Converse and Identity

Necessarily, if I ate a slice of pizza, then that slice of pizza was eaten by me. More generally, it is necessarily true that if a relation holds between two objects in some order, its converse holds of the same objects in reverse order. What is the intimate relationship that guarantees such necessary connections? Timothy Williamson argues that the relationship between converses must be identity, on pain of the massive and systematic indeterminacy of relational predicates. If sound, Williamson’s argument overturns our standard conception of relations, according to which relations are individuated not just by the arguments they take, but by the order in which they take those arguments. I show how one can defend the standard conception against Williamson’s argument. My defense helps us to better understand both the standard conception of relations and the nature of relational predicates.