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This paper presents two experimental findings pertaining to the semantics and pragmatics of superlative modifiers ("at least", "at most"). First, in a scenario with N objects of a given type, speakers consistently judge it true that there are ‘at least N’ and ‘at most N’ objects of that type. This supports the debated position that the ignorance conveyed by superlative modifiers is an implicature, not an entailment, and contrasts with results obtained using an inference-judgment paradigm, suggesting that truth-value judgment tasks are impervious to certain pragmatic infelicities that inference-judgment tasks are sensitive to. The second finding is not predicted by any previous theory: In a scenario with N objects, it is not consistently judged true that there are ‘at most N + 1’ objects, even though it is consistently judged true that there are ‘at least N − 1’ objects. To explain this, we propose a novel pragmatic principle requiring that the scenario depicted by a sentence must be considered possible by the speaker (the Maxim of Depictive Sincerity). Put together, the two findings show that truth-value judgment tasks are impervious to some aspects of pragmatics, but not all.

Diagnosing truth, interactive sincerity, and depictive sincerity