Dunno if it has been thoroughly debated, but I thought I'd come out on the side of "within the context of this story, Erfworld has some kind of reality outside of Parson's perception of it."
http://en.wikipedia.org/wiki/The_Chroni ... Unbeliever
I mean, I think that Parson having the same name as his grandfather might be significant, as might be the similarity of Erfworld to the scenario he was about to game. But it's not entirely "his imagination," or "in his head." Erfworld wished for Parson; that might be significant too (grand-dad again?).
But we have too much detail about things that happen to characters prior to Parson being summoned, or beyond Parson's perception/influence. All that backstory, all that character development... that's not just different parts of Parson's subconscious or whatever. It exists, in itself. I aint got much betterer arguments than that; just, this is the only explanation that seems to make sense to me, given the story so far.
Not to say that that doesn't put Parson in the same kind of situation that Thomas Covenant was in. It may also put the Titans in the same position that the Creator was in, and the Arkentools in a position similar to White Gold. But those are just interesting parallels, not central to my loosely-made argument of the previous paragraph.
Does this community have any consensus on this point?