Minimal sufficiency with covert even

Exclusive particles (e.g. just) express exclusivity inferences by negating focus alternatives to the sentence they modify. Grosz (2012) observes that they can sometimes give rise to what he calls minimal sufficiency readings, which seem to affirm, rather than negate, focus alternatives. Grosz proposes to analyze them in terms of the rank-order reading, a kind of scalar reading of exclusive particles that is independently attested. Coppock & Beaver (2014) put forward a similar analysis based on their unified semantics for different uses of exclusive particles. We point out that these previous accounts fail to capture the distribution of minimal sufficiency readings, in particular, the relevance of distributivity, and propose an alternative analysis where the scalar component of the minimal sufficiency reading comes from a covert version of even, rather than from the exclusive particle itself. Empirical support for this comes from the generalization that an overt even can be added to sentences that have minimal sufficiency readings without changing the meaning, but not to sentences that do not allow for minimal sufficiency readings. We argue that our account not only captures the distribution of the minimal sufficiency reading, but also derives the inferences involved in the minimal sufficiency reading compositionally together with the standardly assumed semantics for exclusive particles and even.