Sorites Arguments
 A pile of 1 grain is not a heap.
 For every integer N>1, if N1 grains is not a heap, then N grains
is not a heap.
 Therefore, a pile of 10^10 grains is not a heap.
If the word heap was clearly defined, then premise 2 would automatically
be false. However, we can not be expected to give precise definitions for
terms that are intentionally vague. Rather, we must simply be careful not
to apply logic to statements that contain vague terms, because then they
can be in a state that is neither true nor false, which allows for problems
to arise.
