Even, comparative likelihood and gradability

A popular view of the semantics of even takes it to presuppose that its prejacent, p, is less likely than all its contextually relevant focus alternatives, q. In this paper I point out three novel problems for this 'comparative likelihood' view, having to do with (a) cases where even p is felicitous though p cannot be considered less likely than q, (b) cases where even p is infelicitous though p asymmetrically entails and is less likely than q, and (c) cases where even interacts with gradable predicates, indicating that merely requiring p to be higher on the scale than q is not enough to make even p felicitous. Instead, both p and q must also yield degrees which are at least as high as the standard of comparison. In response to these problems I develop a revised scalar presupposition for even which resembles the semantics of comparative conditionals, and which requires that for a salient x, retrieved from p, and a salient gradable property G, (i) x's degree on G is higher in all accessible p worlds than in all accessible q-and-not-p worlds and that (ii) in the latter worlds this degree is at least as high as the standard on G. I show how this presupposition accounts for both traditional observations concerning even, as well as for the novel data and propose that the common presence of 'less likely' inferences with even can be indirectly derived from the common use of 'distributional' standards of comparison with gradable properties. A general contribution of the proposal, then, is in attempting to apply tools from research of gradability-based phenomena for a better understanding of scalarity-based phenomena.