Rigidity for Predicates and the Trivialization Problem

According to the simple proposal about rigidity for predicates, a predicate is rigid (roughly) if it signifies the same property across the relevant worlds. Recent critics claim that this suffers from a trivialization problem: any predicate whatsoever would turn out to be trivially rigid, according to the proposal. In this paper a corresponding "problem" for ordinary singular terms is considered. A natural solution is provided by intuitions concerning the actual truth-value of identity statements involving them. The simple proposal for predicates is then defended, by exploiting corresponding intuitions concerning statements involving their nominalizations, in an analogous manner