To what Puritan doctrine does Judge Hathorne attribute John’s decision to confess in Act IV of "The Crucible"?

In Act IV, Proctor tells Hathorne he wants to keep living, and Hathorne asks if he will confess to being a witch. Proctor again tells Hathorne, "I will have my life." At that point, Hathorne yells, "God be praised! It is a providence!" The doctrine Hathorne refers to is the belief in Providence. The Puritans saw God as the ultimate ruler of the universe, and God's Providence was when He planned and carried out everything in the universe in order to achieve his divine ends. Providence is God's will that extends to all his creatures in the universe. Hathorne, therefore, thinks Proctor is confessing because it is God's will that he do so.