What is the name of the paradox where a heap loses grains yet stays a heap?

Take a heap of sand and remove one grain. Still a heap - nobody would say a single grain makes the difference. Remove another. Still a heap, by the same reasoning. Keep going and the reasoning never breaks, yet you end up insisting that one grain is a heap. Run it the other way and you can prove that no quantity of sand is ever a heap at all. The argument is credited to Eubulides of Miletus in the fourth century BC, and it is named from the Greek soros, a heap.

The trouble is not sand, it is vagueness. Words like heap, bald, tall and red have no sharp boundary, and each individual step of the argument looks unimpeachable while the conclusion is absurd. Something has to give, and every option costs something. The epistemicist says there really is an exact grain at which it stops being a heap and we simply cannot know which - tidy logic, strange metaphysics. Others allow statements to be partly true, or true on some ways of sharpening the word and not others.

It stops being a parlour game the moment a threshold has to be drawn in law or medicine. At what point is a person too drunk to drive, or a patient too ill to consent, or an embryo far enough along to have protections? Every one of those is heap-shaped: no single second or single millilitre makes the difference, and yet a line must be put somewhere. The paradox is the reason those lines always look arbitrary, because they are.