I was recently introduced to something called the Sorites Paradox. The person explaining it to me also referred to it as 'the vagueness paradox'. My response, before hearing its explanation, was that perhaps if one is more precise, the paradox ceases to exist. The Sorites paradox can be explained as follows:
Imagine a heap of sand. Take one grain away. Is it still a heap? Presumably so. Now remove another, and another, and another, and... at what point does it cease to be a heap?
However, a heap is an imprecise idea. It is an approximate, not a specific, measure. It makes no sense to talk of heaps in terms of the number of grains of sand; grains of sand are a very precise numerical measure. The paradox arises only when this precise measure is applied to this imprecise concept.
One ought to use only the degree of precision in one's language that is correct to the problem. This is because seeking appropriate degrees of precision helps to solve problems most efficiently. There will be some problems that do not require more than a certain degree of precision in the definition of their terms, and insisting on seeking further precision is unnecessary and, in fact, would just distract from solving the actual problem.
Indeed, it seems that this paradox does not take into account that a heap is an imprecise concept. It assumes that a precise definition of a heap must be necessary in order for it to be meaningful, and that a paradox arises when it is not. The value of having terms like 'heap' or 'pile' is in fact that they are vague. We need not measure them precisely and can use approximations. This is very useful in one's day-to-day existence and does not benefit from being defined more precisely.
This is apparently a paradox that confounds many an Oxford philosophy student, and presumably their professors as well since the solution has not been explained to them to resolve their confusion. I must say that I was very unimpressed.