Deputy Governor Danforth has a completely wrong view of his own discernment and his ability to judge others's truthfulness. When John Proctor, Giles Corey, and Francis Nurse come to the court in Act Three, Danforth tells Proctor, "We burn a hot fire here; it melts down all concealment." He thinks that he and the court are able to ascertain who is truthful and who is not. However, nothing could be further from the truth: this court believes lies and fails to believe honest folk.
When Danforth seems to go on believing Abigail and doubting Mary Warren, Proctor calls Abigail a "whore" and confesses to their sexual relationship. He cries out, "I have known her, sir. I have known her." However, when Elizabeth Proctor lies about his past lechery in order to protect his reputation, Danforth declares, "She spoke nothing of lechery, and this man has lied!" It is certainly ironic that Danforth believes that Proctor has lied, as it is really Elizabeth Proctor who lied to protect him (even Reverend Hale, who has not been super discerning up until now, recognizes this). One would think that such an important magistrate would be better able to figure out who is lying, who has ulterior motives, and so on. Danforth's stark inability to make correct judgments about people is very ironic indeed.
In Act IV Danforth and the judges realize the court is in jeopardy. Rebecca Nurse, Martha Corey, and John Proctor are set to be executed because they will not confess to their crimes of witchcraft. Realizing that these are important people in Salem, Danforth knows it's important to get at least one of them to confess.
After talking with Hale and his wife, Elizabeth, John finally gives in and confesses. It looks like things are going to be okay for the courts. John will live, and they have a signed confession. Until John grows upset that they are planning to post his confession on the church doors.
Danforth asks Proctor
Is that document in your hand a lie? I will not accept it! I will not deal in lies Mister! You will give me your honest confession in my hand, or I cannot keep your from the rope.... Which way do you go Mister?
The irony in this statement is found in Danforth's belief that he doesn't "deal in lies" when the court's entire case has been built on the lies of the girls. All those who have confessed have lied. Proctor, by recanting his false confession (by tearing it up) is actually telling the truth, but Danforth will not listen to it.