Vagueness and the Sorites

Removing one grain never turns a heap into a non-heap, yet repeated removal does — the sorites paradox exposes the logic of vague predicates.

Definition

A predicate is vague when it admits borderline cases and lacks a sharp boundary; the sorites paradox arises because a series of individually compelling tolerance steps leads from a clear case to a clear non-case.

Scope

This topic covers the phenomenon of vagueness and the sorites (heap) paradox it generates. It treats the structure of the paradox, the existence of borderline cases and apparent boundarylessness, and the leading theories: epistemicism (vague predicates have sharp but unknowable boundaries, classical logic preserved), supervaluationism (truth-value gaps with classical logic retained), and degree theories (many-valued or fuzzy logic), along with the problem of higher-order vagueness that besets several of them.

Core questions

• Which premise of the sorites argument should we reject?
• Do vague predicates have sharp boundaries we cannot know (epistemicism)?
• Should we abandon bivalence and admit truth-value gaps or degrees of truth?
• How should higher-order vagueness — vagueness about borderline cases — be handled?

Key concepts

• borderline cases
• tolerance principle
• the sorites series
• epistemicism
• supervaluation and precisification
• higher-order vagueness

Key theories

Epistemicism

Williamson holds that vague predicates do have sharp boundaries, fixed by use, but their location is in principle unknowable owing to margin-for-error constraints on knowledge, so classical logic and bivalence are fully preserved.

Supervaluationism

Fine treats a sentence as true iff it is true on every admissible precisification; borderline sentences are neither true nor false, retaining classical logic at the level of super-truth while denying bivalence for individual cases.

History

The sorites is attributed to the ancient logician Eubulides. Modern treatments revived in the late twentieth century: Fine's 1975 supervaluationism, fuzzy and degree-theoretic accounts, and Williamson's influential 1994 defence of epistemicism, with Keefe's 2000 survey comparing the rival theories.

Debates

Are there sharp boundaries we cannot know?

Whether epistemicism's claim that vague predicates draw sharp but unknowable lines is more credible than abandoning bivalence (supervaluationism, degree theory), and whether any view escapes higher-order vagueness.

Key figures

• Timothy Williamson
• Kit Fine
• Rosanna Keefe
• Crispin Wright
• Eubulides of Miletus

Seminal works

• fine1975
• williamson1994
• keefe2000

Frequently asked questions

What is the sorites paradox?

Start with a heap of sand and remove one grain at a time. Each removal seems too small to turn a heap into a non-heap (the tolerance principle), yet after enough removals no heap remains. The chain of plausible steps leads to a false conclusion, so one of the premises — usually the tolerance principle — must be rejected.