When does a heap of sand stop being a heap?

Nobody knows, and that is the puzzle. Removing a single grain from a heap of sand never seems to turn it into a non-heap. But repeat that step enough times and you're left with one grain, which is obviously not a heap. Every step looks fine, yet the conclusion is false. This is the sorites paradox, from the Greek word for heap, and it is usually traced back to the Greek thinker Eubulides of Miletus.

The trouble lies in vague words. Heap has no sharp edge, and neither do tall, rich, old, blue or bald. The Greeks had a baldness version too: if one more hair never makes a bald man not bald, then no amount of hair ever will. There's even a colour version: if neighbouring colour chips are too similar for the eye to tell apart, step-by-step reasoning would prove we can't tell any colours apart at all.

Philosophers have tried many escapes. Draw a line at, say, 10,000 grains? But it seems absurd that 9,999 grains isn't a heap while 10,000 is. Some argue there really is a sharp line, we just can never know where it is. Others use fuzzy logic, letting statements be partly true, so the sand slides gradually from definitely heap to definitely not. One philosopher simply denied that heaps exist. A colleague replied that the same logic, run with atoms, would prove he was identical with everything in the universe.