Two types of disagreement
Following from Two types of thought, it seems that all types of disagreement and argument fall into two types that correspond to the types of thought. I have yet to find a good example that breaks this schema, but would be eager to find one.
This is a disagreement between two maps, about expectations for an unknown part of the territory. This type of argument is about disagreement in what unknown (likely future) experiences will be. Since I think of Knowledge is testable prediction|knowledge as testable predictions, these types of disagreements are about knowledge.
This is a disagreement between Concept-spaces, about definitions of words (since Definitions are clouds in concept-space and Words are pointers to concept-space). This type of argument likely does not have any possible external validation, and runs the risk of going on forever.
In other words, this is a disagreement about what the Shape of concept-space|shape of concept-space should be. This type of argument is only necessary in contexts where consensus is needed over the shape of a concept-space.