In this paper I argue that the polysemy view is not capable of giving
a unified account of the meanings of CAN, MAY, MUST and SHOULD, wherea
s the unitary meaning view does not encounter the problems facing the
polysemy view. I propose unitary meanings which are rich enough to acc
ount for the range of interpretations these modals can have, but which
are specific enough to account for why they get these interpretations
and not others. Proposing unitary meanings implies that we have to lo
ok for a theory of pragmatics which can explain how we achieve the dif
ferent interpretations of these modals in use. I will argue that adopt
ing the Relevance theory view of what drives interpretation gives us t
he basis for such an explanation.