Modified numerals: Two routes to ignorance
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CitationE Coppock, Alexandre Cremers, Jakub Dotlacil, Floris Roelofsen. 2017. "Modified numerals: Two routes to ignorance." Language,
Modified numerals, such as at least three or more than five, are known to sometimes give rise to ignorance inferences, in that their use suggests that the speaker does not have exact knowledge. However, there have been disagreements regarding the nature of these inferences, their robustness and context dependency, and differences between at least and more than. We first present a series of experiments which sheds new light on these issues and explains some contradicting reports in the previous literature. Our results show that (a) the ignorance inferences of at least tend to be more robust than those of more than, but (b) both modifiers are sensitive to the question under discussion (QUD). We argue that this pattern can be explained if we assume two sources of ignorance: traditional Quantity implicatures, which arise regardless of the modifier but are sensitive to the QUD, and implicatures arising from the maxim of inquisitive sincerity, which are QUD-insensitive but only appear with at least.