What theological argument does john hale use to explain the causes of the events in salem?

With notable exception of John Proctor, Hale gets our vote for most complex character in The Crucible. We say so, because Hale goes through a major personal journey over the course of the play. He starts off with really good intentions. In Act One, Miller writes of Hale: "His goal is light, goodness, and its preservation." This guy has trained and trained to be the best witch-hunter ever, and he's psyched to finally get a chance to show off his stuff. Though he's probably a little full of himself, but ultimately his goal is to valiantly fight the Devil. What could be wrong with that? Well, a whole lot. 

In Act Two, we see that Hale's former confidence is slowly eroding. This is demonstrated by the fact that he shows up at the Proctors' house of his own accord. He's there without the court's knowledge, trying to get an idea of who the Proctors are for himself. This independent action is a big hint that he's probably beginning to doubt the validity of his own conclusions. When John Proctor gets convicted in Act Three, through Abigail's transparent machinations, Hale's confidence is shattered. He quits the court and storms out in anger.