# Bobzien: Higher-Order Vagueness

KRIPKE CENTER LECTURE
Kripke Semantics for Columnar Higher-Order Vagueness
Susanne Bobzien (Yale University)
Thursday, May 16, 4:15-6:15pm
Room 5307, GC

Abstract. Hierarchical higher-order vagueness leads to incoherence when it is used as a means to avoid a sharp boundary in the Sorites paradox (cf. Sainsbury 1990, Wright 1992, Shapiro 2006). The challenge is to provide a compositional notion of higher-order vagueness that (i) allows infinite higher orders, (ii) retains the desired relevance to the Sorites, (iii) allows for a model-theoretic representation that reflects such relevance, but (iv) does not run into any higher-order vagueness paradox. In some recent papers I have introduced the only type of higher-order vagueness that meets this challenge (“columnar higher-order vagueness”) and have set forth some of its elements. In this paper, I explain what columnar higher-order vagueness is, give a formalization of its core properties in terms of an axiomatic modal system, and produce a Kripke semantics for its simplest (i.e. bivalent & classical) form together with a philosophical interpretation of the semantics. I finish with an illustration of how the semantics can be used as an infrastructure for epistemicist and non-epistemicist bivalent theories of vagueness and briefly touch upon possible modifications for three-valued logics.