3.1 Two types of indexical bare plurals

As mentioned in connection with (11), Carlson (Reference Carlson1977) notes that some bare plurals, typically those modified by relative clauses or PP’s with an indexical expression, behave differently from standard bare plurals. The following are some canonical examples of indexical bare plurals:

Indexical bare plurals do not lend themselves to kind-level predication (15a) or to binding by adverbs of quantification. They are also not very good with individual level predicates (15b).

He notes that such bare plurals can be ambiguous between opaque and transparent readings. The following can be read in a way that the content of the description is not included in Bill’s belief worlds or in Sue’s search:¹⁰

Recall that Chierchia’s account, as summarized in Section 2, is that such bare plurals are ∃ generalized quantifiers because they are shifted to argument type by the low ranked ∃ type shift. It therefore predicts full convergence between indexical bare plurals and indefinites, but this has been challenged by Van Geenhoven (Reference Van Geenhoven, Jackson and Matthews1999). One point of difference between the two positions is empirical. While Chierchia argues that such NPs can take wide scope with respect to negation, Van Geenhoven claims wide scope readings to be unavailable. The source of this disagreement, I believe, is due to a distinction in the class of indexical bare plurals that has so far escaped notice.

The examples in (17) show that indexical bare plurals are not a homogeneous class. Some of them, those in partitive constructions, indeed allow wide scope over negation, and this can be made explicit. This scopal flexibility, however, does not hold generally:

While (17a) behaves as predicted by Chierchia, (17b) from Van Geenhoven (Reference Van Geenhoven, Jackson and Matthews1999), is contradictory. This buttresses Van Geenhoven’s arguments against Chierchia. Of course, the acceptability of (17a) does not support Van Geenhoven’s view that these bare plurals are semantically incorporated indefinites.¹¹

We can abstract away from scope interactions, and note that there remains a distinction between the two types when we try to use them in statements with incompatible predicates.¹² In (18a)–(18c) there are no other operators, so distinctions having to do with kind terms vs. semantically incorporated indefinites are irrelevant. However, there is a contrast between (18a) and (18b)–(18c). We understand the first clause in (18a) to apply to some parts and the second clause to apply to other parts. The same option is clearly not available to (18b) and (18c), where we apparently interpret all the people/light bulbs to have the first property so that applying the second property leads to contradiction:

Given that scopal effects are at the heart of the distinction between type shift by nom and type shift by ∃, this distinction clearly merits further attention. I should note in closing that these facts are equally problematic for both approaches to bare plurals, the neo-Carlsonian approaches that treat such bare plurals as kinds and the ambiguity approaches that treat them as object-level indefinites.

3.2 Infelicitous indexical bare plurals

There is a further problem with taking indexical bare plurals to tap into ∃ type shift. Not all bare plurals that are conceptually incompatible with kinds are, in fact, acceptable. The crucial data rests on contrasts in contextually anchored bare plurals of the kind discussed by Condoravdi (Reference Condoravdi1997), those she terms “functional” bare plurals. In addition to her example (19a), I include two others:

I will not be concerned with the particulars of Condoravdi’s approach but rather with what her data implies for Chierchia’s theory.¹³ The bare plurals in (19) pose a challenge because they seem to suggest the operation of iota, rather than ∃. The real problem, however, is that there are structurally parallel sentences such as the ones in (20) where the bare plural appears infelicitous. That this is not an effect restricted to bridging contexts but is more generally true of indexical bare plurals can be seen in (21), where the contextual grounding is lexically encoded in the modifiers inside the noun phrase:¹⁴

One might, of course, appeal to the blocking principle to explain this effect, but we would then have a problem showing why the same does not apply to (19). In addition, it would not explain why the ∃ type shift, which does not have any presuppositions associated with it, does not become available once iota is lexically blocked. Once again, it bears emphasizing that the data in (19) to (21) pose a challenge not only for Chierchia’s theory but for all current theories of bare plurals.

4.1 Extending the scope of Nom

I will take as my starting point the surprising infelicity of certain bare plurals discussed above. The obvious conclusion to draw from the facts is that there are only two covert type shifts in natural language, nom and iota. In languages with definite determiners iota is indeed lexically blocked, as claimed by Chierchia. This entails that if for any reason a bare plural cannot undergo nom, it will simply be unacceptable. We now have to figure out the reason why some indexical bare plurals in English undergo nom, while others do not and are therefore infelicitous.

I start by delinking nom from kind terms. Instead, I build partiality into the function in a somewhat different way. That is, instead of an appeal to the concept of kinds in Chierchia’s (1a), repeated here as (22a), I appeal to a notion of proper variation in size, as shown in (22b):

Let us see how this helps us deal with indexical terms. Recall that Chierchia takes kinds to be individual concepts that live in the domain of quantification U, if and only if, they “identify classes of objects with a sufficiently regular function and/or behavior” and “generally have a plurality of instances (even though sometimes they may have just one or none)” (Chierchia Reference Chierchia1998: 350). As we can see, there is both an appeal to intensionality and an appeal to variation in size in defining the notion of kinds here.

My revision of nom in (22b) preserves the notion of variation in size as integral to nom but it lets in a certain amount of extensionality. Let us consider the requirement of variation in size first. The idea that number morphology plays a role in licensing kind formation goes back to differences I noted in Dayal (Reference Dayal, Barker and Dowty1992) between bare plurals/mass terms and definite singular generics in English and between bare plurals/mass terms and bare singulars in Hindi. There were two conclusions I drew from these comparisons. I located number morphology, rather than definiteness marking, as the locus of the differences since they were maintained across languages with and without determiners. A second conclusion I drew there was that singular morphology would constrain the resulting kind term to singleton instantiation sets. I argued that there were fundamentally two types of operations involved in kind formation: a “plural” kind formation and a “singular” kind formation. The former is what we have been discussing here: nom is defined on predicates whose extensions vary in size from index to index; it is undefined for singular terms “because the number feature clashes with the presuppositions associated with a kind term” (Dayal Reference Dayal, Barker and Dowty1992: 48).¹⁵ This point is highlighted by Chierchia. His definition of nom in (1b) builds in the uniqueness associated with iota and effectively rules out nom(dog), as clashing with the notion of kind. The semantics of plural morphology allows nom(dogs) because now plural individuals of different sizes can be denoted at different indices. The proposed revision in (22b) takes things a bit further. It not only prevents nom from applying to singular terms, it also blocks it from applying to plural predicates if their extension remains constant in size across indices. Let us see what this buys us.

I repeat the crucial contrasts from Section 3:

A crucial difference between (23) and (24) is in the relationship of the bare plural with the noun it is associated with. Take a given campus. While it is readily possible to accommodate a set of students by the mention of a campus, it is not strictly speaking necessary that there be students for a campus to be considered a campus. Similar considerations apply to buses and passengers or gardens and groundhogs. In each case, if we define a function from a given campus/bus/garden to students/groundhogs/passengers in it, we are likely to end up with different sets at different times, and most likely these sets will be of different sizes.

Turning to (24), we see that the connection between the two nouns is much tighter. A car cannot be considered a (complete) car if it does not have wheels. Similarly, while monuments do not, in and of themselves, entail the existence of stones, a given monument made of stone does: the monument cannot exist if the stones are removed. It is the same with a rope, which cannot exist without its fibers. Another way to express this is to say that the noun which provides the functional pivot (e.g., car, rope, monument) and the bare plural it is functionally related to (e.g., wheels, fibers, stones) are co-extensional. If the function is restricted to indices in which the pivot exists, the cardinality of the predicate denoted by the bare plural will remains constant across all of them.

I am suggesting that the infelicity of the bare plurals in (24) is due to this requirement of variation in size but I am aware that this particular implementation of the intuition may not be precise enough. Ivano Caponigro (p.c.) correctly points out that one can conceive of a given rope as having fewer fibers in one world than in another. If the two ropes count as the “same” rope, (22b) fails in its job (see Heller and Wolter 2011 for relevant discussion). There is, of course, a simple way to take care of this problem. We can tap into the intuition that there is a minimum limit on size. There is no world in which we can conceive of the rope without any fibers, so the presupposition on nom could conceivably be stated as: ∃s P_s = ∅. I do not pursue this line here since it does not rule out unacceptable bare singulars, such as the ones in (25a). There are many situations in which the same country does not have a president/monarch so the requirement that there be an index at which the extension of the nominal is empty would be insufficient. It would have to be combined with the requirement of variation in size:

Another alternative to (22b), suggested by an anonymous reviewer, is to have variation in the instantiation set itself instead of in its size: ∃s ∃s′ P_s ≠ P_s′. This would work as well for the contrast we are interested in, since it would rule out the set in (24) where the bare plurals are co-extensional with the pivot of the function. It would also explain cases like (25b) where one might imagine a context in which a platoon is defined in terms of a fixed number of soldiers, but the actual soldiers in a given platoon could change from time to time. The reason I have not adopted this suggestion is that it is not clear to me that the same reasoning would not apply to cars and wheels. After all, the wheels on a typical car get changed several times and yet (24a) is clearly unacceptable, unlike (25b). Furthermore, eliminating reference to size would require a separate explanation for cases like (25a). The function from a given country to its president/monarch yields different (atomic) individuals at different times, but bare singulars are unacceptable. The fact that bare singulars do not seem to undergo nom suggests that rigidity in size is critical.

For the moment, then, I will continue to take (22b) as the appropriate way of constraining nom, though I will return to this question briefly in Section 6 (see Dayal in prep for further discussion of the alternatives considered here). To sum up, (22b) allows nom to apply to predicates that do not include a deictic term, i.e., standard kind denoting bare plurals, as in Chierchia’s original formulation. It privileges bare plurals over bare singulars which are restricted by number morphology to invariably denote an atomic individual. In the case of indexical bare plurals, it makes a crucial distinction. The deictic expression restricts variation to situations with the contextually salient entity in it, in the actual world or in worlds with counterparts of it. The presupposition of variation makes nom undefined for predicative terms where co-extensionality with the deictic term leads to invariance in size. With iota being lexically blocked, such terms are correctly predicted to be infelicitous if ∃ type shift is not in the set of covert shifts. It should be obvious that even if some variant of (22b), such as the ones we have considered above, were to be adopted instead of (22b), the conclusion would remain valid that the infelicity of indexical bare plurals can only be explained if ∃ type shift is removed from the equation.

4.2 Partition-inducing bare plurals

In the last section I argued for expanding the domain of nom to include those indexical bare plurals that meet a reduced bar for intensionality. The fact that such bare plurals show the same scopal behavior as canonical kind denoting bare plurals is no longer surprising. We expect DKP to apply equally to both and yield narrow scope ∃ readings. The question we must now address is the behavior of those indexical bare plurals for which Chierchia’s ∃ type shift seemed to capture the scope facts correctly: parts/slices/pieces of NP. Given that ∃ type shift is no longer among the set of covert options, we need an alternative account of the ability of such bare plurals to take scope over other operators.

Drawing on the discussion of part-of in Chierchia (Reference Chierchia2010), we can take it to be a function from an entity to sets of entities. Extending the account of part to include pieces, slices, etc., we can treat all of them as subdividing the entity denoted by the inner NP into non-overlapping i-parts. Their role, roughly speaking, is akin to that of classifiers, in that they create properties that have the appropriate structure for counting. Phrases headed by such partition inducing nouns can therefore serve as arguments for cardinal expressions or determiners, as shown in (26a):

The question that concerns us here is how to interpret such phrases when there is no cardinal or determiner in the structure. As we know from examples like (26b) they display the scopal properties that ∃ generalized quantifiers have.

In order to address this question, let us consider cardinal phrases which show a similar pattern of behavior. They can be arguments of determiners (27a) or function by themselves as ∃ generalized quantifiers (27b):

A standard view of cardinal expressions in work stemming from Link (Reference Link, Bäuerle, Schwarze, von Stechow, Portner and Partee1983) is that they are predicate modifiers. This allows them to serve as arguments of determiners. When there is no determiner they are taken to shift to a generalized quantifier meaning by a default ∃ type shift (LandmanReference Landman2004, Ionin and MatushanskyReference Ionin and Matushansky2006, ChierchiaReference Chierchia2010, among others). We have argued in the previous section, however, against the possibility of such an option, in order to explain the infelicity of some indexical bare plurals. A further argument for an alternative explanation comes from cross-linguistic considerations. We know that in languages without definite determiners, such as Hindi, Russian, or Chinese, bare plurals cannot interact scopally with other operators. We have captured this fact by allowing them to shift to argumental meaning via iota as well as nom. Interestingly, cardinal expressions in these languages behave like cardinal expressions in English in allowing scope interaction with other operators. That is, they behave like regular indefinites, rather than definites. If we were to allow phrases headed by cardinal expressions to be covertly type-shifted into argumental meaning, we would predict incorrectly that in these languages they would make use of iota, just like bare plurals.¹⁶ An alternative in which covert type shifts do not come into play for cardinal expressions is clearly preferable.

I suggest that cardinal expressions, universally, are ambiguous between predicative and ∃ generalized quantifier meanings. Thus there are two options for their interpretation. (28a) involves a predicative meaning for the cardinal. (28b) involves the existential generalized quantifier meaning. What is ruled out is the derivation in (28c), where the cardinal has a predicative meaning and undergoes ∃ type shift covertly.¹⁷

There remains one final issue to settle. Assuming that cardinal phrases are not in the domain of nom, a derivation like (29a) will be ruled out in languages with determiners due to blocking by the lexical definite. In languages without determiners, however, they are predicted, incorrectly, to be possible under a definite reading due to a covert application of iota, as shown for Hindi in (29b):

In order to rule out the derivation in (29b), we may consider the primary meaning of cardinals to be that of a generalized quantifier. However, in structures where a predicative meaning is required they shift by a covert application of BE (Partee 1986).¹⁸ Assuming that such shifts are repair operations, there is no motivation for a predicative meaning for the cardinal expression in a structure like (29b). Without a determiner above, it is predicted that phrases headed by cardinal expressions will necessarily denote generalized quantifiers and show scope interaction with negation and other operators cross-linguistically. Back to indexical bare plurals, I suggest the same holds for partition-inducing expressions like part-of/slices-of, etc.

4.3 Some predictions for indexical bare plurals

The proposal I am advancing makes an essential distinction within the class of indexical bare plurals. The first type, those that shift via nom, are predicted to undergo DKP in episodic contexts and display obligatory narrow scope, just like kind denoting bare plurals. The second type, those with partition-inducing head nouns, are predicted to behave like regular indefinites in being able to take scope over other operators. However, there are two properties noted by Carlson that apply equally to both types of indexical bare plurals. One is the ability to take narrowest scope in contexts where indefinites cannot take such scope, the other is the ability to have de re readings of the sort that kind denoting bare plurals do not have. Since I am aligning one kind of bare plural with kind terms and another with indefinites, these shared properties call for some further discussion.

Carlson (Reference Carlson1977) notes that the following have differentiated scope readings. That is, they allow different books/puzzles to participate in different sub-events of destruction/discovery. Overt indefinites do not display similar effects. These data are particularly important because they show that the ∃ readings of bare plurals are not a subset of the ∃ readings of indefinites:

Under the present account, (30a) is unproblematic since the bare plural denotes a kind and is subject to DKP. The challenge is to explain (30b). If these bare plurals are like indefinites, (30b) should pattern with the examples in (31), where the generalized existential quantifier takes scope over the adverb and leads to the implausible readings in which the same set of entities is destroyed/discovered multiple times.

So far I have argued that pieces of that puzzle or parts of this machine can have the same semantics as regular indefinites. However, this does not preclude the possibility that they can also be analyzed as simple predicative terms. If so, they would be able to undergo nom as long as they satisfy the presupposition of variation in size.¹⁹ It seems to me that they do. It is possible for there to be different partitions of the same entity at different indices: a puzzle can be made into a 50-piece puzzle in one world and into a 100-piece puzzle in another; a cake can be cut into 6 slices in some world and into 8 slices in another. If so, then it should come as no surprise that they would have the option of aligning with other kind terms in taking lower scope than indefinites that function unambiguously in argument position as generalized quantifiers.

The second property that the two types of indexical bare plurals have in common is the potential for de re readings. Carlson (Reference Carlson1977) notes, albeit somewhat tentatively, that (32a) seems to be ambiguous in the relevant way, while (32b) clearly is not:²⁰

(32a), under the present account, is predicted to have the interpretation in (33a), after the application of DKP. This can be compared to (33b), the representation of (32b):

I assume that the situation index on a bare plural, shifted via nom, must be identified with the situation index at the lowest point in the tree where one becomes available. In an intensional context, this necessarily yields an opaque reading. An indexical expression inside the bare plural (e.g., next and its logical translation ‘next-to-y_i’), however, anchors the interpretation of the bare plural to a set of finite entities of whom the attitude holder could potentially have direct knowledge. This is what I claim is the source of the de re feel of these examples. In other words, the apparent de re reading is a piggy-back effect based on the contextual anchoring provided by the deictic expression. When the bare plural is unmodified or when the modification does not contextually anchor the interpretation, the effect cannot arise. The effect is also unlikely to arise if the anchoring is to a set that is potentially too large for an attitude holder to have direct knowledge of its members. I think the following would not be characterized as allowing a de re construal:²¹

No doubt this issue needs further thought, both in terms of the generalizations as well as implementation (see Dayal in prep), but I hope that the remarks here suggest a way of reconciling the fact that interpreting such indexical bare plurals via nom still leaves room for distinctions between indexical bare plurals and canonical kind terms.

Before ending this section, I would like to acknowledge that the issue of scope interaction with negation for nom shifted indexical bare plurals remains somewhat debatable. Gennaro Chierchia (p.c.) points out that (35a)–(35b) are accepted by speakers in situations where only some of the books were bought or read. The point I would like to emphasize, though, is that this cannot be made explicit, as shown in (36a)–(36b):

The data seems a bit puzzling at first glance but I suggest that the wide scope effect we get for (35a) and (35b) is due to the possibility of a contrastive reading. Take a context in which I bought almost all the things I had intended to buy, including perhaps some books that I wanted to buy. I can utter (35a) to convey that among the things that got left out were books I wanted to buy. Similarly, if I read almost everything I was supposed to read including some books suggested by you, I can say (35b) to convey that among the things I didn’t read were books suggested by you. In fact, as pointed out by an anonymous reviewer, even (36a)–(36b) become acceptable if the verbal constituents are contrastively stressed (and but is changed to and). The point worth emphasizing is that these are not the standard wide scope readings of indefinites. It is only bare plurals that can plausibly be analyzed as having partition inducing head nouns that allow for true wide scope, where conjunctions with affirmative and negative counterparts do not result in contradiction. The case of indexical bare plurals that do not countenance conjunction of incompatible predicates but nevertheless seem to allow a ∃¬ reading no doubt merits further attention. But I would like to suggest that the locus of this inquiry should be the role of modification, not the possibility of the ∃ type-shift.

5.1 Arguments against ∃-force for kind denoting bare plurals

I start with two facts that argue against the ∃ force associated with bare plurals. I give in each case the logical representation that would be derived under Chierchia’s neo-Carlsonian approach as well as under the ambiguity approach. I do this to highlight the fact that the problems are not specific to the neo-Carlsonian position:

(37a) shows that the referents of a bare plural cannot be listed. If all that is involved in interpreting bare plurals in episodic contexts is some form of existential quantification over (instances of) dogs, as shown in (37b)–(37c), there is no reason why they should resist specification via a list. The data in (38) is the problem of incompatible predicates we had encountered earlier in connection with indexical bare plurals. As shown in (38b) and (38c), standard approaches do not have a way of accounting for the oddness of (38a). Since there is no issue of scope interaction and each conjunct would normally be acceptable on its own, their conjunction should be as well. Note that switching to compatible predicates has an ameliorating effect, as shown in (39). I should note that it is important in applying this diagnostic to keep the interpretation of both conjuncts fixed to a single spatio-temporal location.²²

These facts are replicated cross-linguistically. Consider the following Korean paradigm.²³ In the first case, we have a nominative marked bare nominal, in the second a nominative marked bare nominal with the overt plural morpheme. Both are judged unacceptable:

Switching to compatible predicates leads to improvement in the basic version and full acceptability in the plural-marked version.

To sum up, specification is resisted in languages with definite articles. In languages without definite articles, specification is possible under a definite reading of the bare plural, but not under an indefinite reading. Bare plurals seem to resist the conjunction of incompatible predicates universally. In addition to English and Korean, I have tested the data in Hindi and Japanese as well. As already shown, these facts are as problematic for the neo-Carlsonian account which always refers to kinds in the interpretation of bare plurals, as they are for the alternative ambiguity-based accounts that interpret them as object-level indefinites. Since my focus here is on Chierchia’s theory, I will pitch my solution to the problem posed by these facts in relation to the rule of DKP, which is responsible for deriving the existential readings of bare plurals in his theory. However, there are obvious implications for the ambiguity approach as well.

5.2 Bare plurals as definites over a widened domain

There are two modifications I will propose to DKP. The first is to remove existential quantification from it, and simply have the sort mismatch between the predicate and the kind term repaired by taking the extension of the kind, i.e., the maximal entity that instantiates the kind at the relevant index (see also DayalReference Dayal, Maeinborn, von Heusinger and Portner2011a for discussion of this way of deriving definiteness in Chierchia’s system). The second is to require the domain of quantification for a bare plural to be wider (cf. Kadmon and LandmanReference Kadmon and Landman1993). Furthermore, I impose a requirement of proper widening where the instantiations of the kind in the widened domain must properly include the instantiations in the base situation:

The claim of widening immediately accounts for the impossibility of specification, demonstrated in (37). If the instantiation set extends beyond the contextually salient set, it follows that it would not be possible to specify through a list the entities denoted by the bare plural. The explanation for the impossibility of conjoining incompatible predicates, demonstrated in (38), becomes tractable under the claim of maximality. It is parallel to the explanation for the oddness of conjoining incompatible predicates with definites, shown in (43). The same individual cannot have two conflicting properties at the same time:

This line of argumentation, however, begs the question of how to derive the intuition that bare plurals seem to have indefinite readings. In the next section I show that in accounting for the facts in (37) and (38) we haven’t thrown away the baby with the bathwater. The solution rests on both aspects of the proposed modification: maximality and widening.

5.3 Representative group readings

The challenge, in brief, is to reconcile the maximality that clearly helps rule out the conjunction of incompatible predicates with the perception that bare plurals in episodic contexts allow predication to a subset of relevant entities. In order to show that maximality need not be anti-thetical to our intuitive understanding of bare plurals, I will begin with definite determiners which canonically are thought to encode maximality. An interesting fact about them is that although they refer to maximal entities, they can actually allow a weaker reading in which the predication, strictly speaking, only holds of a subset of the group. It is easy to see this when definites are contrasted with universal terms:

In a situation where 3 out of 10 reporters asked questions, (44a) would be false but (44b) may well be accepted. Note that this is independent of the domain restriction for which resource domain variables have been proposed. In both (44a) and (44b) the resource domain variable may restrict the evaluation to reporters at a press conference in the White House on a particular day. The difference between universals and definites remains unaffected even when the common noun has this restricted interpretation.

This phenomenon, known as representative group readings or pragmatically weakened readings, has been studied by Dowty (Reference Dowty, Marshall, Miller and Zhang1987), Taub (Reference Taub, Bach, Kratzer and Partee1989), Brisson (Reference Brisson1998), and Lasersohn (Reference Lasersohn1999), among others. Lasersohn (Reference Lasersohn1999) discusses these facts within a more general perspective on various items that countenance and regulate such effects.²⁴ His main point with regard to data such as (44b) is that statements with definites can be evaluated with respect to subsets of the full set of entities, pragmatic halos in his terms, as long as the gap between the halo and the actual denotation is irrelevant in the utterance situation.

Let us work through a concrete case to see how the account works. Consider a situation in which there are four reporters, a, b, c, and d. Of these a, b, and c ask questions at the news conference. In this scenario, the halos for the definite plural would be the set in (46a), with the halos ordered from tightest on the left to loosest on the right. Assuming the compositional semantics in Lasersohn, the halo of a complex expression is derived by applying normal semantic rules to all possible combinations of elements drawn from the halos of its immediate parts. Under this view a sentence like (46b) may be judged true in virtue of a proposition like (46c), where a particular halo of the definite functions as the argument. That is, a loose halo with only three of the four reporters suffices for truth, as long as the context supports treating them as representative of their group ιx[reporters(s)(x)]:

My claim is that bare plurals present a parallel situation. In the same situation as above, the halos of the bare plural would include larger entities, as represented on the left in (47a). A statement like (47b) is verified on the basis of a loose halo such as the one we see in (47c), as long as the context supports treating them as representatives of their group. This is parallel to what we saw in (46), except that the group represented happens to include other possible reporters:

This is represented diagrammatically in (48):

(48)

With this in mind, let us take a closer look at the “indefinite” reading of bare plurals. A canonical context for such readings might be something like (49). You are looking out of the window, you see dogs, none of them known to you, running around the garden. Your friend asks you the question in (49a). You might respond with (49b):

You know that the dogs you see could not possibly be all the dogs in the world, possibly not even in the neighborhood. You use the bare plural to refer to this larger entity, though the truth of the statement is based on the halo that refers only to the dogs in the base situation. The intuitive characterization of this reading may be that it is an indefinite because world knowledge tells us that only a subset of the dogs in the wider set are involved. The point I am making is that such a reading technically does not involve ∃ quantification over dogs in the way that an actual indefinite like some dogs does. One way to think of this is to say that by choosing a kind term, the speaker signals that the truth of the statement will be verified with respect to a loose halo that refers to a group larger than the contextually salient one. This puts, if you will, empirical bite into the claim of reference to kinds in episodic contexts.

There is an interesting consequence of the account I am proposing. Consider what happens if you utter (49b) when there are no dogs outside. There will not be a halo for ^∩dogs_s′ that will make the sentence true, but the term itself will notbe undefined because the presupposition of existence can be satisfied on the widened domain. In the case of a plural definite on the other hand, the term itself, ιx [dogs(s)(x)], is undefined. We can capture, without stipulation, a difference between definites and bare plurals by appealing to different domains of quantification for presupposition satisfaction.

Another welcome consequence is that it provides a straightforward account of the problem of incompatible predicates. Consider the following paradigm, due originally to Kroch (Reference Kroch1974):

Assume a context in which (50b) will be judged true under a pragmatically weakened reading. That is, a context in which asleep(the townspeople) is true only of a proper subset of the townspeople. The question is why in (50c) those members who are awake cannot make the second conjunct true. The reason, according to Lasersohn, is that the choice of a halo is context sensitive. If their being awake is relevant enough to justify the assertion in the second conjunct, a halo that leaves those people out cannot be supported to make the assertion in the first conjunct.

The same obviously applies to conjunctions with plural definites. Two conjuncts which have incompatible predicates cannot be remedied by applying the predicates to different halos since a subset that is deemed irrelevant to the truth of the first conjunct cannot then be resurrected as relevant in the next conjunct. In this respect, definites differ from indefinites, whose semantics has predication to subsets built into it and need not rely on halos for the relevant reading:

Under the view that a bare plural is a type of definite, the solution to the problem of incompatible predicates with bare plurals follows from our assumptions about maximality and representative group readings. To go back to our White House press conference scenario, whether the plural individual a+b+c represents the contextually salient set of reporters (for the definite) or reporters more generally (for the bare plural), we cannot predicate kept quiet or did not ask questions in the same context by referring to those that are set aside by the halo deemed appropriate for asked questions. Lasersohn’s account, though it incorporates the notion of halos into compositional semantics, leaves to pragmatics the choice of halo appropriate for an assertion. While the semantics proper allows for conjunction of incompatible predicates, the pragmatics of assertion, which regulates the choice of halos, militates against it.

6.1 Scope matters

An important aspect of the semantics of bare plurals has always been the propensity for narrow scope. Let us see if the revisions I have proposed capture this aspect of their behavior, starting with negation:

I believe the facts follow from what we have said so far. Since we are taking bare plurals to be definites, the presupposition of existence will project above negation. If there are no dogs in the base situation, it does not matter. The presupposition can be satisfied in a larger situation. With the presupposition satisfied, DKP comes into play in the computation of the sentence at the level of the predicate bark. If there are no barking dogs in the base situation, either because there are no dogs or because no dog is barking, there will be no halo of the extension of the kind to make it true. (52c) will be false, so (52a), the negative statement will be true, as desired. But now suppose there is one sole dog barking. In a particular context, that one dog may be enough to make (52c) true and, in that case, (52a) will be false, as desired. But now suppose that the one barking dog for some reason doesn’t count as particularly relevant. In such a situation we can ignore that dog and choose a halo without it, making (52c) false and consequently (52a) true.

This last fact goes against the received wisdom about bare plurals and negation but I think it better captures the reality. Consider the White House press conference scenario and assume only one reporter got to ask a question. It may be possible to say in this context either (53a) or (53b), depending on how easy it is for us to treat the sole reporter that asked a question as an outlier:

Finally, we might wonder about cases in which the presupposition of existence cannot be met, as shown in (54):

What seems to be going on is that the first part of the sentence is uttered in a context where the presupposition that dinosaurs exist is entertained, but is subsequently abandoned (see Chierchia and McConnell-Ginet 2000: 384–386 for discussion of apparent cases of presupposition cancellation). But this is not how bare plurals under negation typically behave. Typically, the presupposition of existence is accommodated and the negative sentence evaluated as true either because there are no relevant entities in the base situation, or it is evaluated as true/false depending on whether there is a halo that makes the embedded sentence true. I have suggested that the diagnostic of narrow scope be tweaked to allow for some pragmatic weakening but the rest follows from what we know about negation, definites, and halos. Thus the present account maintains the results of the standard neo-Carlsonian account.

Let us now consider the fact that bare plurals show differentiated scope. These are sentences where they take scope below a temporal adverbial, at a point where indefinites cannot:

There are many issues that come up in relation to such sentences but an intuitively adequate way of characterizing them is to take them as involving quantification over times within a temporal interval. Just to keep things simple, I have taken the quantification to be over sub-situations s of a contextually salient situation S. After the intervention of DKP, we look for a halo of leaves at each s to see if fall can be truthfully predicated of it. Since this is a once-only predicate, we take each sub-situation to license access to a distinct halo for the kind term. This seems reasonable enough but requires further thought when we consider definites in such structures. A variant of (55a) with a definite is also acceptable, as we might expect given the kinship we are claiming between bare plurals and definites. However, we need to be cautious in drawing parallels because the alignment is not perfect.

In contrast to the periphrastic construction, a low pluractional adverbial such as twice yields a more nuanced comparison. With a small time interval like this morning the definite has the implausible reading but with a larger time interval like last year the differentiated scope reading re-emerges:

Descriptively, it is clear what is happening in (56). One can imagine one set of leaves falling and then a new set sprouting subsequently and falling later in the year, but not within a single morning.²⁵

We know that the reason indefinites do not show differentiated scope is because their type does not allow them to be interpreted low enough in the structure, but this does not hold true of definites. Carlson did not compare bare plurals with definites and the literature since then has also not done so systematically. The data discussed here argue for a systematic investigation into the differences between bare plurals and definites, both of which have the same type and can therefore occur as direct arguments of the verb. But clearly bare plurals have more flexibility than definites in allowing reference to distinct individuals within short intervals, thus allowing for distinct halos.

6.2 Bare plurals and discourse

Since I have extended the scope of nom and therefore of the modified DKP to indexical bare plurals, we need to see how proper widening plays out in these cases:

Given the restriction imposed by the modifier to a specific time and place, the requirement of proper widening cannot be satisfied if both properties are involved in the comparison. Because of the anchoring to a particular campus at a particular time, the set of students is fixed regardless of how much we widen the domain of quantification. However, because we are dealing with a complex noun phrase, I suggest that it is possible to satisfy widening with reference to the head noun alone. We can see this graphically:

(58)

The bare plural is felicitous because even though ¬∃x [x ≤ k(s’) ⋀ ¬ in-s(x)], when k = λs ιx[students(s)(x) ⋀ on-the-campus(s)(x)] , it is the case that ∃x [x ≤ k(s’) ⋀ ¬ in-s(x)] iff k = λs ιx[students(s)(x)]. The head noun alone satisfies the presupposition of proper widening so widening can technically be satisfied. The implicit (or explicit) restriction by the indexical effectively blocks reference to a plurality beyond the base situation. The “indefinite” feel of the bare plural is predictably missing because the students on campus cannot represent a larger plurality of students on campus. We thus derive Condoravdi’s “functional” readings, which align bare plurals with definites rather than indefinites. Note that we needed to block nom from applying to wheels on the car, because if it were admitted as a kind term the same reasoning that we have applied to (57a) would apply to it and yield the unavailable reading.

Continuing further with the general issue of relation to discourse, let us move away from functional contexts to contexts in which there is an explicit antecedent. There are two possibilities to consider: an anaphoric link between the antecedent and the bare plural, and a partitive connection. I repeat English and Hindi (10) here to illustrate:

In a language like English the bare plural is unacceptable. In a language like Hindi it is acceptable, but only if anaphorically linked to the children in the first sentence. As far as I know, it is not possible for bare plurals to refer to a subset of a previously mentioned set in any language. This follows under the present account since bare plurals are never interpreted with ∃ force, neither through ∃ type shift, nor through DKP. The only possible reading is an anaphoric one, and that is dependent on whether the language has a lexical definite or not. This is, I believe, an important advantage of treating bare plurals as definites.

6.3 Proper widening and variation in size

Finally, I would like to consider whether we really need to constrain nom by requiring predicates to vary in size across indices and have a requirement of proper widening when bare plurals are used in object-level statements. In order to do so, I will first look at how predicate selection can affect the felicity of bare plurals. I start by noting some predictions of the view that the indefinite feel of bare plurals is due to representative group readings of a definite, interpreted over a widened domain.

It has been claimed that the choice of predicates can influence the availability of pragmatically weakened readings (see DowtyReference Dowty, Marshall, Miller and Zhang1987; TaubReference Taub, Bach, Kratzer and Partee1989; BrissonReference Brisson1998):

(60a)–(60b) can only be verified with respect to a tight halo. That is, the totality of senators must be taken into account. (60c)–(60d), on the other hand, admit loose halos. Not all senators need be involved in the relevant activity.

It is predicted that if a predicate requires a tight halo a bare plural will be inadmissible because it will run afoul of proper widening: if all the senators are already in the base situation, widening cannot add more senators. This prediction is borne out:

Crucially, what we get is infelicity of the otherwise acceptable bare plural senators. This is explained under the view that bare plurals have a presupposition of proper widening but not under a simple view of bare plurals as indefinite.

Coming now from the opposite angle, consider some potential counterexamples to the claim that bare plurals do not tolerate conjunction of incompatible predicates, a feature crucially explained by their being definites. (62a) is a context provided by an anonymous reviewer but other such examples are easy to construct:

An interesting fact about such cases is that there is typically a framing sentence that describes the overall situation, after which follows an elaboration. (62a) most likely follows upon a statement like “There is complete chaos here. People are screaming . . .” The elaboration seems to pick out sub-situations from a partition of the overall situation. Under these circumstances, it appears possible to use different halos for each sub-situation. In the examples I had used to make the case for bare plurals being definites, the situation was held constant and the judgment was that conjoining incompatible predicates led to contradiction. The point was that holding the situation constant precludes a switch in halos for a bare plural. This would not be an obstacle if the bare plural were an indefinite because an ∃ quantifier could still make reference to different subsets.

In a twist on the same theme, certain infelicitous bare plurals seem to improve when they are part of a list. (63b), due to Omer Preminger (p.c.), contrasts with our previous example, repeated here as (63a):

This is a bit of a puzzle but here is how one might try to make sense of it. Suppose, contrary to what we had assumed in Section 3, that fibers even in the context of an indexical is a kind term. Suppose further that in interpreting the phrase fibers are sticking out in (63b), we focus only on a part of the rope, that part where we see some fibers sticking out. Then, we can satisfy proper widening by considering the whole rope which has fibers that are not sticking out. Not only do we get a felicitous bare plural, we also capture the intuition that only some of the fibers in the rope are sticking out. But if we are talking about what those fibers are made of, as in (63a), we look at the whole rope and now proper widening is not possible and the bare plural is ruled out.

The explanation I am giving for (63b) brings us back to the question we had started with: can an appropriate understanding of how proper widening interacts with predicate selection make it possible to eliminate the constraint of variation in size on kind formation? I am clearly not in a position to answer this question in this chapter though the theoretical appeal of such a streamlining is obvious.