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Some DH7, or at least DH7-like thinking, can be relatively easy. For instance, there will often be gaps in someone's argument that they do not consider significant, or a general case they hadn't bothered to think of. You can't make it perfect, but you can patch it up a bit.
Point taken - in some cases, the significance of the gaps is more evident to the outside view.
Maybe they didn't go wrong, and there is no paradox, and it is a matter of relative values as to which is more important.
In which case screaming makes a lot of sense as a strategy.
In that case, we can replace "point out where in their argument they went wrong" with "point out where our underlying value judgments seem to diverge."
If they then try to argue that your values are wrong and theirs are right, either you have to move the discussion up a meta-level or, yes, screaming.
In response to
Better Disagreement
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)
In response to
Better Disagreement
I like this post, even though it doesn't add much to Paul Graham's original essay. I mean, I wouldn't have seen this content if it were not posted on Less Wrong.
For all of my life until this year, I've been confounded by DH2 arguments against myself. Why are my opponents ignoring what I say because I said it angrily, or sadly, or confrontationally, or in passing, or whatever? Well, I don't like when people do that, but it doesn't change the fact that people do it, so I've started to adopt a more pleasant, acceptable tone.
I still don't like it. I don't like that I have to adopt a certain style to be taken seriously. But oh well.
Edit, 4/04/12:
I've started to adopt a more pleasant, acceptable tone.
I was deluded when I said this.
Why are my opponents ignoring what I say because I said it angrily, or sadly, or confrontationally, or in passing, or whatever?
The way you say something may signal that you are trying to diminish their status. If you say it with a sufficiently negative tone, it may even be taken as a signal (a generally reliable signal) that you care more about diminishing their status than about having a truth-seeking discussion.
In other words, what wedrifid said, but less simply and more explicitly.
Depends on how it's done, IME.
I often find that "Hm. So you're saying XYZ? That doesn't really work, because of ABC. But now that I think about it, X'Y'Z' would be consistent with what you're claiming, and not have that problem. Even there, though, A'B'C' suggests it's false." can work all right, although I'm often tempted to add "But of course by this point I've wandered off into a corner and started arguing with myself, which seems antisocial."
I think that in some contexts, like arguing over mathematical proofs (as orthonormal noted), spending a little time arguing with yourself to bring out X'Y'Z' is polite and a sign of good faith. In other cases, I'd rather just trot out A'B'C' early on, as long as it doesn't require too much effort, and deal with both arguments at once without ever explicitly raising X'Y'Z'.
"In the seminal Zucker, Zucker, and Abrams opus Airplane!, one character, played by Leslie Nielsen, asks another to pilot an passenger airliner in an emergency. The would-be pilot responds with incredulity, but is coolly rebuffed by the Leslie Nielsen character. This evinces laughter from the audience, as the exchange involves a confusion between two near-homophones."
You might be interested to know that "Airplane!" was itself essentially a shot-for-shot remake of a "serious" made-for-TV movie with exactly the same plot - with, of course, jokes added in.
I was aware of the genre it spoofed, but I didn't know that it was so specifically targeted. I'm tempted to try to find that made-for-TV movie and watch clips just to increase my appreciation of Airplane!
DH7 does happen between mathematicians now and then. Person A has an idea of a proof for X. Person B could show a problem with Person A's proof (DH6) or an unrelated disproof of X (DH4? DH6?), but the best response is to show A a disproof of X that makes it clear why A's strategy is futile.
This is often done well enough that it doesn't even hurt feelings. But math is kind of a special case.
In this case, I'd even drop my initial thoughts about rudeness. If you can prove that somebody's gone down mathematical blind alley, it's downright polite to do so, since there's no ambiguity about the relevance of the steel man here.
If you come up with a better version of the other person's argument but keep it to yourself and only refute the original version, then later on they may think "Now, in all honesty Gil was right about X ... but no, wait a moment, that's just because I didn't get it quite right. If I'd said X' instead then his argument wouldn't have worked." and stick with their position rather than changing it.
I doubt that this outweighs the effect of antagonizing them at the time by saying "You should have said X', and I'm now going to refute that" in most cases, though.
Ideally, a reasonable counterargument that applies to the strong form will also apply to the weak form without significant editing. If the person one was arguing with would have been receptive to DH7 in the first place, that alone should stop them from making the strong form argument - the countering evidence has already been provided.
Where this fails... well, I said "at first" in my thread-starter for a reason.
The danger you point out is real, but an unqualified dictum such as "DH7 should be kept internal, at least at first" is very specific advice that IMO is going too far. A great deal depends on the quality of the sub-argument to do with strengthening the opponent's position, and the opponent's (and/or audience's, if any) receptiveness to that. You seem to be saying we should always have low confidence in both, while I'd say it depends.
If we imagine arguments as soldiers
Maybe let's not. Applying DH7 already assumes we're interested in truth, not just in winning a debate.
I don't ALWAYS have low confidence in the other arguer's ability to tolerate a steel man version of their own argument. I do have low confidence in the ability of most people, especially me, to decide what constitutes a non-gratuitous steel man. I have an unfortunate, but understandable, bias in favor of my own creations, and I suspect that this bias is widely shared.
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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.")