Dr. Mathieu Paillé

A Unified Semantics for Summative and Integrative Predicates

Abstract: Predicates in natural language can be classed according to whether they are ‘integrative,’ i.e. hold of individuals qua individuals (e.g., This is a comedy), or ‘summative,’ i.e. hold of individuals qua sums of parts (e.g., This is blue; ‘blue’ quantifies universally over its argument’s parts). 

The present talk improves on the theory in Paillé 2020 for summative predicates, in a way that ends up making apparently challenging predictions for integrative predicates (if the two classes are to remain unified). Summative predicates are known to display truth-value gaps (Löbner 2000, Spector 2013, Križ 2015): The square is blue is neither true nor false if the square is partly but not fully blue. I suggest a way to modify the theory in Paillé 2020 to generate such gaps, by modelling strengthening through the trivalent Pexh operator of Bassi et al. (2021). This move raises a non-trivial puzzle: integrative predicates have not been suggested to involve such truth-value gaps, but these are now predicted. I show that in fact, the generation of truth-value gaps with integrative predicates is empirically desirable. I discuss various data involving situations where two integrative predicates hold of an individual, but only one of the predicates is asserted; I suggest such sentences are neither true nor false. Thus, the unified semantics for summative and integrative predicates from Paillé 2020, modified to generate truth-value gaps, can and should be maintained.