Higher-Order Vagueness

Higher-order vagueness is the phenomenon that the distinction between determinate cases, borderline cases, and determinate non-cases is itself vague. Just as there are borderline cases of 'heap,' there are borderline cases of 'borderline case of heap' — cases where it is unclear whether something is borderline. This threatens every theory of vague predicates that proposes a sharp boundary between the determinate and the indeterminate, because the boundary itself becomes subject to the same sorites reasoning that motivated the theory. The challenge is whether any account of vagueness can avoid infinite regress without collapsing into a distinction between determinacy and indeterminacy that is itself precise — and therefore vulnerable to the very problem it was designed to solve.

Higher-order vagueness is not a bug in the theory of vagueness. It is the theory of vagueness looking at itself in the mirror and realizing the mirror is also vague.