How does John Proctor demonstrate alienation throughout "The Crucible"?
The main way that John demonstrates alienation is within himself; he has sinned, and he feels like he is not really a worthy man in the eyes of others, God, the church or himself. So even though he is around people, and interacts with them, he feels alone. Miller writes of him that
"the steady manner he displays does not spring from an untroubled soul...he is a sinner...against his own vision of decent conduct."
So, he feels like he has sinned against himself and his own morals, and this alienates him from his own self-esteem, and everyone else too.
In act one we learn that he doesn't come to town often, and in act two, we see that he is very alienated from his wife. Hale questions why he has alienated himself from the church, not coming very often that past year. He tends to alienate him from Parris and those that like Parris, and from the Putnams and their money-grubbing ways. All in all, he does not have very many connections, and keeps himself aloof from forming alliances and connections. He does, however, join with Francis and Giles in trying to save their wives, and ends up alienating himself further by getting arrested and thrown in jail. He then refuses to confess, which sets the judges against him.
All in all, John Proctor is a very strong figure, but one that feels alienated in his own heart because of his misdeeds, and keeps himself distant from hypocrites and other people he doesn't like. I hope that those thoughts helped; good luck!