Harnessing Vagueness with Productivity

We propose a productivity-based account of vagueness. In this model, predicates remain bivalent over the intended universe, but their extensions may be productive, explaining the persistence of borderline cases as a structural feature of undecidability rather than a semantic gap. We distinguish contrary (term) negation from complementary negation, and show that, for sharp predicates, term negation coincides with logical/complementary negation. We also demonstrate an effective obstruction: no recursively enumerable family of precisifications, each providing a c.e. approximation, can fully capture a productive extension. A uniform escape operator always generates counterexamples. This approach offers a dynamic, one-sided account of vagueness that improves on supervaluationist, fuzzy, and rough-set approaches, explaining the continual emergence of new borderline cases without relying on a predicate–complement partition. Note: This preprint is not peer-reviewed and may contain errors.