Title: CONVERSE PREDICATES AND THE INTERPRETATION OF SECOND ORDER QUANTIFICATION 

 ABSTRACT: In this paper I argue that we cannot interpret second-order quantification as quantification over properties and relations. My argument forges a hitherto unexplored connection between debates typically conducted independently, one metaphysical, about whether there are converse relations, the other logical, about the interpretation of second-order quantifiers. I begin from the semantics of converse predicates. Either we suppose that pairs of mutually converse predicates co-refer or they do not. If we suppose they do co-refer, I argue that we lack an understanding of the relevant class of higher-order predicates which are required for second-order quantification over a domain of relations to make sense. If we suppose they don’t co-refer but pick out distinct converse relations then I argue that even if we do understand the relevant class of higher-order predicates enough to make sense of quantification over relations, we do so only at great theoretical cost. Either way, I conclude that second-order quantification should not be interpreted as quantification over properties and relations.