One grain of sand is not a heap. And for any number n, if n grains of sand are not a heap, then the addition of just one more grain does not make them a heap. But in that case you can never get a heap, for each grain you add leaves you just as much without a heap as before. The paradox is serious because it raises a tension between classical logical and mathematical reasoning, and the ‘vague’ predicates of natural language. Solutions include approaches based on denying the second, inductive premise, on introducing ‘degrees of truth’, and on modifying classical logic into fuzzy logic. But it is generally recognized that no solution is free of problems.