Nov 14, 2008 - Spector (2007) proposes an analysis of indefinite singular and plural ... (23) If the children in a divorced family stay with the mother, they are ...
The semantics and pragmatics of plurals Donka F. Farkas and Henriëtte de Swart
November 14, 2008
Abstract This paper addresses the semantics and pragmatics of singular and plural nominals in languages that manifest a binary morphological number distinction on nouns. We develop our analysis against recent proposals in the literature that posit a strong semantics for the singular while taking the plural morpheme to be semantically vacuous. We propose an alternative account which treats the plural as semantically relevant and the singular as not contributing any number restriction on its own. The main conceptual advantage of our proposal is that it respects Horn’s division of labor so that morphologically marked forms are semantically marked as well. We also discuss a series of empirical challenges to previous analyses and examine how our solution meets them. The proposed account grounds the semantics of singular and plural nominals in bidirectional optimization over form/meaning pairs. Both an inclusive and an exclusive sum interpretation are available for plural nominals under this semantics, so we exploit the strongest meaning hypothesis as a pragmatic principle that decides between the two interpretations in context. The empirical coverage of the approach extends to subtle pragmatic distinctions within English as well as to some cross-linguistic contrasts that have not been discussed in the literature so far.
1. Singulars and plurals: atoms, sums and the inclusive/exclusive sum interpretation.
1.1 The naïve view
The question addressed in this paper is a simple one: What is the difference in meaning between singular and plural nominals in languages where this distinction is morphologically marked?1 Concretely, the question reduces to characterizing the semantic difference between the pair in (1a) and (1b), as it pertains to information conveyed by the contrast in number. 1
We use nominal here as a cover term for DPs and NPs. We limit the discussion to nominals in regular argument position, and ignore special uses in predication, incorporation, etc (cf. de Swart and Zwarts 2008b and references therein for discussion of such constructions). Among the languages that manifest a singular/plural morphological distinction are the languages within the Germanic and Romance families as well as Finno-Ugric languages such as Hungarian and Finnish. We will not deal here with languages that make more fine-grained distinctions in number, involving duals and paucals, cf. Corbett (2000). Languages such as Mandarin Chinese that lack morphological number distinctions will be shown to raise problems for certain analyses, but will not receive a
1
(1)
a.
Mary saw a horse.
b.
Mary saw horses.
A disarmingly simple answer would be to say that singular nominals (such as a horse above) refer to one entity while plural nominals (such as horses) refer to more than one entity. Recast in somewhat more technical terms based on Link (1983), this answer is formulated in (2):
(2)
a.
Singular nominals take values from the domain of atoms.
b.
Plural nominals take values from the domain of sums.
The essential distinction between atoms and sums is based on Link’s proposal, according to which the domain of entities from which nominals take values has the structure of a joinsemilattice whose atoms are ordinary individuals (in this case individual horses) and whose non-atomic elements are all the possible sums of more than one atoms (in this case groups of more than one horse). When a nominal is singular, the domain from which its referent is chosen is the set of atoms in the semilattice denoted by its head noun, while in case it is plural, its reference domain is the set of sums in that semilattice. The classical challenge for this view is the existence of inclusive plurals, plural nominals that appear to be indifferent to the atom/sum divide. Inclusive plurals are exemplified in (3).
(3)
a.
Do you have children?
b.
If you have children you may come to our party.
c.
Sam has no children.
The questioner in (3a) is understood to be interested in whether the addressee has one or more children; a yes answer, therefore, is interpreted as committing the addressee to being a parent. This comes as an unpleasant surprise to our naïve view, according to which the plural in (3a) is interpreted as ranging over sums only, and therefore (3a) is incorrectly predicted as • full-fledged analysis in this paper; cf. Krifka (1995) and Rullmann and You (2003) for proposals. Nor do we go into issues concerning non-morphological encoding of number information of the type discussed for Korean by Kwon and Zribi-Hertz (2006) or for Papiamentu and Brazilian Portuguese by Kester and Schmitt (2007).
2
inquiring about whether the addressee has more than one child. Equally surprising to the naïve view is (3b), whose antecedent is interpreted as covering both families with single children and families with more than one child. Finally, (3c) claims that Sam is not a parent, and not that Sam does not have more than one child, as the naïve view would predict. The first challenge then is to account for the distinction in (1) while at the same time allow for the possibility of plural forms to be interpreted inclusively in examples like (3). In Section 1 of this paper, we discuss a number of proposals that attempt to resolve this puzzle, and point out where they fail. Section 2 exploits bidirectional Optimality Theory to propose a semantics of the singular/plural contrast based on the morphological markedness of the plural form. Section 3 links the inclusive/exclusive contrast to the pragmatics and uses the Strongest Meaning Hypothesis to account for the contrast between (1) and (3). Section 4 refines the analysis to account for singular nominals in DPs conveying sum reference in languages like Hungarian. Section 5 concludes.
1.2 The weak plural/strong singular solution
An immediate solution to the inclusive plural problem sketched above is to treat plural forms as indifferent to the atom/sum distinction while assuming that singular forms have atomic reference. Sauerland (2003) and Sauerland et al. (2005) work out a proposal along these lines, based on an earlier suggestion in Krifka (1989). Krifka (1989) proposes to treat singular forms as more specific than plural ones. Singular nominals, he suggests, have to refer to atoms. Plural nominals, on the other hand, are less specific in that they are always interpreted inclusively: their reference domain includes the entire semilattice. The fact that in ordinary episodic sentences exemplified in (1) plural forms are interpreted as referring exclusively to sums is due, in Krifka’s view, to a pragmatic blocking effect. The existence of the singular form blocks the use of the plural when atomic reference is intended because of a pragmatic rule that forces the choice of a more specific form over a less specific one when the two are equally complex. Since the singular DP is more specific than the plural the singular is chosen when atomic reference is meant. Following Sauerland (2003), Sauerland et al. (2005) work out a detailed implementation of this idea. In their account, there are two number features, SG and PL, located syntactically in the head of a φP node, as in (4), where *boy is a number-neutral predicate: 3
φP
(4)
φ
[SG/PL]
DP
D
NP
the
*boy
In this approach, the plural morpheme on the head noun is the reflex of agreement.2 The proposed semantic contribution of number features is given in (5):
(5)
Semantics of the singular/plural in Sauerland et al. (2005): a.
[[SING]](x) is defined only if #x = 1 [[SING]](x) = x wherever it is defined
b.
[[PLUR]](x) is always defined [[PLUR]](x) = x wherever it is defined
In this approach the plural feature contributes nothing to the interpretation of the phrase it occurs in, while the singular feature contributes a presupposition amounting to atomic reference in our terms. In this view then the singular is ‘strong’ and the plural is ‘weak’ because the plural has no semantic contribution to make while the singular does. In order to derive the exclusive reading of the plural, exemplified in (1), Sauerland et al. (2005) make recourse to the principle of Maximize presupposition proposed in Heim (1991). Given two alternative morphemes, Maximize presupposition forces the choice of the one that has a stronger presupposition. Assuming that the two number features are alternative morphemes, the singular is predicted to be used whenever the atomicity presupposition is met, thus correctly predicting that the singular from in (1a) will receive an atomic (singleton) interpretation, while the plural will receive a sum (‘more than one’) interpretation in (1b). In this analysis, the inclusive (‘weak’) reading of the plural is predicted to emerge whenever the presupposition of the singular is not met. This happens when the cardinality of the referent is an open issue in the context or when mixed reference (atom and group) is 2
The high position of the number feature is crucial, because the analysis posits Quantifier Raising on its sister DP, a detail that is not crucial for us.
4
meant. For the first case, Sauerland et al give the example in (6), in a context where the speaker does not know how many children the addressee has:
(6)
You may bring your children.
As an instance of the second case, they give the example in (7), spoken by a coach who knows that some of the boys on the team have one sister, while others have more than one:
(7)
Every boy should invite his sisters to the party.
In order to capture the number interpretation of plural indefinites within and outside the scope of negation, Sauerland et al. propose the weakening of Maximize Presupposition in (8)3:
(8)
Maximize Presupposition applies to the scope of an existential if this strengthens the entire sentence.
Maximize Presupposition together with the generalization in (8) correctly predict that plural indefinites outside the scope of negation will be interpreted exclusively, as in (9a), while such indefinites within the scope of negation will receive inclusive interpretations, as in (9b):
(9)
a.
Some eggs are still hidden.
b.
There are no eggs in the basket.
The generalization in (8) further predicts inclusive readings of plural forms in downward entailing contexts such as restrictors of universal quantifiers and antecedents of conditionals, an issue to which we return below. On the down side, however, let us note that it is not clear how Maximize Presupposition is to be integrated into an overall theory of grammar, especially given the need to weaken it as in (8).
3
It is at this point that raising the DP sister of φ out of φP becomes crucial.
5
1.3 The strong singular / weak plural solution vs. the Horn pattern
The analysis outlined above, or any alternative in which the singular feature makes a semantic contribution while the plural does not, forces one to distinguish between semantic and morphological markedness. Unlike Sauerland et al, we see this as a major problem especially since, as they note, the field has not yet seen any other reason to distinguish between these two types of markedness. Thus, note that in any strong singular/weak plural theory the singular form is semantically potent while the plural one is not. On the other hand, it is a stable cross-linguistic generalization that in languages that have a singular/plural contrast in nominals, the plural is morphologically marked, i.e., it is encoded in a special morpheme, while the singular is not, i.e., there is no special morpheme signalling singular number (Greenberg 1966, Corbett 2000).4 Under the strong singular/weak plural view, morphological and semantic marking diverge: the singular feature is morphologically unmarked and semantically marked, while the plural feature is morphologically marked and semantically unmarked.5 It is, in fact, this very tension between semantic and morphological markedness that made the existence of inclusive plurals interesting in the first place. McCawley (1981) raises the question of how to reconcile the morphology and the semantics of number given the general tendency of language to pair up morphologically unmarked forms with morphologically unmarked meanings. In this paper, we call this fundamental connection the Horn pattern. Citing structuralist and Prague school work on markedness, Horn (2001: 155) describes it as follows: “… one member of an opposed pair is literally MARKED (overtly signaled) while the other is UNMARKED (signaled via the absence of an overt signal). Semantically, the marked category is characterized by the presence of some property P, while the corresponding unmarked category entails nothing about the presence or absence of P but is used chiefly (although not exclusively) to indicate the absence of P (Jakobson 1939)”. The strong singular/weak plural analyses contradict the Horn pattern because in such approaches the singular forms are assigned a strong semantics (requiring atomic reference, which plays the role of P above), while plural forms are given a weak interpretation, neutral with respect to whether values are chosen among atoms or sums. 4
Exceptions to this generalization involve instances of reversed markedness, cf. de Swart and Zwarts (to appear) for data and discussion. We will be concerned here with the typologically most frequent pattern, where the plural is morphologically marked, but the singular is not. 5 For further discussion of the special status of number within nominal φ features with respect to semantic and morphological markedness within the assumptions of Sauerland (2003) and Sauerland et al. (2005), see Sauerland (2008).
6
A central goal of the present paper is to achieve a reconciliation of the semantics and the morphology of number and thus propose an analysis of number interpretation that conforms to the Horn pattern. Thus, one of our goals is to arrive at a view that meets the desideratum formulated in A:
A.
Plural forms should be semantically marked relative to singular forms so as to preserve the correspondence between morphological and semantic markedness seen elsewhere in language.
Note that only by meeting this desideratum can we explain why singular forms are unmarked morphologically while plural forms are not. Analyses that are in line with the Horn pattern will be called here weak singular/strong plural approaches. They are superior on theoretical grounds to strong singular/weak plural views because they reconcile morphological and semantic markedness.
1.4 Empirical challenges to the weak plural/strong singular view
In addition to the theoretical problem discussed in the previous subsection, the weak plural/strong singular approaches face empirical challenges as well. We discuss here a problem that arises in Hungarian. First, note that just like English and other Indo-European languages, Hungarian has a singular/plural distinction:
(10)
a.
Mari látott egy lovat. Mari saw a
horse.Acc
‘Mari saw a horse’ b.
Mari látott lovakat. Mari saw horse.Pl.Acc ‘Mari saw horses.’
7
The morpheme -(a)k in (10b) is the realization of the plural feature on nominals.6 We see it as realizing the plural feature on verbs as well in (11b), which show that in Hungarian, just like in English, verbs must agree with their subjects in number:
(11)
a.
A gyerek elment. the child
leave.Past
‘The child left.’ b.
A gyerekek elmentek the child.Pl
/*elment.
leave.Past.Pl/leave.Past
‘The children left.’
The problematic data concerns DPs whose determiner entails reference to sums, including but not limited to cardinals bigger than one, exemplified in (12):
(12)
a.
három gyerek three child ‘three children’
b.
sok
gyerek
many child ‘many children’ c.
mindenféle gyerek all.kind
child
‘all kind of children’ d.
több gyerek more child ‘more children’
e.
egy pár a
gyerek
couple child
‘a couple of/some children’
6
The vowel a is in parentheses here because in many phonological analyses it is treated as epenthetic. The quality of this vowel is determined by vowel harmony as well as by morphological considerations that are irrelevant for our purposes.
8
As one can see from these examples, such DPs are formally singular; adding the plural morpheme would result in ungrammaticality in all the examples in (12). Note that these cases involve not only cardinal numerals (12a, and possibly 12b) but other types of Ds as well (12ce), so the analysis of cardinals proposed by Ionin and Matushansky (2006) would not cover all the relevant examples. The fact that these DPs are semantically plural can be seen from the fact that they may occur as subjects of verbs like összegyülni ‘to gather’.
(13)
Egy pár a
gyerek összegyült a téren.
couple child
gather.Past the square
‘Some children gathered in the square’
The singular form of these morphemes comes as an unpleasant surprise to a weak plural/ strong singular analysis, given that the sum reference presupposition is met here. We could claim that the DPs in (12) have the feature [Pl] in the φ node heading their φP, but that the agreement rule mandating the presence of the plural morpheme on the head noun of the DP is suspended in this case. Such an analysis predicts that these DPs are plural, just like the subject DP in (11b), but their plural feature happens not to be realized on their head noun. Attractive as this solution might be, it is not tenable in view of the fact that when any of the DPs in (12) is in subject position, it triggers singular rather than plural agreement:
(14)
a.
Három gyerek elment three child
/*elmentek.
leave.Past /leave.Past.Pl
‘Three children left.’ b.
Mindenféle gyerek jelentkezett / *jelentkeztek all.kind
child
apply.Past
apply.Past.Pl
If the feature PL on the DP were responsible for the plural verb in (11b), as seems natural, and if this feature is present on the DP in (13) as well, as predicted by the solution we just sketched, why doesn’t this feature trigger plural verb agreement in (14)? The DPs in (12) behave like plural DPs when it comes to agreement with discourse pronouns. When these DPs are antecedents of discourse pronouns, the pronouns are obligatorily plural. If (15) is the continuation of (14) and if the three children are to be the antecedent of the direct object pronoun, that pronoun must be plural.
9
(15)
Mari nem látta
őket
/*őt.
Mari not see.Past III.Pl.Acc /III.Acc ‘Mari didn’t see them.’
The data discussed here suggest that the DPs in (12) are morphologically singular but semantically plural, i.e, they involve reference to sums. Subject verb agreement is sensitive to the morphological feature of the DP while discourse pronoun agreement is sensitive to the semantics, i.e., to the sum/atom nature of the referent. If this characterization is on the right track, we see that at least in Hungarian, singular forms can be used in case of sum reference, a state of affairs that contradicts the strong singular/weak plural view. Such a situation seems to call for the opposite approach, one where the singular is weak and the plural is strong. At the same time, in Hungarian, just like in English, plural forms have inclusive uses. In (16) for instance, the addressee is expected to give a positive answer even if she saw a single horse.7
(16)
Láttál
lovakat?
see.Past.II horse.Pl.Acc ‘Have you seen horses?’
These data add a second challenge to the analysis of number, formulated in B.
B.
There are languages with a morphological singular/plural distinction on the nominal, where singular forms may have sum reference in case sum reference is entailed by D.
This generalization poses an empirical challenge to strong singular/weak plural views. The problem for Sauerland et al. (2005) is that the singular forms in (12) do not meet the presupposition required by the feature SG, which, however, appears to be present in such DPs given the agreement data in (14). We end this subsection by noting some further problems with the analysis in Sauerland et al. (2005). While discussing examples such as (17),
7
The contrast between inclusive and exclusive plurals in Hungarian is complicated by the fact that in this language bare nominals (whether singular or plural) can incorporate, an issue discussed at length in Farkas and de Swart (2003). Incorporated singulars are number neutral, but incorporated plurals have sum reference. We will not be concerned with incorporated nominals in this paper, but our proposals are compatible with the analysis of incorporation proposed by Farkas and de Swart (2003).
10
(17)
You are welcome to bring your children.
Sauerland et al. suggest that plural forms are always defined, even if the cardinality of the referent is 0. This has the unfortunate consequence, however, of predicting that (18) is true even in case Mary ate zero apples:
(18)
Mary ate apples.
Note also that examples of the form in (17), but involving a singular DP may also be used in the absence of an existential presupposition:
(19)
You are welcome to bring your spouse.
These data indicate to us that in both (17) and (19) contextual narrowing is at play and therefore that there is no special link between plural forms and lack of existential import. The semantics of plurality we develop below does not rely on existential import, so we leave the contrast between (17) and (19) as a problem for Sauerland et al. that does not concern us. Finally, we will see below that there are complex matters involved in determining when plural forms can be used inclusively and when not. To give an example, note that (20b) is a strange question to ask in case I am in your kitchen and have just spilled some beans on the floor.
(20)
a.
Do you have a broom?
b.
Do you have brooms?
The strangeness of (20b) in the kitchen situation cannot be explained away making recourse to Maximize Presupposition since (20a) is preferred to (20b) even in case there is no reason for me to believe that you have one and only one broom. Note also that Maximize Presupposition does not explain why (20b) rather than (20a) is the appropriate question to ask the salesperson in a store, even if I intend to buy just one broom.
11
1.5 Towards a strong semantics for the plural: attempts and challenges
1.5.1 Spector (2007) and Zweig (2006)
Spector (2007) proposes an analysis of indefinite singular and plural DPs in which both types of DPs are marked with a number feature.8 On the ontological level, Spector assumes that the domain of individuals is structured according to a part-whole relation such that for any two individuals x and y there exists a unique individual x + y (the mereological sum of x and y) that contains both x and y as parts. Atomic individuals are individuals whose only parts are themselves (See Schwarzschild 1996 for details; Rullmann 20032 proposes a similar idea). In Spector’s proposal there are two number features, singular and plural. The singular morpheme has no semantic import, which is what makes this proposal a weak singular approach. Singular indefinite DPs are assumed to denote within the set of atoms because of pragmatic reasons we turn to below. Plural DPs on the other hand denote the set of atoms and sums of which their descriptive content is true. This is due to the contribution of the plural morpheme, given in (21):
(21)
Spector’s (2007) semantics of the plural: [[pl]] = λP.λX(∀x(atomic(x) ∧ x ≤ X) → P(x) = 1)
Here x ≤ X is to be read as ‘x is part of X’ under the ‘part of’ relation just mentioned. This analysis has no trouble, of course, accounting for the inclusive interpretation of plural DPs. The exclusive interpretation of indefinite plural DPs is derived via a complex mechanism of higher order implicature based on a system of scales (whose full justification remains open). The gist of the analysis is as follows. An indefinite singular DP such as a horse implicates ‘no more than one’ because of competition with several horses. Because of this implicature and the weak semantics of the plural morpheme, the singular is more specific than the plural and therefore they form the scale < pl, sg >. The use of an indefinite plural then implicates that the corresponding singular form could not have been used. This implicature is second order because it is the negation of the singular form together with its implicature. For an example like I saw horses, the higher meaning is I saw one or more 8
Another weak singular approach is proposed in Spector (2003), where the plural is analyzed as ambiguous between an exclusive and an inclusive interpretation, the latter having to be licensed, in a manner similar to N(egative) P(olarity) I(tems) by certain operators. For critical discussion of this proposal, see Farkas (2006).
12
horses, and the higher order implicature is It is not the case the I saw exactly one horse, which, together, give the exclusive interpretation of the plural. Returning to desideratum A, we observe that the analysis preserves the Horn pattern at the level of strict semantic meaning, but goes against it at the level of semantic meaning + first order implicature. The main theoretical issue the analysis raises is the introduction of a brand new type of implicature. On the empirical side, the analysis focuses on bare plurals, and does not straightforwardly extend to definite plural DPs. Such DPs have exclusive readings just like bare plurals, but differ from them in that there is no obvious definite counterpart to several. It is therefore unclear how the horse gets its atomic value, and how the horses gets its exclusive plural interpretation in examples like (22a) and (b):
(22)
a.
Mary touched the horse.
b.
Mary touched the horses.
Note, incidentally, that definite plural DPs, just like bare plurals, are susceptible to inclusive interpretations. Thus, the generalization in (23) covers divorced families with one or more children and not only those with more than one child.
(23)
If the children in a divorced family stay with the mother, they are better fed than if they stay with the father.
We conclude that an account of the interpretation of plural indefinites that relies crucially on the competition between a and several is not on the right track. Finally, note that the higher order implicature account makes no predictions concerning the pragmatic conditions that make the use of an inclusive plural unacceptable in (20b), when uttered in the kitchen. In view of the empirical and theoretical challenges faced by Spector’s (2007) analysis, we cannot adopt it as a general analysis of the singular/plural morphological contrast on nominals. We turn now to an account that is similar in spirit to the one just sketched, namely Zweig (2006). Zweig’s main focus is the treatment of ‘dependent bare plurals’, plurals within the scope of a quantifier, exemplified in (24), about which he has many interesting and accurate observations.
13
(24)
a.
Ten students live in NY boroughs.
b.
Most/all students read papers.
We discuss here only those parts of the paper that extend the account to number interpretation in general. For Zweig, both singular and plural nominals are number neutral semantically. The difference is that the plural contributes a ‘plurality’ generalized conversational implicature giving rise to the exclusive interpretation. This implicature disappears in downward entailing contexts, as implicatures usually do (see Chierchia 2006), thus giving rise to the inclusive interpretation when plural nominals are within the scope of negation or in the antecedents of conditionals. The account is admittedly incomplete in that the question of how the crucial plurality generalized implicature arises is not discussed, except to note, correctly, that for dependent plurals, the mechanism cannot be that of Sauerland (2005) et al. Normally, generalized conversational implicatures arise because of competition of paradigmatic alternative forms or some other factor that involves the semantic contribution of the item in question. Such an implicature cannot, by definition, simply get attached to a morpheme or feature. Switching to a conventional implicature would help in this regard, but would become problematic because of the fact that conventional implicatures are not cancellable and therefore the existence of the inclusive reading of plurals would be lost. In the absence of a foundational discussion of the status of the plurality implicature, Zweig’s proposal is hard to evaluate. On the empirical level, this account, just like the others discussed here, has nothing to say about the broom contrast in (20). There is a further empirical issue that has gone unmentioned so far. Spector (2003, 2007) and Farkas (2006) observe that a plural form is inappropriate in an inclusive-plural friendly environment when the possibility of having a sum as a witness is ruled out for pragmatic reasons:
(25)
a.
# Sam doesn’t have Roman noses.
b.
#Does Mary have high school diplomas?
Human beings normally have one nose, and it is unusual for a person to have more than one high school diploma. Strong singular/weak plural analyses cannot handle the infelicity of (25), because the plural noun should be compatible with atomic reference. Spector (2007)
14
stipulates a possibility presupposition associated with scalar implicatures in general.9 For Zweig, the facts in (25) remain mysterious.
1.5.2 Farkas and de Swart (2003)
None of the proposals discussed so far fully meets the desideratum formulated in A. As far as we know, there is only one analysis of the singular/plural contrast which respects the Horn pattern, and attempts to account for inclusive plurals at the same time, namely the one proposed by Farkas and de Swart (2003). Farkas and de Swart (2003) sketch an account of number interpretation whose main advantage, from the present perspective, is that it achieves the desired reconciliation between the semantics and the morphology of number. The proposal treats number as a privative feature, PL and assumes that singular forms lack number morphology altogether. Singular forms are interpreted as referring to atoms by default, whenever such forms introduce a discourse referent. The presence of the plural morpheme indicates that this default is not in force. Plural forms therefore will be used whenever reference to sums or reference to sums and atoms is intended. Under this account the plural does semantic work while the singular does not. Besides the conceptual advantage of respecting the Horn pattern, the proposal has no difficulty handling the Hungarian data reviewed in Section 1.4 above: the D in the examples in (12) ensures sum reference, thus exempting these DPs from being under the jurisdiction of the default rule. The only difference between English and Hungarian is that in Hungarian the use of a redundant plural feature is prohibited in such cases. Note also that the account deals with the data in (25) as well because the use of a plural needs to be justified by the need to suspend the default atomic interpretation from arising. At the heart of this solution lies the assumption that a discourse referent is interpreted as atomic by default. The main problem with this assumption is that it predicts atomic default reference for nominals independently of the facts of number morphology in the language. Thus, unmarked nominals are predicted to have default atomic reference not only in languages like English or Hungarian, but also in languages that lack a morphological plural feature, such as Chinese. This, however, is not the case. In Chinese, unmarked nominals are number neutral, rather than interpreted as atomic, as emphasized by Krifka (1995), on the basis of examples such as (26): 9
The extension of the presupposition from number interpretation to scalar implicatures in general rests on a single example involving or which we do not find particularly convincing.
15
(26)
Wò kànjiàn xióng le. I
see
[Mandarin Chinese]
bear Asp
‘I saw a bear/some bears.’
The empirical generalization we draw from contrasting the interpretation of non-plural forms in English-type languages and Chinese type languages is formulated in C.
C. The interpretation of an ‘unmarked’ singular form in a language depends on the existence of ‘marked’ plural forms. In the absence of morphologically plural forms, unmarked forms are number neutral.
Here, we concentrate on languages that have a morphological singular/plural distinction in the nominal domain. But number is not a semantic universal (von Fintel and Matthewson 2008). Even though we will not develop an analysis of Chinese-type languages in this paper, any account of the semantics of number morphology has to be compatible with the data in these languages, at least in principle. Therefore, we will not pursue here the line explored in Farkas and de Swart (2003).
1.6 Conclusion
In this section we saw why we must go beyond the naïve (and attractive) view of number interpretation according to which singular nominals are interpreted as referring to one entity while plurals are interpreted as referring to more than one entity. The main stumbling block is the existence of contexts where plural nominals are interpreted inclusively, as well as the number system in languages like Hungarian, where singular nominals receive a non-atomic interpretation (cf. subsection 1.4). We also reviewed some earlier approaches to the problem of number interpretation and briefly discussed the major challenges they face. We established the following desiderata:
A comprehensive account of number interpretation must: (i)
account for the existence of the inclusive as well as the exclusive interpretation of both definites and indefinite plurals; 16
(ii)
respect the Horn pattern and be in line with the morphological markedness facts (generalization A);
(iii)
account for the choice between inclusive and exclusive plural interpretation in context;
(iv)
account for subtle contrasts in the choice of a singular and plural form in inclusive friendly environments (examples 20, 25);
(v)
predict the possibility of certain singular forms referring to sums in languages like Hungarian (generalization B, examples 12);
(vi)
be compatible with the number neutral interpretation of nominals in languages that do not have a morphological mark for plurals, such as Mandarin Chinese (generalization C, example 26);
In the remainder of this paper we work out a detailed proposal of number interpretation and discuss how it meets the desiderata established in (i)-(vi).
2. The semantics of singular and plural nominals
In languages with a binary morphological number distinction, speakers have a choice between the use of a singular and a plural form. As one would expect, and as we saw in Section 1, this choice is not free, but rather, it depends on what meaning is conveyed by the alternative form. An account that respects the Horn pattern should posit a weak semantics for the singular and a strong semantics for the plural in order to explain why the singular is systematically morphologically unmarked across languages, while the plural is marked. For languages with a singular/plural distinction then, one seeks an analysis in which the singular form is not associated with any special number semantics while the plural, being morphologically marked, is treated as being associated with number semantics. That semantics, however, has to be subtle enough to allow both inclusive and exclusive plural interpretations. We work out such an account below. To preview, we propose that in languages with a binary number distinction, there is a single, privative morphological feature [Pl] on nominals, which gets assigned two related interpretations: exclusive sum reference and inclusive sum reference. The interpretation of singular forms is derived as a result of the existence and interpretation of plural forms. The analysis is rooted in a bidirectional OT model based on Mattausch (2005, 2007), a set-up that captures the harmonization of unmarked forms with unmarked meanings, 17
and of marked forms with marked meanings.10 We focus here on the semantics of number interpretation on argumental nominals, nominals that introduce a variable (or discourse referent) for which atom/sum reference has to be decided. We do not discuss here issues concerning the interpretation of the feature [Pl] when it occurs as an agreement features on verbs and VPs for instance. We concentrate on N-headed nominals, and leave detailed discussion of pronouns and coordinate DPs for future work. In this section we show how Mattausch’s model accounts for the interpretation of singular and plural nominals. The account derives both inclusive and exclusive sum readings as optimal interpretations of plural forms. Section 3 goes on to propose a pragmatic account of the choice between the two interpretations in context. Sections 2 and 3 complete the semantics and pragmatics of number interpretation in English. We turn to issues of crosslinguistic variation in Section 4.
2.1 Bi-directional optimization over form-meaning pairs
Mattausch proposes an abstract way of modelling the association of forms and meanings as an optimal communication strategy. Suppose there are two forms, one marked (m), one unmarked (u) and suppose there are two meanings, a more common meaning α and a less frequent meaning β. Their combination leads to four possible form-meaning pairs: 〈u,α〉, 〈m,α〉, 〈u,β〉, 〈m, β〉. The question is which pairs are the optimal, most harmonic pairings of form and meaning. In order to model this situation, Mattausch proposes four bias constraints on the relation between form and meaning:
(27)
Bias constraints *m,α: the (marked) form m is not related to the (frequent) meaning α. *m,β: the (marked) form m is not related to the (infrequent) meaning β. *u,α: the (unmarked) form u is not related to the (frequent) meaning α. *u,β: the (unmarked) form u is not related to the (infrequent) meaning β.
The bias constraints in (27) mitigate against all possible form-meaning combinations. Furthermore, there is a general markedness constraint * MARK on forms, which penalizes the 10
Mattausch’s work goes back to ideas developed by Jäger (2003) and Blutner (1998, 2000, 2004). For a slightly different bidirectional OT set-up, see Beaver (2004). For a comparison of different bidirectional OT models, see Beaver and Lee (2004).
18
use of the marked form. *MARK models a notion of economy, a preference of simpler forms over more complex ones. All constraints are soft, but how easily they can be violated depends on their strength. The ranking of *MARK with respect to the bias constraints reflects the balance of economy considerations with faithful correspondence relations between forms and meanings in the process of optimal communication. The ranking of the four bias constraints and the markedness constraint constitutes the grammar of the language. Mattausch derives the constraint ranking from iterated learning over several generations in a computational model. In the initial training corpus, a grammar is used in which all four bias constraints are ranked equally high. Due to learning effects, the rankings can shift, and the association between forms and meanings shifts along with the rankings. Learning is driven by frequency distributions in a corpus. It is crucial to start out with a frequency asymmetry between meanings α and β, α occurring say 90% of the time, and β 10% of the time. There is an even distribution of marked and unmarked forms over the meanings α and β, so that 45% of the unmarked forms are associated with meaning α, and 5% of the unmarked forms with meaning β, and the same distribution of meanings α and β (45-5%) holds for the marked forms. Adjustment of constraint values is dependent on comparisons of forms and comparisons of meanings.11 When it comes to the association of meanings to a particular form, a bias constraint *u,α will be promoted when the learner observes the use of an unmarked form to express the meaning β, and demoted when an unmarked form is found with the meaning α. A bias constraint *m,α is promoted when the learner observes the use of a marked form expressing the meaning β, and demoted when the marked form is found with the meaning α. Because of the discrepancy between the number of α meanings and the number of β meanings in the training corpus, any form is much more likely to correlate with the meaning α than with β. In the interpretive dimension, this demotes *u,α, *m,α and promotes *u,β and *m,β, roughly in accordance with the frequencies of the input training corpus. The ranking of * MARK is not determined in the comparison of meanings, for a markedness constraint on forms is not concerned with meanings. When it comes to the comparison of forms, a bias constraint *u,α is promoted when a marked form is used to convey the meaning α, and demoted when an unmarked form is used to convey α. A bias constraint *m, α is promoted when an unmarked form is used to convey 11
In the terminology of Jäger (2003) and Mattausch (2005, 2007), this is the distinction between speaker mode and hearer mode of learning. The speaker mode is production oriented, so it involves comparison of forms to convey a particular meaning. The hearer mode is interpretation oriented, and involves comparison of meanings for given forms.
19
the meaning α, and demoted when a marked form is used to convey β. The markedness constraint *MARK interacts with the bias constraints. *MARK favors the use of unmarked forms for α as well as β. But given that meaning α is more frequent than meaning β, the compromise between optimization over forms and optimization over meanings is to promote *m,α more than *m,β. Balancing the constraints leads to a new frequency distribution in the corpus, in which more than half of the infrequent meanings β are expressed by marked forms. The evolutionary perspective comes in when the bidirectional learning algorithm is integrated with the iterated learning model of Kirby and Hurford (1997). The iterated learning model of Kirby and Hurford (1997) is based on the idea that learners produce language according to their acquired grammar. This means that the corpus frequencies produced by the first generation, after adjusting the OT grammar are slightly different from the frequencies of the original training corpus. Instead of having an equal distribution of marked and unmarked forms for the meanings α and β, the corpus will now contain more instances of the rare meaning β expressed by marked forms. The second generation learner is exposed to the set of frequencies in the speech of the first-generation learner, and will reinforce the tendency to avoid marked forms for the more frequent meaning. The frequencies produced by the secondgeneration learner will be slightly different from those of the first-generation learner, and will constitute the input for the third generation learner. By iterating this process over multiple generations we end up with a stable ranking that reflects the Horn pattern:
(28)
Horn’s distribution of pragmatic labor {*u,β; *m,α} >> *MARK >> {*u,α; *m, β}.
We started with an original training corpus with 50-50% frequencies for marked and unmarked forms, but as a result of iterated learning, an asymmetric distribution of meanings develops into a grammar in which there is a 100% association of the unmarked meaning with the unmarked form and a 100% association of the marked meaning with the marked form. In this way, Mattausch (2005, 2007) models the emergence of Horn’s division of pragmatic labor as the optimal communication strategy that arises under evolutionary pressure.
20
2.2 Morphological and semantic markedness in the domain of number
In this subsection we apply Mattausch’s abstract model to the interpretation of singular and plural nominals. In order to do that we have to identify values for u, m, α and β in the bias constraints and formulate a markedness constraint for *MARK. On the formal side, recall that we are concerned with languages that make a binary morphological number distinction between singular and plural nominals and which display the typologically frequent pattern in which the plural is morphologically marked, whereas the singular remains unmarked. Because of this asymmetry, the singular form is (u) and the plural is (m). As mentioned above, we assume that the morphological mark on plural forms is the presence of the privative feature [Pl]. On the semantic side, we follow Link (1983), and take the domain of interpretation from which variables (discourse referents) are assigned values to consist of atoms and sums, the latter built from the former by means of the join operation ⊕. The domain from which a variable introduced by a non-pronominal nominal is given values is determined by the head noun, which identifies the relevant join semi-lattice, and by the number information, which further restricts it in terms of atomic/sum reference. We take a nominal to have atomic reference iff the values of the variable it introduces are restricted to atoms in the relevant join semi-lattice. We take a nominal to have sum reference iff the values of the variable it introduces include sums. Such a nominal will be said to have exclusive sum reference iff its value domain includes only sums; a nominal has inclusive sum reference iff its value domain includes not only sums but atoms as well. What about semantic markedness? We take atomic reference to be the unmarked meaning (α), and sum reference (whether inclusive or exclusive) to be the marked meaning (β). Atomic reference qualifies as the unmarked meaning because the conceptualization of sums is dependent on atoms: atoms may exist independently of sums, but not the other way around. Support for this view is found in psychological research that suggests the special nature of sum reference. Recent psychological research suggests that non-human primates and children under two represent small sets of objects as object-files, and do not establish a singular-plural distinction based on atoms vs. sums (Hauser, Carey and Hauser 2000, Feigenson, Carey and Hauser 2002, Feigenson and Carey 2003, 2005). The evidence comes from a variety of nonlinguistic tasks such as the following. Infants watch while sets of crackers are placed into two
21
different buckets (e.g. two in one bucket, three in another). When encouraged to crawl to one of the buckets, infants reliably choose the bucket with more crackers with numbers up to three. Nevertheless, when one set of crackers exceeds three (in four vs. two, six vs. three or even fous vs. one comparisons), infants up till 20 months are at chance. All they would need to do to succeed on a one vs. four comparison is to represent one as a singular individual, and four as a plurality, but they fail to do so, and do not show a preference for the bucket containing more crackers. This suggests that they do not have a prelinguistic equivalent to the singular-plural distinction. The three-item limit is expected when infants’ representation is object-based, as the object-file system is assumed to be subject to the same working memory limit of three to four items we find in representations underlying midlevel attention in adults. Wood, Kouider and Caregy (2004) and Kouider, Halberda, Wood and Carey (2006) assume that by the time children learn the meanings of linguistic markers for the singularplural distinction, they must have distinguished between singletons and sets (or sums, in our terms). They find that children over two who have started to produce the plural marker understand that a plural markers signal reference to multiple objects. Their experiment uses a preferential looking paradigm with a single novel object on one screen, and one depicting a set of eight novel objects on another. When confronted with nonsense words, twenty-four-monthsolds but not twenty-month-old infants looked at the screen that matched the carrier sentence with respect to the singular-plural distinction when number was expressed on the verb (is/are), on the noun (the blicket/the blickets) and with quantifiers (a blicket/some blickets). The results suggest a strong correlation between the linguistic and cognitive developmental process, where learning the semantic force of number marking on linguistic expressions may make the distinction between sets (sums) and individuals (atoms) explicit or more salient. In sum, representations of individual objects and object arrays are available from ten months onward. The representation of multiple objects as sums is paired up with the acquisition of linguistic markers of plurality (around 24 months). Given the long time period between ten months and 24 months, it seems fair to say that it takes time for children to learn to construct a sum-based representation out of atomic objects. We take the results from the acquisition of number and developmental psychology to provide support for the hypothesis that sum reference is marked and atomic reference is unmarked. Given what was said so far, the bias constraints we need for pairing up singular and plural forms with their domain of interpretation in the lattice are as follows:12 12
We are talking about ‘nominals’, because we want to include DPs such as the children, and bare NPs such as children. We use ‘pl’ for variable introducing nominals marked with the feature [Pl] and ‘sg’ for variable
22
(29)
Bias constraints for number: *pl,atom: the plural form is not related to atomic reference. *pl,i/e sum: the plural form is not related to (inclusive/exclusive) sum reference. *sg,atom: the singular form is not related to atomic reference. *sg,i/e sum: the singular form is not related to inclusive/exclusive sum reference.
The markedness constraint on forms is *FUNCTN, the constraint proposed by de Swart and Zwarts (2008a, 2008b, 2009) as the central economy constraint in the nominal domain:
(30)
*FUNCTN: avoid functional structure in the nominal domain
*FUNCTN prefers ‘bare’ nominals without articles, number morphology, classifiers, etc. over nominals involving the functional projections that host these expressions. The elaborate structures we find in the nominal domain support the view that *FUNCTN is a soft, violable constraint, that can be overruled by faithfulness constraints driving the expression of sum reference, discourse referentiality, definiteness, etc (cf. de Swart and Zwarts 2008a, Hendriks et al. 2009: chapter 7). However, its influence is pervasive, even in languages in which such faithfulness constraints are ranked high, as argued by de Swart and Zwarts (2008b) in relation to a range of bare nominal constructions in Germanic and Romance languages.
2.3 Distribution of atomic/sum reference over singular/plural nominals
If we use these values as the instantiation of Mattausch’s model in the domain of number, we obtain the ranking in (31) as an evolutionary stable pattern.
(31)
The Horn pattern for number {*sg, i/e sum; *pl, at} >> *FUNCTN >> {*pl, i/e sum; *sg, at}
• introducing nominals that lack a number feature. The [Pl] feature is shared by the DP/NP and N. We are talking here of ‘variable introducing nominals’, because we leave the discussion of predicative nominals (‘Mary and John are good children’), as well as incorporated nominals outside the scope of our discussion (cf. footnote 1).
23
The optimization over form-meaning pairs under this ranking is spelled out in the bidirectional tableau 1, where singular and plural forms are paired up with their respective domain of interpretation in the lattice.
*sg, i/e sum
*pl at
*FUNCTN
*pl, i/e sum
*
*
*
*
*
*
*
*
*
*sg, at
Tableau 1: Optimization over singular/plural form-meaning pairs
All possible form-meaning combinations are listed in the first column. Atomic reference is represented as at, exclusive sum reference as sum, and inclusive sum reference as at∪sum. The four bias constraints, plus the markedness constraint *FUNCTN are ranked across the top, where the left-right order reflects a decreasing order of strength. The two bias constraints *sg, i/e sum and *pl, at are ranked above the markedness constraint *FUNCTN, but their mutual order is irrelevant, which is reflected in the dotted line between the two columns. Similarly, the two constraints *pl, i/e sum and *sg, at are both ranked below *FUNCTN, and their mutual order is also irrelevant, as marked by the dotted line. Because of the set-up with the bias constraints, all pair-meaning combinations incur one or more violations, marked by an asterisk * in the relevant cell. But the bias constraints penalizing the combination of singular forms with (inclusive or exclusive) sum reference and the combination of plural forms with atomic reference are ranked above the markedness constraint *FUNCTN, and drive the optimization over form-meaning pairs. The constraints mitigating against the combination of plural forms with (inclusive or exclusive) sum reference, or the combination of singular forms with atomic reference are ranked below *FUNCTN, and are de facto inactive in the optimization process. The tableau shows that we assign the (unmarked) singular form the (unmarked) meaning of atomic reference under strong bidirectional optimization, because is marked as a bidirectionally optimal pair ().
24
Intended sum reference calls for the use of a plural form. Both sum and at ∪ sum qualify as non-atomic reference, so plural forms have exclusive or inclusive sum reference. Accordingly, both and qualify as bidirectionally optimal pairs (). In line with Horn’s distribution of pragmatic labor then, unmarked forms pair up with unmarked meanings, and marked forms pair up with marked meanings. We spell out the truth conditions we obtain for singular and plural nominals under bidirectional optimization. There are three bidirectionally optimal pairs in Tableau 1. The singular form always conveys atomic reference, for there is no better interpretation for this form, and no better form to express this meaning. This takes care of the semantics of sentences like (1a), repeated here as (32a), with the truth conditions spelled out in (32b).
(32)
a.
Mary saw a horse.
b.
∃x: [x ∈ Atom & *Horse (x)] [Saw(m,x)]13
The singular DP contributes a variable x which is bound by an existential quantifier ∃ as a result of the contribution of the indefinite article.14 *Horse is the number neutral predicate (cf. Section 1.2 above). The condition x ∈ Atom is there because variables have to be marked for the type of value they have, and since there is no [Pl] feature on this nominal, the OT system discussed above imposes an atomic interpretation upon the singular nominal. The condition x ∈ Atom in (32b) is not contributed by the presence of a particular piece of morphology in (32a) but rather, by the absence of the feature [Pl]. The account we propose, therefore, allows explicit semantic information to be contributed on the basis of the OT system. As we saw above, the bidirectional optimization process uniquely fixes the interpretation of singular forms, but leaves two interpretations open for forms marked with the feature [Pl]. They correspond with the two meanings of exclusive and inclusive plural interpretation established in Section 1.1 for sentences like (1b) and (3a), repeated here as (33a) and (34a). Their truth conditions are spelled out in (33b) and (34b), respectively.
13
Throughout the paper we use First Order Predicate Logic formulas with restricted quantification. We put square brackets around the Restrictor and the Nuclear Scope, and use capitals to distinguish logical predicate constants from their naturel language counterparts. We disregard matters that are not directly relevant to us such as tense interpretation. 14 For the purposes of this paper, it is irrelevant whether we derive existential force of the indefinites in a static or a dynamic fashion; we focus strictly on truth conditions.
25
(33)
(34)
a.
Mary saw horses
[exclusive plural]
b.
∃x:[x ∈ Sum & *Horse(x)] [Saw(m,x)]
a.
Do you have children?
b.
? [∃x: [x ∈ Sum ∪ Atom & *Child(x)] [Have(addressee,x)]]
[inclusive plural]
The interpretation of [Pl] marked forms is driven by the bidirectional OT system. Because they are marked, such forms are incompatible with the unmarked meaning of atomic reference. This leaves open two possibilities: inclusive or exclusive sum reference. We assume that the feature [Pl] contributes inclusive or exclusive sum reference to the compositional semantics of nominals marked with it. This interpretation is imposed by the OT system we discussed above. Given that the semantics does not decide between the two interpretations (both are strong bidirectional pairs), a disambiguating principle is needed to ensure one or the other interpretation in contexts like (33) and (34). In Section 3 below, we appeal to the Strongest Meaning Hypothesis to do so. Note that since our analysis has not implicated particular determiners, it carries over straightforwardly to the definites in examples (22) and (23), repeated here as (35)-(37):
(35)
(36)
(37)
a.
Mary touched the horse.
b.
∃!x: [x ∈ Atom & *Horse(x)] [Touch(m,x)]
a.
Mary touched the horses.
b.
∃!x: [x ∈ Sum & *Horse(x)] [Touch(m,x)]
a.
In case of a divorce, the children will stay with the mother.
b.
GENs: [Divorce(s)] [∃!xs: [x ∈ Sum ∪ Atom & *Child(x)] [Stay_with_mother_of_x(x)]]
We take it that the prepositional phrase in case of a divorce restricts a generic operator, and that the rest of the sentence is the Nuclear Scope of this operator. An issue that is orthogonal to our present concerns is how the presupposition of the definite article is to be met. One possibility is to assume that there is a further contextual restriction of the relevant situations
26
introduced by the Restrictor to situations involving divorce and children; another possibility is to accommodate children in each situation quantified over by GEN. The definite article the combines with both singular and plural nouns, so number information on the DP percolates up from N. Other determiners, such as several or two convey plurality by themselves, and finally, the indefinite article a(n) or one can only occur with singular nominals. We take these distinctions to be lexically encoded in the relevant determiners. For the indefinite article, we assume that it is lexically restricted to atomic reference. We come back to the issue of determiners marked for sum reference in Section 4 below. Finally, note that the analysis of number in noun-headed nominals proposed here extends to number contrasts with pronominals for both English, where plural forms are suppletive, and a language like Hungarian, where sometimes they are not. Plural forms, we suggest, are marked with the feature [Pl] and require inclusive or exclusive sum reference, while ‘singular’ forms bear no number feature and receive an atomic interpretation by the same bidirectional OT mechanism we postulate for non-pronominal DPs. So far, we have captured the semantics of singular and plural indefinite and definite nominals as a result of bidirectional optimization over form-meaning pairs. The analysis is grounded in the morphological markedness of the plural, and respects Horn’s division of pragmatic labour. It thus captures the generalization that in languages with a binary number contrast, the singular is morphologically unmarked while the plural is morphologically marked. The analysis predicts atomic reference for singular nominals and inclusive or exclusive sum reference for plural nominals. In the next section we turn to the issue of the fate of these two interpretations of the plural.
3. The pragmatics of the plural
A welcome result of the analysis developed so far is that plural nominals are predicted to be interpretable as having either inclusive or exclusive sum reference. In Section 1 we saw that both interpretations are indeed available for such nominals. We also saw however, that the choice between them is not free: exclusive sum reference is the rule in upward entailing environments, as exemplified in (33) and (36), whereas inclusive readings are typically found in downward entailing environments such as negation, questions, or antecedents of
27
conditionals, as exemplified in (34) and (37).15 In Section 2 we developed a semantics that characterizes the space of meaning for plural nominals. In this section, we turn to the problem of predicting the choice between these two interpretations. We first propose a solution that relies on the independently motivated S(trongest) M(eaning) H(ypothesis), a pragmatic principle that can be constrained under contextual pressure (Section 3.1). We then examine in further detail the balance between semantics and pragmatics in order to shed light on the factors that govern the choice of form in downward entailing environments in cases exemplified in (20) and (25) above (Section 3.2).
3.1 Strongest meaning hypothesis for number
Dalrymple et al. (1998) propose the SMH to account for the contextual choice between a range of interpretations for reciprocals. Winter (2001) extends the principle to instances of Boolean conjunction and quantification. Zwarts (2004) exploits the SMH as part of his interpretation procedure for the preposition round. We will exploit SMH here to account for the choice between the inclusive and the exclusive sum interpretation of plural nominals. The SMH applies when an expression is assigned a set of interpretations ordered by entailment. The SMH chooses the strongest element of this set that is compatible with the context. Returning now to the interpretation of plural nominals, recall that the bi-directional optimization process developed in Section 2, assigns to the feature [Pl] in nominals the family of interpretations in (38):
(38)
Semantics of [Pl] a.
[[Pl]] = λx. x ∈ Sum
(exclusive interpretation of plural)
b.
[[Pl]] = λx. x ∈ Sum ∪ Atom
(inclusive interpretation of plural)
Note now that these two meanings are ordered by (truth-conditional) strength: (38a) asymmetrically entails (38b). This relationship, we claim, is crucial in determining the choice between interpretations in context because they fall under the jurisdiction of SMH. Our hypothesis is formulated as SMH_PL (the Strongest Meaning Hypothesis for Plurals): 15
Whenever relevant, the notion of downward entailment can be refined to ‘Strawson entailment’, e.g. in conditionals (cf. von Fintel 1999). Obviously, questions are not downward entailing, but they are subject to the same principle of scale reversal, as evidenced by the well-known fact that NPIs are licensed in all these environments (cf Ladusaw 1996 for an overview of the issues in NPI licensing).
28
•
SMH_PL:
the Strongest Meaning Hypothesis for plurals: prefer the stronger interpretation of
the plural nominal over the weaker one, unless the former conflicts with the context.
In upward entailing environments exemplified in (33) and (36), the SMH_PL favors the exclusive interpretation over the inclusive one because the exclusive interpretation is stronger in these contexts: (38a) asymmetrically entails (38b). In downward entailing environments and questions, the SMH_PL leads to the inclusive interpretation, because of scale reversal under monotonicity reversal (Fauconnier 1979, Sauerland 2003). The weaker, inclusive reading of the plural in such contexts leads to a stronger claim for the sentence as a whole (34, 37). We predict that, other things being equal, a plural is interpreted inclusively in downward entailing contexts and exclusively in upward entailing ones. This is indeed the situation we find in (33)/(34) and (36)/(37). The statement that Mary saw a plurality of horses is stronger than the claim that Mary saw one or more horses, so in line with the SMH_PL, we prefer the exclusive plural interpretation in (33b). Similarly, the statement that Mary touched a plurality of horses is stronger than the claim that Mary touched one or more horses, so SMH_PL favors the exclusive plural interpretation in (36b). If the question operator ranges over atomic and sum values for children, we obtain a more encompassing question than if we took it to range over sum values only, so we prefer the inclusive sum interpretation in (34b) and (37b). A yes or no answer therefore is more informative (i.e., stronger) if the question involves an inclusive plural, than in case the plural receives an exclusive interpretation. The SMH as advanced by Dalrymple et al. (1998), Winter (2001) and Zwarts (2004) is a pragmatic principle, and as such it can be overridden by contextual pressure. If SMH_PL is indeed responsible for the choice of interpretation for plural nominals, we expect pragmatic pressure to render it inoperative making inclusive interpretations available in upward entailing environments, and exclusive interpretations available in downward entailing environments and questions, under pragmatic pressure. As we saw in (33) and (36), exclusive sum reference is indeed the norm in upward entailing environments. Normally, we expect the speaker to know what Mary saw or touched (one horse or more than one horse). If Mary saw/touched one horse, the speaker should use a singular form, which is the best expression for conveying atomic reference, given the high ranking of the constraint *pl, at (cf. Tableau 1) (32, 35). If Mary saw/touched more than one horse, the speaker should use the plural form, given the equally high ranking of *sg, i/e sum. Under the assumption that the speaker knows what Mary saw, there is no possibility to 29
weaken (33a) or (36a) to an inclusive plural interpretation under the bidirectional optimization process spelled out in Section 2. This suggests that weakening to inclusive sum reference would only be possible in upward entailing environments in contexts where the speaker is assumed to lack information concerning the atomic/sum nature of the referent of the nominal. The examples in (39) illustrate just such a case:16
(39)
a.
(situation: speaker walks into basement, and notices mouse droppings): Arghh, we have mice!
b.
(situation: speaker walks into unknown house, and notices toys littering the floor): There are children in this house.
Crucially, the utterances in (39) are felicitous in situations in which the speaker finds positive indirect evidence for the presence of mice and children, but has no way of telling how many there are. Although the one-or-more interpretation is weaker in upward entailing contexts, it is a better fit in a situation of ignorance, where both atomic and sum reference are compatible with the speaker’s knowledge. Analogous cases are discussed in Zwarts (2004) in terms of a constraint FIT outranking the constraint STRENGTH. We will not spell out the interpretative tableaux here, but refer the interested reader to Zwarts (2004) for a way to do so. Note now that we find exclusive interpretations of plural forms in questions like (40):
(40)
a.
Does a worm have #an eye/eyes?
b.
Does/do #the wing/the wings of a butterfly have many colours?
Given that eyes and wings naturally come in pairs, the use of the singular in these questions is distinctly odd. Furthermore, note that an inclusive plural interpretation is highly unlikely here, a fact that is expected under our analysis. The stronger, inclusive interpretation favoured by SMH_PL in
downward entailing contexts and questions is cancelled here under pragmatic
pressure, thus predicting the exclusive interpretation in these contexts. Note that alternative analyses have to resort to pragmatics in order to rule out the possibility of an inclusive plural here. Relying on SMH_PL for choosing between inclusive and exclusive plural has the advantage of predicting the relevance of pragmatic factors and thus the unavailability of inclusive readings in examples such as (40).
16
The example in (39a) was suggested by a participant in ‘A bare workshop 2’ (LUSH, June 2008).
30
3.2 Choice of form
We examine here further cases where inclusive interpretations are unavailable in questions and downward entailing contexts and which therefore are problematic for ‘weak plural’ analyses. Consider the examples in (41):
(41)
a.
Does Sam have a Roman nose/ #Roman noses?
b.
Do you have #a high school diploma/high school diplomas?
c.
Does the stem of this plant leak a white liquid when you break it?
c’
#Do the stems of this plant leak a white liquid when you break them?
The examples in (41) are the mirror image of those in (40) in the sense that people naturally have only one nose, and one high school diploma, and plants naturally come with a single stem. Recall that such examples are problematic for the strong singular/weak plural analyses discussed in Section 1. In Sauerland et al. (2005), the principle of Maximize Presupposition must be invoked here, while in Spector (2007) an extra presupposition of ‘possible sum reference’ has to be added to the semantics of the plural (see Section 1.5.1 above). Under our analysis, the infelicity of the plural in (41) falls out as a restriction on the SMH_PL
by the bidirectional optimization approach. Questions normally favour an inclusive
interpretation of the plural, along the lines of Section 3.1 above. But in (41) the context imposes atomic interpretation for the relevant nominals. The use of the plural form is ruled out by the bidirectional OT system: sum values are pragmatically excluded and therefore the best form to express the intended meaning is the singular. Our analysis therefore predicts that even in environments in which the inclusive plural interpretation is favoured by the SMH_PL, when sum values are pragmatically excluded, the singular form is imposed under bidirectional optimization. Here then pragmatic pressure rules out sum values, which renders a plural form inappropriate given the OT system we have set up. In (40) and (41) the choice between singular and plural forms was sharp because the pragmatic pressure in favour of an exclusive plural or an atomic interpretation is strong. Let us now turn to examples such as (42), where the contrast is more subtle in the sense that both forms can be used, but the way they are interpreted is not the same.
(42)
Do you have an MA degree/ MA degrees? 31
Although it is in principle possible for students to accumulate several MA degrees, the normal situation is for a person to have a single such degree. This makes the use of the singular nominal the default in (42), just as in (41b). The most salient pragmatic distinction in the case of MA degrees is that between having one MA degree and having none. If the speaker is interested in this distinction, a singular is the optimal form to use because sums are not relevant. The marginal cases in which the addressee has more than one MA degree are taken to be special cases of having one such degree. The use of the plural form in a pragmatic situation where sum values are highly unusual signals that it is not the one/none distinction that is of interest to the speaker, but rather, the pragmatically more marked distinction between none, one on the one hand, and several on the other. The plural form here then will tend to be interpreted as exclusive, rather than as inclusive. The pressure here involves the relevance of sum reference, rather than the issue of whether sum reference is possible or not. In (41) sum reference is pragmatically ruled out; in (42), sum reference is pragmatically marginal and therefore the use of a plural form signals the importance of sum reference and thus, highlights the speaker’s interest in such values. In (42) the pragmatic pressure for the exclusive interpretation of the plural is rooted in general world knowledge about people’s higher degrees. Another source of pragmatic pressure that regulates the choice of the singular over the plural form is the relevance of atomic vs. sum values for the particular situation of utterance. This, we claim, is what regulates the choice of form in the broom example in (20), repeated here as (43).
(43)
a.
Do you have a broom/ #brooms?
[at home]
b.
Do you have #a broom/ brooms?
[in the store]
Recall that if the speaker spills some crumbs on the floor in the addressee’s kitchen, and kindly offers to help in cleaning it up, she would ask (43a), using a singular form; the use of the plural in such a case would be distinctly odd. If, however, the speaker is wondering whether the store she is in sells brooms, what she would ask a salesperson is (43b), using a plural form; the use of the singular here would be just as odd as the use of the plural in (43a). Note that there is no presupposition in the kitchen situation that the addressee would have only one broom, unlike in (41); nor is there any general knowledge that would lead us to assume that people have only one broom, if any, as in the case of (42). But just like in (42), what is assumed to be relevant given the situation, is the contrast between the addressee 32
having one broom vs. no broom whatsoever. How many brooms the addressee has is irrelevant for the purpose at hand, as long as she has one. Choosing the plural, therefore, is marked, since this form explicitly brings in the possibility of sum values, under our account. In the store, on the other hand, the general assumption is that if a store sells any brooms, it will sell several. Here then the pragmatically relevant contrast is that between several brooms and none whatsoever, and therefore the use of the plural form is the natural one. The two cases just discussed (the brooms and the MA degrees) contrast with the much discussed examples involving children. In the case of inquiring about children, the relevant pragmatic contrast is that between being a parent (i.e., having one or more children) vs. not being a parent (having no children whatsoever). Once it is established that one is dealing with a parent, the relevant question is how many children there are. The contrast between having several vs. none or one is not pragmatically relevant in our culture. This situation then fits an inclusive plural interpretation in downward entailing environments, which is what SMH_PL favours as well. The account we worked out is flexible enough to capture these subtle facts. In the OT system, what licenses the possibility of a plural nominal is the requirement that sums be among the values given to the variable the nominal introduces. Pragmatic pressure to include or exclude such values is predicted to play a role in whether a singular or a plural will be chosen. The account we have proposed then allows pragmatic pressure to be felt at two points: (i) at the choice between inclusive and exclusive interpretations for a plural form because that choice is regulated by the pragmatically sensitive SMH_PL principle and (ii) at the choice between a singular and a plural form, because that choice is regulated by the OT system which requires that sum values be relevant when a plural form is used.
3.4 Taking stock
In section 2, we took Horn’s division of pragmatic labor to heart, and developed an analysis of the singular/plural contrast in line with the view that unmarked forms are paired with unmarked meanings, and marked forms with marked meanings. For languages that establish a morphological singular/plural distinction on nominals, we assume that singular forms are unmarked and plural forms are marked, and that atomic reference constitutes the unmarked meaning while non-atomic reference is the marked meaning. Applying the model developed by Mattausch (2005, 2007), we derive three strongly optimal form-meaning pairs, namely 33
, and . The polysemous semantics of the plural (inclusive and exclusive sum reference) is thus grounded in the claim that reference that includes sums constitutes the marked meaning. Nothing in our analysis of nominal number interpretation makes crucial reference to determiners. We therefore predict that bare and definite plurals in English will be alike as far as number interpretation is concerned. The analysis in Section 2 then meets desiderata (i) and (ii) formulated in Section 1.6. In Section 3, we claimed that the choice between inclusive and exclusive plural interpretation is governed by the Strongest Meaning Hypothesis. We thus predict that, other things being equal, exclusive plural interpretations are preferred in upward entailing environments, while inclusive plural interpretations are preferred in downward entailing environments and questions. Given that SMH_PL is a pragmatic principle, it can be overruled by contextual pressure. The choice of a singular or plural form in typical problem cases like (20) and (25) is governed by the interaction of the SMH_PL with the bidirectional analysis. The proposals in this section meet desiderata (iii) and (iv). What remains to be investigated is the cross-linguistic validation of the analysis set up so far. Recall that in Section 1 data from Hungarian and Chinese were crucial in rejecting previous accounts of the singular/plural distinction. The last two desiderata in Section 1.6 concern the use of the singular with sum-reference entailing determiners in Hungarian and the number neutral interpretation of nominals in languages that lack morphological number marking, such as Chinese. In the next section we give a detailed account of the first problem, thus meeting desideratum (v). A full-fledged analysis of languages lacking morphological number goes beyond the scope of this paper. The proposals in Hendriks et al. (2009: Chapter 9) and de Swart and Zwarts (2008a) are compatible with the analysis developed here while at the same time predicting that the atom/sum distinction does not play a role in the interpretation of unmarked nominals in such languages. We will simply note here that in contrast with Farkas and de Swart (2003), we do not take atomic reference to be the default interpretation for nominals. Our current analysis is subtler in that it claims that if number interpretation is marked in a language, atomic reference is the unmarked interpretation and sum reference is the marked interpretation. This account then no longer predicts that in languages where number distinctions are not morphologically marked, unmarked nominals will be interpreted as atomic.
34
4. Plural determiners: a cross-linguistic perspective
So far we have concentrated on the interpretive contribution of the morphological number feature [Pl] when it occurs in nominals in argument position in languages like English, where a morphological distinction between singular and plural nominals is operative. With respect to determiners, we have assumed that they are either unmarked for number altogether (as in the case of the or some in English) or they come with lexical number restriction concerning the atomic or sum nature of the referent of the variable they introduce, as is the case with several, three or a(n). In English then, the definite determiner the combines with both singular and plural nouns, so in this case the restriction to atomic or sum reference is due only to morphological information coming from the noun. Indefinite singulars on the other hand contrast with bare plurals. We follow the literature in assuming that the primary role of the indefinite article a is to introduce a new discourse referent (Kamp and Reyle 1981, Kamp and van Eijck 1996). With Farkas and de Swart (2003), Hendriks et al. 2009, Chapter 7, de Swart and Zwarts 2008a, 2009). We further assume that there is no morphological number feature on this determiner. In our view, plural morphology contributes the requirement that the variable be given values that include sums. In the absence of an overt determiner, we take it that it can also introduce a new discourse referent via accommodation of a presupposition.17 Within the category of indefinites DPs, just like in the case of definites, number interpretation is primarily driven by the morphological singular/plural contrast on the noun, though the contrast may be reinforced by determiner choice. A DP headed by several can only refer exclusively to sums, while a DP headed by a(n) can only refer to atoms. The indefinite determiner some, however, has no inherent lexical restrictions pertaining to number interpretation. The core analysis set up in Sections 2 and 3, illustrated with English, extends to other languages that have a morphological number distinction such as Germanic or Romance languages as well as to non-Indo European language such as Hungarian. In DPs whose determiner does not contribute number information, we expect the effect of the feature [Pl] on the nominal to be the same as in English.
17
This view is spelled out in a revised version of Discourse Referential theory in which nouns and verbs come with thematic arguments, but discourse referents are normally introduced by determiners (articles, quantifiers). Farkas and de Swart (2003) take plurality to be a predicate that applies to discourse referents, not to thematic arguments. Thus they posit the existence of a presupposed discourse referent to which the plurality predicate applies. The presupposition of existence is bound by a determiner, or accommodated in the case of bare plurals.
35
In Section 1, however, we noted a contrast between English and Hungarian which has so far remained unaddressed. We saw there that in Hungarian, if the determiner is lexically marked for sum reference, such as három ‘three’ or sok ‘many’, the DP must be singular in form, rather than plural, as in English. These facts are problematic for a strong singular/weak plural account which has to treat the singular form of these DPs as different from ordinary singulars. In this section we extend the present account to cover this contrast between English and Hungarian. We first briefly review the facts, then discuss their implications and then work out an analysis.
4.1 A contrast between English and Hungarian
As outlined in Section 1.4, Hungarian is like English in distinguishing between singular and plural nominals, with the singular remaining unmarked and the plural being marked by the presence of the morpheme -(a)k. The facts of number interpretation in English that we discussed so far are parallel in Hungarian and therefore the analysis proposed for English extends to Hungarian as well. Recall, however, that there is a difference between the two languages when it comes to DPs whose determiner is lexically marked for sum reference. In English, such DPs have to be morphologically plural, while in Hungarian they have to be morphologically singular. We repeat the key relevant Hungarian facts in (44) (see examples in (12) above):
(44)
a.
három gyerek
[Hungarian]
three child ‘three children’ b.
sok
gyerek
many child ‘many children’
These DPs are singular in form (and trigger singular agreement with the V when in subject position) and yet they have exclusive sum reference. This environment then neutralizes the semantic contrast between singular and plural forms in Hungarian. We therefore conclude that in languages with a morphological number contrast, when the D is marked for sum
36
reference, there are two options: (i) mark the N (and therefore the DP) with the feature [Pl] (as in English); (ii) leave the N (and therefore the DP) unmarked, i.e., singular in form. In English then we have plural DPs such as three children, many children contrasting with their singular Hungarian counterparts, három gyerek, sok gyerek. The difference between the two languages is purely morphological -- the semantic interpretation of the DPs is identical. We turn to an account of these facts after we review their significance for competing analyses of number.
4.2 Implications for the weak/strong singular debate
Note that if we analyze a determiner such as three as a generalized quantifier expressing existential quantification over a discourse referent x with cardinality of at least three, the semantics of the DP three children / három gyerek is spelled out as in (45), where we use Nsg as shorthand for the Hungarian case, where the N (and the DP) are singular in form, and Npl as shorthand for the English case, where the N (and the DP) are marked with the feature [Pl]: 18
(45)
a.
||three Nsg|| = λP ∃x: [N(x) & |N| ≥ 3] [P(x)]
(weak singular)
b.
||three Nsg|| = λP ∃x: [N(x) & Atom(x) & |N| ≥ 3][P(x)
(* strong singular)
c.
||three Npl|| = λP ∃x: [N(x) & |N| ≥ 3] [P(x)]
(weak plural)
d.
||three Npl|| = λP ∃x: [N(x) & Sum(x) & |N| ≥ 3][P(x)
(strong plural)
In order to obtain the intended meaning, the fact that the N is singular should have no interpretive consequence here. The weak interpretation of the singular in (45a) yields the desired interpretation, but the strong singular semantics in (45b) does not, which is why the Hungarian facts are problematic for ‘strong singular’ accounts while being at least compatible with a ‘weak singular’ account such as the one we propose. When the N is plural, both the weak and the strong plural analyses yield the right interpretations. Under a weak plural account, the plural feature does not contribute any number information, while the determiner introduces a plural discourse referent (45c). Under the strong plural analysis advocated here, 18
The semantics spelled out in (45) may be an oversimplification, given the more fine-grained analyses of the differences in meaning between three children and at least three children that have been offered in the recent literature (cf. Nouwen and Geurts 2007 and references therein). However, the observations made in these works are tangential to the issues at stake in this paper, because they focus on the role of the determiner, not the singular/plural distinction on the noun. So we ignore these complications in this paper.
37
the plural morphology on the noun conveys (exclusive) sum reference (45d). Note that the contribution of the plural morphology here is redundant, given that sum reference is already entailed by the contribution of the determiner. The presence of the plural morphology here is not needed but it isn’t harmful either. This contrasts with the assumption that singular nominals have a semantically potent singular feature, which leads to harm in (45b). The facts with determiners like many or several are parallel to those given in (45). We see in (45) that the contrast between English and Hungarian does not raise any problems for the semantic analysis of the plural feature proposed here. It is, however, problematic for a strong singular hypothesis since it leads to a contradictory interpretation for the Hungarian case schematized in (45b). We take these facts to constitute an important argument in favor of the weak singular/strong plural approach. The particular weak singular/strong plural analysis developed in Section 2 derives atomic reference for singular nominals under bidirectional optimization. We crucially need this mechanism in Hungarian as well in order to assign the correct interpretation of ordinary Hungarian singular and plural definites and indefinites such as a gyerek ‘the child’ and a gyerekek ‘the children’, which behave just like their English counterparts. Note now that the analysis does not predict atomic reference for the singular forms in (44). Crucially, our account is based on a competition between two forms available to express two distinct meanings. But the truth interpretations in (45) show that there is no difference in meaning between a singular and a plural noun form when the determiner that heads the DP lexically entails sum reference: the contribution of the plural morphology in this case is redundant. Because there is no crucial interpretive difference between three Nsg and three Npl we claim that the bidirectional optimization over form-meaning pairs spelled out in Section 2 above does not apply in these cases. In view of the equivalence between singular and plural nominals in DPs headed by ‘semantically plural’ determiners, both English three Npl and Hungarian három Nsg are compatible with the analysis developed so far in this paper. But there is one further issue that needs to be addressed. Although the singular/plural contrast on nouns is semantically neutralized in contexts where the determiner entails sum reference, the choice between a singular or a plural form is not free. In both languages under consideration, the alternative form is ungrammatical, that is, *három gyerekek (‘three child_pl) is as ill-formed in Hungarian, and *three child is ungrammatical in English. So languages typically grammaticalize just one of the two options. The question that needs to be answered is what drives the choice between these two forms in the grammar. This is a question that has not been addressed in the current literature on number interpretation. In the 38
next section we work out an analysis in which the presence of the feature [Pl] in the English three children, many children is treated as resulting from an agreement-like requirement imposing the presence of [Pl] on sum denoting nominals. Its absence in the corresponding Hungarian három gyerek, sok gyerek is seen as a choice dictated by economy considerations that militate against the use of marked forms when redundant. We work out these intuitions in the next subsection, relying on a unidirectional OT syntactic analysis.
4.3 A unidirectional OT analysis
We claim that the contrast between English and Hungarian nominals headed by a semantically plural determiner instantiates a shallow syntactic difference, which arises in a situation in which two forms are available for independent reasons, but there is no difference in meaning associated with them in the context at hand. This calls for a unidirectional syntactic OT analysis that establishes a more fine-grained distinction within the set of languages under consideration. We embed our analysis in an OT typology of number in a classical OT formulation in terms of markedness and faithfulness constraints. Recall that in Section 2 we exploited the economy constraint *FUNCTN that favours the least number of functional layers on top of the NP. If we assume that the plural feature [Pl] lives in the functional projection of NumP and cardinals and indefinite determiners live in D, the presence of such expressions constitutes a violation of *FUNCTN. Such violations are motivated by the need to satisfy faithfulness constraints that are ranked above *FUNCTN. One of these, is the constraint FPL, favouring the expression of sum reference in a functional layer above NP.19
(49)
FPL:
Sum reference must be encoded in the functional structure of the nominal.
Languages that do not establish a morphological singular/plural distinction on the noun (such as Mandarin Chinese, cf. Section 1.5 above) rank FPL below *FUNCTN (see de Swart and Zwarts (2008a). We assume that FPL outranks *FUNCTN in both English and Hungarian. The cases in Sections 2 and 3 dealt with cases where the semantic contribution of plural forms was
19
Note that the formulation of the constraint FPL here is slightly different from that in de Swart and Zwarts 2008a, 2009, where we did not deal with the complexities of cardinals and indefinite plural determiners, but focused on ‘plain’ definites and indefinites.
39
not redundant and we saw that English and Hungarian are alike in those cases. For these cases we can identify FPL with the bias constraints *pl, at and *sg, i/e sum. The grammar FPL >> *FUNCTN then corresponds with the grammar {*sg, i/e sum; *pl, at} >> *FUNCTN >> {*pl, i/e sum; *sg, at} we proposed earlier. But the formulation of FPL is more general, and allows the expression of number distinctions by other elements in the functional layer above the NP as well. Under the assumption that the Hungarian semantically plural determiners három and sok satisfy FPL, there is no reason to attach a plural morpheme to the noun. In fact, the markedness constraint *FUNCTN forbids its realization as a redundant expression of plurality in the nominal domain. Tableaux 2 and 3 illustrate the optimization process for the plural definite a gyerekek (‘the children’) and the cardinal három gyerek (‘three child’).
Meaning:
FPL
*FUNCTN
∃!x: [Sum(x) & Child(x)] a gyerek
*
*
the child.sg
a gyerekek
**
the child.pl
Tableau 2: expressive optimization for definite plurals (Hungarian)
Meaning:
FPL
*FUNCTN
∃x: [Child(x) & |Child| ≥ 3]
három gyerek
*
three child.sg három gyerekek
**
three child.pl
Tableau 3: expressive optimization for plural cardinals (Hungarian)
40
In both the definite plural, and the cardinal plural, we find a violation of *FUNCTN because of the presence of an expression in the functional projection of D.20 Of course, the input meaning involves sum reference, and the high ranking of FPL in the grammar of Hungarian requires satisfaction of this constraint at the expense of the economy constraint *FUNCTN. Given that the definite article a does not convey number information, the optimal plural nominal form incurs a second violation of *FUNCTN in Tableau 2. In Tableau 3, there is no reason to use a plural form of the nominal, given that the lexical semantics of the cardinal D három entails sum reference, and may therefore be taken to satisfy FPL. A singular form of the noun is more economical, and is therefore preferred. In OT terms, the use of a singular noun in combination with an inherently plural determiner exemplifies the emergence of the unmarked. The ranking FPL >> *FUNCTN is sufficient to account for Hungarian, but does not yet capture the cross-linguistic contrast between Hungarian három gyerek (‘three child’) and English three children. To capture the intuition that the use of a plural noun in English in these cases is motivated by agreement in number between the plural determiner and the noun we posit an additional constraint MAXPL.
(50)
MAXPL:
Mark with [Pl] nominals that have sum reference.
Unlike FPL, MAXPL favours redundant marking of plural morphology on the noun, at the expense of extra violations of *FUNCTN. The advantage of this multiplication of plural marking is the emphasis on sum reference. MAXPL is inspired by de Swart’s (2006, 2009) analysis of negative concord in terms of semantic agreement. De Swart posits a constraint FNEG
requiring faithfulness to the expression of negation, and MAXNEG requiring a reflection
of negation on an indefinite argument within the scope of negation on the form of the nominal. The high ranking of MAXNEG in negative concord languages leads to a multiplication of negative forms even in context in which they are not needed to satisfy FNEG, and thus convey semantic negation. Along similar lines, we suggest that the use of plural nominals in contexts in which the determiner already conveys sum reference, and thereby satisfies FPL is governed by a high ranking of MAXPL. We assume that the grammar of Hungarian has the ranking FPL >> *FUNCTN >> MAXPL, whereas English exemplifies the grammar { FPL, MAXPL } >> *FUNCTN. For Hungarian, the introduction of the new constraint does not affect the optimization patterns spelled out in Tableaux 2 and 3, because MAXPL is ranked too 20
The presence of the definite determiner a is licensed by a high ranking of the faithfulness constraint FDEF governing the expression of definiteness (see Hendriks et al. 2009, chapter 7, de Swart and Zwarts 2008a, 2009).
41
low to have an effect. For English, the new ranking leads to the optimal form three children for the expression of cardinality information over children, as illustrated in Tableau 4:
Meaning:
FPL
MAXPL
*FUNCTN
∃x:[Child(x) & |Child| ≥ 3] three child
three children
*
* **
Tableau 4: expressive optimization for plural cardinal meaning (English)
Sum reference is entailed by the cardinal determiner three, so FPL is satisfied, just like in Hungarian. However, the constraint MAXPL maximizes the expression of plurality by forcing it to appear on the noun as well. The high ranking of this constraint in English leads to a preference of agreement between the determiner and the noun over a more economical form. In Hungarian, the constraint MAXPL is ranked below *FUNCTN, where it is inoperative. Independent support in favor of our analysis comes from L1 acquisition. Children acquiring a double negation language such as standard English sometimes go through a phase in which they multiply negation as if they were speaking a negative concord language. Along similar lines, Hungarian children sometimes mistakenly use the form *három gyerekek (‘three children’) before they acquire the grammatical három gyerek (‘three child’). Even though anecdotal, this evidence suggests that child grammar favours agreement both for negation and number marking. The analysis of the contrast between Hungarian and English is not in conflict with the bidirectional optimization process developed in Section 2, but covers a niche where the competition in form evades the competition in meaning. With inherently plural determiners, the determiner entails sum reference for the nominal as a whole, and thus makes irrelevant the semantic competition between singular and plural forms. In languages with a morphological singular/plural distinction, this creates room for a new competition between unmarked (singular) and marked (plural) forms. In the absence of a difference in meaning, the optimal expression is selected on purely formal grounds. The competition here is between economy of
42
form (exemplified by Hungarian), and agreement between D and N (exemplified by English).21 We conclude that Hungarian and English are both members of the class of languages with a full-fledged morphological singular/plural distinction on the noun, and a grammar in which FPL is ranked above *FUNCTN. However, there are subclasses within this general class, that exploit contrasts in form for other purposes than to express a distinction between atomic and sum reference. Given that agreement in number between determiner and noun is available only in languages with a morphological singular/plural distinction (instantiating FPL >> *FUNCTN), we predict such subtleties not to occur in languages lacking number morphology.
5. Conclusion
The three main ingredients of our account of the puzzles of number marking dealt with in this paper are a bidirectional OT analysis of the competition between marked and unmarked forms, the Strongest Meaning Hypothesis extended to plurals, and a unidirectional analysis of agreement in plural marking within DPs. The analysis of number interpretation and number morphology developed here has two main advantages over competing proposals. Unlike the strong singular/weak plural approaches, it respects Horn’s division of labor, which we take to be a strong conceptual advantage. Our approach is close in spirit to Spector’s proposals. The crucial distinction is that we do not have to resort to the special notion of higher order implicatures. The tools we use instead are established techniques for optimisation over formmeaning pairs and the independently motivated principle of the Strongest Meaning Hypothesis. On the empirical side, an advantage of the account we propose is that it does not crucially rely on what the determiner is and therefore it generalizes to both indefinite and definite DPs. The interaction of the SMH_PL with pragmatic factors allows us to achieve a better empirical coverage than previous analyses when it comes to accounting for the subtle or not so subtle contrasts found in the choice between inclusive and exclusive interpretations of plural forms, as well as the choice of singular or plural forms in inclusive plural friendly environments. Finally, we saw that the analysis we propose fairs well with respect to cross21
We use the term ‘agreement’ here to cover not only cases where morphological features are shared but also cases where the presence of a morphological feature on one node is connected to the presence of a semantic constraint on another. Our account therefore is compatible with a morphological treatment of English which does use [Pl] as a feature on Ds.
43
linguistic data and accounts for the difference between English and Hungarian when it comes to number marking on DPs whose D entails sum reference.
References
Beaver, David (2002). The optimization of discourse anaphora, Linguistics and Philosophy 27, 3-56. Beaver, David and Hanjung Lee (2004). Input-output mismatches in OT, in Reinhart Blutner and Henk Zeevat (eds.). Optimality theory and pragmatics, Palgrave/MacMillan, 112153. Blutner, Reinhard (1998). Lexical pragmatics, Journal of Semantics 15, 115-162. Blutner, Reinhard (2000). Some aspects of optimality in natural language interpretation, Journal of Semantics 17, 189-216. Blutner, Reinhard (2004). Pragmatics and the Lexicon, in: Laurence Horn and Gregory Ward (eds.). Handbook of pragmatics, Oxford: Blackwell, 488-514. Chierchia, Gennaro (2006). Broaden your views: implicatures of domain widening and the “logicality” of natural language, Linguistic Inquiry 37, 535-590. Corbett, G. ( 2000). Number, Cambridge University Press, Cambridge. Dalrymple, Mary, Kanazawa, Makoto, Kim, Yookyung, Mchombo, Sam and Peters, Stanley (1998). Reciprocal expressions and the concept of reciprocity, Linguistics and Philosophy 21, 159-210. Farkas, Donka F. and Swart, Henriëtte E. de (2003), The semantics of incorporation: from argument structure to discourse transparency, CSLI Publications, Stanford: CA. Farkas, Donka F. ( 2006). The unmarked determiner, in: S. Vogeleer and L. Tasmowski-de Rijk (eds.). Non-definiteness and plurality, John Benjamins, Amsterdam, 81-106. Fauconnier, Gilles (1979). Implication reversal in natural language, in: F. Guenther and S.J. Schmidt (eds.). Formal semantics and pragmatics for natural languages, Reidel. Feigenson, Lisa and Susan Carey (2003). Tracking individuals via object files: evidence from infants’ manual search, Developmental Science 6, 568-584. Feigenson, Lisa and Susan Carey (2005). On the limits of infants’ quantification of small object arrays, Cognition 97, 295-313. Feigenson, Lisa, Susan Carey and Marc Hauser (2002). The representations underlying infants’ choice of more: object files versus analog magnitudes, Psychological Science 13, 150-156. 44
von Fintel, Kai (1999). NPI-licensing, strawson entailment and context-dependency, Journal of Semantics 16, 97-148. von Fintel, Kai and Lisa Matthewson (2008). Universals in semantics, the Linguistic Review 25, 139-201. Greenberg, Joseph (1966). Language Universals, Mouton, the Hague. Hauser, Marc, Susan Carey and L.B. Hauser (2000). Spontaneous number representation in semi-free-ranging rhesus monkeys, Proceedings of the Royal Society of London: Biological Sciences, 267, 829-833. Heim, Irene (1991). Artikel und Definitheit, in: Arnim von Stechow & Dieter Wunderlich (eds.). Handbuch der Semantik, Berlin: De Gruyter. Hendriks, Petra, de Hoop, Helen, Swart, Henriëtte de, and Zwarts, Joost (2009). Conflicts in Interpretation, Equinox Publishing (to appear). Horn, Laurence (2001). A natural history of negation, CSLI Publications, Stanford CA. Ionin, Tania and Ora Matushansky (2006). The composition of complex cardinals, Journal of Semantics 23/4, 315-360. Jakobson, Roman (1939). Signe zéro, in: Mélanges de linguistique offerts à Charles Bally, Genève (also in Selected Writings II). Jäger, Gerhard (2003). Learning constraint sub-hierarchies, in: R. Blutner and H. Zeevat (eds.). Pragmatics and Optimality Theory, Houndmills: Palgrave MacMillan, 251-287. Kamp, Hans and Uwe Reyle (1993). From discourse to logic, Dordrecht: Kluwer Academic Publishers. Kamp, Hans and Jan van Eijck (1996). Representing discourse in context, Johan van Benthem & Alice ter Meulen (eds.). Handbook of Logic and Linguistics, Amsterdam: Elsevier, 179-237. Kester, Ellen-Petra and Christina Schmitt (2007). Papiamentu and Brazilian Portuguese: a comparative study of bare nominals, in M. Babtista and J. Guéron (eds.). Noun phrases in Creole languages: a multi-faceted approach, Amsterdam: Benjamins, 107-144. Kirby, Simon and Jim Hurford (1997). The evolution of incremental learning: language, development and critical periods, in: Antonella Sorace, Caroline Heycock and Richard Shillcock (eds.). Proceedings of the GALA ’97 conference on language acquisition HCRC, Edinburgh University. Kouider, Sid, Justin Halberda, Justin Wood and Susan Carey (2006). Acquisition of English number marking: the singular-plural distinction, Language learning and development 2, 1-25. 45
Krifka, Manfred (1989). Nominal Reference, Temporal Constitution and Quantification in Event Semantics". In R. Bartsch, J. van Benthem, P. von Emde Boas (eds.), Semantics and Contextual Expression, Dordrecht: Foris Publication. Krifka, Manfred (1995). Common nouns: a contrastive analysis of English and Chinese, in G.N. Carlson & F. J. Pelletier (eds.), The Generic Book, Chicago University Press 1995, 398-411. Kwon,
Song-Nim
and
Anne
Zribi-Hertz
(2006).
Bare
objects
in
Korean:
(pseudo)incorporation and (in)definiteness. In: S. Vogeleer and L. Tasmowski-de Rijk (eds.). Non-definiteness and plurality, John Benjamins, Amsterdam, 107-132. Link, Godehard (1983). The logical analysis of plural and mass nouns: a lattice-theoretic approach, in: R. Bäuerle et al. (eds.), Meaning, use and interpretation of language, de Gruyter, Berlin, 302-323. Mattausch, Jason (2005). On the optimization and grammaticalization of anaphora, PhD dissertation, Humboldt University Berlin, published as ZAS Papers in Linguistics 38. Mattausch, Jason (2007). Optimality, bidirectionality & the evolution of binding phenomena, Research on Language & Computation 5, 103-131. McCawley, Jim (1981). Everything that linguistis have always wanted to know about logic (but were ashamed to ask), Chicago: University of Chicago Press (2nd edition 1993). Nouwen, Rick and Bart Geurts (2007). At least et al.: the semantics of scalar modifiers, Language 83, 533-559. Rullmann, Hotze (2003). Bound-variable pronouns and the semantics of number, in: Proceedings of the Western Conference on Linguistics, WECOL 2002, vol. 14, 243-254. Rullmann, Hotze and Aili You (2003). General number and the semantics and pragmatics of indefinite bare nouns in Mandarin Chinese, ms. UBC. Sauerland, Uli (2003). A new semantics for number, in: SALT 13, 258-275. Sauerland, Uli, Anderssen, J. and Yatsushiro, J. (2005). The plural is semantically unmarked, in: S. Kepser and M. Reis (eds.), Linguistic Evidence, de Gruyter. Sauerland, U. (2008). On the Semantic Markedness of Phi-Features, in Harbour, D. et al. (eds.), Phi Theory, Oxford: Oxford University Press, 57-83. Spector, Benjamin (2003). Plural indefinite DPs as plural polarity items, in: J. Quer et al. (eds.). Romance Languages and Linguistic Theory 2001, Amsterdam: John Benjamins, 295-313.
46
Spector, Benjamin (2007). Aspects of the Pragmatics of Plural Morphology: On Higher-Order Implicatures, in Sauerland, U. and P. Stateva (eds.), Presuppositions and Implicatures in Compositional Semantics, Palgrave-Macmillan, 243-281. Swart, Henriëtte de (2006). Marking and interpretation of negation: a bi-directional OT approach. In: Zanuttini, Raffaella, Héctor Campos, Elena Herburger and Paul Portner (eds.). Negation, tense and clausal architecture: cross-linguistic investigations. Georgetown: Georgetown University Press, 199-218. Swart, Henriëtte de (2009). Expression and interpretation of negation: an OT typology, Dordrecht: Springer (to appear). Swart, Henriëtte de and Joost Zwarts (2008a). Article use across languages: an OT typology, in: Atle Grønn (ed.). Proceedings of Sinn und Bedeutung 12, University of Oslo, 628644. Swart, Henriëtte de and Joost Zwarts (2008b). Less form, more meaning: why bare nominals are special, Lingua (in press). Swart, Henriëtte de and Joost Zwarts (2009). Optimization principles in the typology of number and articles, Bernd Heine and Heiko Narrog (eds.). Handbook of linguistic analysis, Oxford University Press (to appear). Winter, Yoad (2001). Plural predication and the strongest meaning hypothesis, Journal of Semantics 18, 333-365. Wood, Justin, Sid Kouider and Susan Carey (2004). The emergence of the singular/plural distinction, poster presented at the biennial International Conference on Infant Studies, Chicago. Zwarts, Joost (2004). Competition between word meanings: the polysemy of around, in: Proceedings of Sinn und Bedeutung, Konstanz, 349-360. Zweig, Eytan (2006). The implications of dependent plural readings, in C. Davis et al. (eds.). Proceedings of NELS 36, pp. 735-746.
47
