Frege famously held that the ontological categories correspond to the the logico-syntactic types. For instance, something is an object just in case it can be referred to by a singular term, and likewise for all the other categories. This view faces an expressibility problem: in order to express the view, we need to generalize across categories; but by the view itself, any one variable can only range over a single category. We provide a sharp formulation of the problem, show that there is no easy way out, and then explore some of the hard ways.
(Joint work with Bob Hale)