Boxuan Zheng
Shandong University
The dominant conception of vagueness treats it as a form of semantic under-determination. On this view, vague expressions fail to determine a unique boundary of application, and vagueness arises from the existence of multiple admissible precisifications. However, such accounts face significant difficulties. Philosophically, they threaten to undermine the contentfulness of ordinary language. Formally, they often struggle to preserve a fully compositional treatment of vague expressions.
Meanwhile, approaches that treat vagueness as a form of semantic over-determination have received comparatively little attention. On this kind of view, vagueness arises not because language determines too little, but because it determines too much. Very roughly, a vague predicate is associated with multiple admissible patterns of application rather than a single uniquely privileged one. Yet this approach has not been developed into a systematic account.
This paper develops a use-sensitive, bivalent theory of vagueness grounded in semantic over-determination. Drawing on a Wittgensteinian conception of language use, I argue that vagueness arises from the coexistence of multiple equally legitimate patterns of use. These patterns largely converge on paradigm cases while diverging at the boundaries, thereby generating multiple admissible boundaries of application. Because these patterns substantially overlap in their application and belong to a shared linguistic practice, the resulting phenomenon is vagueness rather than ambiguity.
Formally, the paper introduces an additional parameter U representing use patterns. This yields a compositional semantic framework capable of modelling the proposed account of vagueness. The framework explains the Sorites paradox without abandoning bivalence. I conclude that semantic over-determination offers a more satisfactory explanation of vagueness than traditional under-determination approaches.
