Harnessing Vagueness with Productivity

<p>We propose a productivity-based account of vagueness. Predicates remain bivalent over the intended universe, but their extensions may be productive, explaining the persistence of borderline cases as a structural failure of effective decidability rather than a semantic gap. We distinguish contrary (term) negation from complementary negation and prove that, for sharp predicates, term negation coincides with logical/complementary negation. We further show an effective obstruction: no effectively enumerable family of precisifications, each providing a c.e. approximation, can capture a productive extension; a uniform escape operator always produces counterexamples. The model yields a dynamic, one‑sided account of vagueness that improves on supervaluationist, fuzzy, and rough‑set approaches by explaining the perpetual emergence of new borderline cases without appealing to a predicate–complement partition. Note: This preprint is not peer-reviewed and may contain errors.</p>