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kpreid comments on Better Disagreement - Less Wrong
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An application of this hierarchy:
Jack the Scarecrow. My crystal healing pills will give you eternal life. For $50.00 each, you need never die, suckers.
--
DH0: "I'm not interested for myself, but can I buy you a border collie and give her some? If you're going to live forever, you're going to need a smart friend to make the really tricky decisions."
DH1: What, exactly, is your profit margin on these crystal healing pills? If we don't live forever, would you still make money off of them?
DH2: Any post that ends in the word "suckers" directed at the readers is difficult to read charitably.
DH3: > My crystal healing pills will give you eternal life.
WRONG.
According to this hierarchy, D3 is arguing on a higher level than DH0, DH1, and DH2. And, well, maybe that's correct. "Higher" doesn't necessarily mean "more subtle." But in the absence of this hierarchy, I'd have been tempted to order the arguments from low- to high-level as 0 < 3 < 2 < 1.
(EDITED to remove potential applause light; EDITED again to better hit the idea of DH2)
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.")