Plural Expression and Converse Relations

Abstract Since the work of George Boolos in the 1980s, philosophers have become more comfortable making use of plural reference and plural quantification in their theorizing. Plausibly, part of the reason is that it sometimes has a philosophical payoff. Mereological nihilists, for example, can do justice to the apparent truth of everyday claims involving singular reference or singular quantification over composite objects by paraphrasing them as claims involving plural reference or plural quantification over only mereological simples. But the analogous question of whether predicates can plurally express multiple relations has not received attention. I show that answering affirmatively can have philosophical payoffs of its own, illustrating this by explaining how it allows the directionalist about relations to articulate their position in such a way that it avoids Timothy Williamson's (1985) challenge. The result is an expanded range of formal tools which the philosopher can make use of in their theorizing.