As a central project in Constructing the World, David Chalmers motivates an approach to constructing a space of epistemically possible worlds through his defense of the Generalized A Priori Scrutability Thesis: there is a compact (i.e., sufficiently small to make the thesis interesting) primitive class of statements that a priori entails all epistemically possible statements. I argue that Chalmers’ preferred solution to what I call reference-fixing problems that arise for the semantics that he develops that work—primarily in defense of the Generalized A Priori Scrutability Thesis, but in favor of which he also offers substantial independent motivation—generates counterexamples to the thesis.  This tension demonstrates that, at most, only one of these two central projects of Constructing the World may be defended.