Pragmatic inferences with numeral modifiers: novel experimental data

We present results from two experiments that investigate the nature of pragmatic inferences triggered by numeral modifiers (namely at least and more than when embedded under universal quantifiers). We have found that while both types of modifiers give rise to implicatures, they differ in the extent to which they trigger such inferences, contra current theoretical analyses (e.g. Büring 2008, Schwarz 2013). We also found that the precise nature of the inferences in question is one that favours a theory positing a rather modest set of alternatives for modified numerals (as in Büring 2008, contra Schwarz 2013). Background — Geurts and Nouwen (2007) argued that superlative modified numerals (SMNs, e.g.”at least 3”) differ from comparative ones (CMNs, e.g. ”more than 3”) in giving rise to epistemic inferences, which may disappear in certain embedded contexts (cf. Buering 2007). While it is (relatively) uncontroversial that these two kinds of quantifiers differ with respect to the ignorance inferences they trigger, it is an open question how this difference extends to other pragmatic inferences. Two inferences are of relevance here: variability effects akin to free choice and scalar implicatures. Consider the sentence Every student read at least 3 / more than 2 books. Assuming the scale of numbers as the relevant scale, such a sentence would give rise to implicatures of the kind not every student read more than 3 books, suggesting in turn that at least some student read 3 books. Variability effects are (only slightly) different: they say that not every student read the same number of books. Experiments — In 2 experiments, we investigated both kinds of inferences, whilst also comparing CMNs to SMNs. Both experiments consisted of short dialogues in Dutch between a researcher and an interviewer; the researcher makes a claim and the interviewer poses a question about the claim. Participants had to read these dialogues and rate how well the interviewer has understood the researcher’s claim on a Likert scale from –3 (the claim is not understood) to 3 (the claim is understood). Both experiments used the same target items, varying only in the interviewer’s question. The following box gives a translation of such an item. Researcher: During the event every street was guarded by more than 6/at least 7 policemen. Exp1. Interviewer: Were they all guarded by the same number of policemen? Exp2. Interviewer: How did you find out that there were streets guarded by 7 policemen? The interviewer’s question in Exp1 targets a variability inference connected to the researcher’s claim (i.e., not every street has the same number of guards) and is inconsistent with this inference. The question in Exp2 targets and requires the inference triggered by scalar implicature (i.e., not every street was guarded by more than 7/at least 8 policemen). Aside from the modified numerals, Exp1 also tested the variability effects in the n or more disjunctions and Exp2 tested scalar implicatures under three determiners (every, all, some) and the implicature of disjunction under all. (The items with every and all showed almost identical behavior, so they are merged from now on under the heading Quant.) All experimental items (6 in Exp1, 14 in Exp2) were rotated through lists in a standard way, so that each participant only saw one condition per item. Contradictory controls (6 in Exp1, 10 in Exp2) as well as semantically and pragmatically well-formed items (13 in Exp1, 10 in Exp2), and fillers were added to every list. There were 68 participants in Exp1, and 43 in Exp2. The data, summarized in the boxplots below, were analysed with mixed-effects ordered probit regression models, including the maximal converging random effect structure for subjects and items. In both experiments Quant+CMNs (and SMNs) were rated significantly lower than the semantically and pragmatically well-formed items (p < .0001) and significantly higher than the self-