At least ignorance inferences come at a processing cost: Support from eye movements

We present results of an eye-tracking reading study that directly probes ignorance effects of the superlative numeral modifier at least in embedding and unembedding environments. We find that interpreting a numeral (phrase) modified by at least in a context with an ignorant speaker is costlier than in a context with a knowledgeable speaker, regardless of whether at least is in an embedding environment or not. In line with online studies testing scalar implicatures using a similar paradigm, this finding is taken to suggest that the observed processing cost is due to the derivation of ignorance interpretations via a pragmatic mechanism. Our results, given the paradigm we employ, further enable us to adjudicate not only between semantic and pragmatic accounts of ignorance, but also among various pragmatic proposals, favouring neo-Gricean accounts that derive ignorance as a quantity implicature (Büring 2008; Cummins & Katsos 2010; Schwarz 2013; Kennedy 2015). We find no evidence indicating that ignorance with at least in interaction with a universal modal involves an extra operation, like covert movement.