Why won't Danforth postpone the hangings?
This is in Act Four. Parris (and Hale) are worried that news of the revolt in Andover will inspire a similar revolt in Salem. Danforth is defiant and stubborn and says "There is no rebellion in Andover!" Recall the description Miller (the author) gives of Danforth in an earlier section:
Danforth is a grave man in his sixties, of some humor and sophistication that does not, however, interfere with an exact loyalty to his position and his cause.
His sophistication (being cultured and having diverse knowledge) does not interfere with the position he has taken. In other words, he is stubborn. He also will not allow anyone to challenge him as Deputy Governor and this is because of his pride. Hale arrives and pleads with Danforth to pardon the others. Danforth says he can't because twelve have already been executed for the same crime of witchcraft. He won't postpone the executions or pardon anyone because it will suggest he was wrong and the court convictions were incorrect. He says:
Postponement now speaks a floundering on my part; reprieve or pardon must cast doubt upon the guilt of them that died till now.
Danforth is more worried about his own reputation and the integrity of the court. He would rather go ahead with more executions than even suggest that he and the court have made a grave mistake.