Semantic Accounts

A semantic account addresses the problem of contingently empty restrictors solely by alter- ing the truth conditions given by standard theories of generalized quantifiers. If a semantic account succeeds in altering the truth conditions in such a way that they no longer conflict with the responses elicited by empty-restrictor sentences, then progress is made in resolving the problem of perceived contingently empty restrictors.

The semantic view originates in de Jong and Verkuyl (1984), where it is claimed that the trivial truth predicted by accounts of generalized quantifiers and classical logic for sen- tences where ‘every’ applies to an empty restrictor is based on marked, ‘lawlike’ uses of such sentences. De Jong and Verkuyl argue that the ordinary truth conditions for definite determiners involve a requirement that the extension of the restrictor phrase is non-empty, causing occurrences of sentences to be assigned the value ‘undefined’ when this requirement is not met. This undefinedness is the source of the resulting sense of oddness: for given that occurrences of sentences with perceived empty restrictors lack truth values, it is unsurpris- ing that assessors struggle to assign them values. For example, de Jong and Verkuyl’s truth conditions for ‘every’ are as follows:3

JEvery NβKc      = 1ifJNKc⊆JβKcandJNKc6=∅ = 0ifJNKc*JβKcandJNKc6=∅ =undefined ifJNKc=∅

De Jong and Verkuyl uphold the standard truth conditions for indefinite quantifier expres- sions, treating sentences featuring such expressions as defined even with the presence of an empty restrictor.4

A significant difficulty thus arises for the account of de Jong and Verkuyl with respect to accommodating all of the data that composes the problem of contingently empty restrictors. Definite Variance was originally noted in Lappin and Reinhart (1988), hence the earlier pa- per by de Jong and Verkuyl did not perceive any pressure to reconsider the truth conditions of indefinite determiners. Yet this results in their account’s predicting that sentences where an indefinite determiner combines with an empty restrictor will always prompt judgements of valuedness, which is contradicted by the data.

More generally, in order to predict the Definite Variance data, there are three options available for a semantic account. It must either: modify the truth conditions for indefinite determiners so that the application to an empty restrictor yields undefinedness, claim that indefinite determiners are semantically ambiguous between a version with the standard semantics and a version with modified semantics, or propose an extra-semantic explanation

3_{De Jong and Verkuyl (1984), p.36.} 4_{De Jong and Verkuyl (1984), p.28.}

of the oddness response that sometimes arises with respect to indefinite DPs. I will now show that all of these options are problematic.

Let us begin by considering the first response, where the semantics for indefinite deter- miners are altered to incorporate a non-emptiness requirement. The first argument against this approach is that it erodes the distinction between definite and indefinite determiners by undermining the distinct properties that are commonly attributed to each class.5 For example, as stated in §(1.2.3), Keenan (2003) shows indefinite DPs to be intersective. How- ever, modifying the truth conditions for indefinite determiners means that such determiners need not denote intersective quantifiers.6 A second argument against incorporating a non- emptiness requirement into the semantics for indefinite determiners is that such a movestill

fails to yield the correct predictions for the Definite Variance data. For Definite Variance in- cludes the observation that sentences with indefinite DPs and empty restrictorsvaryin their propensity to generate the oddness response. Modified truth conditions for indefinite de- terminers would predict that sentences with indefinite DPs and empty restrictorsinvariably

trigger the oddness response, as is supposed to be the case for such sentences with definite DPs.

Turning now to the second option, Geurts (2007) (p.261) suggests that the best way for de Jong and Verkuyl to salvage their account is to claim that indefinite determiners are seman- tically ambiguous between presuppositional and non-presuppositional readings, with the context sometimes making one reading more salient. That is, each occurrence of an indefi- nite determiner denotes either the quantifier proposed by theories of generalized quantifiers or a second quantifier which is identical apart from being undefined when its first argument is empty. According to this approach, we can continue to distinguish a class of quantifiers with properties such as intersectivity, but we must deny that determiners such as ‘no’ invari- ably denote quantifiers from this class; for they will sometimes denote the presuppositional copies that lack these properties. I will consider, and reject, this type of approach in §(4.2.2). The third option presumably involves endorsing one of the other responses to the prob- lem of contingently empty restrictors with respect to indefinite DPs. That is, while the odd- ness consistently elicited by occurrences of definite DPs is attributed to their truth condi- tions, the oddness sometimes elicited by occurrences of indefinite DPs is attributed to pro- cessing effects, implicatures or pragmatic presuppositions. One objection to such a proposal is that it would be preferable on grounds of methodological simplicity to advance a uni- form explanation of the oddness response elicited by occurrences of definite and indefinite DPs with perceived empty restrictors. A second objection is that many of the criticisms of processing and implicature accounts, to be set out in subsequent subsections, will straight- forwardly apply to an account that endorses the relevant response solely with respect to indefinite DPs. Finally, if this third approach were to associate pragmatic presuppositions with indefinite DPs, then it would plausibly count as the type of position to be considered, and rejected, in §(4.2.4).

In summary, de Jong and Verkuyl’s semantic account in particular has been seen to fail to predict the differing judgements associated with the Definite Variance data, thereby lacking descriptive adequacy. I then argued that semantic accounts in general are unable to develop

5_{Lappin and Reinhart (1988), p.1027.}

6_{To see this, note that the modified truth conditions for (e.g.) the determiner ‘no’ are compatible with situa-}

tions whereQno(A)(B)holds butQno(A∩B)(B)fails to hold (i.e. ifA6=∅butA∩B=∅); thusQnofails to be

de Jong and Verkuyl’s approach into an approach that predicts the Definite Variance data, since all three options for such a development face insurmountable difficulties. We may therefore conclude that semantic accounts inevitably lack descriptive adequacy.