Arthur Dimmesdale definitely is a character who has a rather tragic end, and yet he is able to meet that tragic end with dignity and honour. Firstly, he dies young, and secondly he dies at the peak of his career, when he is already respected and loved by his parishioners. Thirdly, he dies before he can enjoy real happiness with the woman that he loves. Yet note how he responds to his premature death and how he is so accepting both of his early demise and of the various pain and sufferings he has experienced up until that point. In a conversation with Hester, he says:
God knows, and he is merciful! He hath proved his merc, most of all, in my afflictions. By giving me this burning torture to bear upon my breast! By sending yonder dark and terrible old man to keep the torture always at red-heat! By bringing me hither, to die this death of triumphant ignominy before the people! Had either of these agonies been wanting, I had been lost forver! Praise be his name! His will be done! Farewell!
The easy acceptance with which Dimmesdale is shown to meet his tragic end clearly shows that he is a character who does not rage against his fate, but sees a divine hand in both his sufferings before his death and his premature demise. One of the striking aspects of this quote is that Dimmesdale clearly recognises he is dying, yet is able to see God's providence in both his death and in what has come before it. He is a man who dies with honour, and therefore could be argued to be a tragic hero.