The meaning of the plural · and not just multiple entities are in the denotation of the plural...
Transcript of The meaning of the plural · and not just multiple entities are in the denotation of the plural...
The Inclusive Plural The Distribution Experimental Evidence Analysis Typological Outlook
Plurality and Referentiality
Scott Grimm
Universitat Pompeu Fabra
April 10, 2013
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The meaning of the plural
What is the difference between cat and cats?
While seemingly simple, the contrast between one X and morethan one X has stirred a large debate in semantics
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The meaning of the plural
One might think that cats simply means more than one cat
Classic challenges:
(1) Q: Do you have children? A: Yes, I have one.# No, I have one.
(2) Ed didn’t see dogs.False if Ed saw even a single dog.
(3) If you have children, raise your hand.True for those with one child.
For these cases, it seems to be necessary that individual entities,and not just multiple entities are in the denotation of the pluralform
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The inclusive plural
Based on such examples, many researchers have argued that thesemantic form of plural nouns is inclusive
I designating one or more (including atomic entities), ratherthan exclusive, i.e. more than one.
This analysis has a long history: see Krifka 1989, Ojeda 1991among others
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The Inclusive Plural
The Distribution
Experimental Evidence
Analysis
Typological Outlook
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Sauerland et al. 2005
Sauerland et al. (2005) relate the inclusive reading todownward-entailing (DE) environments
I Claim: “number marking on indefinites in a downwardentailing environment does not affect truth conditions”.
Elaborated on and extended in Zweig 2009 among others, whobuild upon this claim
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Sauerland et al. 2005
Denotations of singular and plural nouns include both atoms andsums, but the singular φ-feature additionally includes an atomicitypresupposition.
(4) a. JSGK = λx ∈ De : ATOM(x).x
b. JPLK = λx ∈ De .x
Use the principle of “maximize presupposition” (Heim 1991)
I the form with the strongest presupposition must be selected,unless a presupposition failure would arise
Downward entailing contexts are crucial for this analysis
I reverse which interpretation is stronger
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Sauerland et al. 2005
For positive contexts the singular has stronger presuppositions andmust be selected, if appropriate.
(5) Ed saw dogs.
I dogs includes both atoms and sums
I If the atomic interpretation was licensed, by maximizepresupposition, the singular form must be chosen
I The use of the plural implies that an atomic interpretation isnot licensed, and from this the exclusive reading is derived.
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Sauerland et al. 2005
In negative contexts, singulars are logically weaker than plurals
(6) Ed didn’t see dogs.(⇒ Ed didn’t see a dog)
Further assumption: Maximize presupposition applies if thisstrengthens the entire utterance
I then, maximize presupposition is not in effect since selectingthe singular with its atomicity presupposition would notstrengthen the entire utterance
I there is no further implicature that atoms have been excluded,allowing the plural to be interpreted inclusively
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Beyond Downward Entailing Contexts
While these analyses have drawn attention to the more intricatebehavior of plural nouns:
I downward-entailing contexts are neither necessary norsufficient conditions for licensing of the inclusive pluralreadings
Alternate Hypothesis: The inclusive plural, which is always abare plural, can be connected with another use of the bare plural:kind-level (instances of a kind)
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The Distribution
The inclusive plural theory makes a strong prediction:
Prediction: Inclusive Plural ⇐⇒ Downward-Entailing environment
Form of Prediction: Two different predictions depending ondefinition of downward-entailing environment:
I strict
I NPI-licensing
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The Distribution
Facts: A closer look at the distribution will show that the inclusivereading is a much broader phenomenon.
Alignment with either variety of downward-entailing fails to be anecessary and sufficient condition for licensing of the inclusiveplural readings
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Inclusive Plural =⇒Strict Downward-Entailing environment?
Does the inclusive plural reading only occur in strictDE-environments?
The inclusive plural reading can be found outside strictDE-environments, e.g. opaque contexts:
(7) Sherlock Holmes should question local residents to find thethief. (inclusive reading available)
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Inclusive Plural ⇐⇒ NPI-licensing environment?
Is the inclusive plural reading described completely and only byNPI-licensing environments?
Inclusive Plural ; NPI-licensing environment
I Positions which do not license NPIs may license the inclusivereading, as in the restrictor of both
(8) #Both students who saw anybody reported to the police.(NPI not OK)
(9) Both students who saw spies reported to the police.(inclusive plural)
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Inclusive Plural ⇐⇒ NPI-licensing environment?
NPI-licensing environment ; Inclusive Plural
I Positions which do license NPIs may fail to license theinclusive reading, as with emotive factives,
(10) I am surprised that anything was there. (NPI OK)
(11) I am surprised that boxes were in the office.(exclusive plural only)
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The Limits of the Inclusive Reading
New question: In the contexts where the inclusive reading ispossible, does it always occur?
If not, what governs the variation?
Farkas (2006) and Farkas and de Swart (2010) already discusslimitations due to knowledge about the world and differentcontexts:
(12) a. Is Sarah wearing shoes(/*a shoe)?
b. Is Sarah wearing a hat(/*hats)?
(13) a. Do you have a broom? (asked in your kitchen after Ispilled peas on your floor)
b. Do you have brooms? (asked in a store)
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Confounding Factors
The example sentences used to (i) support the inclusive pluralreading or (ii) test it experimentally are of a limited type:
I involve the verb have in questions. (Sauerland et al. 2005,Kahn et al. 2010, Pearson et al. 2010)
(14) Do you have children?
This use of have is known as the existential have construction(Partee 1999)
Since an existential construction in an interrogative contextactually puts the existence of the NP in question:
I inclusive plural contexts could also be aligned with“non-referential” contexts
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Number Neutrality and Referentiality: ExperimentalEvidence
Two studies investigate the conditions under which a plural form ispermitted to refer to a single object
Two hypotheses:
I Inclusive plural should appear in interrogative environment
I Inclusive plural should appear in “non-referential” context
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Number Neutrality and Referentiality: ExperimentalEvidence
Presented interrogative phrases with nouns designating physicalobjects in contexts disposed towards interpretation of the entity as:
I spatiotemporally anchored
I non-referential/generic/kind-level
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Experiment 1
Presented 40 speakers (Mechanical Turk) with pictures displayingeither one or multiple instances of a physical object.
Example:
One pair of stimuli presented a photo of a woman asking Is thewoman in this picture holding mugs?, permitting a yes or noanswer.
Manipulation: whether the woman was holding one mug or two.
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Experiment 1: Stimuli
Is this woman holding mugs?
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Experiment 1: Stimuli
Is the mug in this picture sitting next to laptops?
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Experiment 1: Results
When presented with multiple objects, the participants almostuniformly answered yes (92%), when presented with a singleobject, only a minority of participants answered yes (32%).
This statistically reliable result (χ2 (df =1, N = 240) = 76.56 p <.001) is unexpected under the inherently inclusive plural analysis:
I these indefinite plurals are within an interrogative context, acontext initially used to argue for the inclusive plural reading
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Experiment 1: Results
plural sing
yesno
Responses by Number Category
Number Category
Responses
020
4060
80100
120
140
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Experiment 1: Results
bookshelf laptop mug tube woman
yesno
Responses by Entity Type
Entity Type
Responses
05
1015
2025
30
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Experiment 2
Study 2 presented questions within a “rules-and-regulations”environment, which is known to fosternon-referential/generic/kind-level construals (Carlson 1995; Cohen2001).
Participants were presented with questions they were told couldhave come from a corporate environment, along with facts aboutan employee, and were asked to answer as they thought theemployee should answer
All other aspects of the design were as in the prior study.
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Experiment 2: Stimuli
Did your team terminate projects this fiscal quarter?
Employee facts: employee’s team has terminated exactly oneproject this fiscal quarter
What answer should the employee give?Yes/No
Manipulation: whether the employ’s team completed one or threeprojects
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Experiment 2: Results
In contrast to Experiment 1, participants largely preferred theinclusive plural reading for the critical items (78% yes responses).
plur sing
YesNo
Responses by Number Category
Number Category
Responses
020
4060
80100
120
140
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Experiment 2: Results
Some sophisticated participants left comments showing that theyunderstood the difficulty of these uses of the plural:
Even though the question uses the plural of the word‘projects’, the intent seems to want the employee todisclose whether any projects were terminated, not justwhether more than one project was terminated.
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Interim Discussion
Singular Plural
Spatiotemporally bounded .32 .92
Rules and Regulations .78 .99
Table: Percentage of yes responses
A generalization emerges:
I referential uses of the plural are exclusive
I non-referential uses permit inclusive readings
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Interim Discussion
Two puzzles:
i how referentiality comes to disfavor the inclusive reading
ii how these particular contexts (questions, negation, etc.) cometo favor the inclusive plural reading
Two major components to the analysis:
I distinction between weak referential contexts and referentialcontexts (building on Krifka 1995)
I structured approach to discourse (building on Roberts 1996)
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The Analysis: Kind and Object Readings
A central assumption since Carlson (1980) is nouns lead a doublelife:
I they designate a type of thing, i.e. referring to a kind
I they designate individual objects of that type in the world
In the analysis here, both types of information are relevant tostructuring discourse, and both can be queried as a QuestionUnder Discussion (QUD).
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Krifka 1995
In Krifka’s analysis, three elements of meaning are present incommon nouns:
I concepts (a broader notion than kinds)
I objects
I number
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Krifka 1995
These different elements are related by:
I R, a realization relation between concepts and the instances ofthe concept at the level of objects
I OU, an operator which, given a concept and a set of objects,provides a measure, n, of the number elements of whichqualify as instances of the concept.
n is assumed to be greater than 0.
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Krifka 1995: denotation of common nouns
The denotation of common nouns, where i is a variable of type sranging over possible worlds:
(15) λyλiλnλx [Ri (x , y) ∧ OUi (y)(x) = n]
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Krifka 1995: denotation of common nouns
Two different types of derivation for a common noun:
I quantified object reading: the number argument is filledduring composition
(16) Quantified Object:λnλiλx [Ri (x ,DOG) ∧ OUi (DOG)(x) = n]
I instance of a concept reading: the bare plural denotesinstances of a kind/concept and number argument isexistentially closed
(17) Instances of a Concept:λiλx∃n[Ri (x ,DOG) ∧ OUi (DOG)(x) = n]
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Krifka 1995: denotation of common nouns
Allows two possible interpretations for a given plural noun:
I plural marker is interpreted as a number marker
I diverging from Krifka, is interpreted here as more than one
I the plural noun enters the derivation as a kind/concept andthe plural marker is not interpreted
I Since n is assumed to be greater than 0, interpretationsucceeds when at least one entity realizes the kind dog
(18) a. JdogsK := λiλx [Ri (x ,DOG) ∧ OUi (DOG)(x) ≥ 2]
b. JdogsK := λiλx∃n[Ri (x ,DOG) ∧ OUi (DOG)(x) = n]
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The Structure of Discourse and the Question UnderDiscussion
Roberts (1996)’s theory of discourse:
I focus on “regulating discourse”
I main organizational force comes from the Question UnderDiscussion (QUD)
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The Structure of Discourse and the Question UnderDiscussion
Partition theory of questions (Groenendijk and Stokhof 1984)
I guarantees that answers are strongly exhaustive
I establishes entailment relations between questions
I a question q1 entails question q2 iff answering q1 gives acomplete answer to q2
(19) J?K = λP<s,<−→e ,t>> λwλv [P(w) = P(v)]
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QUDs
Combining the theory of common nouns and this theory ofquestions, can derive different QUDs:
I query the kind, existence or number of objects
(20) What (kinds of things) did Ed see? (Kind QUD) :?(λiλy∃n∃x [Ed see x in i ∧ Ri (x , y) ∧ OUi (y)(x) = n])
(21) Did Ed see dogs? (Existential QUD) :?(λi∃x∃n[Ed see x in i ∧ Ri (x ,DOG) ∧ OUi (DOG)(x) =n])
(22) How many dogs did Ed see? (Quantitative QUD) :?(λiλn∃x [Ed see x in i ∧ Ri (x ,DOG) ∧ OUi (DOG)(x) =n])
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QUDs: Entailment relations
Entailment relations among the different QUDs shows furtherstructure.
A complete answer to the Kind QUD gives a complete answer tothe Existential QUD
I Kind QUD entails Existential QUD
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QUDs: Entailment relations
The Existential QUD and Quantitative QUD do not stand in anentailment relation:
I an answer to Existential QUD resolves whether Ed saw anydogs or not, but not the number of dogs he might have seen
Instead, implied precedence relationship between Existential QUDand Quantitative QUD
I an element of the question alternatives to How many dogs didEd see? will be undefined if there do not exist any dogs in therelevant domain (recalling n > 0)
I How many dogs did Ed see? is typically an appropriatequestion only when Did Ed see dogs? is affirmatively resolved
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QUDs: Entailment relations
The question alternatives for the closed proposition correspondingto Ed saw dogs can be derived in two different fashions
I these two readings clearly relate to the two modes ofdiscourse, kind/concept-oriented and object-oriented
(23) Did Ed see dogs? (Existential QUD):?(λi∃x∃n[Ed see x in i ∧ Ri (x ,DOG) ∧ OUi (DOG)(x) =n])
(24) Did Ed see dogs ? (Quantitative QUD):?(λi∃x [Ed see x in i ∧ Ri (x ,DOG) ∧ OUi (DOG)(x) ≥ 2])
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Analysis: Polar Interrogatives
Return to the basic example:
(25) Do you have children?
The respondent must decide which QUD is relevant:
(26) (Existential QUD) :?(λi∃x∃n[You have x in i ∧ Ri (x ,CHILD) ∧OUi (CHILD)(x) = n])
(27) (Quantitative QUD) :?(λi∃x [You have x in i ∧ Ri (x ,CHILD) ∧OUi (CHILD)(x) ≥ 2])
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Analysis: Polar Interrogatives
Recall the precedence relation:
I the Quantitative QUD is only licensed when the ExistentialQUD has been resolved, due to the precedence
For Do you have children?
I this question is put forth precisely when the Existential QUDhas not been resolved
I since Existential QUD has not been resolved, the ExistentialQUD is the immediate QUD
I in turn licensing the inclusive reading of the plural.
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Analysis: Polar Interrogatives
Prediction: the range of answers should be different if
I quantity is relevant to the QUD
I or, the Existential QUD is previously resolved
Manipulating the context so that quantity is relevant to the QUD:
(28) Context: Several colleagues are looking for a meetingplace. B has an office in the building:A: Do you have chairs in your office?B: ?Yes, one/ No, only one.
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Analysis: Polar Interrogatives
Recall the experiments:
In the questionnaire environment, there is no presumption thatany, e.g., projects were completed
I licenses the Existential QUD, and inclusive reading
When speakers saw a particular situation, where it was plausiblethat the type of object under discussion, e.g. a mug, was fixed
I licenses the Quantitative QUD, and exclusive reading
I Although the Quantitative QUD was preferred, the ExistentialQUD was still a plausible option, as the variation in responsespresumably demonstrates
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Analysis: Conditionals
Same explanation carries over to antecedents of conditionals.
Examples from the literature:
(29) If you have children, raise your hand. (Bale et al. toappear)Existential QUD: Do you have children?
(30) If you have ever seen horses in this meadow, you shouldcall us. (Farkas and de Swart 2010)Existential QUD: Were there horses in this meadow?
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Analysis: Conditionals
Manipulating the context shows that the Quantitative QUD canalso be possible in the antecedent.
(31) If John ate apples at lunch, he will be sick.Existential QUD: Did John eat any apples?Quantitative QUD: Did John eat a plurality of apples?
Two interpretations:
I Existential: if John has eaten even one apple, then he will besick, e.g. in the case where he is allergic
I Quantitative: if he ate a sufficient number of apples, with thelower bound being two, then he will be sick.
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Analysis: Negation
Objects under negation provide the most recalcitrant examples ofinclusive readings
This is expected: negation denies the existence of entitiesdesignated by the noun
I consistent with the Existential, but not the Quantitative, QUD
(32) Ed didn’t see dogs.Existential QUD: Did Ed see any dogs??Quantitative QUD: Did Ed see a plurality of dogs?
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Analysis: Negation
An exclusive reading is still possible under negation
(33) I FAILED Algebra in High School–FAILED IT.. . . You have to do a LOT of NOTHING to fail a class. Ididn’t turn in assignments, I didn’t ask for help and that’swhy I got an F.(from http://www.city-data.com/forum/)
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Analysis: Negation
Two readings:
I no assignments were handed in
I two or more assignments were not handed in
For the second reading, the Existential QUD, Did the student turnin any assignments?, is presumably resolved via world knowledgethat a class typically has many assignments and the speaker mostlikely did at least one of them
I Quantitative QUD is then appropriate
This sentence is a counter-example to the claim that bare pluralsalways scope under negation
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Analysis: Other Phenomena
I Existentials
I Effect of Focus
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Existentials
Even within the context of existentials, scenarios can beconstructed where the “inclusive reading” is available.
Scenario: Miles climbs up to the attic. Upon seeing feathersdistributed throughout the attic, says: “There are birds in theattic!” Later it was determined that only one bird had been livingin the attic. Did Miles say something false?
The intuition I have harvested from casual queries is ‘no’.
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Existentials
This scenario hinges upon an indirect evidential context
I the speaker has no commitment to particular entities
Most existentials are uttered within a direct evidential context
I the speaker does have a commitment to particular entities
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Effect of Focus
Pearson et al. 2010: experimental exploration of the Sauerlandtheory
I Experimental paradigm to test whether a scalar implicature,or something like it, is calculated for the plural.
Logic of experiment:
I Set up an environment where the implicature is likely to becancelled
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Effect of Focus
Exprimental Items
[Singular] Instruction: Point to the card where Big Bird has akite. Cards displayed:(i) Big Bird with more than one kite.(ii) Big Bird with nothing.(iii) Face down card.
[Plural] Instruction: Plural. Point to the card where Big Birdhas kites. Cards displayed:(i) Big Bird with one kite.(ii) Big Bird with nothing.(iii) Face down card.
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Effect of Focus
Expect that:
I cancelation should not be possible in the singular condition,since the atomicity requirement is built into the semantics ofthe singular.
I in the plural condition, participants should select the visiblecard showing only one of the mentioned object, rather thanchoosing the face-down card.
Results:
For both singular and plural conditions, the face-down card wasnearly always selected (96% of trials)
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Effect of Focus
Second version: insert only
I “the addition of only to our stimuli may create a linguisticcontext that would facilitate implicature cancelation for theplural.”
[Singular] Instruction: Point to the card where Big Bird only has akite. Cards displayed:(i) Big Bird with more than one kite.(ii) Big Bird with nothing.(iii) Face down card.
[Plural] Instruction: Point to the card where Big Bird only haskites. Cards displayed:(i) Big Bird with one kite.(ii) Big Bird with nothing.(iii) Face down card.
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Effect of Focus
Results of second experiment:
I in the singular condition, samre results—chose the face-downcard on 96% of trials,
I in the plural condition, chose the face-down card on 35% oftrials
So with the description ‘only has a kite’, participants almost alwaysrejected an option that showed multiple kites, whereas thedescription ‘only has kites’ frequently led to accepting an optionwith a single kite
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Effect of Focus
But these are exactly the results the QUD-account would predict:
For experiment 1:
I Referential context: expect that the Quantitative QUD is ineffect
For experiment 2:
I only induces an alternative set, and this can be {a kite, kites}or {kites, balloons, toys, . . . }
I corresponds to Quantitative QUD (number is relevant) andKind QUD (number not relevant), respectively
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Beyond English
Have argued that inclusive readings are linked to weakly referentialcontexts
I How does this relate to the cross-linguistic facts?
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Typological Outlook: Armenian
The account here makes certain typological predictions:
I Broad prediction: there is an interaction between referentialityand plurality
I Specific prediction: the inclusive plural reading is bound upwith weak referential uses:will only be found when languages permit plural forms to referto instance-of-a-kind readings, otherwise there should be nooverlap
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Typological Outlook: Armenian
Interaction between plurality and referentiality is not frequentlydiscussed, but it appears to be pervasive
Armenian allows bare singulars and has a plural marker
Sigler (1995) shows that
I bare singulars are only permitted in non-specific contexts
I cannot establish pronominal reference
I cannot be discourse-linked
I obligatory narrow scope
I cannot appear with ‘certain’
I plural marking only when nominal is speciif:“If a semantically plural noun phrase is specific, in the senseof referring to entities already introduced into the discourse,then it is marked plural, but not obligatorily so.” (p. 154)
Similar facts hold for Turkish and Persian
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Typological Outlook: Aari
Aari is an Omotic language, spoken in the Gemu-Gofa highlands ofsouth-west Ethiopia.
Nouns may inflect for case and number, but only when marked asdefinite (Hayward 1990, reported in Corbett 2000)
Similar dependence on definiteness has been noted for
I Korean -tul
I Kambera (Austronesian) has three articles (Klamer 1998: 92,141):
I singular and definite
I plural and definite
I for proper names
Indefinites do not express number
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Typological Outlook: Japanese
Plural marking in Japanese is even more restricted:
I used with pronouns
I used with proper names when human
I not used otherwise
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Typological Outlook: Accessibility Hierarchy and Number
Thinking in terms of the accessibility hierachy
I number marking descends to different levels of referentialaccessibility, depending on the language
Number marking in Japanese :
non-specific < specific < definite < proper name <pronoun
Lots of work to do to sort this out!!
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Typological Outlook: Specific Prediction
Specific prediction: the inclusive plural reading is bound up withweak referential uses:
I will only be found when languages permit plural forms to referto instance-of-a-kind readings, otherwise there should be nooverlap
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Typological Outlook: Specific Prediction
Armenian is known not to permit the inclusive reading for plurals(Bale and Khanjian 2008)
However, it employs the bare singular, but not the plural, in weakreferential contexts (generic statements, non-specifics)(Dum-Tragut 2009).
Armenian then exemplifies the typological prediction:
I the inclusive plural aligns with weak referential uses
I the inability to use the plural form for weak referentialstatements corresponds to an absence of the inclusive pluralreading
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Summary
Given a different account of inclusive plurals
I Downward-entailing contexts are neither a necessary orsufficient condition for inclusive plural readings
I Inclusive readings are related weak referential contexts
I Whether the inclusive or exclusive reading obtains depends onthe QUD
I The connection between plurality and referentiality receivescross-lingusitics support
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Thanks
Thanks!
Thanks to Chris Potts for much advice, Pranav Anand, LucasChampollion, Cleo Condoravdi, Donka Farkas, Beth Levin, AsyaPereltsvaig and Matthew Wagers for discussion, as well as to theaudiences at NELS 41, California University Semantics andPragmatics 3 and SemLab at UC Santa Cruz. Thanks toMarie-Catherine de Marneffe for providing her modeling skills.
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