I read about the sorites paradox, especially "what is a heap?" and was a bit puzzled about the reasoning.
Isn't it fairly straightforward to say, "fiftenn grains is not a heap" and "fifteen thousand grains is a heap" and then say, "even if we cannot give a single precise number where "not a heap" ends and "is a heap" begins, we can narrow down the range within which it occurs, right? In other words, a sort of "bounded fuzziness" applies, where we know for sure what is a heap and what is not a heap (the "bounded" part) while we cannot say exactly where the transition occurs (the "fuzziness" part). It also reminds me of Alexander the Great's solution to the Gordian Knot problem, in a way. People are getting confused because they are using the wrong tools, not because of the nature of the problem itself.
the argument seems reminiscent of the supposed paradox about achilles and the tortoise, you can calculate the exact time at which Achilles catches and passes it.
The sorites paradox -- the paradox of the heap and similar paradoxes exploiting more important concepts than heap -- is a terrific topic. It's great to see people thinking about it. You wrote, "we cannot say exactly where the transition occurs." Some philosophers would respond, "It can't occur exactly anywhere, because heap (or bald or tall or rich ...) isn't a concept that allows exact status-transitions. To say that there's an exact point of status-transition, even a point we can't know or say, is to misunderstand what vague concepts are." Some philosophers would also object to your suggestion that the fuzziness can be "bounded," if by that you mean "sharply bounded." They'd say that any boundary around the fuzzy cases must itself be a fuzzy boundary: like the boundary between heap and non-heap , the boundary between definitely a heap and not definitely a heap isn't precise to within a single grain. (This phenomenon is usually called "higher-order...