The meaning of the plural · 2013-04-10 · Number Neutrality and Referentiality: Experimental...

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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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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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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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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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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plural sing

yesno

Responses by Number Category

Number Category

Responses

020

4060

80100

120

140

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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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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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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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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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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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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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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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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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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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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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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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The meaning of the plural · 2013-04-10 · Number Neutrality and Referentiality: Experimental...

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