One Grain at a Time

Start with a million grains of sand. Clearly a heap. Remove one grain. Still a heap. Remove another. Still a heap. Keep going. At some point you are left with a single grain. Nobody would call that a heap.

This is the Sorites paradox, from the Greek word for "heap." The problem is devastating because it applies to nearly every concept we use. When does a person become tall? When does water become hot? When does a town become a city? There is no sharp boundary, yet we act as if there is.