I don't understand the author's point about the two heaps. Clearly there are two separate propositions at play -- the "heapness" of either pile, and whether or

I don't understand the author's point about the two heaps. Clearly there are two separate propositions at play -- the "heapness" of either pile, and whether or not the two heap-like entities are identical. The first requires fuzzy logic because the definition of "heap" is vague. The second does not because the rules (take a grain off one for each grain removed from the other) are precisely defined. There is no inherent contradiction just because two different systems are in use at once.