There is an extensive literature pertaining to NPs that interlocutors perceive to contingently denote the empty set. A paradigm instance of acontingently non-denotingNP is ‘American king’: for the intersection of the set of Americans and the set of kings is empty relative to the current time and actual world, although the intersection is non-empty relative to some
close counterfactual scenarios. When a non-denoting NP occurs as the restrictor for a DP, I shall refer to it as an ‘empty restrictor’.
The problem posed by perceivedcontingently empty restrictors (that is, restrictors that interlocutors take to be contingently empty) begins with the observation that the standard truth conditions for generalized quantifiers indicate that empty restrictors should pose no obstacle to the assigning of the predicted truth values. For example, the truth conditions for ‘every’ predict that occurrences of sentences where the restrictor is contingently empty will be unproblematically true, since the empty set is a subset of any set. The truth conditions for ‘some’ predict that occurrences of sentences where the restrictor is contingently empty will be unproblematically false, since the empty set has an empty intersection with any set.
However, it has been shown in the literature that sentences with perceived contingently empty restrictors exhibit an unexpected pattern of acceptability. Not only do occurrences of such sentences frequently elicit an oddness response instead of judgements that accord with the values predicted by the standard truth conditions, but the eliciting of a judgement of oddness or valuedness seems to correlate with certain properties of the sentence in a pre- dictable way. To explain these claims, it is important to begin by clarifying what it means for an occurrence of a sentence to elicit a sense ofoddnessin an assessor. The following defi- nition demarcates the phenomenon the literature has been concerned with, whilst avoiding prematurely judging the source or nature of the oddness response:
Oddness Response definition:An occurrence of a sentence elicits anoddness response
if and only if: (i) an assessor has a sense that the occurrence is defective or infelicitous, and (ii) the assessor encounters difficulty in assigning it a truth value relative to the relevant context.
The second part of the definition is intended to prevent a sense that a certain sentence con- stitutes a bizarre thing to utter relative to some or all CGs from counting as an oddness response, if it is simultaneously straightforward to assign it a particular truth value relative to a given CG. For example, an occurrence of the sentence ‘There are no kings and there are no kings’ would be strange relative to any ordinary CG, since there is normally a pragmatic expectation that the second conjunct of a conjunction will contribute new information. How- ever, the conditions under which this pragmatically bizarre sentence would be true – that is, if and only if there are no kings within the relevant domain – are nevertheless discernible, allowing an assessor to assign it a value. Also note no oddness response is elicited if an assessor struggles to assign a truth value to an occurrence of a sentence that she neverthe- less considers an appropriate contribution to the discourse, due to factors such as epistemic limitations.
Having clarified what I mean by an ‘oddness response’, we are in a position to set out the data pertaining to sentences with perceived contingently empty restrictors that naturally elicit judgements of oddness and judgements of valuedness. Consider the natural responses to occurrences of the following three sentences, relative to a CG where ‘American king(s)’ is (correctly) perceived to be a contingently empty restrictor:
1. (a) ?Every American king lives in New York. (b) (?) No American kings live in New York.
The first type of data is illustrated by the contrast between (1a) and (1b). Lappin and Rein- hart (1988) claim that a consideration of the former invariably triggers the oddness response, whereas the latter may sound odd or acceptable depending on the context and assessor. They propose (p.1023) that ‘[t]he relevant distinction here is between [DPs] with weak de- terminers and those with strong determiners’ (see §(1.2.2) for a definition of ‘strength’); though their support for this diagnosis of the contrast is solely based on their consideration of a pair of sentences where the determiners ‘no’ and ‘two’ combine with empty restrictors. Nevertheless, the view that the contrast between (1a) and (1b) centres upon the contrast be- tween (in the terminology advanced in §(1.1.3)) definite and indefinite determiners has been widely endorsed in the literature. For instance, Reinhart (2004) (p.52.) reports that, ‘about half the participants’ she has surveyed in various classes assign a value to each of a series of sentences where an indefinite determiner applies to a contingently empty restrictor, whereas the rest of the participants react with an oddness response to each of the sentences.1 I shall therefore refer to the phenomenon illustrated by these data as ‘Definite Variance’.
The second type of data is illustrated by (1c), and consists of the observation that the value predicted by standard truth conditions can be easily assigned in the case of ‘there’- sentences with perceived contingently empty restrictors.2 I shall refer to this phenomenon as ‘‘There’ Acceptability’. ‘There’ Acceptability is unexpected in light of the problems asso- ciated with assigning the standard values to non-‘there’-sentences with contingently empty restrictors.
Theproblem of contingently empty restrictorsinvolves accounting for these data by explain- ing why judgements of oddness arise in cases where standard accounts predict truth values, in addition to explaining why definite and indefinite determiners vary in their propensity to elicit a sense of oddness when combined with empty restrictors. Furthermore, the fact that ‘there be’ constructions allow assessors to assign the predicted value requires explanation.
The following subsections will consist of a survey of the available accounts of sentences with contingently empty restrictors that are prevalent in the literature. I shall discuss four types of account: semantic, processing, implicature andpragmatic presuppositional. These cat- egories are not intended to be totally precise, since certain accounts seem to straddle their boundaries: for example, the account of Reinhart (2004) could be classified as a processing or a pragmatic presuppositional account. Nevertheless, the categories are sufficiently sharp to structure the discussion of the existing positions. It should also be noted that the litera- ture has mainly focused on the task of explaining Definite Variance, thus the discussion in the following subsections will only pertain to this aspect of the problem of perceived contin- gently empty restrictors; developing an account that can explain ‘There’ Acceptability will be tackled later, after progress has been made in finding an account that is able to explain Definite Variance.
I will assess the proposed solutions to the problem of contingently empty restrictors according todescriptive adequacy(the accuracy of the judgements they predict with respect to empty-restrictor sentences with definite determiners, indefinite determiners and ‘there be’ phrases),explanatory adequacy(the plausibility of their explanation of Definite Variance
1Reinhart’s (2004) report suggests that some assessors consistently judge occurrences of sentences where an
indefinite determiner applies to a contingently empty restrictor to be valued, and other assessors consistently judge them to be odd. Definite Variance would receive equal support from a scenario where each assessor varies in her response to an occurrence of such a sentence, potentially due to contextual features.
and ‘There’ Acceptability) andgenerality(the extent to which they rely upon independently motivated mechanisms with general applicability). Such desiderata are frequently invoked implicitly or explicitly in the assessment of accounts of any linguistic phenomenon.
I will conclude that pragmatic presuppositional accounts are most promising, though modifications are required to allow such accounts to meet all three desiderata. Such modifi- cations will be implemented in a later section.