Interpreting quantifiers in subject position

Interpreting quanti�ers in subject position Jon Ander Mendia Abstract In this paper we argue that collective readings of quanti�ed NPs in subject position involve a form of hidden distributivity (Dowty 1987). We argue that there are two di�erent types of collective predicates, and that the best way to model this contrast is by means of two separate syntactic structures corresponding to di�erent aktionsarten (Taub 1989, Brisson 1998). Borrowing the basic mechanism to exploit this idea from Brisson (2003), we argue instead that a semantics without covers (Schwarzschild 1996) is both empirically more adequate and conceptually more appealing. Keywords: Aktionsart, distributivity, quanti�cation, event semantics 1 Introduction1 This papers investigates the interaction, �rst noted by Vendler (1957), between the aktionsart of a verb and its availability to get collective interpretations. Concretely, we will concentrate on examples like the following: (1) a. The boys are a nice group b. *All the boys are a nice group On the basis of contrasts like the one in (1), we will argue that we have to distinguish at least two ways of collective predication, one of which involves covert distributive quanti�cation (cf. Brisson 1998, 2003). The resulting picture is one where there seems to be a di�erence between the mechanisms by which quanti�ed expressions, on the one hand, and non-quanti�ed expressions, on the other, arrive at collective interpretations. 1This paper is a revised version of one of the qualifying papers written during 2010 in partial full�lment of my MA at the University of the Basque Country. I thank Javier Ormazabal for many valuable comments and suggestions. In addition, I am also grateful to Myriam Uribe-Etxebarria, Urtzi Etxeberria, Ricardo Etxepare, Seth Cable and the audiences at the 6th Meeting of the European Research Nets in Linguistics. This research has bene�ted from the research grant BFI07.98 by the Basque Government. All errors are my own. 33 Interpreting quanti�ers in subject position Jon Ander Mendia 2 Collective & distributive interpretations Since the seminal work by Vendler (1957), it is common to assume that there are at least three kinds of predicates with respect to their ability to generate collective/distributive interpretations: (2) John and Mary � � � � � � � � � a. met. b. woke up. c. lifted a piano. Example (2) above shows a case of a collective interpretation of a sentence, where the conjoined subject can only be true of both John and Mary together. In contrast, the predicate woke up in (2) can only be true of each of the members denoted by the subject NP, no modi�er can make wake up be interpreted collectively.2 Finally, the sentence in (2) has the property of being ambiguous between both interpretations and, for this reason, predicates of this kind are usually referred to as ‘mixed’ predicates: they can be true in a collective as well as in a distributive interpretation. However intuitive it may look, the distinction between the three types of predicates is hard to state formally. Spelling out a de�nition that discriminates each type from the others is di�cult because often the interpretation of the predicates changes depending on the subject. The remainder of this section is devoted to clarify the typology of predicates that will be relevant for the present paper with respect to the collective/distributive distinction. 2.1 Two types of collective predicates As it has been previously noticed in the literature (Dowty 1987; Winter 2001), the quanti�er all can be used to signal the di�erence between two types of collective predicates: (3) a. All the girls gathered in the hall. b. *All the girls are a good team. The di�erence between both types of collective predicates amounts to the grammaticality of all in subject position. Verbs like gather can host the universal quanti�er all in subject position, whereas predicates like be a good team cannot. 2That is, wake up is ‘lexically distributive’ (Winter 2001). Consider the fact that sentences like John and Mary woke up together or John and Mary woke up at the same time are still distributive. The question about what predicates qualify as collective is a di�cult, however. For the purposes of this paper, I will concentrate only on lexical predicates, setting aside the case of other types of predicates that may also be interpreted collectivelly–like, for example, re�exives (resemble, see each other, VP themselves) or predicates modi�ed by adverbials (together, as a group, at the same time). Iberia: IJTL �Volume 7 (2015), 33–67 http://revistas.ojs.es/index.php/iberia/ 34 Interpreting quanti�ers in subject position Jon Ander Mendia It is important to note that the di�erence, then, is stated in terms of grammaticality: (3b) is plainly ungrammatical, and not merely odd or weird. Indeed, when all modi�es a plural DP in subject position three outcomes are possible, depending on the predicate at hand: (3a) and (3b) show two of them, namely, that the sentence may be grammatical or not. The third possible outcome is that where, in the presence of all, a sentence that would otherwise be ambiguous between a collective and a distributive interpretation loses the collective interpretation (examples from Dowty 1987, attributed to B. H. Partee and B. Ladusaw, respectively). (4) a. The trees are denser in the middle of the forest. b. The trees are all denser in the middle of the forest. (5) a. The students voted in favor of the proposal. b. The students all voted in favor of the proposal. The sentences in (4a)/(5a) above without all are ambiguous. In the case of (4a), it can mean two things: under the distributive reading, it means that the individual trees in the middle of the forest are thicker than those in the outskirts; under the collective reading, it means that in the middle of the forest the trees are closer to each other than they are at the outside. Similarly, (5a) without all has a collective reading similar to pass the proposal, but in (5b) that reading is no longer available; the sentence can only be distributive, with a meaning that can be paraphrased as to cast an individual vote in favor. The e�ect of this meaning shift can also be observed with predicates that are only acceptable in the collective reading because the distributive reading is in con�ict with world knowledge. Consider the following examples: (6) a. The senators passed the pay raise. b. #All the senators passed the pay raise. (7) a. The short athletes won the relay race. b. #All the short athletes won the relay race. The sentences in (6a)/(7a) above are only acceptable in the collective reading; in the case of (6a) because we know that single senators do not have the legal power to pass a pay raise by themselves. Similarly, we know that relay races are run in teams, and so the only adequate interpretation for (7a) is a collective one, where the short athletes form a single team. The observation, then, is that with all in subject position–as in (6b) and (7b)–the collective reading is no longer available and the distributive reading is enforced, resulting in pragmatic oddness. Iberia: IJTL �Volume 7 (2015), 33–67 http://revistas.ojs.es/index.php/iberia/ 35 Interpreting quanti�ers in subject position Jon Ander Mendia This is something we do not expect, not at least if collectivity were a homogeneous property of predicates: on the one hand, some collective predicates cannot be interpreted with all, even if all,per se, does not disallow collective readings, as illustrated by the contrast between (3a) and (3b) above. On the other hand, some mixed predicates lose their collective reading with all in subject position, even if, again, this e�ect cannot be attributed to all alone, as observed in (4) through (7). We know that all is not the sole responsible for this meaning shift because there are indeed mixed predicates that remain ambiguous despite the presence of all, as illustrated by the two ambiguous examples in (8). (8) a. All the students built a raft. b. All the artists painted a horse. This discussion suggests that there are at least two types of collective predicates. So far, it is evident that the collective vs. distributive distinction is not as well-behaved as expected, even if we accept the existence of lexically distributive or collective predicates (Winter 2001).3Moreover, note that the presence of all has an interesting e�ect: whenever it a�ects the meaning of a predicate and triggers a meaning shift with respect to the relevant collective/distributive distinction, the e�ect is always to the detriment of the collective interpretation. That is, there are no cases where an otherwise ambiguous predicate loses the distributive interpretation in the presence of all, and this suggests that the collective reading may be more complex than the distributive reading. 2.2 A pervasive contrast The di�erences between the two types of collective predicates in the previous section were claimed on the basis of the behavior that some predicates show when they combine with all. But, in fact, the observed pattern is not exclusive of all: there is a wide variety of quanti�ed NPs (QNPs henceforth) that pattern alike. (9) a. All the b. Exactly four c. More less than four d. At least / at most four e. Few / many f. Most of the g. Some � � � � � � � � � � � � � � � � � � � � � � � � � � � � � students gathered in the hall. 3By ‘lexical’ here we mean predicates like breath and be a group. For instance, if several people breath, no matter how this is expressed, it is entailed that each of them breathes. Similarly, be a group can never be true of a simple atomic individual (setting aside ‘group-denoting’ NPs, which might be considered atomic individuals. I will not discuss here, but see Lasersohn (1995); Schwarzschild (1996); Landman (2000); a.o.) Iberia: IJTL �Volume 7 (2015), 33–67 http://revistas.ojs.es/index.php/iberia/ 36 Interpreting quanti�ers in subject position Jon Ander Mendia (10) a. *All the b. *Exactly four c. *More / less than four d. *At least / at most four e. *Few / many f. *Most of the g. *Some � � � � � � � � � � � � � � � � � � � � � � � � � � � � � students are a good team. The examples in (9) and (10) show how the attested pattern is reproduced with a variety of di�erent QNPs. Interestingly, this state of a�airs holds not only for English, but also for Romance and Basque.4 (11) a. Todos los all.�� D.�� b. Exactamente cuatro exactly four c. Más / menos de cuatro more less of four d. Al menos / como mucho dos at least at most two e. Muchos / pocos many few f. La mayoría de D.�� most of g. algunos some � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � estudiantes se reunieron en el student.�� re�. meet.�� in the vestíbulo. hall (12) a. *Todos los b. *Exactamente cuatro c. *Más / *menos de cuatro d. *Al menos / *como mucho cuatro e. *Muchos / *pocos f. *La mayoría de g. *Algunos � � � � � � � � � � � � � � � � � � � � � � � � � � � � � estudiantes son un buen grupo. student.�� be.�� one good team 4In general, the situation is the same for more Germanic (German, Dutch) as well as Romance (French, Italian, Portuguese, Romanian, Catalan) languages. Iberia: IJTL �Volume 7 (2015), 33–67 http://revistas.ojs.es/index.php/iberia/ 37 Interpreting quanti�ers in subject position Jon Ander Mendia (13) a. Ikasle guztiak student all.D.��� b. Zehazki lau ikasle exactly four student c. Lau ikasle baino gehiago / gutxiago four student than more less d. Gutxienez / gehienez lau ikasle at least at most four student e. Ikasle gutxi / asko student few many f. Ikasle gehienak student most.D.��� g. Ikasle batzuk student some � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � atondoan bildu ziren. hall.��� meet ��� (14) a. *Ikasle guztiak b. *Zehazki lau ikasle c. *Lau ikasle baino gehiago / *gutxiago d. *Gutxienez / *gehienez lau ikasle e. *Ikasle gutxi / *asko f. *Ikasle gehienak g. *Ikasle batzuk � � � � � � � � � � � � � � � � � � � � � � � � � � � � � talde on bat dira. team good one.��� ��� Moreover, Spanish and Basque also show exactly the same shift in meaning we observe with mixed predicates in English (see examples (4) and (5) above): certain kind of mixed predicates lose their collective meaning with all in subject position. This is illustrated bellow: examples (15a)/(16a) below are both ambiguous, whereas the examples in (15b)/(16b) lack the collective interpretation. (15) a. Los D.��.���� melones watermelon.�� de of la D.��.� cesta basket pesan weigh.�� mucho. a-lot ‘The watermelons of the basket weigh a lot.’ b. Todos all.�� los D.�� / algunos some.�� melones watermelon.�� de of la D.��.� cesta basket pesan weigh.�� mucho a-lot ‘All the / some watermelons of the basket weigh a lot.’ Iberia: IJTL �Volume 7 (2015), 33–67 http://revistas.ojs.es/index.php/iberia/ 38 Interpreting quanti�ers in subject position Jon Ander Mendia (16) a. Saskiko basket.�������.�� meloiek watermelon.D.���.�� asko a-lot pisatzen weigh dute. ��� ‘The watermelons of the basket weigh a lot.’ b. Saskiko basket.�������.�� meloi watermelon guztiek all.D.���.�� / batzuk some.���.�� asko a-lot pisatzen weigh dute. ��� ‘All the / some watermelons of the basket weigh a lot.’ So, summing up, in the light of the data presented here, it becomes apparent that there is a di�erence between collective predicates, which, consequently, do not constitute a homogeneous kind. The di�erence can be tracked by combining QNPs of all sorts with the relevant predicates: the classical collective predicates are either grammatical or ungrammatical, whereas the classical mixed predicates either lose or maintain the collective interpretation. Moreover, the fact that this very same di�erence holds in both English and Spanish, but also in a typologically isolated language such as Basque, suggests that it may be a re�ect of some pervasive feature of natural language. In the next section, we will review some of the most in�uential proposals that have focused on this puzzle. 3 Previous proposals 3.1 Dowty’s observation Taking into consideration the contrast between the so-called collective predicates for English, Dowty (1987) suggested that there are two distinct kinds of collective predicates: (17) Collective Predicates from Dowty (1987): a. Pure Collective: meet,gather,see each other,disperse ... b. Pure Cardinal: be a team,be numerous,be a majority,be a nice group ... The di�erence between both types is that Pure Collective predicates have an (implicit) entailment about the subject that Pure Cardinals lack: a Distributive Sub-entailment (DS henceforth). Now, what is a DS? Consider what is required of individual students for the sentence the students gathered in the hall to be true. Clearly, every student in the group referred to by the NP the students (or, at least, almost every student) must come into the hall and remain long enough so that they are all in that place at a common time. Thus, gather entails the distribution of Iberia: IJTL �Volume 7 (2015), 33–67 http://revistas.ojs.es/index.php/iberia/ 39 Interpreting quanti�ers in subject position Jon Ander Mendia some property of the members of its subject (namely, that each of them undergoes a change of location), but ‘gathering’ itself can only be true of the group qua group (Dowty 1987, pp. 101). Another way to express this more complex meaning is by the following conjunction: (18) All the girls gathered ≈[The girls gathered] & [Every girl contributed to the gathering] By virtue of making all sensible to the presence of DS, Dowty can use all to test what class a collective predicate belongs to. According to him, all is a universal quanti�er that distributes over the DS down to every individual in the denotation of the subject that all is modifying (akin to the suggestion in Link 1983 that all introduces a ‘part-take’ operator). Pure Cardinal predicates lack DS and therefore all does not have anything to operate on, and so the ungrammaticality of sentences like all the children are a big group is explained. Dowty did not provide a formal account of this distinction, and so it di�cult to imagine what the DS of some predicates may be. For example, consider paint a building: could mixed the paint count as a DS? And calculate the amounts of paint? Those are tasks that someone could very well perform in a collaborative e�ort to paint a big building. In addition, it is a mystery why these DS are only relevant for all and not for, say, plural de�nites, demonstratives or coordinated NPs; all these DPs behave di�erently from all QNPs in the relevant respect, as illustrated below. (19) a. The students are a nice group. b. Those students are a nice group. c. Mary and John are a nice couple. d. *All the students are a nice group. Dowty did not acknowledge either that the same di�erence can be observed with quanti�ers other than all, even though the contrast is pervasive (recall the data in section 2.2). Moreover, even though Dowty notes the existence of the meaning shift e�ect triggered by all (that is, the loss of the collective reading when QNPs combine with some mixed predicates), he acknowledges that an explanation in terms of DS is not su�cient to account for it. For instance, if sentences like (20) below had DS, the collective reading should still be available with all, but it is not. (20) (All) the bottles are too heavy to carry Iberia: IJTL �Volume 7 (2015), 33–67 http://revistas.ojs.es/index.php/iberia/ 40 Interpreting quanti�ers in subject position Jon Ander Mendia In general, the argumentation for the existence of DS is somehow circular: the proof of the existence of DS is the distribution of all, and the distribution of all with respect to collective predicates is explained in terms of DS. Thus, a better insight is needed to shed some light on the distribution of all with respect to the collective/distributive predicate distinction. 3.2 Taub’s Generalization Building on the observations by Dowty (1987), Taub (1989) investigates further the properties of DS and makes the following generalization: (21) T���’�G������������� The collective predicates that disallow all are the collective predicates denoting states and achievements. In order to support the generalization, Taub provides the following examples: (22) Collective States: a. *All the boys are a big group. b. *All the students are numerous. (23) Collective Achievements: a. *All the senators passed the pay raise. b. *All the students elected a president. (24) Collective Activities: a. All the boys carried the piano around for an hour. (25) Collective Accomplishments: a. All the students gathered in the hallway. b. All the girls built a raft. Taub’s Generalization is superior to Dowty’s observation in terms of DS in two respects. First, Cardinal Predicates fall directly into the generalization, since they are all states. Second, the generalization predicts that collective states and achievements will be ungrammatical with all in subject position, whereas mixed states and achievements (like be too heavy and elect) will lack the collective reading if they combine with all. Thus, Taub’s generalization provides a desirable description of the phenomena by reducing the availability of all to the kind of aktionsart of the predicate and, as shown in examples (22) through (25), the observation seems Iberia: IJTL �Volume 7 (2015), 33–67 http://revistas.ojs.es/index.php/iberia/ 41 Interpreting quanti�ers in subject position Jon Ander Mendia Moreover, these facts are true of virtually every type of QNP, and not only of those headed by all. (43) Todos los all.�� D.�� Exactamente cuatro exactly four Más / menos de cuatro more less of four Al menos / como mucho cuatro at least at most four Muchos / pocos many few la mayoría de D.�� most of Algunos some � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � estudiantes están students be � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � reunidos. meet.���.�� agrupados. group.���.�� juntos. toghether.�� unidos. unit.���.�� pegados. glue.���.�� atados. tie.���.�� (44) Ikasle guztiak student all.D.��� Zehazki lau ikasle exactly four student Lau ikasle baino gehiago / gutxiago four student than more less Gutxienez / gehienez lau at least at most four Ikasle gutxi / asko student few many Ikasle gehienak student most.��� Ikasle batzuk student some � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � taldekatuta group.��� bilduta meet.��� elkartuta toghether.��� batuta unit.��� itsatsita glue.��� lotuta tie.��� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � daude. ���-be In a system relying on structural di�erential between predicates, these contrasts cannot be straightforwardly accounted for. In fact, Dowty (1979) explicitly rejects the idea of having a DO predicate as part of the meaning of stative predicates. Here I will just sketch two ways of thinking about these cases. Note �rst that all the predicates considered above are ‘derived’, in the sense that they all involve a participial expression. In fact, all of the examples involve predicates that usually denote activities (like atar (‘tie’), pegar, ‘glue’, etc.) and so, by assumption, they Iberia: IJTL �Volume 7 (2015), 33–67 http://revistas.ojs.es/index.php/iberia/ 48 Interpreting quanti�ers in subject position Jon Ander Mendia must have a DO component in their meaning. In some syntactic frameworks, like the neo-constructionist approaches to grammar, the structure of any derived form must include the non-derived form (see, for example, the proposals in Borer 2005; Ramchand 2008, a.o.). Thus, in these frameworks, it should be possible to access the DO component of verbs like ‘tie’ and ‘glue’ in Spanish before they combine with the copula and turn into states. In any case, a putative integration of such neo-constructionist frameworks with Brisson’s approach raises a number of question. Whether these predicates are construed along the syntactic derivation or are rather inserted as a whole lexical unit is something that is still debated. And even if we argue for the former approach, it is not straightforward how semantic operations, such as the insertion of D, can be applied to morphological units below the ‘word level’. In Spanish there is another set of examples that seem to point in this direction: collective achievement verbs with the morphological pre�xco(n)- are usually good with QNPs in subject position, and also allow for collective readings:13 (45) a. Todos all.�� los D.��.���� ríos river.�� con�uyen meet.�� más more adelante. ahead ‘All the rivers join ahead.’ b. Todas all.�� las D.��.� líneas line.�� convergen converge.�� en in el D.��.���� mismo same punto. point ‘All the lines converge on the same place.’ The examples in (45) do not involve derived predicates nor participial constructions and the only interpretation they have is collective, in spite of being achievements. Thus, one could think that the pre�xco(n)- is responsible for the licensing the collective reading. Furthermore, given that this is the only interpretation possible, it could be that that co(n)- is some sort of overt Doperating on verbal roots.14 On the other hand, it may be that collective readings in (43) / (44) and (45) are licensed by di�erent means. Thus, a second way of thinking about the examples in (43) and (44) is to take seriously the di�erence between the two kinds of copulas. All the examples mentioned in Basque and Spanish are composed with the locative copula stare, which is believed to bear some aspectual meaning that the plain 13The pre�xco(n)- stems from the preposition con (‘with’) and its meaning is similar to together. Consider also the English pairs operate vs. cooperate,author vs. coauthor,variation vs. covariation, and so on. 14It may be helpful to think about the di�erences between join and conjoin in English. While both predicates need to be related to a plurality of some sort, only conjoin is obligatorily collective: the kid joined the two dots and formed a line vs. #the kid conjoined the two dots and formed a line. Iberia: IJTL �Volume 7 (2015), 33–67 http://revistas.ojs.es/index.php/iberia/ 49 Interpreting quanti�ers in subject position Jon Ander Mendia copula essere lacks; hence, it is believed to be more complex. Within the Spanish linguistic tradition there is a long standing debate about the precise nature of [estar + participle] constructions. For some researchers, constructions of this type are passives in disguise, whereas for others they are not. The point about which both views agree is the acceptance of an aspectual di�erence between [ser + participle] and [estar + participle] (see Mendikoetxea 1999, pp. 1623). On the basis of this di�erence, it could be the copula estar which introduces the DO head.15 The fact that the estar participial structures considered here all have a resultative meaning–as opposed to ser participials, which never do–points in this direction. But note, however, that whatever the meaning of this DO would be, it couldn’t be the same as the one advocated by Dowty (1979) or Brisson (1998), for it could non-agentive and the resulting derived predicate would still be stative. The take away message from this has been to point out the existence of a particular set of predicates that, on the surface, do not fall under Taub’s generalization and hence are problematic for Brisson’s approach. We will have not much more to say about these cases and we will set the issue aside for further research. In the remainder of the paper we concentrate on pointing out more pressing problems that follow from the non-quanti�cational approach to the semantics of all. 4.2 Intermediate readings The lack of intermediate readings with QNPs headed by all poses a problem for the cover-based analysis of all. In order to understand better what a intermediate reading is, consider the following example by Schwarzschild (1996, pp. 67): Two merchants are attempting to price some vegetables. The vegetables are sitting before the merchants, piled up in several baskets. To determine their price, the vegetables need to be weighed. Unfortunately, the merchants do not have an appropriate scale. Their grey retail scale is too �ne, meant to weigh only a few vegetables at a time, and their black wholesale is coarse, meant to weigh huge truckloads. Realizing this, one of the merchants says: (46) The vegetables are too heavy for the grey scale and too light for the black scale. If the sentence in (46) were uttered out of the blue it could have, at least, the following readings: 15I am thankful to an anonymous reviewer for pointing out this possibility. Iberia: IJTL �Volume 7 (2015), 33–67 http://revistas.ojs.es/index.php/iberia/ 50 Interpreting quanti�ers in subject position Jon Ander Mendia (47) a. ������������: each of the vegetables is too heavy ... b. ����������: all the vegetables together are too heavy ... c. �����������: this consist of two (groups of) readings, non-maximal distributive and non-maximal collective.16 d. ������������: its both distributive and collective, as it distributes over groups of vegetables. Sentence (46) is false in the context if we consider either individual vegetables or the whole vegetable pile; it can only be true if we consider sub-pluralities. That is, instead of going down to every member of the denotation of the NP, or building a plural entity like a ‘group’ for all the vegetables together, the sentence takes junks or piles of vegetables into account, baskets of vegetables in this case. This signals that the distribution is made over sub-pluralities of the NP. With this example, Schwarzschild shows the existence of intermediate readings with plural de�nites. Observe that, crucially, this reading is impossible for the same sentence with all, and so (48) is odd in the context described above. (48) All the vegetables are too heavy for the grey scale and too light for the black scale. In general, intermediate readings are absent with quanti�ed subjects. However, nothing in the de�nition of good-�t cover that Brisson (1998, 2003) provides for the interpretation of all rules out the intermediate reading. Imagine a context where �vegetables�={a, b, c, d, e, f}. According to her de�nition, repeated below for convenience, in order to be a good-�t cover every member of the denotation of the NP must be (i) a member of a cell such that this cell is a member of the cover, and (ii) a subset of the denotation of the NP. (49) Good Fit: for a variable Cov of Uand a NP denotation X,Cov is a good-�t with respect to Xi� ∀y[y∈X→∃Z[Z∈Cov &y∈Z&Z⊆X]] (50) a. Cov1 ={{a},{b},{c},{d},{e},{f},{g,h}} b. Cov2 ={{a, b, c, d, e, f},{g,h}} c. Cov3 ={{a, b, c, },{d, e, f},{g,h}} 16In the �rst case, the sentence is true for all the vegetables but one, two, three ... In the second case, the sentence is true in a collective reading even if do not compute the vegetables very accurately (if there are 10, for example, then we take 8 into account). Iberia: IJTL �Volume 7 (2015), 33–67 http://revistas.ojs.es/index.php/iberia/ 51 Interpreting quanti�ers in subject position Jon Ander Mendia Thus, Cov3 is also a good-�t cover for the NP vegetables, but there is no interpretation that corresponds to that cover. In fact, the theory allows intermediate readings for any sentence that allows all in subject position, even though these readings are not always available. 4.2.1 A possible solution for Covers How can an account with covers rule out undesired interpretations like (48)? Given that be heavy in (48) is a stative predicate and, therefore, it has no DO predicate, we could argue that in those cases some economy condition bans the insertion of D. The rationale would be the following: in the presence of all,Dmediates between two possible readings, collective and distributive, and for doing so it crucially depends on the presence of the head DO. Since states and achievements lack DO, Dcan only apply to the VP node and thus only a collective reading is possible. In other words, with states and achievements Dis doing no disambiguating labor whatsoever, and on this grounds some economy condition bans it from applying. This way of thinking seems to �t well within Brisson’s analysis; in fact, with these cases in mind, Brisson follows Fox 2000 in adopting an economy condition that bans the insertion of an operator–Din this case–in those places where it does not a�ect the meaning of the predicate (the de�nition was introduced above in (31); see Brisson 2003, pp. 172–174 for discussion). This would not prevent the theory from generating intermediate readings, but from generating them with state and achievement predicates. Nevertheless, such a proposal makes strong predictions: 1. It predicts the absence of collective and intermediate readings with achievements in the presence of all, due to the lack of the head DO. 2. It predicts intermediate readings for collective (or mixed) activities and accomplishments, since they both have a DO predicate. In the following subsections I will consider each of the predictions in more detail, and conclude that each of these predictions is too strong and is not supported by the data. 4.2.2 Collective achievements Assume then that Dis not allowed with states and achievements because of some economy condition and thus neither collective nor intermediate readings will be allowed with all. However, Brisson (2003, pp. 173) acknowledges the existence of intermediate readings with achievements: For example, suppose we are teachers at Wading River Elementary School. The students are holding elections for class president, so each grade will elect its own president. In this context, it is possible to say the following. Iberia: IJTL �Volume 7 (2015), 33–67 http://revistas.ojs.es/index.php/iberia/ 52 Interpreting quanti�ers in subject position Jon Ander Mendia (51) All the students elected a president. This sentence does not mean that each individual student elected a president. It means that the third graders elected a president, the fourth graders elected a president, and so on. Examples of this kind constitute a real problem for the proposal. Her solution is to admit that in these cases Dcan be inserted in the VP and thus it distributes over the contextually salient sub-pluralities that are grouped by the di�erent cells of the cover. But it poses a serious conceptual weakening of the proposal, since it opens the possibility for predicates without a DO component to have collective readings with all in subject position. This is something we want to avoid, given examples like (48). Why is it then that (51) can have an intermediate reading and (48) above cannot? According to this explanation, there is no principled answer. 4.2.3 Activities and accomplishments An economy condition banning Dfrom states and achievements would obviously not a�ect mixed activities and accomplishments, and so the prediction is that they should have intermediate readings. However, it seems that intermediate readings with all are impossible also in these cases. In order to illustrate the point, consider the following example (adapted from Landman 2000): (52) a. The boys are touching the ceiling. b. All the boys are touching the ceiling. According to Landman, the sentence in (52a) is true in a context in which the boys form a pyramid and just the boy on the top of the pyramid touches the ceiling with the tip of his �nger. An appropriate situation can be that of a human pyramid building contest between girls and boys. As expected, the same meaning is absent for the example in (52b). Consider now the same contest with other participants: it is di�erent several groups of boys, girls and teachers that compete against each other. The sentence in (52a) can still mean that every group of boys managed to build a pyramid and touch the ceiling, but the same meaning is absent from (52b). Again, nothing in the de�nition of good-�t cover prevents us from building subsets that exhaust the denotation of the NP and, since the predicate has a DO predicate by assumption, nothing precludes the intermediate reading. However, this interpretation is absent or at least very hard to obtain.17 17In this example the collective reading is also absent, possibly due to the lexical properties of the verb touch. So, it may be tempting to conclude that that the unavailability of the collective Iberia: IJTL �Volume 7 (2015), 33–67 http://revistas.ojs.es/index.php/iberia/ 53 Interpreting quanti�ers in subject position Jon Ander Mendia The discussion in the last subsections has tried to rescue an analysis of all as related to covers by imposing an economy condition that bans the insertion of Din those predicates where it can only apply to one constituent–namely, to the VP. There are two major problems with this amendment: the presence of intermediate readings with some achievements and the lack of intermediate readings with mixed activities and accomplishments. Maintaining the current de�nition for good-�t cover opens the door for intermediate readings. Since it is the de�nition of good-�t that provides us with the best empirical results for interpreting all, it must be that we rule out intermediate readings by other means. In the previous sections we have explored the consequences of not allowing the insertion of Dwith neither states nor achievements, and concluded that such an approach is untenable. In the next section I will point out a further conceptual problem of analyzing all as a modi�er operating over covers. 4.3 Overlapping The need for an economy condition on Duncovers an obscure point in Brisson’s theory: there is some degree of overlapping in the theory between the work done by the values of the covers, on the one hand, and the place where Dis inserted, on the other. In the economy condition de�ned above in (31) that precludes Dfrom quantifying over a singleton domain, and so covers of the form {a, b, c, d} would be unavailable. That is, inserting Don VP and selecting a cover over a singleton domain of the form {a, b, c, d}is not allowed. While this is expected in cases like the boys are a big group, it is not clear that the same condition should hold for all. Note that, by assumption, all is associated with D–it always requires D– (cf. Link 1983) and so no economy condition should be able to ban Din its presence. In addition, as a consequence of this ban, the theory of covers allows two reading correlates with the lack of an intermediate reading as well. This does not seem to be the case: sentences with mixed predicates also lack the intermediate reading. Consider the following example: (i) Context: A football tournament is going to take place in the elementary school of Amurrio, were students and professors will play against each other. The school is really small and there will be only three teams: two teams formed by students and another team formed by professors. Given that professors are lazier than students ... a. The students will play �rst against each other. b. #All the students will play �rst against each other. In that context only the intermediate reading is available, since only groups of students can form a team and play against each other. The example shows that the relevant reading is absence from the all variant even in this kind of rigid contexts. Iberia: IJTL �Volume 7 (2015), 33–67 http://revistas.ojs.es/index.php/iberia/ 54 Interpreting quanti�ers in subject position Jon Ander Mendia di�erent ways of obtaining collective interpretations. On the one side, there is the strategy of choosing a cover of the form {a, b, c, d}, where all the relevant individuals form a single set; this is the strategy employed by plural NPs with states and achievements. Alternatively, Dcan be inserted on DO–when it is present in the structure–and then take a cover of type {{a},{b},{c},{d}}, where DO is interpreted distributively, and this results in the collective interpretation of the big VP. This is because every individual xin {{a},{b},{c},{d}} will be the agent of a DO-ing event. The distinction is accounted for by the aforementioned economy condition ban the insertion of Din those environments were its e�ects would otherwise be vacuous (as it is the case of collective states and achievements). But the resulting picture is still problematic on empirical grounds. By banning the insertion of covers with collective states and achievements we are no longer in a position to allow for exceptions, which is probably the greatest achievement of cover-based theories. As an illustration, consider the following examples, were �girls�={a, b, c, d}. (53) a. The girls built a raft. Cover1={{a, b, c},{d, e, f}} b. The girls are a nice team. The sentence (53a) is good in a context were all the girls but one collaborated in the building of the raft (simply imagine that the missing girl was sick and could not join her peers). To render the (53a) true in such a context, a cover like Cover1is necessary, a cover that will left out an element that would otherwise be withing the denotation of �girls�(the girl din this case). By the same reasoning, one can utter a statement like (53b) to express admiration for a team of girls, even though there is some girl among them, namely d, that is not a member of the team. However, in this case, the economy condition on Dprecludes us to insert it here, and hence no covers can be selected, and so �girls�has to be interpreted maximally. The prediction, then, is that a non-maximal reading should be absent from sentences like (53b), contrary to fact. This problem weakens signi�cantly the conceptual and empirical grounds over which this particular implementation of Dand covers is stated. Even though the basic idea of linking the interpretation of all with the aktionsart of verbs seems to be appealing, the details of Brisson’s account lead to some undesired empirical predictions, in addition to the theory internal issues we just considered. 4.4 The case of di�erent QNPs Lastly, we would like to point out what is probably the most problematic consequence of excluding all from the rest of QNPs. As we saw in section 2, the same pattern that all displays holds also for many other QNPs. Since the behavior of all the QNPs seems to persist, we expect that the rest of QNPs will show Iberia: IJTL �Volume 7 (2015), 33–67 http://revistas.ojs.es/index.php/iberia/ 55 Interpreting quanti�ers in subject position Jon Ander Mendia the same behavior of all in the same relevant environments. Moreover, whatever e�ect the presence of all may have with respect to the collective and distributive interpretation of the predicate, there is no reason to believe that it should extend to other kind of QNPs, because only all involves covers. This observation alone is already problematic, given the data in section 2: it seems unlikely that all the QNPs in question behave as pragmatic modi�ers and that they are not contributing to the truth-conditions of the sentence. In addition, the identical distribution of all and the rest of QNPs as a robust cross-linguistic pattern clearly speaks for a uni�ed account. Moreover, consider the examples in (54) in the scenario we depicted for (51), where only an intermediate reading is available. (54) a. Some of the students elected Leah (... and some others elected Bill). b. Ten students elected a representative. c. ??Most students elected Leah. The example in (54a) is acceptable in this context, where di�erent classes elect their own class presidents. Sentences in (54b)/(54c), however, do not allow this interpretation.18 This is a remarkable fact, since it shows that the intermediate reading, which under Brisson’s account is generated only with all, is also present with some: in this case, all and some pattern together, but not most. But this begs for explanation, since by assumption some is not related to D.19 The important fact to be noted here is that, if accept that all is not a quanti- �er, we are loosing an apparently interesting generalization: all the QNPs we con- 18In the case of most, the reason may be that it is obligatorily distributive (as suggested by Reinhart 1997). The case of (54b) is more controversial, and judgements vary. The collective reading is fully available, but speakers struggle with the intermediate reading. 19As pointed out by Seth Cable (p.c.), there are cases where all does di�er from other QNPs: (i) a. Some of the boys are touching the ceiling. b. All the boys are touching the ceiling. (ii) a. Most of the boys built a raft. b. All the boys built a raft. The example in (i-a) allows collective and possibly intermediate readings more easily than (i-b); on the other hand, (ii-a) is preferable under its distributive reading, whereas in (ii-b) there seems to be no preference for any of the interpretations. This shows that, contrary to what the data in section 2 suggests, all QNPs do not pattern alike with respect to the distributive–collective (and intermediate; see section 4.2 below) readings they allow. A �ne grained analysis of these di�erences is out of the scope of the present paper, and so I will stick to the picture outlined in 2, and bear these considerations in mind for further research. Iberia: IJTL �Volume 7 (2015), 33–67 http://revistas.ojs.es/index.php/iberia/ 56 Interpreting quanti�ers in subject position Jon Ander Mendia sidered in this paper behave similarly in three typologically di�erent languages so far. In the next section we argue that retaining the traditional analysis of all as a Generalized Quanti�er (Barwise & Cooper 1981, Keenan & Stavi 1986) avoids most of these problems. 5 No covers In the previous section we have seen that a version of Dwith covers as spelled out by Brisson (1998, 2003) makes some undesirable predictions. On the one hand, it overgenerates intermediate readings in contexts in which they are impossible, and, on the other hand, we loose an interesting generalization that concerns the behavior of more QNPs besides all. Finally, the theory is redundant in that there is some degree of overlapping between the means by which it generates collective interpretations. From this point of view, it is interesting to provide the system with a mechanism to treat all QNPs in a way that they all get the same interpretations in the relevant contexts. For that, we have two main possibilities: either we provide a sort of good-�t de�nition for each QNP and continue using covers to interpret them, or we get rid of covers for the semantics of QNPs. An alternative then is to provide a good-�t de�nition for each di�erent quanti�er, where a good-�t is simply a relation between a cover and a de�nite DP denotation. Consider, for example, the following de�nition for most (based on Nakanishi & Romero 2004): (55) Good Fitmost: For some cover of the universe of discourse Cov and some NP denotation X,Cov is a good-�tmost with respect to Xi�: ��{x∶x∈X∧x∈Y∧Y⊆X}�>1�2�X� According to (55), the quanti�er most requires a cover where the cardinality of the union of all the cells containing just members of �NP�will be greater than the cardinality of the set denoted by the DP divided by two. This de�nition, however, will not help with the problem of intermediate readings pointed out in the previous section. It seems that getting rid of covers and providing some other denotation for QNPs seems a step worth considering. Ideally, we would avoid intermediate readings and, at the same time, retain some consistency in the semantics of QNPs. 5.1 QNPs as Generalized Quanti�ers The most straightforward theory available for interpreting QNPs is that of Generalized Quanti�ers (GQ henceforth; Barwise & Cooper 1981), were quanti�ersdeterminers denote properties of properties: Iberia: IJTL �Volume 7 (2015), 33–67 http://revistas.ojs.es/index.php/iberia/ 57 Interpreting quanti�ers in subject position Jon Ander Mendia Moreover, there is an important factor that must be taken into account: the availability of the pair-list reading varies depending on the type of quanti�cational subject (examples from Szabolcsi 1997). (71) a. Which/what boy did two dogs bite? b. ??Fido bit X and King bit Y. (72) a. Who did two dogs bite? b. Fido bit X and King bit Y. (73) a. Who did the dogs bite? b. Fido bit X and King bit Y. From this discussion we can conclude that, indeed, there are some di�erences between all and the rest of quanti�ers.24 However, it does not seem that there is conclusive evidence against the quanti�cational status of all. Brisson centers the gist of her argument on the di�erences between every and all, but we have seen that these di�erences are not exclusive of all, but hold for the rest of quanti�ers too.25 6 Conclusion From the results obtained in this work, we can conclude that there are at least four types of di�erent predicates with respect to the collective/distributive distinction: (74) Collective predicates26 a. BAD with subject QNPs: be many,be a good team,be a family ... b. OK with subject QNPs: meet,be together,gather ... 24Note that we have skipped from the discussion some more obvious di�erences, like the fact that all can �oat, or that it can combine with plural de�nites. 25As we mentioned above, it may be true that all is not a true quanti�er after all. But then, either we need more evidence than the one provided here, or there might be a wide variety of what we call ‘QNPs’ that are not quanti�cational, in the sense that they show the same kind of di�erences with every and other ‘well-behaved’ quanti�er-determiners. 26The former correspond to correspond to Dowty’s pure ‘cardinal’ predicates, whereas the latter correspond to pure ‘collective’ predicates. Iberia: IJTL �Volume 7 (2015), 33–67 http://revistas.ojs.es/index.php/iberia/ 64 Interpreting quanti�ers in subject position Jon Ander Mendia (75) Mixed predicates a. OK with subject QNPs: lift a piano,build a raft ... b. BAD with subject QNPs: elect a president,win a relay race ... Using covers to interpret QNPs has a series of undesired consequences that can be overcome if we adhere to the classic version of Generalized Quanti�er Theory. In this paper we have pointed out a number of problems that previous proposals have to face and we have concluded that covers can be dispensed with at no cost, and with the additional bene�t of (i) precluding systematic intermediate readings with QNPs in subject position and (ii) simplifying the semantics of QNPs. If correct, the proposal uncovers a di�erence between the mechanisms that allow collective readings for non-quanti�cational versus quanti�cational NPs: the latter depend on speci�c syntactic environments, whereas the former do not. Moreover, the di�erences have been shown to hold for English, Spanish and Basque; nevertheless, since the relevant di�erences are grounded on strong cross-linguistic generalizations, it is expected that more languages pattern similarly. References Barwise, Jon & Robin Cooper. 1981. Generalized quanti�ers and natural language. Linguistics and Philosophy 4(2), 159–219. Borer, Hagit. 2005. The normal course of events. Oxford: Oxford University Press. 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Dordrecht: Kluwer. Lasersohn, Peter. 1998. Generalized distributivity operators. Linguistics and Philosophy 21(1), 83–93. Lasersohn, Peter. 1999. Pragmatic halos. Linguistics and Philosophy 75(3), 522–571. Link, Godehard. 1983. The logical analysis of plurals and mass terms: a lattice theoretical approach. In R. Bauerle, C. Schwarze & A. von Stechow (eds.), Meaning, use and interpretation of language, Berlin: De Gruyter. Mendikoetxea, Amaya. 1999. Construcciones con se: medias, pasivas e impersonales. In Nueva gramática de la lengua española, vol. 2, 1631–1722. Madrid: Espasa Calpe. Mittwoch, Anita. 1982. On the di�erence between eating and eating something: activites versus accomplishments. Linguistic Inquiry 13(1), 113–122. Moltmann, Friederike. 2005. Part structures in situations: the semantics of individual and whole.Linguistics and Philosophy 28(5), 599–641. Iberia: IJTL �Volume 7 (2015), 33–67 http://revistas.ojs.es/index.php/iberia/ 66 Interpreting quanti�ers in subject position Jon Ander Mendia Nakanishi, Kimiko & Maribel Romero. 2004. Two constructions with most and their semantic properties. In Keir Moulton & Matthew Wolf (eds.), Proceedings of NELS 34, vol. 2, 453–468. Parsons, Terence. 1990. Events in the semantics of English: a study in subatomic semantics. Cambridge, MA: MIT Press. Pustejovsky, James. 1991. The syntax of event structure. Cognition 41(1), 47–81. Ramchand, Gillian Catriona. 2008. First phase syntax. Cambridge: Cambridge University Press. Reinhart, Tanya. 1997. Quanti�er scope: How labor is divided between QR and choice functions. Linguistics and Philosophy 20(4), 335–397. Rooth, Mats. 1985. Association with focus: University of Massachusetts, Amherst dissertation. Rooth, Mats. 1992. A theory of focus interpretation. Natural Language Semantics 1(1), 117–121. Schwarzschild, Roger. 1996. Pluralities. Dordrecht: Kluwer. Szabolcsi, Anna. 1997. Ways of scope taking. Dordrecht: Kluwer. Taub, A. 1989. Collective predicates, aktionsarten and ‘all’. In Emmon Bach, Angelika Kratzer & Barbara Hall Partee (eds.), Papers on quanti�cation, Amherst: University of Massachusetts at Amherst. Vendler, Zeno. 1957. Verbs and times. The Philosophical Review 66(2), 143–160. Winter, Yoad. 2001. Flexibility principles in Boolean semantics: the interpretation of coordination, plurality and scope. Cambridge, MA: MIT Press. Received: 2015/04/29 Revised: 2015/07/02 Accepted: 2015/09/21 Jon Ander Mendia Department of Linguistics / University of Massachusetts Amherst [email protected] Iberia: IJTL �Volume 7 (2015), 33–67 http://revistas.ojs.es/index.php/iberia/ 67