authority. The spectacle of the proceedings and their strong faith is a significant reason they initially believe the girls.

However, John Proctor, Giles Corey, Francis Nurse, and Mary Warren challenge the court's authority in act three by exposing Abigail and the girls as frauds. After Mary testifies that the girls are lying, Danforth and Hathorne become primarily concerned with their own well-being and maintaining their positions of power. Instead of attempting to listen to their opposition, Danforth and Hathorne remain resolute and take a hard stand against anyone challenging the court. Danforth even tells Francis Nurse,

But you must understand, sir, that a person is either with this court or he must be counted against it, there be no road between. (94)

Once it becomes clear that Abigail Williams's reputation is certainly questionable and there is sufficient evidence that the girls are lying, Danforth and Hathorne become defensive and callously wield their authority by having their enemies arrested. By act four, Danforth and the other leading court officials are solely focused on maintaining their positions of power and carrying out the executions. Danforth reveals his motivation to look past Abigail's transgressions by saying,

Now hear me, and beguile yourselves no more. I will not receive a single plea for pardon or postponement. Them that will not confess will hang. Twelve are already executed; the names of these seven are given out, and the village expects to see them die this morning. Postponement now speaks a floundering on my part; reprieve or pardon must cast doubt upon the guilt of them that died till now. While I speak God’s law, I will not crack its voice with whimpering. If retaliation is your fear, know this—I should hang ten thousand that dared to rise against the law, and an ocean of salt tears could not melt the resolution of the statutes. (129)

Danforth is evidently more concerned with his reputation and authority than he is with saving innocent lives. He also understands that pardoning Proctor and Rebecca Nurse will cast doubt upon his previous rulings. Essentially, Danforth, Hathorne, and the other officials are more concerned about their legacy, reputation, well-being, and status than they are about fairly administering justice, which is why innocent citizens like Proctor and Rebecca die.

Miller's construction of the legal system of Salem is an interesting one.  On one level, Miller suggests that part of the reason why men like Danforth and Hathorne are hesitant to view the girls as liars is because to do so would contradict their belief of what it means to be a "good Christian."  Miller establishes that Salem is driven feverishly to embrace a construct of spirituality in dogmatic terms.  Religious devotion in Salem is blindly accepted without much in way of reflection or proposal of alternate construction.  Power and authority speak to what it means to be a "good Christian" and everyone else follows.  Danforth speaks to this in his own testimony of what he has witnessed in presiding over the trials:

 I tell you straight, Mister-I have seen marvels in this court. I have seen people choked before my eyes by spirits; I have seen them stuck by pins and slashed by daggers. I have until this moment not the slightest reason to suspect that the children may be deceiving me. Do you understand my meaning?

Leaders like Hathorne and Danforth are shown to sincerely believe in the court's cause.  They believe that their work is reflective of a "good Christian." To accept that the girls were lying is a repudiation of that, challenging their dogmatic notion of spirituality.  To accept that the girls are lying and that the premise of witches in Salem is false goes against their perception of what it means to be a "good Christian."  The loss of such a view of faith is unfathomable for men like Danforth and Hathorne as well as majority of Salemites.

The other reason why men like Danforth and Hathorne cannot accept that the girls are lying is because of power.  Miller develops the Salem legal system as one predicated upon the notions of power.  Hathorne and Danforth have gained great power and prestige as a result of their presiding over the trials.  They are known.  They are respected.  They have control over others' lives in Salem.  Miller shows how power is seductive, its trappings so alluring that even the truth can be rejected in the name of control and consolidation of greater power.  If the court accepts that the girls are lying, the trials are over and their power goes away.  Miller shows that there were people in Salem who directly benefited from the trials, and some of them wore judicial robes.

All of these men have a vested interest in the continuation of the witch trials. Judge Danforth, for example, takes himself as an authority figure very seriously. The witch trials give him an opportunity to wield that authority over others. He's on the biggest power trip of his life and doesn't want it to end any time soon. A moment's reflection would tell him that the whole witch craze is based on nothing more than lies and fabrications, but he really doesn't care. All that matters to him is that he gets to hold the power of life and death in his hands. Despite proclaiming to be a devout Christian, he's actually playing God.

Much the same thing can be said of Reverend Parris. He's also an authority figure in Salem, kind of a big deal in town. But as with Danforth he abuses that authority for his own ends. The witch craze presents him with an opportunity to bolster his prestige in the eyes of the townsfolk. At the same time, he needs to cover up what his niece and the other girls were getting up to in the forest that night. The witch craze is a classic diversion tactic that will take the focus off Abigail and put it onto innocent people such as Elizabeth Proctor.

Hathorne, unlike Danforth, lacks experience as a judge. He's still making his way in the world, still in the foothills of a judicial career. He sees the witch trials as a golden opportunity to make a name for himself. Fiercely ambitious, he's prepared to resort to unscrupulous methods to get the verdict he wants. Innocent people are just stepping stones for Hathorne on his way to the top. If he can establish a reputation at the Salem witch trials, he figures that that will launch him on a long and successful career as a judge.

Danforth is interested in maintaining the authority of the court. To admit that innocent people have been sentenced and killed as the result of fraud would greatly undermine the authority of the court in the public's esteem. 

As the court is generally reliant upon public opinion as the basis for its authority, Danforth energetically defends the court's position that it has not done anything falsely and that the evidence used in the court has all been valid. 

Parris wants to continue to side with the court and associate himself with this body of power. He fears that, as something of an outsider, his position in Salem is insecure. By aligning himself with the power of the court, he bolsters his own position as a minor authority in the town. For him, undoing the work of the court and recognizing the trials as fraudulent will reverse the progress he has made regarding the stability of his position. His position would become even more unstable than it was at the opening of the play. 

Hathorne's reasons for disbelieving the claims made by Proctor and Mary Warren are more legally oriented. He simply does not believe Mary Warren. She either is lying in her confession in Act III, or she was lying in court earlier. Both ways she is untrustworthy and, for Hathorne, unconvincing.

How would it make them look if they convicted "innocent" people and the girls were lying?  They would look like fools!  You know the saying from the Bible, "Pride goes before a fall"?  These men took pride in who they were--they were godly, righteous, logical thinkers.  If they could be taken in by a bunch of silly girls, who would ever be able to trust or respect the men ever again?  Plus, the blood of innocent people would be on their heads.  It's so much easier to live with one's conscience if you don't even entertain the thought that your witnesses were lying.  The entire reputation of the men and the court rested on their believing the girls.

Specific Evidence:

There are several instances where they refer to the law and how it "binds" them. 
Act Two (where Herrick comes to arrest Elizabeth): "I have nine men outside.  You cannot keep her.  The law binds me, John, I cannot budge"

After that, Reverend Hale say "The court is just"

About a page after that, Giles Corey even says to Hale, "It is fraud, you know it is fraud!  What keeps you, man?"

Soon after, Hale talks for a couple of paragraphs--those would really work as to why they have trouble doubting "little girls".

Look at Act Three also--where Francis Nurse and Giles Corey go to bring evidence.  You can feel the haughtiness and pride in the words of Hathorne and Danforth.