Supervaluationism and Necessarily Borderline Sentences

The supervaluationist theory of vagueness is committed to a particular notion of logical consequence known as global validity. According to a recent objection, this notion of consequence is more problematic than is usually thought since i) it bears a commitment to some sort of bizarre inferences, ii) this commitment threatens the internal coherence of the theory and iii) we might find counterexamples to classically valid patterns of inference even in the absence of a definitely-operator (or similar device). As a consequence, the supervaluationist theory itself is in trouble. This paper discusses the objection.