The contradiction puzzle for logicality

Abstract

We submit a new puzzle for logicality. It has been argued that the logicality of language is reflected both in the exclusion of contradictions and tautologies, and in the tendency to maximize information in various interpretive phenomena, such as scalar implicatures. We discuss that these two lines of research take on different and intimately conflicting notions of information. This becomes apparent when we focus on contradictions, that are treated as uninformative on the first line, but would qualify as (maximally) informative assuming the second. We suggest that a more adequate and unitary notion of information for logicality is halfway between the one famously introduced by Bar-Hillel and Carnap and the one defended more recently by L. Floridi, namely stronger than the former but weaker than the latter. Adopting this solution, both tautological and contradictory constructions turn out to be uninformative, but for different reasons. This, in turn, grounds the novel prediction of a differentiated speaker reaction as a function of whether the triviality in question is a contradiction or a tautology, both in grammatical and in ungrammatical cases.