1. Introduction

This paper examines a characteristic which I will call "multiple plurality", where the conjunction of two morphologically plural predicates requires a subject whose denotation consists of at least four individuals. I argue that this should be taken as evidence that plural expressions only include plural entities in their extension, and as evidence for the existence of cumulative ("non-Boolean") conjunction on predicates.

As an example, think of the following situation: a teacher is asked to send all the children of medium height to participate in a play; however, the class only consists of tall children and short children. The teacher can explain why no children were sent by uttering (1) in Hebrew or (2) in English:

(1) ha-yelad-im gvoh-im ve-nemux-imthe-child-pl tall-pl and-short-pl (2) The children are tall and short. The two sentences above appear like straightforward translations of one another; however, they are not exactly synonymous. English (2) can also be uttered by a parent of two children, one tall and one short, while Hebrew (1)requires at least two tall children and two short children to make the sentence true. It is natural to attribute this characteristic of multiple plurality in Hebrew to the plural morphology that appears on each of the conjuncts. A similar thing happens in Spanish: each conjunct is marked with plural morphology, and the sentence receives a multiple plurality interpretation.

(3) Esos ni~no-s son alto-s y bajo-sthose child-pl are tall-pl and short-pl \Lambda This paper was presented at WCCFL 20 at USC, and in a different form at TLS at the University of Texas; travel support from the Graduate School--New Brunswickis gratefully acknowledged. I thank the participants at both conferences for their comments and insights. I owe particular thanks to Chris Barker, Rajesh Bhatt, Jos'e Camacho, Sandy Chung, Veneeta Dayal, Beto Elias, Manuel Espa~nol Echevarr'ia, Ed Keenan, Chris Kennedy, Hilda Koopman, Frida Morelli, Vieri Samek-Lodovici, Barry Schein, Phillippe Schlenker, Roger Schwarzschild, Yael Sharvit, Karina Wilkinson, and Yoad Winter. Of course, the responsibility for the views expressed in this paper, as well as any resulting inadequacies, is solely my own.

c fl 2001 Ron Artstein. WCCFL 20 Proceedings, ed. K. Megerdoomian and L. A. Bar-el, pp. 29-42. Somerville, MA: Cascadilla Press.

(For reasons unclear to me, Spanish speakers only accept this sentence with esos ni~nos "those children" in the subject, not with los ni~nos "the children". While many speakers of Spanish and Hebrew require that there be at least two children of each height, some are content with two of one height and only one of the other; all speakers reject the sentences if there is one child of each height. I will ignore this variability now, accepting the majority judgment.)

The goal of this work is to explain how the multiple plurality requirementcomes about, and the consequences this has on our understanding of plurality and conjunction. Multiple plurality receives a straightforward explanation if we accept the following assumptions.

(4) Plural morphology in (1) and (3) is interpreted literally as semantic plurality: the morphologically plural expressions only include pluralities in their extension. (5) Cumulative (plural-forming, "non-Boolean") conjunction is available foradjectives as well as for nominals.

Literal interpretation of the plural morphemes (Chierchia 1998) ensures thateach conjunct will be instantiated by at least two individuals; cumulative conjunction (Krifka 1990) allows conjoined adjective phrases like tall and shortto have a denotation with mixed referents, some of which are tall while the others are short. Cumulative conjunction of plural predicates thus results in amultiply plural predicate.

However, cumulative conjunction and multiple plurality are not as common as we might expect them to be. This is because the availability of cumulative conjunction is restricted by two additional factors.

(6) Cumulative conjunction of adjectives is only available in cases of conjunction weakening.

(7) Syntactic number agreement is needed independently of semantic interpretation of plural morphology.

Conjunction weakening (Winter 1996, 1998) allows cumulative conjunction of non-nominals only when their meanings are incompatible, that is when intersective ("Boolean") conjunction is contradictory; syntactic number agreement does not allow the coordination of singular adjectives to be plural, blocking the cumulative conjunction of singular adjectives. The rest of the paperexamines the above four claims in detail.

2. The representation of plurality

In order to account for the facts in (1)-(3) we need a theory of plurality. I will assume a structured domain of individuals, where plural objects are of the same type as singular individuals, namely type e (Leonard and Goodman1940). The choice of representing pluralities as mereological sums rather than sets is just a matter of convenience, in order to keep the types low. The domain of individuals has the structure of a free i-join semilattice (in the terms of Landman 1991), which is isomorphic to a structure where plurals are freely formed sets of individuals. My claim is that expressions that bear plural morphology only include plural objects in their extensions, and thus contrast with expressions that lack number marking. English tall is unspecified for number; it has both singular and plural objects in its extension, and is closed under plural formation (8).

Hebrew gvoh-im has an overt plural morpheme, so it only has plural elements in its extension; it is the closure under plural formation of singular gavoah, minus the singular individuals (9). I use direct interpretation and set notation in my representation; in the metalanguage AT is a function which returns the set of atomic individuals that make up a plural object, and PL is the set of all plural objects (individuals that are not atomic).

(8) [[tall]] = faj8a1 2 AT(a)[a1 2 [[tall]]]g (9) [[gvoh-im]] = faja 2 PL ^ 8a1 2 AT(a)[a1 2 [[gavoah]]]g

The assumption that morphologically plural expressions do not include singularities in their denotation is not unproblematic. Examples like (10) below (van Eijck 1983) suggest that morphologically plural common nouns like men should include singularities (individual men) in their extension, because the sentence is false if even one man walks.

(10) No men walk.

The argument goes as follows: examples like (10) suggest that singularities need to be included in the extension of plural expressions; this assumption does not pose other problems to the semantics of plurals; so it is safe to conclude that as a general rule, extensions of plural expressions include singular individuals. The above argument rests crucially on the second premise, that the inclusion of singularities in the extension of plural expressions does not do any harm. An obvious challenge to this premise is that a sentence like I saw boys in the park is judged false if I only saw one boy. This can be argued to be a matter of pragmatics: the sentence may be semantically true, but pragmatically inappropriate given the alternative expression I saw a boy in the park. This pragmatic account does not generalize to the cases of multiple plurality. A situation with one tall child and one short one cannot be characterized by the Hebrew sentence (1). Yet there is no alternative sentence with singular expressions: sentence (11) is ungrammatical (the source of ungrammaticality will be discussed in more detail in section 5). 20 (11)*ha-yelad-im gavoah ve-namuxthe-child-pl tall. sg and-short. sg

If the plural expressions gvoh-im and nemux-im include singularities in their denotations, we expect Hebrew (1) to be semantically true for two children, one of whom is tall and the other short, just like English (2). The pragmatic account given above fails to explain why the sentence is inappropriate.

Chierchia (1998) makes another argument against including singularities in the extension of plural expressions: he argues that it explains why mass nouns do not appear in the plural. In his theory, expressions with plural morphology receive a denotation that is disjoint from that of the corresponding singular expressions; mass nouns are inherently plural, so with plural morphology they end up denoting nothing. In response to examples like (10), Chierchia rejects the naive interpretation that no requires disjointness of its restrictor (men) and scope (walk); instead he proposes that no operates on the ideal generated by its restrictor, where an ideal p

(a) is defined as the set of all elements which are components of the join of a:

fbjb ^

W a

g. This allows him to maintain the idea that plural expressions only include pluralities in their extension. Chierchia has provided a solution for the problem of the quantifier no; something similar could be done for only (Hoeksema 1983), treating it as a quantifier of some sort. However, the problem posed by (10) is much more pervasive. Plural expressions appear to include singularities in their denotation in a variety of negative contexts (the following are modeled after examples by Karina Wilkinson and Roger Schwarzschild, respectively). (12) It is not the case that students from Germany came to the conference. (13) Students from Germany failed to come to the conference.

In a situation where one student from Germany came to the conference, arethe above sentences true or false? A naive interpretation of it is not the case as propositional negation and of failed to come as the complement of came would predict that if plural expressions denote literal pluralities, the sentences are true in the above situation, but if plural expressions include singularities in their extension then the sentences are false. On the most accessible reading, sentences (12) and (13) are indeed false, pointing toward the inclusion of singularities in the denotation of plural expressions. However, I believe that at least (12) can also be construed as true, if there is a pitch accent on students. The source of the ambiguity is the negative expression, and the latter interpretation looks like a case of "external negation" (Horn 1985), where it is exactly plurality which is denied.

It appears then that Chierchia was right in identifying the negative expression in (10) as the reason the common noun men looks as if it ranges over singularities and pluralities alike, but he was wrong in describing this as a lexical property of the quantifier no. Rather, the applicability of men to singularities should be tied to the fact that it appears in a negative context, in a way that is yet to be explained. The ambiguity of (12) shows that even in negative contexts it is possible to pick out plural denotations for common nouns.

I conclude that the assumption that plural expressions include singularities in their extension is no less problematic than the assumption I make, that plural expressions only denote pluralities; the difference between negative and positive contexts should be addressed through an examination of the semantics of negative expressions. In the meantime it is safe to assume that plural morphology is interpreted literally as semantic plurality; this literal interpretation forms the first part of the explanation of multiple plurality. 3. Cumulative conjunction of predicates

The other element in the account of multiple plurality is the interpretation of conjunction. The most basic meaning of the English word and andits counterparts in other languages is often considered to be propositional conjunction--a binary operation on truth values that is true in case both of the operands are true, false otherwise. This accounts for the use of and between sentences. The use of and between other constituents can be explained via a general type shifting paradigm which interprets all constituent coordination at the propositional level (Gazdar 1980; Partee and Rooth 1983). I will call this use intersective conjunction. Some uses of the word and, however, appear to fall outside this paradigm. For example, sentence (14) is not equivalent to (15). (14) John and Mary met. (15) John met and Mary met.

Given our theory of plurality, this non-equivalence receives a natural explanation if the coordinate subject of (14) is taken to denote a plural object, the join of John and Mary. Following Link (1983), I will assume that when and coordinates individuals of type e it can denote the join operation; I use the symbol \Phi in the metalanguage to stand for this operator.

(16) [[John and Mary]] = [[John]] \Phi [[Mary]]

This use of and will be called cumulative conjunction; it is argued to apply in the nominal domain, at least for referring nominals (Hoeksema 1988). Cumulative conjunction on type et will be defined in (22) below. My claim is that the multiple plurality requirement in (1) is evidence for the existence of cumulative (plural-forming) conjunction not only on nominals, but on adjectives as well (cf. Krifka 1990; Sharvit 1999). An alternative possibility is that the coordinate predicate in (1) may actually be a nominal, perhaps with the adjectives as modifiers of a null pronoun, meaning something like "tall ones and short ones" (Hilda Koopman, personal communication). Hebrew does allow lexical adjectives to act as nominals in certain contexts, as in the following sentence.

(17) ha-namux (ha-ze) hu sofer mefursamthe-short the-this PR writer famous"The/this short [person] is a famous writer"

Notice however that predicative nominals usually require a pronominal cop-ula (glossed as PR in the above example), while the adjectives in (1) appearwithout such an element. Furthermore, a nominal interpretation is impossible when the adjective is modified by a degree phrase. (18)*ha-namux mi-meter va-xeci (ha-ze) hu sofer mefursam the-short than-meter and-half the-this

PR writer famous"The/this shorter than 1.50m..."

However, a cumulative reading is possible with degree-modified adjectives, as seen below in (19); this sentence is also subject to a multiple plurality requirement (thanks to Rajesh Bhatt for pointing out the relevance of this example). (19) ha-yelad-im gvoh-im mi-meter va-xeci ve-nemux-im mi-meter ^slo^simthe-child-pl tall-pl than-met and-half and-short-pl than-met thirty

"The children are taller than 1.50m and shorter than 1.30m." I conclude that the predicates in (1) and (19) are indeed adjectives, so we need cumulative conjunction outside the nominal domain as well.

The need for cumulative conjunction on categories other than nominals is independent of multiple plurality. Take for example the following sentence.

(20) Students from Germany and from Switzerland met at the conference.

On the most natural reading of (20), the PP from Germany and from Switzerland does not pick out individuals who are both from Germany and from Switzerland. Rather, it picks a collection of individuals, based on a cumulative inference such as the following (Scha 1981). (21) Hans is from Germany. Fritz is from Switzerland.

Hans and Fritz are from Germany and from Switzerland. In order to capture this kind of inference, cumulative conjunction of the PPs should have the meaning below. This is an instance of the general paradigm for cumulative conjunction of type et (Link 1983; Krifka 1990). (22) [[from Germany and from Switzerland]] = faja = a1 \Phi a2 ^ a1 2 [[from Germany]] ^ a2 2 [[from Switzerland]]g

Coordination of the predicative adjectives in (1) and (2) is interpreted much the same way: the cumulative conjunction of tall and short is analogous to the meaning in (22) above; the fact that the Hebrew adjectives bear plural morphology will give rise to the multiple plurality requirement.

As an illustration of conjunction with multiple plurality we can take an English sentence similar to (20) above, where instead of coordinating PPs we coordinate full NPs, which are marked for number. The subject NP in (23) getsa meaning through cumulative conjunction, which is given below in (24).

(23) Students from Germany and students from Switzerland met at the conference. (24) [[students from Germany and students from Switzerland]] = faja = a1 \Phi a2 ^ a1 2 [[students from G.]] ^ a2 2 [[students from Sw.]]g

Assuming that each of the plural conjuncts only includes pluralities in its extension, we get a multiple plurality meaning for the conjoined NP subject. A similar interpretation of the conjoined plural predicates in (1) will give rise tothe multiple plurality requirement.

(25) [[gvoh-im ve-nemux-im]] = faja = a1 \Phi a2 ^ a1 2 [[gvoh-im]] ^ a2 2 [[nemux-im]]g

Notice that multiple plurality arises in the above example because the denotations of gvoh-im ("tall-pl") and nemux-im ("short-pl") are necessarily disjoint. The objects a1 and a2 in the above formula must therefore be non-overlapping, and since each of them is a plurality, their join a is a multiple plurality. If a1 and a2 were allowed to overlap then a simple plurality of children, each of whom is both tall and short, would suffice to make sentence (1) true. But this is impossible, given the lexical meanings "tall" and "short". 4. Conjunction weakening

If cumulative conjunction is available for predicates, we should expect to see cumulative conjunction with all kinds of coordinated expressions. However, we only see cumulative conjunction when the predicates are incompatible in their meaning, as are "tall" and "short". In other cases the only reading we get is one with intersective (propositional) conjunction. (26) ha-yelad-im gvoh-im ve-raz-imthe-child-pl tall-pl and-thin-pl

(27) The children are tall and thin.

Sentences (26) and (27) are virtually identical in meaning; unlike (1) and (2) they entail the sentence the children are tall, and the Hebrew sentence does not have a multiple plurality requirement. This is all expected if and is interpreted as intersective conjunction. But how come the above sentences are not ambiguous between an intersective and a cumulative reading? The answer lies in the strongest meaning hypothesis (Winter 1996, 1998, following work on reciprocals by Dalrymple et al. 1994,1998). This hypothesis states that plural predicates receive an interpretation using "the logically strongest truth conditions ... that are not contradicted by known properties ofthe singular predicate(s)" (Winter 1998, p. 323). Applied to coordination, the strongest meaning hypothesis states that the weaker form, i. e. cumulative conjunction, is only available when the stronger (intersective) one is contradictory (this idea is already present in Krifka 1990). Given the architecture ofour theory, the strongest meaning hypothesis is a filtering strategy: from the two meanings for coordination it selects the strongest one which is consistent. A similar architecture is advocated by Dalrymple et al. (1994, 1998).An alternative is Winter's own rendering of the strongest meaning hypothesis. In his theory conjunction is always intersective; plural objects are formed only in the nominal domain, as a result of type shifts that apply to DPs. In this architecture, the strongest meaning hypothesis has to be seen as a repair strategy: coordination of predicates is always strong (intersective), but when the result is contradictory the meaning is weakened. Weakening is a general process that applies to a variety of constructions, and in the case of coordinate structures it yields a reading which is virtually identical to what would be derived via cumulative conjunction.

I believe that multiple plurality gives reasons to adopt the view that the strongest meaning hypothesis is a filtering strategy rather than a repair strategy. Sentence (28), with plurality marked on each conjunct, is subject to a multiple plurality requirement, so it requires at least two children of each age; sentence (29), with plurality marked above the conjunction, does not have such a requirement, and it can be true with one child of each age. These judgments are very robust (I have not found a good English gloss for ben; the construction

ben n means "n years old").

(28) ha-yelad-im bn-ei ^se^s ve-bn-ei ^sevathe-child-pl ben-pl six and-ben-pl seven

"The children are six years old and seven years old." (29) ha-yelad-im bn-ei ^se^s ve-^sevathe-child-pl ben-pl six and-seven

"The children are six and seven years old." The above readings are indeed the result of conjunction weakening: sentences with similar structures but non-contradictory predicates do not have such readings. In (30) and (31) the predicates are compatible; the sentences are synonymous, and each of them entails both of the sentences ha-yelad-im ^sxor-ei `enayim ("the children are black-eyed") and ha-yelad-im ^sxor-ei se`ar ("the children are black-haired"). Neither sentence exhibits multiple plurality.

(30) ha-yelad-im ^sxor-ei `enayim ve-^sxor-ei se`arthe-child-pl black-pl eyes and-black-pl hair

"The children are black-eyed and black-haired." (31) ha-yelad-im ^sxor-ei `enayim ve-se`arthe-child-pl black-pl eyes and-hair

"The children are black-eyed and -haired." In (28) and (29), however, the predicates turn out to be contradictory on the intersective interpretation of and. I take the denotation of ben to be a relation between individuals and lengths of time;

[[ben]](a; t) is true if a is anindividual of age t. The words ^se^s and ^seva denote the lengths of six years and seven years, respectively (numerals denote length in years by convention; for ages that are not measured in years the unit length must be given explicitly, as in ben ^si^sa xoda^sim "six months old"). Given these meanings, we can derive the denotations of the predicates bnei ^se^s ve-bnei ^seva and bnei ^se^s ve-^seva. Iuse lambda abstraction and variables in the metalanguage for clarity; the metalanguage symbols 6 and 7 stand for the lengths of six years and seven years, respectively.

(32) [[bnei ^se^s ve-bnei ^seva]] = [[bnei ^se^s]] u [[bnei ^seva]]

= la:[[bnei]](a; 6) u la:[[bnei]](a; 7) = la:[[bnei]](a; 6) ^ [[bnei]](a; 7) (33) [[^se^s ve-^seva]] = lP: P(6) ^ P(7)

[[bnei ^se^s ve-^seva]] = lTla: T(ly:[[bnei]](a; y))([[^se^s ve-^seva]]) = la: lP: P(6) ^ P(7)(ly:[[bnei]](a; y)) = la:[[bnei]](a; 6) ^ [[bnei]](a; 7)

We see that on the strong interpretation of and, the predicate bnei ^se^s ve-^seva turns out to have an identical meaning to bnei ^se^s ve-bnei ^seva. This meaning is contradictory, so the strongest meaning hypothesis will apply. The strongest meaning hypothesis must yield different readings for (28) and (29): the former must receive a multiple plurality reading, while the latter must not. However, a repair strategy that only looked at the meanings in (32)/(33) would not be able to assign these sentences distinct meanings.

The current model will give each predicate the meaning derived independently by cumulative coordination. In (28), where two full predicates are coordinated, the predicate will receive a reading akin to (25). (34) [[bnei ^se^s ve-bnei ^seva]] = faja = a1 \Phi a2 ^ a1 2 [[bnei ^se^s]] ^ a2 2 [[bnei ^seva]]g

In (29), coordination takes place at the level of the object, below the predicate. I will assume that transitive verbs allow a cumulative relation between their subjects and objects (Scha 1981); plural morphology on transitive bnei restricts its subject to pluralities, in a manner analogous to that in (9).

(35) [[bnei ^se^s ve-^seva]] = faj[[bnei]](a; 6 \Phi 7)g

= faja 2 PL ^ 8a1 2 AT(a) 9b1 2 AT(6 \Phi 7) [[[ben]](a; b)]

^ 8b1 2 AT(6 \Phi 7) 9a1 2 AT(a) [[[ben]](a; b)]g

Our model thus produces the desired readings: the meaning in (34) is multiply plural while that in (35) is not.

In Winter's system the strongest meaning hypothesis will have to weaken the meaning derived through intersective conjunction in (32)/(33). Coordination of the nominals ^se^s and ^seva could in fact receive a cumulative interpretation (precisely because they are nominals), but according to Winter's assumptions the plural marker on the predicate in (29)/(33) is inherently distributive, so the meaning of the predicate turns out to be the same. So if we want to sustain the architecture of Winter (1996, 1998) and still get distinct weakened readings, the weakening process must have access to the units below the level of the conjoined predicate. Let us be a bit more explicit about what a modification of Winter's theory would look like if we want it to account for the multiple plurality facts. Winter defines weakening at the propositional level based on the normal universal form of the proposition, which is derived from the proposition's basic meaning relative to a tuple of predicates involved. We have seen that the basic meaning of the predicates in (28) and (29) is the same, namely the one derived in (32)/(33). The difference must be attributed to the tuple of predicates which make up the normal universal form: for (28) it will be the two unary predicates bnei ^se^s and bnei ^seva, whereas for (29) it will be the single binarypredicate bnei. In Winter's system pluralities are not mereological sums but rather sets of individuals, and predication takes place on the individuals that make up these sets. The normal universal forms of (28) and (29) will thereforebe as follows.

(36) [[ha-yelad-im bnei ^se^s ve-bnei ^seva]]

= 8a 2 [[ha-yelad-im]]8b 2 f[[bnei ^se^s]]; [[bnei ^seva]]g : b(a)

(37) [[ha-yelad-im bnei ^se^s ve-^seva]]

= 8a 2 [[ha-yelad-im]]8t 2 f6; 7g : [[bnei]](a; t)

The weakened reading is derived from the normal universal form in light of some known lexical properties of the predicates involved, in this case the knowledge that a child cannot be six and seven years old at the same time. In the weakened reading, the universal quantifiers of the normal universal form are replaced by the requirement that the number of relations be maximal, given the above lexical knowledge. Now for both sentences, the weakened reading will be true if each child is either six or seven, since any additional instantiations of the relations in (36) and (37) would contradict the lexical knowledge.

We still haven't derived distinct meanings for the two sentences above, that is we haven't accounted for the multiple plurality requirement of (28).

Worse, the weakened reading as it stands does not even capture the correct truth conditions without multiple plurality: the relations in (36) and (37) are maximized if all of the children are of one age (say six), so in such a case the sentences are predicted to be true, contrary to intuition. One line of defense (Yoad Winter, personal communication) is that in the above situation the sentences are pragmatically inappropriate, just like a disjunction implies that both of the disjuncts are applicable. I believe this line of defense doesn't hold, inlight of the following contrast.

(38) The children are six or seven--in fact, they're all six. (39)#The children are six and seven--in fact, they're all six.

Sentence (38) shows that the disjunction gives rise to a conversational impli-cature, which is cancelable with additional context. This is not the case in (39), where the addition makes the sentence contradictory. The requirement thateach of the conjuncts should be instantiated is therefore stronger than a conversational implicature. In a weakening theory, this requirement has to be explic-itly made part of the strongest meaning hypothesis; however, this requirement is already built into the definition of cumulative coordination, so in the archi-tecture advocated here, where the strongest meaning hypothesis chooses between two independently constructed meanings, no additions have to be made(Heycock and Zamparelli 1999, 2000 make a similar observation: cumulative or "split" coordination requires at least one element from each conjunct; thisis built into their semantics through the set product operation, which is isomorphic to the cumulative conjunction used here).

Now we can see how a weakening theory would deal with the multipleplurality requirement of sentence (28): we first require that every conjunct

be instantiated by at least one relationship (as deemed necessary by the dis-cussion in the preceding paragraph), and then add the requirement that every plural conjunct be instantiated by at least two relationships. This complicatesWinter's definition of a weakened reading, but it seems necessary in light of the data.

How does this compare to my proposal? In the modification I proposedto the weakening theory, plural morphology plays a double role: predicates

that apply to plural arguments must have a plural denotation (which includessingular individuals), regardless of morphology; in addition, the definition of weakened readings must refer explicitly to plural morphology. This latter is remarkably similar to the claim that morphologically plural expressions, in-cluding plural predicates, literally denote pluralities. In my theory this applies generally, while in the modified weakening theory it is specific to the weakening process. The main difference between the theories, then, comes out to be that I accept cumulative conjunction, whereas the modified weakening theory derives these effects in a roundabout way. The weakening theory fits in well with Winter's program, which sets out to show that conjunction is always intersective, and any apparent cumulative effects come about as the result of independent processes. The cost, however, is the admission of a weakening process which includes an ad-hoc mechanism that is built specifically to mimic cumulative conjunction and multiple plurality.

5. Conjunction of singular predicates

Admitting non-propositional conjunction for predicates leads to the expectation that the cumulative conjunction of two singular predicates should yield a plural predicate. After all this is what happens with the coordinationof proper names, e. g. John and Mary, as well as other nominals. But for APs and VPs this is hopelessly wrong.

(11)*ha-yelad-im gavoah ve-namuxthe-child-pl tall. sg and-short. sg

(40)*dani ve-yosi gavoah ve-namuxDanny and-Yossi tall. sg and-short. sg (41)*John and Bill eats a doughnut and drinks coffee (respectively).

The sentences above are all ill formed, even though the intended meaning is perfectly clear. Having a coordinate subject in (40) or the word respectively in (41) doesn't help. Based on the interpretation of conjoined plural predicates, I have argued above that the semantics should allow cumulative conjunction; it would seem odd if this were not available for singular predicates. Indeed, it seems to me that the problem in the above sentences is not with the meaning, but with the syntax.

We may note that coordination of singular NPs in Hebrew is syntactically plural, but coordination of singular APs is singular. We can check this with words that are ambiguous between nouns and adjectives, like sini ("Chinese")and yapani ("Japanese"). We can put these words in a context where they must be interpreted as one category rather than the other: only nouns can be modified by locative PPs, and only adjectives can be modified by the adverbial meod ("very"). We now get a stark contrast between (42) and (43). (42) ha-xaver-im ^sel dana hem sini mi-beijing ve-yapani mi-tokyothe-friend-pl of Dana pl. Chi. sg from-Beijing and-Jp. sg from-Tokyo (43)*ha-xaver-im ^sel dana hem meod sini ve-meod yapanithe-friend-pl of Dana pl. very Chinese. sg and-very Japanese. sg

I believe the above contrasts are not due to a difference in meaning, or to dif-ferences in the availability of cumulative conjunction between nouns and adjectives. Indeed, when the adjectives are plural as in (44) below, we do get acoherent reading, with cumulative conjunction and multiple plurality.

(44) ha-xaver-im ^sel dana hem meod sini-m ve-meod yapani-mthe-friend-pl of Dana pl. very Chinese-pl and-very Japanese-pl

I conclude that on top of the semantic interpretation of plurality, there are syntactic requirements of agreement. Cumulative conjunction is available for adjectives in general, but we cannot see it on singular ones because such constructions are ruled out by syntax.

6. Conclusion

In this paper I argued that multiple plurality outside the nominal domain should be taken as evidence that plural morphology on an expression excludes singularities from its denotation, and that cumulative conjunction is an operation that is generally available. The limited occurrence of cumulative conjunction is the result of the strongest meaning hypothesis and syntactic number of conjoined adjective phrases.

A question that remains open is why does the strongest meaning hypothesis exist in the first place, that is why should natural language employ such a filtering strategy when it tolerates ambiguity in many other places? And why should this filtering strategy apply to adjectives, while coordinated nominals routinely receive a cumulative interpretation? Adopting Winter's architecture, where the strongest meaning hypothesis is a repair strategy, only reverses the question: why does natural language employ such a repair strategy, while other structures are simply understood as contradictory? I do not have an answer to this question, but the data suggest that it may be related to the questionof syntactic number: how come coordinated singular APs form a singular AP, whereas coordinated singular NPs form a plural NP. The difference does not seem to lie in the semantics of coordination, because cumulative coordination is available for plural adjectives. Another question concerns speaker variation: as I mentioned in the introduction, some speakers of Hebrew and Spanish accept sentences (1) and (3)with a weaker multiple plurality effect, whereby only one of the conjuncts must have a plural referent (all speakers reject the sentences if all conjuncts have single referents). My theory does not predict that such variation should be possible. At the moment I do not see how this can be treated without an adhoc stipulation, so I leave the question open.

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