Inclusive and exclusive plurals reconciled

Donka F. Farkas and Henriëtte de Swart

Naïve view of number

Singular horse means ‘one’ Plural horses means ‘more than one’

‘singular’: atomic reference ‘plural’: sum reference (Link 1983)

Apparent success:

(1) Mary saw a horse. (atom only)

(2) Mary saw horses. (sum only)

Problem: inclusive plurals

(3)Do you have children? Yes, I have one/two/…

(4)If you have children, you may come to our party.

(5)Mary didn’t solve problems from this list.

Inclusive plural: atom + sum

Exclusive plural: sums only

WPlH/SSgH

Weak Plural/Strong Singular Hypothesis (WPlH/SSgH).

The plural carries no meaning (WPlH). The singular is marked for atomic reference

(SSgH). Sauerland et al. (2005): [[sg]](x) is defined only if #x = 1

Dominant view in the literature: Krifka 1989, Sauerland 2003, Sauerland et al. 2005.

Empirical problem with SSgH

SSgH: singular is marked for atomic reference. Problem: Hungarian

Singular N is used when D entails sum reference:

Három/sok gyerek elment. A gyerekek elmentek

three /many child left the child.Pl left.Pl

‘Three/many children left.’ ‘The children left.’

Conceptual problem with WPlH

Typological generalization: In languages with a morphological distinction between singular and plural nominals, the singular is unmarked and the plural is marked (Greenberg 1966, Corbett 2000).

How to reconcile morphology and semantics of number given Horn’s distribution of pragmatic labor? (McCawley 1981).

Challenge 1: respect Horn pattern

Horn pattern for number: singular form is semantically and morphologically unmarked. ergo: we expect the marked plural form to be semantically marked.

WPlH/SSgH in conflict with Horn’s distribution of pragmatic labor: anti-Horn pattern!

Challenge 2: typological variation

Farkas and de Swart (2003), Farkas (2006): sg has atomic reference by default. Effect of pl: lift default and allow for sum reference.

OK for Hungarian, but problem for Chinese. Chinese nominals: absence of morphological

number leads to number-neutrality. (i.e. nominal compatible with both atomic and sum reference).

Challenge 3: choice of interpretation

What is responsible for the choice between inclusive and exclusive interpretation of the plural in a particular context?

(1) Mary saw horses. (sum only; exclusive plural)

(2) Do you have children? (atom+sum; inclusive plural)

Challenge 4: choice of form

(3) Do you have #a child/children?(6) Do you have an MA degree/MA degrees?(7) Does Sam have #Roman noses/a Roman nose?(8) Does a worm have #an eye/eyes? Inclusive plural reading in (6) less likely than in (3).

Noses come in singleton sets: pl not natural in (7). Eyes come in pairs: sg not natural in (8).

Not predicted by WPlH. What governs choice of form?

Ingredients of analysis

Privative feature [pl] (no feature for sg). Polysemous semantics for [pl]

(no semantics for sg). Syntax-semantics interface in bi OT. Strongest Meaning Hypothesis reconciles

inclusive/exclusive readings. Bi OT analysis restricts cancellability.

Morpho-syntax of nominal number

Morpho-syntax of nominal number:

- [pl] on plural NPs (in NumP)

- no number feature on singular NPs (in English/Hungarian type languages) or morphologically unmarked nouns (in Chinese type languages).

Number morphology in OT

O(ptimality) T(theory): presence/absence of number morphology depends on interaction of constraints (Hendriks et al. 2007):

*FunctN: avoid functional structure in the nominal domain.

FPl: intended reference to sums is parsed by an expression in NumP (feature [pl]).

Cross-linguistic variation

Reranking of constraints ~ two grammars:

*FunctN >> FPl (Chinese) (no number)

FPl >> *FunctN (English) (sg/pl distinction) Typological evidence in favor of FPl rather

than Fsg (sg unmarked form). Cognitive primacy of atomic reference

(atomic reference unmarked meaning).

Plural is semantically marked

English: sg/pl distinction. Feature [pl] is assigned a family of interpretations (polysemous semantics):

a. [[pl]] = x. x Sum (exclusive interpretation of plural)

b. [[pl]] = x. x Sum Atom (inclusive interpretation of plural)

The two meanings are ordered by (truth-conditional) strength: (a) asymmetrically entails (b).

Result 1: Chinese/Hungarian OK

Chinese: no [pl] feature anywhere; morphologically unmarked nouns are number-neutral.

Hungarian: morphologically unmarked (sg) nouns are number neutral, and therefore compatible with D that entails sum reference.

Why do English singular forms have atomic reference? Bi-directional Optimality Theory.

Horn pattern in bi OT

Mattausch (2006): distinguish unmarked forms (u) and marked forms (m) along with common, unmarked meanings () and infrequent, marked meanings (). Bias constraints block all form-meaning combinations.

In evolutionary setting, stable ranking arises: {*u, ; *m,} >> *Struct >> {*m, ; *u, }

Horn’s division of pragmatic labor emerges.

Bidirectional optimization

*sg,sum/atsum

*pl,at *FunctN *pl,sum/atsum

*sg,at

<sg,at> *

<sg,atsum> *

<sg,sum> *

<pl, at> * *

<pl, atsum> * *

<pl, sum> * *

Result 2: Horn pattern of number

Morpho syntax ([pl]) + polysemous semantics of [pl] in bi OT in line with Horn pattern:

- Morphologically unmarked form (sg) gets unmarked interpretation (no semant. for sg): Chinese.

- Morphologically marked form (pl) gets marked interpretation (sum reference always involved).

- Morphologically unmarked form (sg) gets complement of marked interpretation (atomic reference): English.

Strongest Meaning Hypothesis

Family of interpretations permits inclusive/exclusive interpretations.

Strongest Meaning Hypothesis (Dalrymple et al. 1998, Winter 2001, Zwarts 2003) determines choice between incl/excl plural.

SMH_PL: prefer the stronger interpretation of [pl] over the weaker one, unless the former conflicts with the context.

Result 3: inclusive/exclusive choice

In upward entailing (episodic) contexts, the SMH_PL favors the exclusive interpretation, entails the inclusive one. (Mary saw horses)

In downward entailing contexts/ questions, SMH_PL favors the inclusive interpretation, because of scale reversal under monotonicity reversal (Fauconnier 1976, Sauerland 2003). (Do you have children?)

Benefits of SMH_PL

Natural extension of analysis to inclusive plural interpretations with definites (unlike Spector 2005):

If the children in a divorced family stay with the mother, they are well fed.

Support for SMH_PL (1)

SMH_PL is a pragmatic principle, which can be overruled by context, so we expect possible weakening of inclusive to exclusive interpretation in e.g. questions.

We find this with Does a worm have #an eye/ eyes? Pragmatic knowledge: eyes come in pairs weakening to exclusive plural interpretation.

Support for SMH_PL (2)

SMH_PL is a pragmatic principle, which can be overruled by context, so we expect possible weakening of exclusive to inclusive interpretation in episodic contexts.

(Speaker enters unknown living room littered with toys): There are children in this house.

Bi OT restricts cancellability

Under the assumption that the speaker knows what Mary saw (one horse or more than one horse), Mary saw horses cannot be weakened to an inclusive interpretation: intended atomic reference calls for a singular form in bi OT analysis. (vs. Zweig 2006).

Competition between forms

Inclusive interpretation of the plural not falsified by Does Sam have a Roman nose/#Roman noses?, but pl form is nevertheless infelicitous. Why?

Not only pair <pl,atomsum> is relevant, but also <pl,atom>. But <pl,atom> is a suboptimal pair, because of high ranking of bias constraint *pl,atom.

Conclusion: when sum values are pragmatically excluded, sg form is preferred under bidirectional optimization.

Result 4: choice of form

Why the contrast between Do you have children? And Do you have an Ma degree/ MA degrees?

Use of the plural signals that sum values are relevant, a situation that is culturally more striking with MA degrees than with children.

Do you have a broom/#brooms? (kitchen) Do you have #a broom/brooms? (store)

Conclusions

Analysis in line with Horn’s division of pragmatic labor (vs. WPlH).

Analysis accounts for typological variation: English/ Chinese/ Hungarian (vs. SSgH)

SMH_PL reconciles inclusive/exclusive plural (like WPlH) for indefinites and definites alike.

Bi OT restricts cancellability of SMH_PL (beyond WPlH) and accounts for form choice

Acknowledgments

We are grateful to the financial support provided by UCSC and Utrecht University (UU/UC collaboration program).

Thank you!