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gjm comments on Better Disagreement - Less Wrong
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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.