Implicatures of modified numerals: quality or quantity?

This paper presents a theory of modified numerals that derives a three-way distinction in the implicature profile between superlative modifiers, comparative modifiers, and bare numerals. In contrast to the recent proposal by Schwarz (2016a), and drawing on elements from Coppock and Brochhagen’s (2013) inquisitive analysis, the proposal decouples ignorance implicatures from upper-bounding implicatures, and thereby captures an important difference between more than and at least, which differ in their ignorance implicatures but both lack an upper-bounding implicature. At the same time, it accounts for the context-sensitivity in the ignorance implicatures of modified numerals found by Westera and Brasoveanu (2014), and addresses a problem with Coppock and Brochhagen (2013) pointed out by Schwarz (2016b). The key feature of the proposal is the fact that ignorance implicatures may arise in two different ways, namely, both from the Maxim of Quantity and from the Maxim of Quality.