Research Group
in Analytic Philosophy

Abstract

Hierarchical higher-order vagueness leads to paradoxes when employed to avoid sharp boundaries in the Sorites (e.g. Sainsbury, Wright, Shapiro). I suggest this paradoxicality results from a (con)fusion of higher-order vagueness (iterated modalities) with borderline nestings (mixed-order non-empty predicates). Columnar higher-order vagueness is a paradox-proof family of higher-order vagueness that avoids such confusion. It is compositional and compatible with bivalent & non-bivalent semantics, and classical & non-classical logics. I explain what columnar higher-order vagueness is; give a formalization of its core properties in terms of an axiomatic modal system, and provide a Kripke semantics for its simplest (i.e. bivalent & classical) form together with a philosophical interpretation of the semantics that utilizes both viewpoint sensitivity and extensional context sensitivity. If there is time, I illustrate how the semantics can be used as an infrastructure for epistemicist – and non-epistemicist – bivalent theories of vagueness and touch upon possible modifications for three-valued logics.