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, whereas the unitary meaning view does not encounter the problems facing the polysemy view. I propose unitary meanings which are rich enough to account 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 look for a theory of pragmatics which can explain how we achieve the different interpretations of these modals in use. I will argue that adopting the Relevance theory view of what drives interpretation gives us the basis for such an explanation.
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Marjolein Groefsema (1995) studied this question.
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