Higher‐Order Vagueness and Borderline Nestings: A Persistent Confusion

Abstract

This paper shows that authors who have recently argued that higher-order vagueness is incoherent, paradoxical, illusory or non-existent 1 invariably confound elements of higher-order vagueness (of the kind relevant to the Sorites paradox) with elements of a different paradigm of borderline borderline cases; and that, once the elements of that other paradigm are removed from the description of higher-order vagueness, the basis for the claims of paradoxicality, etc., disappears. 2 The paper sets out in detail the two paradigms (higher-order vagueness and borderline nestings) and their logics (iterated modalities vs. mixed-order non-empty predicates), illustrates how the prevalent notion of hierarchical higher-order vagueness gains its persuasiveness largely from a conflation of these paradigms, and shows how the alternative of columnar higher-order vagueness not only preserves coherence, but also is the sort of higher-order vagueness that is relevant to the Sorites paradox. As a corollary, the paper provides support for the increasing number of vagueness theorists who renounce clear borderline cases (such as Sainsbury, Wright, Williamson, Shapiro, Fara, Raffman, Cobreros and Smith). 3