Rigid designators for properties

Here I defend the position that some singular terms for properties are rigid designators, responding to Stephen P. Schwartz's interesting criticisms of that position. First, I argue that my position does not depend on ontological parsimony with respect to properties - e.g., there is no need to claim that there are only natural properties - to get around the problem of "unusual properties." Second, I argue that my position does not confuse sameness of meaning across possible worlds with sameness of designation, or rigid designation. Third, I argue that my position does not founder by way of failing to assign rigidity the work of grounding a posteriori necessity.