The Character of Mr. Square the Philosopher, and of Mr. Thwackum the Divine; With a Dispute Concerning —
This person who Mr. Thwackum winds up fighting with is Mr. Square, another one of Squire Allworthy's hangers-on.
Mr. Square reads a lot of abstract philosophy.
He always likes to think about things like morality as theoretical problems rather than real-life issues with serious consequences.
Mr. Square and Mr. Thwackum have totally opposite views on human nature.
Mr. Square thinks we are all born good and go bad over our lifetimes.
Mr. Thwackum (who is also a clergyman) thinks we are all born evil and can only be saved by God.
So—there is pretty much no way to force these two guys to agree, since their views are so different.
All that's left is for them to squabble all the time.
The question they are arguing over right now is: "Can any honour exist independent of religion?" (3.3.4)
Mr. Square says that all humans are born good, no matter what religion they belong to.
Mr. Thwackum calls Mr. Square one of the enemies "to the true Church" (3.3.6).
He argues that only Christians can receive divine grace from God, which means only Christians can truly have honor.
Mr. Square replies that they obviously have different definitions of honor (oooh, snap. Oh wait, no, this argument is boring. Clearly, even the narrator thinks so, since he's not jumping in with any of his own comments.)
Squire Allworthy thinks this whole discussion is pointless, and since when did we get to the topic of "true honour" (3.3.9) anyway?