James Ryerson in the New York Times:
The “paradox of the heap” seems at first like a trick, a brainteaser that must have some clever catch. But it reveals itself, as it defies easy understanding, to be a philosophical problem. You might approach it as a puzzle, only to end up devising a solution so deep that it would challenge our thinking about language, knowledge and the nature of reality. By the time of her death from brain cancer in July at 48, Delia Graff Fara, a philosopher at Princeton, had done just that.
Start with a heap of sand. If you remove a single grain, it remains a heap. Repeat this process enough times, however, and you have a heap of sand that contains, say, one grain. This is absurd: One grain is not a heap. Something has gone wrong, but it is not obvious what. Either there is a precise number of grains at which point a heap becomes a nonheap, or there is no such thing as a heap, or classical logic is flawed (perhaps it is only ever sort of true that something is a heap). Which bullet to bite?
This paradox, which originated with the ancient Greeks, is troubling because it is ubiquitous. It applies not just to being a heap but also to being tall, or red, or bald, or soft — or any other gradient-like property. When Fara began working on this paradox as a graduate student at the Massachusetts Institute of Technology in the 1990s, philosophers had come to view it as an instance of a larger problem: vagueness. We want to take seriously our talk of hot and cold weather, bald and full-haired men, day and night, but the boundaries that distinguish such things can seem blurry to the point of incoherence.