI 2015 31 / 64
D-indefinites vs. d-numerals: Hungarian (Farkas 1997)
D-indefinites in Hungarian: Analysis
Arguments for a domain variableFarkas: having a domain variable allows a restriction on the typeof variable that can act as a licensorNeed this as possible licensors vary across types of d-indefinites
domain variable d-indefinites d-numeralsintensional w-variable no noextensional w-variable yes noindividual variable yes yes
Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities: d-numerals & d-indefinites ESSLLI 2015 32 / 64
Cross-linguistic variation
Cross-linguistic variation
Look at other descriptions of d-indefinites.Examine variation with respect to
I licensors for the d-indefinitesI distribution possibilities (participants/ space/ time)
Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities: d-numerals & d-indefinites ESSLLI 2015 33 / 64
Cross-linguistic variation
Cross-linguistic variation
Caveat: The descriptions are often in terms of possible scenariosIt is not clear that scenarios correspond to different readings.
(22) Two men carried suitcases in threes.Verifying scenarios
a. Man 1 carries three suitcases & Man 2 carries three suitcases�!⇡ Two men carrying three suitcases each.
b. Man 1 carries three suitcases at t 1 & t 2
Man 2 carries three suitcases at t 2& t 3 ...�!⇡ Two men carrying three suitcases at a time.
c. Man 1 carries three suitcases at t 1
Man 2 carries three suitcases at t 2& t 3 ...�!⇡ Two men carrying three suitcases at a time.
Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities: d-numerals & d-indefinites ESSLLI 2015 34 / 64
Cross-linguistic variation Telugu (Balusu 2006)
D-numerals in Telugu (Balusu 2006)
In Telugu reduplicated numerals give rise to distributive readings(Balusu, 2006)Have three possible readings (23a-c)
(23) pilla-lukid-Pl
renDu2
renDu2
kootu-lu-nimonkey-Pl-Acc
cuus-ee-rusee-Past-3PPl
a. The kids each saw 2 monkeys. Participant keyb. The kids saw 2 monkeys in each time interval. Temp. keyc. The kids saw 2 monkeys in each location. Spatial key
Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities: d-numerals & d-indefinites ESSLLI 2015 35 / 64
Cross-linguistic variation Telugu (Balusu 2006)
D-numerals in Telugu (Balusu 2006)
In Telugu a distributive and a collective reading is possible with asimple numeral and a plural DP (24)
(24) iithese
pilla-lukid-Pl
renDu2
kootu-lu-nimonkey-Pl-Acc
cuus-ee-rusee-Past-3PPl
a. These kids saw 2 monkeys. collectiveb. These kids saw 2 monkeys each. distributive
) distributivity does not require special marking.
Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities: d-numerals & d-indefinites ESSLLI 2015 36 / 64
Cross-linguistic variation Telugu (Balusu 2006)
D-numerals in Telugu
D-numerals require distribution wrt to a plural dimension(participants, space, time)Weak licensing restrictions: Licensing of d-numerals does notrequire an overt licensorWithout an overt licensor distribution in time or space fulfillsdistribution requirement.
(25) renDu2
renDu2
kootu-lumonkey-Pl
egir-i-niyyijump-Past-3PPl
a. 2 monkeys jumped in each time interval. Temp. keyb. 2 monkeys jumped in each location. Spatial key
Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities: d-numerals & d-indefinites ESSLLI 2015 37 / 64
Cross-linguistic variation Telugu (Balusu 2006)
D-numerals in Telugu:
Balusu distinguishes two meaning componentsI An assertion including a distribution requirementI A plurality requirement (variation across the distributed share)
For the example (25) this corresponds toI There was an event e such that for every relevant part e’ of e, two
monkeys jumped in e’.I the cardinality of monkey pairs jumping in e is greater than one
(26) a. Assertion:9e9⇡(e)[8e’2 ⇡(e)9X[two-monkeys(X) ^ jumped(X,e’)]]
b. Plurality requirement (felicity condition)|{X: two-monkeys(X) ^ jumped(X,e)}|>1
Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities: d-numerals & d-indefinites ESSLLI 2015 38 / 64
Cross-linguistic variation Telugu (Balusu 2006)
D-numerals in Telugu: temporal and spatial key
⇡(e) is a partition of e: division of e into a set of non-overlappingsubsets or partsPlural events can be partitioned by having different
I participantsI locationsI times
Events cannot be partitioned by other criteria:a scenario with monkeys’ foreheads of different colours, with 2monkeys for each colour does not allow a distributed reading.Balusu (2006, 8)
Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities: d-numerals & d-indefinites ESSLLI 2015 39 / 64
Cross-linguistic variation Telugu (Balusu 2006)
D-numerals in Telugu: temporal and spatial key
The plurality requirement in (26) is not a conjunct in the
assertion.If the same two monkeys jumped in every cell of the partition, asentence (25) is not false, but infelicitous.The plurality requirement is either a presupposition or animplicature. (Balusu, 2006, 8)
Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities: d-numerals & d-indefinites ESSLLI 2015 40 / 64
Cross-linguistic variation Telugu (Balusu 2006)
D-numerals in Telugu: temporal and spatial key
The superevent e is the key.A partition ⇡ on the event, based on temporal or spatialinformation provides the units of key.⇡ = { e 1 ... e n }For each cell of the partition (subevent e’) have the participant Xdescribed by D-num+NP provides the share.The plurality condition postulates that the share-sum containsmore than a single share.
Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities: d-numerals & d-indefinites ESSLLI 2015 41 / 64
Cross-linguistic variation Telugu (Balusu 2006)
D-numerals in Telugu: participant key
Balusu: Participant-key readings arise through event-keydistribution with a trivial partition ⇡(e) = e.With a trivial partition key = units of key
�!the D-numeral does not distribute in these cases.In these cases distribution comes from
I the quantifier for quantified subjects
I distributive predication for plural subjects
Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities: d-numerals & d-indefinites ESSLLI 2015 42 / 64
Cross-linguistic variation Telugu (Balusu 2006)
D-numerals in Telugu: participant key
Balusu: Participant-key reading with a quantified subject
(27) a. 9E[8y[kid(y)!9e2E 9⇡(e) [8e’2⇡(e) [9X[two-monkeys(X) ^saw(y,X,e’)]]]]]
b. |{X: two-monkeys(X) ^9y[kid(y) ^ saw(y,X,E)]}|>1(28) 9E[8y[kid(y)!9e2E [8e’2{e}[9X[two-monkeys(X) ^
saw(y,X,e’)]]]]](29) 9E[8y[kid(y)!9e2E [[9X[two-monkeys(X) ^ saw(y,X,e)]]]]]
Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities: d-numerals & d-indefinites ESSLLI 2015 43 / 64
Cross-linguistic variation Pereltsvaig 2012
Participant key vs. event key: Pereltsvaig 2012
Pereltsvaig (2012) argues that distributivity over individuals cannotgenerally be reduced to distributivity over events.Argument 1: There are languages that have two distinct markersfor distributivity over individuals and distributivity over events.Argument 2: The marker for event distributivity tends to bemorphologically more complex than the marker for distributivityover individuals. German: jeweils vs. jeArgument 3: There are distributive markers (like binominal each)that only distribute over individuals.These observations are unexpected if event distributivity is takento be the basic case.
Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities: d-numerals & d-indefinites ESSLLI 2015 44 / 64
Cross-linguistic variation Tlingit (Cable 2014)
Distributive numerals in Tlingit
Can have implicit licensing by temporal iteration and spatialdistribution (6= Albanian, Hungarian d-numerals, Kaqchikel)Like in Telugu, other dimensions of event-identification are out:cannot group girls by colour of their dress in (30b)
(30) a. AxMy
yéetson
nás’gigáathree.DIST
xáatfish
aawashaatcaught
My son caught three fish each time / each place (ex 21bhandout Cable)
b. Dáxgáatwo.dist
shaax’wsáanigirls
keihas
kwdik’énjumped
The girls jumped in twos. (Pairs of girls jumping at thesame time). 27 handout Cable
Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities: d-numerals & d-indefinites ESSLLI 2015 45 / 64
Cross-linguistic variation Tlingit (Cable 2014)
Distributive numerals in Tlingit
With plural arguments have a participant-distributive interpretationand an event-distributive interpretation (31)
(31) AxMy
kaamale
yátx’ichildren
nás’gigáathree.DIST
xáatfish
has aawashaatthey.caught
(i) My sons caught three fish each(ii) My sons caught fishes in threes. / My sons caught threefishes each time.
Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities: d-numerals & d-indefinites ESSLLI 2015 46 / 64
Cross-linguistic variation Tlingit (Cable 2014)
Distributive numerals in Tlingit
In Tlingit adverbial d-numerals and adnominal d-numerals thathave to be distinguished on syntactic grounds. (Cable, 2014)Participant-distributive interpretation and event-distributiveinterpretation are possible for both adverbial and adnominald-numerals.The Tlingit adverbial and adnominal d-numerals are notambiguous.Participant-distributive interpretation and event-distributiveinterpretation are possible scenarios for a single meaning.
Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities: d-numerals & d-indefinites ESSLLI 2015 47 / 64
Cross-linguistic variation Tlingit (Cable 2014)
D-numerals in Tlingit
AssumptionsCUMULATIVITY CONDITION on arguments of predicates
(32) For any entities x1, ... , xn, y1, ... , yn,if [[P]](x1)...(xn) = T,and [[P]](y1)...(yn) = T,
then [[P]](x1 + y1)...(xn + yn) = T.
Verbs are (Cumulative) Relations Between Events and Themes(Kratzer 2008)
(33) P<e,✏t>: predicates from individuals (e) and events (✏)to truthvalues.
Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities: d-numerals & d-indefinites ESSLLI 2015 48 / 64
Cross-linguistic variation Tlingit (Cable 2014)
D-numerals in Tlingit
Specific assumptions
The predicate Participant
(34) Participant(e,x) iff x bears a ‘theta relation’ to eiff x is Agent of e, or x is Theme of e, or x is Goal of e,...
the binary maximality operator
(35) a. Pair addition: hx1, x2i + hy1, y2i =df hx1+x2 , y1+y2ib. �<x ,y>. Q(x)(y) =df the pair h↵,�i such that h↵,�i 2 *{hx,yi :Q(x)(y)}, and if h�, �i 2 *{hx,yi : Q(x)(y)}, then � ↵ and � �.
numerals have distinct type n
Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities: d-numerals & d-indefinites ESSLLI 2015 49 / 64
Cross-linguistic variation Tlingit (Cable 2014)
D-numerals in Tlingit
Cable’s semantics for adnominal d-numerals:
(36) Tlingit adnominal d-numerals[[ -gáa ADN ]] = �n n : [ �Q <e,t>: [ �P <e,✏t> : [ �e ✏:9x. Q(x) ^ P(x)(e) ^he,xi = � <e’,y>. y<x ^ |y|=n ^ e’<e ^Participant (e’, y)]...]
n n is the numeral -gáa
ADN
attaches toQ <e,t> is the noun combining with the adnominal numeralP <e,✏t> is the eventive verb of the sentencethe d-numeral+N is the theme of P (as P(x)(e) and P is a predicatebetween events and their themes)e is a sum of subevents e’
Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities: d-numerals & d-indefinites ESSLLI 2015 50 / 64
Cross-linguistic variation Tlingit (Cable 2014)
D-numerals in Tlingit
Require a partition of e with distributive properties
(37) [[ -gáa ADN ]] = �n n : [ �Q <e,t>: [ �P <e,✏t> : [ �e ✏:9x. Q(x) ^ P(x)(e) ^he,xi = � <e’,y>. y<x ^ |y|=n ^ e’<e ^Participant (e’, y)]...]
the pair <e,x> is the sum of pairs <e’,y>the e’ are proper parts of e (no trivial partition: variation)y is a participant in e’ for the pairs <e’,y> partitioning ey is a proper part of x (need more than one y in the partition pairsto sum up to x �!covariation)y is a plurality of cardinality n
Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities: d-numerals & d-indefinites ESSLLI 2015 51 / 64
Cross-linguistic variation Tlingit (Cable 2014)
D-numerals in Tlingit
This formula applies to -gáa ADN in theme position.In Tlingit the d-numeral can modify a subject.
(38) [[ -gáa ADN ]] = �n n : [ �Q <e,t>: [ �P <e,✏t> : [ �e ✏:9x. Q(x) ^ P(x)(e) ^he,xi = � <e’,y>. y<x ^ |y|=n ^ e’<e ^Participant (e’, y)]...]
the pair <e,x> is the sum of pairs <e’,y>the e’ are proper parts of e (no trivial partition: variation)y is a participant in e’ for the pairs <e’,y> partitioning ey is a proper part of x (need more than one y in the partition pairsto sum up to x �!covariation)y is a plurality of cardinality n
Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities: d-numerals & d-indefinites ESSLLI 2015 52 / 64
Cross-linguistic variation Tlingit (Cable 2014)
D-numerals in Tlingit
Cable proposes the following semantics for adverbial d-numerals:
(39) Tlingit adverbial d-numerals[[-gáa ADV]] = �nn : [ �P<e,✏t> : [ �xe : [ �e✏:P(x)(e) ^he,xi = �<e0,y>. y<x ^ |y|=n ^ e’<e ^Participant (e’, y)]...]
Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities: d-numerals & d-indefinites ESSLLI 2015 53 / 64
Cross-linguistic variation Tlingit (Cable 2014)
D-numerals in Tlingit
Cable’s proposal above is the version for themesTlingit also allows d-numerals in subject position
(40) Context: We have three dogs. Six girls came over to bathethem. Each dog was bathed by a team of two (different) girls.
Dáxgaanáxtwo.DIST.HUM
shaax’wsáanigirls
nás’kthree
keitldog
has aawashúch.3plS.3O.bathed
‘Three dogs were each bathed by two girls.’ Judgment: True inthis scenario Cable (2014, ex 33b)
Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities: d-numerals & d-indefinites ESSLLI 2015 54 / 64
Cross-linguistic variation Tlingit (Cable 2014)
Cable’s analysis of d-numerals in Tlingit
Cable’s proposal works for Telugu and TlingitI the distributive morpheme on the numeral introduces a variation
across events and themesI the d-numeral does not need a licensor (locative or temporal key
readings possible)
This analysis will not carry over to languages where locative ortemporal key readings are not freely available.
Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities: d-numerals & d-indefinites ESSLLI 2015 55 / 64
Cross-linguistic variation D-numerals cross-linguistically: temporal/locative key
D-numerals cross-linguistically: temporal/locative key
Languages where locative or temporal key readings are not freelyavailable:
(41) ?? BeniBen
zuricaught
nga
DISTtrethree
peshqfish
(Albanian)
Not: Ben caught three fish each time / each place (Rushiti,2015)
(42) *MartinekMartin-ERG
bi-natwo-DISTR
egunkari(-ak)newpaper(-s).ABS
erostenbuying.IMPF
dizkitdoes.3PL-DO.1SG.IO
(Basque)
intended: ‘Martin buys me two newspapers (on eachoccasion).’ (Pereltsvaig, 2012, ex7b)
Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities: d-numerals & d-indefinites ESSLLI 2015 56 / 64
Cross-linguistic variation D-numerals cross-linguistically: temporal/locative key
D-numerals cross-linguistically: subjects
Cross-linguistic variationI In Tlingit the d-numeral can be in subject position.I In Basque the d-numeral cannot be in subject position.I In Albanian the d-numeral in subject position has much stricter
licensing conditions (quantificational PP)
Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities: d-numerals & d-indefinites ESSLLI 2015 57 / 64
Cross-linguistic variation D-numerals cross-linguistically: subjects
D-numerals cross-linguistically: subjects
In Basque the d-numeral cannot be in subject position.Albanian: d-numeral in subject position requires Q-PP
(43) *Hirunathree.na
emakumeekwomen.erg
ogibread
erosibuy
zuten.aux
(Basque)
Not: each loaf was bought by three women. Trask (2003, 128,ex 89b)
(44) a. ??NgaDIST
dytwo
vajzagirls
lanëbathed
trethree
qenëdogs
(Albanian)
b. NëIn
çdoevery
zyrëoffice
punoninwork-imp
ngaDIST
trethree
punëtorë.workers
’Three workers were working in every office’ (Rushiti, 2015,ex 24a/ 20a)
Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities: d-numerals & d-indefinites ESSLLI 2015 58 / 64
Cross-linguistic variation D-numerals cross-linguistically: adverbials
D-numerals cross-linguistically: adverbials
In Basque adverbial expressions do not license -na d-numerals.
(45) *igandero,sunday-each
ManuelekM-erg
binatwo-na
egunkarinewspaper
erosten ditu.buy-hab aux(3plA.3sE)
Every Sunday M. buys two newspapers.(46) *Manuelek
Manuel-ergbeti
alwaysbinatwo-na
pizzapizza
jateneat-hab
dituaux(3plA-3sE)
Manuel always eats two pizzas. (ex Ricardo Etxepare, pc)(47) *Ni
me-absikusterasee-nmz-allative
etortzencome-hab
deneanis-rel-loc
ManuelekManuel-erg
binatwo-na
oparipresent
ekartzenbring-hab
dizkitaux(3plA-1sD-3sE)
When he comes to see me M brings two presents (each time).(Cabredo Hofherr, 2015)
Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities: d-numerals & d-indefinites ESSLLI 2015 59 / 64
Cross-linguistic variation D-numerals cross-linguistically: adverbials
D-indefinites cross-linguistically
Other studiesI Gil (1982, 1988): Georgian reduplicated numeralsI Farkas (1997); Brasoveanu and Farkas (2011): Romanian cîte +
indefI Zimmermann (2002): German je/jeweilsI Choe (1987); Oh (2001, 2005): Korean -ssikI binominal eachI Rushiti (2015): Albanian -nga+numeralI Basque -na: Trask (2003); Pereltsvaig (2012)
Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities: d-numerals & d-indefinites ESSLLI 2015 60 / 64
Cross-linguistic variation D-numerals cross-linguistically: adverbials
Conclusion
A compléterD-indefinites cannot be reduced to narrow scope (Henderson,2012)Cross-linguistic variation in licensing of d-numerals
I Temporal/ locative key freely available (yes/no)I World variables license (yes/no)I Extensional world variables license (yes/no)I Pluractional marking license (yes/no)I Subject position possible (yes/no)
Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities: d-numerals & d-indefinites ESSLLI 2015 61 / 64
Cross-linguistic variation D-numerals cross-linguistically: adverbials
References I
Balusu, R. (2006). Distributive reduplication in Telugu. In Proceedings ofNELS 36, pp. 39–53.
Brasoveanu, A. and D. Farkas (2011). How indefinites choose their scope.Linguistics and Philosophy 34, 1–55.
Cable, S. (2014). Distributive numerals and distance distributivity in Tlingit(and beyond). Language 90(4), 562–606.
Cabredo Hofherr, P. (2015). The basque distributive suffix -na. in progress.Choe, J.-W. (1987). Anti-quantifiers and a theory of distributivity. Ph. D.
thesis, UMass at Amherst.Farkas, D. (1997). Dependent indefinites. In F. Corblin, D. Godard, and J.-M.
Marandin (Eds.), Empirical Issues in Syntax and Semantics 1, pp.243–268. Peter Lang.
Farkas, D. (2015, February). Dependent indefinites revisited. Talk atJournées (Co-)Distributivité 2015, CNRS Pouchet, Paris.
Gil, D. (1982). Distributive Numerals. Ph. D. thesis, UCLA.
Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities: d-numerals & d-indefinites ESSLLI 2015 62 / 64
Cross-linguistic variation D-numerals cross-linguistically: adverbials
References II
Gil, D. (1988). Georgian reduplication and the domain of distributivity.Linguistics 26, 1039–1065.
Henderson, R. (2012). Ways of pluralizing events. Ph. D. thesis, UC SantaCruz.
Henderson, R. (2014). Pluractionality in Mayan. In under review.Oh, S.-R. (2001). Distributivity in an event semantics. In Proceedings of
Semantics and Linguistic Theory XI (SALT 11), pp. 326–346.Oh, S.-R. (2005). Plurality markers across languages. Ph. D. thesis,
University of Connecticut.Pereltsvaig, A. (2012). Distributivity is not uniformly over events. In
P. Cabredo Hofherr and B. Laca (Eds.), Verbal plurality and distributivity,pp. 211–221. Berlin: de Gruyter.
Rushiti, B. (2015, 26 Feb). Distance distributivity in Albanian: the case of-nga. Talk at Journées (Co-)Distributivité 2015, CNRS Pouchet, Paris.
Cabredo Hofherr/Tovena (CNRS/Paris 7) Event pluralities: d-numerals & d-indefinites ESSLLI 2015 63 / 64
Cross-linguistic variation D-numerals cross-linguistically: adverbials
References III
Trask, L. (2003). The noun phrase: nouns, determiners and modifiers;pronouns and names. In J. I. Hualde and J. Ortiz de Urbina (Eds.), AGrammar of Basque, pp. 113–170. Berlin: Mouton de Gruyter.
Zimmermann, M. (2002). Buy buying two sausages each. On The SyntaxAnd Semantics Of Distance-Distributivity. Ph. D. thesis, U. Amsterdam.
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