Scope, monotonicity and maximal informativity cannot be underestimated! A compositional analysis of an apparent linguistic illusion

Vera Hohaus (The University of Manchester)
Ryan Walter Smith (University of Manchester)

We offer a compositional analysis of a type of inversion illusion, focusing on under-over sentences like Chomsky’s importance cannot be underestimated. Such sentences are normally construed as being equivalent to Chomsky’s importance cannot be overestimated, i.e. that Chomsky is very important. This reading, however, is often claimed to be illusory; the correct interpretation is argued to be one in which Chomsky is extremely unimportant. Building on Hohaus & Bade’s (2023) analysis of depth-charge sentences (Wason & Reich 1979), our analysis derives both readings compositionally via the different scopes of a negated modal with respect to a comparative contributed by under- and their interaction with maximal informativity. Both cases of alleged but empirically robust illusions can be understood from a unified semantic perspective, highlighting the value of rigorous formal analysis.