Equatives, Measure Phrases and NPIs

Standard semantic accounts of the equative ascribe it an ‘at least’ meaning, deriving an ‘exactly’ reading when necessary via scalar implicature. I argue for a particular formulation of this scalar implicature account which considers that (i) equatives license NPIs in their internal arguments, and (ii) equatives whose internal arguments are measure phrases (MPs) are, in contrast to clausal equatives, ambiguous between ‘at most’ and ‘exactly’ interpretations. The analysis employs particular assumptions about MPs, scalar implicature and the notion of set complementation to enable ‘at least’ readings to be sensitive to the direction of a scale, thereby becoming ‘at most’ readings in certain constructions.