Trivalent Exh and summative predicates

Abstract

Many expressions display 'homogeneity': they quantify as universals in positive sentences, but as negated existentials in negative sentences. This paper aims to partly rethink work claiming that homogeneity is the result of exhaustification. I focus on 'summative' predicates like colour adjectives, and the claim that they are universal in positive sentences because they exclude one another. Three puzzles arise on this approach: the existence of truth-value gaps in non-homogeneous situations, the existence of non-maximality, and contrasts between sentential negation and other downward-entailing environments. I show that all of these difficulties can be resolved if exhaustification is trivalent rather than bivalent.