The social and philosophical changes described in chapter 13 ofThe Scarlet Letterconsist on the changes in the view that the villagers had of Hester, and on the changes in the view that Hester had on herself.
The first change comes with the acceptance that, over a long period of time, Hester had achieved among her peers, regardless of the scarlet letter. This social acceptance comes as a shocking change, considering the hades that the villagers put her through at the beginning of Hester's exit from prison. The change was so dramatic, that even the "A" on Hester's chest was re-visited and redefined as something that sets Hester apart...as a good and "able" person.
Thus it was ... Individuals in private life...had quite forgiven Hester Prynne for her frailty; nay, more, they had begun to look upon the scarlet letter as the token, not of that one sin, for which she had borne so long and dreary a penance, but of her many good deeds since.
The philosophical change happens to Hester. Long gone are the days where she would shock the villagers with her femininity and beauty, her long hair, and her demeanor of high dignity. In high contrast, the new Hester staunchly adopted a totally puritanical way of dress, covering her head completely with a headpiece or a bonnet, using austere clothing, and detouring significantly from a feminine or coquettish look. This is because Hester no longer welcomed passion into her life. She switched passion for analysis and self-contemplation; the scarlet letter did sear a tremendous brand of pain within Hester's heart. Now that she no longer had to detour her thoughts to figure out ways to avoid the public, or defend herself, she could finally sit back and analyze what her life had become.
Yet another significant change is in Hester's view of the world as well. She is described in the story as a woman with such a different set of mind, that she could be described as Anne Hutchinson; a woman capable enough to defy the system and form a sect, a cult, and then a religion, of her very own. Hester had completely invalidated the paradigms of her society. She had another way to see things
As a first step, the whole system of society is to be torn down, and built up anew. Then, the very nature of the opposite sex, or its long hereditary habit, which has become like nature, is to be essentially modified, before woman can be allowed to assume what seems a fair and suitable position.
These are heavy-hitting thoughts for a woman of Hester's generation, and would have been considered rebellious, sacrilegious, and even immoral. However, Hester has long passed beyond the morality of puritanism, as she has seen it for the lie that it actually is.
These are then the major changes that the chapter treats in the novel.