Hawthorne suggests in The Scarlet Letter that redemption for sin comes through the gateway of accurate self-knowledge. Paradoxically, this "gateway" is the result of sin. In describing Hester's and Dimmesdale's sin, Hawthorne alludes to the Biblical original sin of Adam and Eve. The results of Adam's and Eve's sin was knowledge of good and evil, which Hawthorne metaphorically likens to self-knowledge and critics expand to mean knowledge of humanity: Dimmesdale's sin gives him an empathy with the sinners of humanity, and Hester's sin eventually leads her to minister to and care for the ill of humanity. In other words, both come to know and understand humanity once they come to know and understand themselves.
Hawthorne's suggestion, which is made through this illustrative logical circle of sin -- self -- others, is that redemption for one's sin originates in knowledge of and understanding of one's self to such a depth that its natural extension is to know and understand humanity. Hawthorne implies that such knowledge and understanding leads to an embrace of others. This is sharply contrasted to the Puritan community's practice of expelling humanity, such as Hester, when humanity in the form of the individual is caught in sin. Further, Hawthorne suggests that the embrace of humanity via the individual other leads from redemption to the renewal of purity, a purity that is opposite of the Puritan community's hollow, meaningless purity -- which is the purity of expulsion.