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I offer an integrated theory of the meaning of only in which the prejacent, while not presupposed, is both entailed and backgrounded, hence tends to project (following a general proposal about projection due to Simons et al. 2010). Moreover, I argue, contra Beaver & Brady (2008), that only is not conventionally associated with focus, the focus effects arising instead pragmatically. But I do adopt aspects of their semantics for only, including the presupposition of a pre-order over the elements of its domain.
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Craige Roberts (2010) studied this question.
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