Sorites

Also called “the heap,” this paradox arises for any predicate (e.g., “… is a heap”, “… is bald”) whose application is, for whatever reason, not precisely defined. Consider a single grain of rice, which is not a heap. Adding one grain of rice to it will not create a heap. Likewise adding one grain of rice to two grains or three grains or four grains. In general, for any number N, if N grains does not constitute a heap, then N+1 grains also does not constitute a heap. (Similarly, if N grains does constitute a heap, then N-1 grains also constitutes a heap.) It follows that one can never create a heap of rice from something that is not a heap of rice by adding one grain at a time. But that is absurd. Among modern perspectives on the paradox, one holds that we simply haven’t gotten around to deciding exactly what a heap is (the “lazy solution”); another asserts that such predicates are inherently vague, so any attempt to define them precisely is wrongheaded.