We teachers of argument have nothing to apologize for.
Argument has no determinable function in the sense Walton needs, and even if it did, that function would not ground norms for argumentative practice.
Papers by Asen and Rehg get us halfway to an understanding of the activity of arguing in the public sphere.
I lay out the basics of "design theory"--a/k/a the normative pragmatics of arguing, particularly in contrast to other approaches.
As seen in the OJ Simpson criminal trial, arguing can be both noncooperative and normatively good.
Given the pragmatic turn recently taken by argumentation studies, we owe renewed attention to Henry Johnstone's views on the primacy of process over product.