Implicature Accounts

Implicature accounts uphold the standard truth conditions for generalized quantifiers, but propose that it is difficult for us to access the truth values of sentences with empty restrictors due to their pragmatic infelicity. This infelicity arises due to an implausible conversational implicature that interferes with normal communication practices. Different implicature ac- counts might predict that an assessor will react by always accommodating the implausible implicature, always refusing to accommodate the implausible implicature (thereby inferring that the speaker has violated a conversational maxim), or considering both strategies. The oddness response will then be attributed to an assessor’s reluctant acceptance of an implau- sible implicature, her inference that a maxim has been violated, or her confusion about how to proceed with making sense of the assertion.

It is important to begin by clarifying the notion of a conversational implicature. Grice and the neo-Griceans (e.g. Atlas and Levinson (1981), Horn (1984), Horn (1989), Levinson (2000)) propose that all cooperative discourse is governed by maxims of Quantity, Quality, Relation and Manner, and that participants in a conversation assume ‘that talkers will in general (ceteris paribus and in the absence of indications to the contrary) proceed in the manner that these principles prescribe’.12 _{In cases where a speaker appears to violate a}

maxim, conversation participants are frequently induced to make certain inferences about the information that the speaker intended to convey. A proposition p, distinct from the proposition literally expressed by an occurrence of a sentence S, is aconversational implicature

of S if the occurrence of S involves the violation of a maxim and hearers are therefore likely

to infer that the speaker intended to convey that p.

The most detailed version of an implicature account is given by Abusch and Rooth (2004), who begin by noting that both (1a) and (1b) are entailed by occurrences of (2):

2. There are no American kings.

The reason for this is that, assuming Keenan-style semantics for coda-less ‘there’-sentences (see §(1.2.3)), an occurrence of (2) is true relative to a contextcand domain of discourseD

just in caseJAmerican kingKc ∩D = ∅. Hence in every context where an occurrence of (2)

is true, occurrences of (1a) and (1b) will feature empty restrictors and will therefore be true according to standard accounts of generalized quantifiers. However, neither (1a) nor (1b) entails (2). This means that (2)asymmetrically entails(1a) and (1b).

It is commonly held that a speaker’s using a sentence S when a distinct sentence S’ that the speaker was in a position to assert asymmetrically entails S violates Grice’s first maxim of Quantity (‘Make your contribution as informative as is required (for the current purposes of the exchange)’). Abusch and Rooth therefore endorse a principle that may be stated as follows: If S’ asymmetrically entails S and S’ is an assertional alternative to S, then an indi- vidual’s uttering of S relative to a CGcimplicates that he does not believe the proposition that would be expressed by an occurrence of S’ relative toc.13 _{The fact that a speaker utters}

(1a) instead of (2) therefore results in the conversational implicature that she does not be- lieve (2) to hold, hence she must believe (1a) to be true without believing that its restrictor is empty. This results in utterances of (1a) eliciting a sense of oddness for an assessor rela- tive to contexts where she was under the impression that the CG entailed (2), since she is required to accommodate another interlocutor’s apparent belief that (2) fails to hold.

It should be clear that the same implicature is predicted to arise when (1b) is uttered. If the oddness response were to be invariably triggered by the presence of the implicature, then the prediction would emerge that all occurrences of sentences with definiteand indefi- niteDPs with empty restrictors that are predicted to be true by theories of generalized quan- tifiers trigger the oddness response. Implicature accounts must therefore complicate the picture described so far in order to capture the Definite Variance data. Abusch and Rooth tackle this issue by claiming that a sense of oddness may be avoided with indefinite DPs be- cause hearers are able to infer that the speaker fails to believe (2) relative to some restricted set of beliefs pertaining to a relevant situation (the hearer need not establish what beliefs this restricted set involves), rather than that he fails to believe (2) tout court. Since there is no implicature that the speaker fails to believe (2) relative to the entire belief state encapsulated in the CG, the attempted reconciliation between the information the hearer took the CG to include and the information she infers the speaker took it to include is unnecessary, hence the oddness response is avoided. Presumably, those individuals who judge sentences with indefinite DPs to be odd are being less charitable to the speaker and refraining from con- sidering the speaker’s salient beliefs alone. Abusch and Rooth attribute hearers’ consistent failure to apply this interpretation strategy to occurrences of sentences with definite DPs to a property that only the quantifiers denoted by indefinite DPs possess.14

13_{Abusch and Rooth (2004), p.11. Note that it is not explained what makes something an ‘assertional alterna-}

tive’.

14_{In more detail, Abusch and Rooth point out that the following property is possessed by the quantifiers}

My primary objection to Abusch and Rooth’s account is that it is psycholinguistically implausible to suppose that interlocutors routinely assume that speakers possess restricted belief states that potentially cohere poorly with their overall belief states. That is, it does not seem that a natural response to an utterance of (1b) would be the assumption that the speaker possesses some relevant set of beliefs compatible with the possibility that there are some American kings, but that the speaker’s belief state as a whole entails that there are no American kings.

An alternative implicature-based account of definite determiners is sketched in Peters and Westerst˚ahl (2006) (pp.125-6.), who propose that it is uninformative to assert sentences where an ‘every’-headed DP applies to a known empty restrictor because the trivial truth of the sentence is already guaranteed by the restrictor’s emptiness. This proposal differs from that of Abusch and Rooth insofar as it attributes the oddness response elicited by (1a) to an assessor’s assumption that the speaker is violating the first Gricean maxim of Quantity, by accepting the stronger claim (2) at the same time as issuing a claim that is uninformative in light of the prior acceptance of (2). In other words, while Abusch and Rooth attribute the oddness response to an assessor’s struggle to accommodate an implausible conversational implicature, Peters and Westerst˚ahl attribute it to an assessor’s refusal to accommodate the implicature and subsequent inference that a speaker has violated a conversational maxim. However, Peters and Westerst˚ahl include no discussion of the behaviour of indefinite de- terminers with respect to empty restrictors, meaning that their proposal is insufficiently developed to display even descriptive adequacy.

Geurts (2007) (p.257) offers a powerful objection to any implicature account, based on the observation that conversational implicatures of this form can normally becancelledby explicitly stating the stronger claim that is typically the assertional alternative. For example, it is commonly held that occurrences of sentences of the form ‘Many Nβ’ conversationally implicate the proposition that not all Nβ, since ‘All Nβ’ asymmetrically entails ‘Many N

β’; yet this implicature may be cancelled as follows: 3. Many orphans are sick - in fact, all orphans are sick.

An utterance of (3) seems felicitous, and the implicature that would otherwise arise is can- celled. Yet compare (3) with the following:

4. ?Every American king lives in New York - in fact, there are no American kings. If Abusch and Rooth (2004) are correct that (2) is the stronger assertional alternative to ev- ery trivially true occurrence of a sentence with ‘American kings’ as its restrictor, and that the oddness response arises only due to the presence of the implicature that the speaker

B0)(B). For example, from the fact that the set of kings is a subset of the set of males, we can infer that ‘No inhabitant of New York is a king’ is true iff ‘No male inhabitant of New York is a king’; on the other hand, ‘Every male inhabitant of New York is a king’ may be true when ‘Every inhabitant of New York is a king’ is false, in cases where there are some female inhabitants of New York. Thus when a hearer assumes there to be a restricted belief state concerning a salient situation that the speaker is basing his utterance on, the hearer can assess the uttered sentence at the same time as supposing that the speaker had in mind an alternative sentence where some aspect of the salient situation further restricted the explicit restrictor. Crucially, in the case of indefinite DPs, whatever additional restriction the speaker has in mind will yield a sentence with the same truth value as the one he uttered.

fails to believe (2), then the implicature should be cancelled for occurrences of (4) and no sense of oddness should arise. This prediction just seems to be straightforwardly false: as Geurts (p.257) notes, ‘it is fairly obvious that this inference doesn’t behave as an ordinary implicature’, since it seems clear that (4) is infelicitous. The sense of oddness with respect to the first part of the sentence persists, although we might find ourselves concurring with the additional claim that there are no American kings. Without an explanation of the difficulties in cancelling the purported implicature, all implicature accounts of sentences with empty restrictors become implausible. Indeed, they must propose a special type of non-cancellable conversational implicature, which would involve the abandoment of a key characteristic of conversational implicatures.

A second objection that targets all implicature accounts concerns the difficulty of apply- ing them to Definite Variance data that emerges with respect to occurrences of sentences that theories of generalized quantifiers predict to be false. That is, sentences that state the empti- ness of a restrictor ‘N’ fail to entail those of the form ‘Det Nβ’ when ‘Det’ is replaced with a determiner that is predicted to combine with an empty restrictor to yield falsity (e.g. ‘some’, ‘three’, etc.). Implicature accounts would therefore need to provide an alternative explana- tion of the source of the oddness response that sometimes arises in such cases in order to attain descriptive adequacy. Yet the reduced parsimony of such an account would render it less appealing than an account that provided a uniform explanation of Definite Variance data with respect to all determiners, thereby undermining its explanatory adequacy.

In summary, the implicature account proposed by Abusch and Rooth lacks explanatory adequacy with respect to Definite Variance. It was also seen that all implicature accounts must commit themselves to non-cancellable conversational implicatures, which further un- dermines their plausibility. Moreover, the fact that Definite Variance data arises with respect to occurrences of sentences that are predicted to be false when the restrictor is empty threat- ens both the descriptive and explanatory adequacy of implicature accounts.