Sorites Arguments

  1. A pile of 1 grain is not a heap.
  2. For every integer N>1, if N-1 grains is not a heap, then N grains is not a heap.
  3. 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.