ABSTRACT
This chapter provides a rigorous definition in a framework analogous to possible worlds semantics; it is neutral between epistemic and supervaluationist accounts of vagueness. The definition is shown to have various desirable properties. But under natural assumptions it is also shown that 2nd-order vagueness implies vagueness of all orders, and that a conjunction can have 2nd-order vagueness even if its conjuncts do not. Relations between the definition and other proposals are explored; reasons are given for preferring the present proposal. The terminology of “nth-order vagueness” presupposes that a hierarchy of orders of vagueness has been defined. Formally, higher-order vagueness corresponds to contingency in which worlds are possible. The chapter also provides to clarify the structural issues without addressing deep questions about the nature of vagueness. For simplicity, predicate and quantifier structure is suppressed. An alternative definition of validity in the formal semantics would have permitted the counterintuitive situation of higher-order vagueness without first-order vagueness.
