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He himself, on the other hand, with characteristic humility, avowed his belief that if Providence should see fit to remove him, it would be because of his own unworthiness to perform its humblest mission here on earth. (9.3)
Dimmesdale sees everything—his life, work, and death—as being out of his power. Maybe that's why he keeps begging Hester to reveal his secret. He can't take a single action for himself; it's not what he believes.