Logical theories are paradox-ridden. There are solutions to paradoxes of set theory (like the Russell Paradox) and of semantics (like the Liar Paradox), but they are costly. The standard solution to the semantic paradoxes enforces a strict separation of object language and metalanguage, and expects that in cases of interest the metalanguage will be more expressive than the object language. Linguists can be comfortable with this solution, though perhaps philosophers cannot. Paradoxes of vagueness (like the paradox of the heap) are harder to for linguists ignore but can be addressed by accepting the necessity of a certain amount of arbitrary regimentation in the semantics of words. Such regimentation seems to be unavoidable, does little or no harm, and even can support the development of a theory of vagueness.