1. The semantics and pragmatics of the plural Donka F. Farkas and Henriëtte de Swart 3 rd workshop on OT and interpretation, Groningen, November 7, 2008

2. 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)

3. 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

4. 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.

5. 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 leftthe child.Pl left.Pl ‘Three/many children left.’‘The children left.’

6. 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). There are some exceptions to this generalization, that can be treated as instances of reverse markedness (de Swart & Zwarts 2008).

7. Challenge 1: respect Horn pattern How to reconcile morphology and semantics of number given Horn’s distribution of pragmatic labor? (McCawley 1981). 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!

8. 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).

9. 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)

10. 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?

11. Ingredients of analysis Asymmetry in form: privative feature [pl] (no feature for sg). Syntax-semantics interface in bi-OT. Strongest Meaning Hypothesis (pragmatics) reconciles inclusive/exclusive readings. Bi OT analysis restricts cancellability.

12. Morpho-syntax of nominal number Morpho-syntax of nominal number: asymmetry - [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).

13. 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.

14. Markedness: form/meaning Unmarked form (u) = singular; marked form (m) = plural. Based on morphological complexity (feature [pl]) Unmarked meaning (  ) = atomic reference; marked meaning (  ) = inclusive/exclusive sum reference. Based on conceptual complexity: conceptualization of individuals prior to sets (e.g. language acquisition).

15. Avoid complex forms: *FunctN Markedness constraint: *FunctN. Bias constraints + markedness constraint in Mattausch’s system: {*sg,i/e sum; *pl,at} >> *FunctN >> {*sg,at; *pl,at}

16. Bidirectional optimization *sg,i/e sum *pl,at*FunctN*pl, i/e sum *sg,at  * * * * *  * * * *

17. Result 1: Horn pattern of number Morpho syntax ([pl]) + semantics in bi OT in line with Horn pattern: - Morphologically unmarked form (sg) gets unmarked, interpretation (atomic reference). - Morphologically marked form (pl) gets marked interpretation (sum reference always involved).

18. Result 2: cross-linguistic variation Morphologically unmarked form (sg) gets complement of marked interpretation under competition with pl (English, Hungarian). In the absence of competition, no atomic reference for sg (Chinese).

19. Polysemous semantics of plural 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). Semantics of [pl] always involves sum reference.

20. Pragmatics of Plural 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.

21. 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?)

22. Overruling 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.

23. Overruling 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 basement, and notices mouse droppings): Arghh, we have mice!

24. 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, because of high ranking of constraint *pl,at. (vs. Zweig 2006).

25. 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 is relevant, but also. But 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.

26. Result 4: choice of form Why the contrast between Do you have ?a child/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)

27. Plural determiners If sg/pl contrast on nouns has semantic import, why do we find cross-linguistic variation between English and Hungarian? Három/sok gyerek elment.A gyerekek elmentek three /many child leftthe child.Pl left.Pl ‘Three/many children left.’‘The children left.’ No semantic difference between Hungarian and English: plural D entails sum reference.

28. Unidirectional OT analysis Competition between economy (why mark plural on noun when D already entails sum reference) and agreement (reflect in noun that entire DP is plural). MaxPl: nouns in nominals that have sum reference are marked as plural. English: MaxPl >> *FunctN Hungarian: *FunctN >> MaxPl

29. English vs. Hungarian  x[Child(x) & |Child|  3] FPlMaxPl*FunctN three child * *  three children ** FPl*FunctNMaxPl  három gyerek three child.sg * * három gyerekek three child.pl **

30. Conclusions Analysis in line with Horn’s division of pragmatic labor (vs. WPlH). 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 Analysis accounts for typological variation: English/ Chinese/ Hungarian (vs. SSgH)

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