Formal pragmatics has been largely preoccupied with strengthening inferences: the observation that utterances often receive an interpretation that is stronger than their literal content. For instance, (1) implicates that (2) is likely to be false and (3) is normally interpreted to exclude the possibility that (4) is true.

(1) I haven't got a lot to do.
(2) I have nothing to do.
(3) I have a lot of things to do.
(4) I have a million things to.

In this talk, I turn to cases where speakers assert an alternative they do not believe to be true, to convey an alternative that can be truthfully asserted in that context. In particular, I look at two rhetorical figures, meiosis and hyperbole, through the lens of scalar alternatives. Meiosis is a type of ironic understatement. An example would be someone for whom (1) is true uttering (2). Hyperbole is a kind of overstatement, for instance, when someone for whom (3) but not (4) is true asserts (4). 

My first goal is to try and see how we can capture these rhetorical figures using the standard scalar language of formal pragmatics. My ultimate goal is to try and approach these figures, as well as connected notions like irony, with the same formal rigour as we normally approach a phenomenon like scalar implicature.

My second goal is to try and relate the case of hyperbole to evaluative (roughly, connotative) dimensions of meaning. My approach here is related to that of Kao et al. (NAS 111.33, 2014) within the Rational Speech Act framework but I will show how the scalar underpinnings that I argue for can improve on such proposals.