Your example makes me wonder where “Their argument is not even wrong.” (i.e. semantically incoherent) fits. It seems to me to be in the vicinity of DH2 and DH3, but not exactly either one.
I’d say that the incoherent speaker is arguing at DH(-1). DH0 would be an improvement. You would be counterarguing at DH(No) - argument by pointing out conversational emptiness.
(edited to clarify that it is the person who makes the incoherent argument who is arguing badly, and the person arguing against that who is doing something entirely outside the hierarchy.
Other DH(No) arguments-that-are-about-non-argument include “We aren’t actually arguing about the same thing” and “let me take some time to do more reading before I reply.”)
Your example makes me wonder where “Their argument is not even wrong.” (i.e. semantically incoherent) fits. It seems to me to be in the vicinity of DH2 and DH3, but not exactly either one.
I’d say that the incoherent speaker is arguing at DH(-1). DH0 would be an improvement. You would be counterarguing at DH(No) - argument by pointing out conversational emptiness.
(edited to clarify that it is the person who makes the incoherent argument who is arguing badly, and the person arguing against that who is doing something entirely outside the hierarchy.
Other DH(No) arguments-that-are-about-non-argument include “We aren’t actually arguing about the same thing” and “let me take some time to do more reading before I reply.”)