Foil
Character Role Analysis
Arthur
Arthur starts out as Jack's enemy, when Jack calls him a sissy and social relationship deteriorate rapidly.
I liked him. I liked his acid wit and the wild stories he told and his apparent indifference to what other people thought of him. (12.2)
And yet despite this, he picks a fight with the kid. And they keep fighting periodically, even going into Mr. Mitchell's little Thunderdome of the Pacific Northwest.
It was supposed to be banter, but it turned easily cruel. (23.1).
And they keep going back and forth like that. Frenemies? You betcha! But in hoity-toity literary terms, we call that "foils."
Rosemary Wolff (AKA Mom)
Mom is a bit of a foil too, since she's kind of on Jack's side, but stands (ineptly at times) against some of the things he wants to do. Jack spars with Mom, starting from the beginning when he "saw that the time was right to make a play for souvenirs" (1.4) on their way to Utah. She often opposes his wishes, like when Roy gets him his Winchester. "After a few days of this, my mother caved in" (3.4), but it won't be the first time she puts her foot down. At the same time, Jack really, really loves his mother… to the point where he would rather stand by her than escape Dwight for Paris:
I was my mother's son. I could not be anyone else's. (16.38)
That sets her pretty solidly in foil territory: someone who challenges Jack not to stop him, but to help make him a better person.