The heap (sorites) paradox
Take one grain from a heap of sand. Still a heap. Keep going…
Eubulides of Miletus, 4th century BCE
Rohan's rice
Rohan's mother tipped a whole sack of rice onto a sheet to dry in the sun. "That," she said, "is a heap of rice." Nobody disagreed.
Rohan, who was supposed to be helping, picked out one grain. Still a heap, obviously. One grain cannot turn a heap into not-a-heap. So he took another. And another. Each time, the same rule applied: one grain makes no difference.
By evening there were three grains on the sheet. Rohan's rule had never failed, so, he announced, three grains must still be a heap. In fact, by his rule, one grain was a heap. Even zero grains.
His mother said that was ridiculous. Rohan asked her to tell him exactly which grain had done it.
The puzzle
Removing one grain never turns a heap into a non-heap, yet removing enough grains clearly does. Where is the line?
See it for yourself
What's really going on
Words like heap, tall, bald, old and crowd are vague: they have clear cases at both ends and a blurry zone in the middle. The paradox comes from pretending a vague word has a sharp edge.
Some philosophers say there really is a sharp cut-off that we just can't know. Others say statements in the blurry zone are partly true, a bit like a dimmer switch rather than an on–off switch. Scientists and engineers dodge the problem by defining sharp cut-offs on purpose, such as 'an adult is 18 or over'.
Still argued about. Philosophers still argue over which explanation of vagueness is right.
Think about it
How many hairs can someone lose before they are 'bald'? Is your answer a single number?