Remove one grain at a time. When does a heap stop being a heap?
A million grains of sand is a heap. Take one away and it's surely still a heap. Repeat that step enough times and logic forces you to call a single grain a heap. This 2,400-year-old puzzle shows how badly our everyday words handle gradual change.
The sorites paradox takes its name from the Greek word for heap, and is traditionally credited to Eubulides of Miletus, a philosopher of the fourth century BC. The argument has two innocent-looking premises: a million grains is a heap, and removing one grain never turns a heap into a non-heap. Apply the second premise again and again and you reach the conclusion that a single grain is a heap. Each step seems valid, yet the conclusion is plainly false.
The same trick works on almost any vague word: tall, rich, old, blue. The ancient Greeks had a version about baldness called the falakros: one more hair never stops a bald man being bald. Run the argument the other way and adding grains one at a time never creates a heap at all. Bertrand Russell argued that all of natural language is vague to some degree.
Philosophers have tried many ways out. Some deny that heaps exist at all, a bold move defended by Peter Unger. Others set a fixed cut-off, say 10,000 grains, but that seems arbitrary: why should 9,999 grains be so different? Timothy Williamson and Roy Sorensen defend 'epistemicism', the view that there really is a sharp boundary but we can never know where it lies. Supervaluationism allows borderline cases to lack a truth value, and fuzzy logic lets 'heap' be true by degrees, though that raises the question of where each degree begins.
The paradox matters beyond sand. Laws, medicine and ethics constantly draw lines across continuous scales: adulthood, poverty, life and death. The heap reminds us that such lines are often useful rather than natural, and that an argument built from many tiny, reasonable steps can still lead somewhere unreasonable.
Source: Wikipedia — Sorites paradox · Text summarised from Wikipedia (CC BY-SA 4.0)
