The Greeks are generally credited with introducing the problem of vagueness into philosophy in the guise of the sorites paradox. The sorites argument is concise, relatively easy to comprehend, and also seemingly quite intractable. The argument can be explicated informally as follows: suppose that we have a heap of sand. Remove one grain of sand from that heap. The heap of sand remains. Remove another, and again, the heap remains. Continue this process until one grain remains. Certainly this one grain of sand does not constitute a heap, yet we are at a loss when asked to give an account as to when a transition occurred from heap to non-heap. More formally, the argument may be couched as a mathematical induction. The first premise, or the base step, states that the predicate in question is true of some object(s). The second premise. or induction step, states that if the predicate is true of some object, then it is true of the succeeding or preceding object. The conclusion states that the predicate (heap) is true for any number of grains (including 0). Thus we have seemingly good premises, seemingly good reasoning and yet end up with an unacceptable conclusion. (Abstract shortened by UMI.)