Self-knowledge and self-confidence do not seem like identical things to me, though I am interested in further exploring the idea that self-knowledge might lead to self-confidence.
Hale is the character who would seem to complicate this debate most. He is most confident when he is least self-aware. When he blindly trusts and believes that the accusations of witchcraft are real, he is willing to send almost everyone to the gallows, including Elizabeth Proctor, a humble and upstanding mother.
It is when he begins to realize his folly and to thereby gain self-knowledge regarding his own over-confidence that he begins to grow feeble and lackluster.
With him in mind, I don't think we can reasonably argue that self-knowledge leads directly to potency and strength.
This would be a great question for the discussion board. I would be interested in the answers...
This statement probably points to the Proctors more than anyone else in the play, in my opinion. Elizabeth and John are having trouble from the beginning because of John's infidelity with Abigail Williams. Their scenes are filled with tension and an "over the top" attempt to please each other. She does not tell him until later that she loves him dearly and that she never expected him to love her because she is so plain. She has gone through life and marriage and children believing that she does not deserve this beautiful speciman of a man...that he is too handsome and too good for the likes of her. During the conflict of the witch trials, Elizabeth's personal insecurities and her confession to John bring them closer together. It also gives her the strength to back him on his decision to go to his death instead of lying, living, and defacing the honor of his name. John knows himself, but he and Elizabeth learn a lot about her, their relationship, and each other which allows them to make certain decisions for their future. It gives them the strength they need to do what has to be done.