Scoop up a heap of sand and let it fall away one grain at a time: at what exact moment does it stop being a heap? This episode explores the Sorites paradox, first formulated by Eubulides of Miletus, and shows how a valid chain of modus ponens can start from premises everyone accepts and end at the false conclusion that a single grain is a heap. The hosts extend the puzzle to the bald man, the ocean, paint-chip gradients, and the impossible second when a person becomes old.

From there they survey the attempted solutions: Peter Unger's denial that heaps exist and A. J. Ayer's devastating reply that this would make Unger identical to the universe, the epistemicism of Williamson and Sorensen, the neuroscience of subitizing, multi-valued logic, supervaluationism and super-true tautologies, fuzzy logic, Diana Raffman's hysteresis, and how economi ...