Sorites

The sorites paradox is a family of philosophical puzzles about vague predicates, traditionally illustrated by questions about heaps and other borderline cases. The term comes from Greek soros, meaning “heap,” and the paradox is associated with Eubulides of Miletus, a 4th century BCE Greek philosopher who introduced several sorites-like arguments. The core idea is that a chain of small, seemingly harmless steps can lead from a clearly true premise to an apparently false conclusion, challenging how we apply binary predicates to vague concepts.

A classic formulation involves a heap of sand. If removing one grain from a heap yields another heap, and if this step can be repeated, then after removing many grains one by one, we would still have a heap, contradicting the idea that eventually we no longer have a heap. A related version uses baldness: if removing a single hair does not make a man non-bald, repeated removals should not turn a bald man into a non-bald, yet a sequence of removals can produce a bald individual from a non-bald starting point. These examples illustrate a basic tension between intuitive judgments about vague terms and the rules of logical deduction.

The paradox highlights the problem of vagueness in language and logic. Responses include supervaluationism, which allows for truth to depend on precise but unarticulated interpretations; epistemic theories, which posit sharp boundaries that are simply unknown; and approaches such as fuzzy logic or gradualist and contextualist theories, which allow degrees or context-dependent thresholds. The sorites remains central to debates on how language maps to the world and to questions about rational argument in the presence of vague concepts.