Ignorance implicatures of modified numerals

Modified numerals, such as at least three and more than five, are known to sometimes give rise to ignorance inferences. However, there is disagreement in the literature regarding the nature of these inferences, their context dependence, and differences between at least and more than. We present a series of experiments which sheds new light on these issues. Our results show that (a) the ignorance inferences of at least are more robust than those of more than, (b) the presence and strength of the ignorance inferences triggered by both at least and more than depends on the question under discussion (QUD), and (c) whether ignorance inferences are detected in a given experimental setting depends partly on the task that participants are asked to perform (e.g., an acceptability task versus an inference task). We offer an Optimality Theoretic account of these findings. In particular, the task effect is captured by assuming that in performing an acceptability task, participants take the speaker’s perspective in order to determine whether an expression is optimal given a certain epistemic state, while in performing an inference task they take the addressee’s perspective in order to determine what the most likely epistemic state of the speaker is given a certain expression. To execute the latter task in a fully rational manner, participants have to perform higher-order reasoning about alternative expressions the speaker could have used. Under the assumption that participants do not always perform such higher-order reasoning but also often resort to so-called unidirectional optimization, the task effect finds a natural explanation. This also allows us to relate our finding to asymmetries between comprehension and production that have been found in language acquisition.

Superlative-modified numerals and negation: A multiply negotiable cost

Comparative-modified numerals (CMNs) and superlative-modified numerals (SMNs) are reported to exhibit a polarity sensitivity contrast: unlike CMNs, the use of SMNs is said to be sensitive to embedding under negation. This contrast is however neither well studied nor well understood, such that the existing views in the literature disagree vastly on both the basic facts and related expectations. In this paper we investigate this contrast in three offline experiments. We show that there is strong empirical support for this reported contrast under negation, but none of the existing analyses of the contrast can capture it in full, though we do seem to require insights from each.

How obligatory irrelevance, symmetric alternatives, and dense scales conspire: The case of modified numerals and ignorance

Buccola & Haida (2019) explore the consequences of a semantic-pragmatic theory in which relevance is closed under speaker belief. A primary consequence of this closure condition, they show, is that the Maxim of Quantity commits speakers to expressing their epistemic state about every relevant proposition. We argue that this commitment, dubbed Strong Epistemic Transparency, explains the contrast in ignorance inferences exhibited by non-strict comparative expressions like at least vs. strict ones like more than (hence the class A/B distinction of Nouwen 2010). We also discuss how our analysis might be extended to account for the observations of Cummins, Sauerland & Solt (2012) and Enguehard (2018) that the modifier more than does not block scalar inferences of round numerals.

Modified Numerals

This chapter discusses the use of experimental methods for probing the semantics and pragmatics of numeral modification. Modified numerals, like ‘at least 3’ or ‘more than 2’, are interesting from a theoretical point of view because they give rise to a range of implicature-like inferences depending on the form of the modifier and the immediate linguistic context. The chapter discusses both studies that aim to counter or support existing theoretical proposals in the literature and studies that bring in entirely new theoretical issues. It also reflects on methodological issues in this area.

Comparative modified numerals revisited: scalar implicatures, granularity and blindness to context

We present a theory of the pragmatics of comparative modified numerals such as “more than~5”. Our proposal is based on the assumption that they trigger alternatives derived from discrete “granularity scales”. This is sufficient to explain the basic pattern of scalar implicatures from comparative numerals; we then show how extra assumptions of blind exhaustification and QUD uncertainty refine the prediction in that we can explain how and when comparative numerals trigger irrelevance inferences.

Up to n: Pragmatic inference about an optimal lower bound

This paper focuses on English directional modified numerals up to n, which triggers opposite inference patterns in speaker-uncertainty and authoritative-permission contexts. I propose that these opposite inference patterns are due to pragmatic inference about an unspecified semantic lower bound of up to n, based on its similarities to gradable adjectives and vague characteristics. The value of the semantic lower bound in different contexts is predicted by a general pragmatic principle of interaction between informativity and applicability independently motivated in previous probabilistic models on gradable adjectives.