The Sorites

Eubulides of Miletus · c. 4th century BCE

The puzzle

One grain of sand isn’t a heap. Adding a single grain to a non-heap doesn’t make a heap. Therefore no heap exists.

Domain

Vagueness

Attribution

Eubulides of Miletus

Date

c. 4th century BCE

Note

Heaps obviously exist. So one of the two innocent-looking premises must be false, and neither obviously is. The Sorites is the central problem of vagueness. Most predicates we actually use — “tall,” “rich,” “old,” “bald,” “alive” — have no sharp boundary, but classical logic insists every predicate must. Three lines of response: reject classical logic for vague terms, accept fuzzy degrees of truth, or accept (with Williamson’s epistemicism) that the sharp lines exist but we cannot know where. The political form of the puzzle (“how many votes constitute consent,” “at what week does a fetus become a person”) is structurally identical and just as unresolved.