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TheOtherDave comments on The Sin of Persuasion - Less Wrong
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I'm not certain that the dividing line between those two senses is as crisp as you make it sound, but I guess I mean something like the latter sense. That is, I can imagine someone articulating their arguments for -P in such a way that their arguments are more compelling than mine are for P, even when P is true.
The dividing line comes from the fact that an impartial audience is not at all the same thing as a rational audience, and there's a lot more to rhetoric than making arguments that are logically sound and tenable.