Are modals polysemous, or do they have a single meaning?

Modals have several distinct uses, and the question of whether they are genuinely polysemous or have a single abstract meaning is an issue that has long been debated in the literature. This problem is linked to the question of the balance of semantics and pragmatics in the analysis of modality: theories which treat modals as monosemous tend to give them a skeletal semantics and make pragmatics and the context do more of the work of interpretation. We argue that modals are not uniform but that the interpretation of different modals varies in the way context applies to them: more specifically we argue that senses of 'may' are clearly distinct, and that this distinction can be accounted for on the basis of different types of pragmatic processes that take place in deriving those senses, not only 'saturation' as is the case with Papafragou's (2000) model, but also pragmatic processes of the 'optional' variety, such as 'modulation', in the sense of Recanati (2004). For 'can', we argue that the senses are less distinct from each other than is the case with 'may', and that different types of pragmatic processes of the 'optional' variety are at play with this modal. Therefore, 'may' [and 'must'] are more polysemous in nature rather than 'can' [and 'should'].