PLAN DE GESTIÓN DE COMUNICACIONES

Despite the arguments in §(4.2) against all accounts that attribute inherent existence pre- suppositions to DPs, the following objection may be raised: we should attribute inherent presuppositions at least in the case of ‘the’-headed DPs, in order to account for the unique- ness and familiarity conditions often attributed to such DPs (as discussed in §(1.1.3)). From this it would follow that, firstly, it is too strong to conclude that no DPs have inherent ex- istence presuppositions. Secondly, the oddness response sometimes elicited by occurrences of ‘the’-headed DPs with empty restrictors would then be over-determined if one were to continue to invoke the failure of existence presuppositions inherited from topic position. For these reasons, it might be argued that we should reconsider the rejection of inherent existence presuppositions for DPs in general.

However, I must resist this argument. For, firstly, if I were to attribute to ‘the’-headed DPs a lexically-encoded presupposition that entails the non-emptiness of the restrictor, then this would constitute the abandonment of a uniformly Inherited approach to the existence presuppositions of definite DPs. Secondly, it would be difficult to reconcile with the view that occurrences of sentences that include non-topical ‘the’-headed DPs with perceived empty restrictors are understood as valued. In this subsection, I will therefore show that we may capture the sense in which ‘the’ imposes a cardinality constraint on a set even when it occurs outside of the topic without resorting to inherent presuppositions.

As noted in §(1.1.3), it has frequently been claimed that ‘the’-headed DPs impose a uniqueness or familiarity condition in a manner that distinguishes their meanings from DPs headed by ‘every’ and ‘a(n)’. For instance, generalized quantifier theoretic approaches that adapt Russell’s (1905) analysis treat ‘the’-headed and ‘a(n)’-headed DPs alike by means of the quantifier that relates pairs of sets with non-empty intersections, adding a uniqueness or familiarity condition in the case of ‘the’.30On the other hand, most contemporary linguistic approaches analyse ‘the’-headed and ‘every’-headed DPs alike by means of the quantifier that relates pairs of sets where the first is a subset of the second, adding a cardinality con- dition in the case of ‘the’.31 These strategies are supported by the observation that, unlike (15b) and (15c), there is a clear sense in which (15a) cannot be truthfully asserted relative to a context where interlocutors are assuming the existence of multiple salient kings or no kings:

15. (a) As for Yasma, she’s talking to the king. (b) As for Yasma, she’s talking to every king.

(c) As for Yasma, she’s talking to a king.

30_{For example, this sort of approach is pursued by Szab ´o (2000), though he treats the uniqueness condition as}

a pragmatic inference separate from the truth conditions.

31_{Presumably, contemporary approaches disprefer an analysis that equates ‘the’ with ‘a(n)’ on the grounds}

that the two determiners exhibit distributional dissimilarities (e.g. acceptability in existential ‘there’-sentences) that are normally captured by treating them as denoting quantifiers with divergent logical properties (e.g. in- tersectivity, etc.).

However, the condition that distinguishes DPs headed by ‘the’ from those headed by ‘every’ and ‘a(n)’ cannot be reduced to an existence presupposition associated with topicality, since the definite DP in (15a) is obligatorily non-topical, due to the left dislocation undergone by ‘Yasma’. It might therefore be argued that ‘the’ encodes an inherent existence presupposi- tion. As previously stated, this conclusion would prove problematic for my proposal.

I will follow contemporary theories of generalized quantifiers (e.g. Peters and West- erst˚ahl (2006)) in treating ‘the’ by means of the quantifier that relates pairs of sets where the first is a subset of the second, additionally encoding a cardinality condition as part of the as- serted content. The cardinality constraint on the restrictor’s extension will act as a condition for truth rather than a condition for definedness. For simplicity, I will assume that ‘the’ is lexically ambiguous between a singular version ‘thesg’ and a plural version ‘thepl’; though,

as observed by Westerst˚ahl (1985), postulating ambiguity may ultimately lack motivation, suggesting the cardinality constraint should instead vary as a function of the determiner’s NP argument. WhereAandBare subsets of the domainDdetermined byc:

JThesgKc={hA, Bi:A⊆B&|A|= 1}. JTheplKc={hA, Bi:A⊆B&|A|>1}.

From these semantics, it follows that ‘the king(s)’ will, like ‘every king’, denote the set of all subsets of D of which the extension of ‘king(s)’ is a subset, and have as its minimal witness set the extension of ‘king(s)’. Furthermore, the minimal witness set associated with ‘the king’ will, like that associated with ‘a king’, be a subset of the extension of ‘king’ with cardinality 1; though ‘thesg’ differs from ‘a(n)’ insofar as there is auniqueminimal witness

set consisting of the extension of ‘king’ whenever there is a minimal witness set at all. The difference in the natural understanding of (15a) – (15c) is attributed to the fact that a true assertion of (15a) is understood to attribute a particular cardinality to the set of (contextually relevant) kings in a manner achieved by neither (15b) nor (15c).32

32_{A related type of structure that is frequently held to carry inherent existence presuppositions is overt parti-}

tives. For example, truthful assertions of (16b) require an appropriate number of contextually salient kings, in contrast with (16a). Again, this cannot be reduced to an existence presupposition inherited from topic position, since the partitives in (16b) are obligatorily non-topical:

16. (a) As for Yasma, she’s talking to (three / few / many / most / all / some) kings.

(b) As for Yasma, she’s talking to (three / few / many / most / all / some) of the (four / few / many) kings.

Westerst˚ahl (1985) shows that analyses of the definite article may be generalized to partitives, a strategy I shall adopt. If we represent the most general form for a partitive as ‘Det1of the Det2N’ (where Det2is possibly the

null determiner), we may alter his analysis to accord with my truth conditions for the definite article as follows:

JDet1of the Det2Kc={hA, Bi:JDet1Kc(A)(B) &JTheplKc(A)(D) &JDet2Kc(A)(D)}.

It follows that both ‘Det1of the Det2 kings’ and ‘Det1kings’ denote the set of all subsets ofDfor which the

extension of ‘kings’ stands in the relation specified by ‘Det1’, with the minimal witness set in both cases being

the one specified by ‘Det1’. The difference between the natural understanding of occurrences of (16a) and

minimal variants of the form of (16b) derives from the fact that the truth of the latter require the cardinality of the extension of ‘kings’ to exceed 1, and the relation specified by ‘Det2’ to hold between the extension of ‘kings’

and the domain of discourse. For example, an occurrence of ‘One of the four kings is in the yard’ is true if and only if the set of kings in the yard is of cardinality 1 or greater, the set of kings is of cardinality exceeding 1 and the set of kings is of cardinality 4 or greater. On the other hand, the truth conditions of ‘One king is in the yard’ only require the first of these conditions to hold.

It has been widely observed that the cardinality condition associated with ‘the’-headed DPs often pertains to some proper subset of its restrictor’s extension. For example, West- erst˚ahl (1985) argues that ‘the’ is invariably interpreted relative to acontext set, represented by a variable that intersects with the extension of the NP’s extension within the semantics. The variable representing this context set is very similar to the covert variables invoked by semantic accounts of domain restriction (see §(3.1.1)), hence my insertion of such a variable into the semantics for ‘the’ would be tantamount to endorsing a semantic mechanism of domain restriction for at least some occurrences of DPs. In order to maintain my neutrality regarding the mechanism by which domain restriction should be modelled, I will there- fore refrain from representing the possible influence of context sets within the semantics for ‘the’. Instead, I will assume that ‘the’-headed DPs frequently receive domain restricted understandings, which are brought about by whatever mechanism brings about domain restricted understandings in general, and which coincide with a means of information stor- age that accords with my file card-based analysis of domain restriction (see §(3.4)). When domain restriction occurs with respect to ‘the’, individuals understand the cardinality con- dition to apply to the proper subset of the restrictor’s extension involved in the domain restricted understanding. Hence I will maintain the above semantics for ‘the’, though an advocate of a semantic account of domain restriction should modify them by inserting an appropriate covert variable.

One of the major criticisms of analyses of ‘the’ that treat the uniqueness or familiarity condition as a requirement for truth is that they predict that assessors will invariably judge occurrences of sentences for which the condition fails as false. This prediction is in conflict with the observation that oddness responses often emerge in such circumstances. However, this criticism is inapplicable to my proposal, since I preserve the Strawsonian insight that ‘the’-headed DPs may additionally carry information structure-dependent existence pre- suppositions. Therefore, the non-emptiness of the restrictor is presupposed if and only if the restrictor is part of the topic, with the perceived emptiness of the restrictor’s yielding the oddness response. When non-topical, a known empty restrictor will simply yield a judgement of falsity rather than oddness, due to the failure of the cardinality condition. I therefore take it that the ‘uniqueness condition’ often attributed to ‘the’-headed DPs is part of a lexically-encoded condition for truth, whereas the ‘familiarity condition’ emerges due to a topicality-inherited presupposition that an appropriate file card is present in the common ground.

The historical interest in ‘the’-headed DPs with empty restrictors has yielded a richer discussion of the nuances of assessors’ judgements than is contained in the literature on contingently empty restrictors in general, and it is worth briefly measuring my proposal against the nuanced data that has been raised. Firstly, my proposal accords with the recent experimental results presented in Abrus´an and Szendr˝oi (2013), where participants judged sentences that included ‘the’-headed DPs with empty restrictors to be false a sufficiently sig- nificant proportion of the time to pose problems for any proposal that takes such sentences to be semantically undefined. The authors conclude that their results support an analy- sis where occurrences of sentences with ‘the’-headed DPs assert a cardinality condition, in addition to carrying a pragmatic presupposition that is sensitive to factors that include top- icality.

about occurrences of sentences that include ‘the’-headed DPs with empty restrictors which are held to prompt judgements of valuedness. For instance, Lasersohn (1993) holds that oc- currences of sentences may be assigned the value false in cases where, even if we suspend our belief that the restrictor is empty, other beliefs suffice to falsify the information expressed (e.g. (16a), asserted while demonstrating an empty chair). Von Fintel (2004) offers a devel- opment of this proposal, observing that occurrences of sentences are naturally judged to be false when there is a contextually salient entity whose properties are in principle enough to falsify the sentence (e.g. (16b), where Australia serves as the contextually salient entity). Schoubye (2009) claims that sentences are naturally judged false when they are understood as proffered (though unsuccessful) answers to a QUD with some true answers, which he takes to explain assessors’ natural inclination to assign values to occurrences of sentences where focus occurs on the DP (e.g. (16c), where the question of who is bald is the obligatory QUD). Schoubye also takes his proposal to explain the fact that occurrences of sentences for which a possible congruent QUD is of practical relevance to the assessor are naturally judged as valued, even when they cannot be empirically falsified (e.g. (16d), where a non- factive mental state is attributed (meaning there is no independent means of falsifying the sentence) but the question of who hates the addressee’s mother is of sufficient practical rel- evance to render it the likely QUD):

16. (a) The king of France is sitting in that chair.

(b) The king of France is on a state visit to Australia this week (c) [The king of FRANCE]F is bald.

(d) The king of France hates your mother.

My proposal attributes the fact that (16a) – (16d) are naturally judged false to the idea that ‘The king of France’ is naturally understood as non-topical in each case. I concur with Ebert and Ebert (2013) that, when (16a) is presented without an indication of the intended prosody or QUD, but it is specified that it should be assessed relative to a context where a chair is salient and empty, then an assessor is likely to imagine an occurrence where the topic is ‘that chair’. In other words, it is plausible to argue that, when we consider out-of-context sentences for which the envisaged context has been indicated to include the salience of a particular item, this overrides the default preference for the narrowest focus compatible with neutral prosody (see §(3.3.2)). Similarly, it is plausible to claim that individuals who consider (16b) or (16d) out-of-context are likely to assume that state visits, Australia, this week or the addressee’s mother are more likely things for imaginary interlocutors to be discussing than the king of France, perhaps because they are assumed to be salient or of practical relevance. Finally, my proposal predicts ‘The king of France’ to be obligatorily non-topical in (16c), which means that no existence presupposition emerges and fails. My proposal is therefore compatible with the fact that assessors naturally assign the value false to (16a) – (16d), on the grounds that these sentences are indeed semantically false and no existence presupposition emerges to trigger an oddness response.

In sum, I have argued that it is not necessary to attribute inherent existence presupposi- tions to DPs headed by ‘the’. I sketched truth conditions that include a cardinality constraint on the quantifier’s first argument. An existence presupposition is therefore predicted to arise for ‘the’-headed DPs if and only if they are construed as topical, with the failure of the

lexically-encoded cardinality constraint otherwise resulting in straightforward falsity. This analysis, though preliminary, serve to show that the proposal that the existence presuppo- sitions associated with some occurrences of DPs are inherited from their being construed as topical cannot be challenged based on intuitions surrounding ‘the’-headed DPs.

Summary of §(4.3)

In §(4.3.1), I developed an account whereby the oddness response elicited by some occur- rences of DPs with perceived empty restrictors is attributed to an existence presupposition triggered by the DP’s topicality. I argued that a DP’s occurring as a sentence topic signals that interlocutors are assuming for the purposes of the conversation that there is a file card for the DP. Given my view that the file card associated with a DP represents an arbitrary non-empty minimal witness set, it follows that a topical DP directly presupposes the non- emptiness of the DP’s minimal witness sets, which means that it indirectly presupposes the non-emptiness of the DP’s restrictor.

In §(4.3.2), I discussed the fact that occurrences of monotone decreasing DPs with empty restrictors are apparently able to elicit the oddness response, which conflicts with the pre- dictions of the account developed. I showed that it is plausible to attribute the oddness response in such cases to sources other than the topicality of the DP, before arguing that this does not undermine the account of non-monotone decreasing DPs given in §(4.3.1). In §(4.3.3), I argued that we need not attribute inherent presuppositions to DPs that involve the definite article. Rather, the data that is sometimes taken to motivate such an attribution may be handled by semantically encoding a cardinality requirement as a condition for truth, at the same time as allowing pragmatic existence presuppositions to be inherited from topic position.