An influential view about the relationship between publicity and linguistic meaning is brought into question. It has been thought that since public languages are essentially public, linguistic meaning is subject to a kind of epistemic cap so that there can be nothing more to linguistic meaning than can be determinately known on the basis of publicly available evidence (Epistemic Thesis). Given the thinness of such evidence, a well-known thesis follows to the effect that linguistic meaning is substantially indeterminate. In this paper, we consider the sort of reasons offered for the Epistemic Thesis and uncover an unexamined presupposition about the epistemic requirements of communication and the establishment of meaning conventions. We show this presupposition is undermined by independently motivated considerations about communication and convention, giving us good reason to reject the Epistemic Thesis and its corollary about indeterminacy.