The Sorites Paradox - Some Doubtful Thoughts

It has been asked how, if at all, one might resolve the Sorites paradox. I am not convinced a solution is possible, and in this paper I will explain the responses I have become aware of, and why they fail. In the end, I will conclude that there is no solution to the paradox, but I will offer a few suggestions for a way forward. The first response might simply be to reject the first premise of the argument.