Higher-Order Vagueness

Overview

Higher-order vagueness refers to the phenomenon where the concept of vagueness itself becomes vague. This arises when we encounter predicates that are borderline cases of borderline cases, making it difficult to determine whether the predicate applies even to the determination of its own vagueness.

Key Concepts

The core idea is a recursive problem of vagueness. If a predicate like ‘tall’ is vague (there’s no exact height that definitively makes someone tall), higher-order vagueness asks whether the predicate ‘is vague’ is itself vague when applied to ‘tall’.

Deep Dive

Consider a spectrum of heights. Vagueness means there’s no sharp cut-off. Higher-order vagueness questions the sharpness of the boundary for where vagueness begins or ends. It’s a meta-linguistic problem about the applicability of vagueness.

Applications

This concept is crucial in formal semantics, philosophy of language, and logic, especially in dealing with fuzzy logic and the semantics of natural language where precise boundaries are often absent.

Challenges & Misconceptions

A common misconception is that it implies an infinite regress of vagueness. However, it highlights the inherent complexity in defining boundaries for vague predicates, not necessarily an unending chain.

FAQs

• What is the main issue with higher-order vagueness? It questions the clarity of applying the concept of vagueness itself.
• Does it mean all concepts are infinitely vague? No, it points to the difficulty in precise demarcation for vague concepts.