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Dan_Moore comments on The Truth about Scotsmen, or: Dissolving Fallacies - Less Wrong
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Just focusing on the logical issue, and not a strategy for persuasion:
Just because your discussant has a fallacious argument, it doesn't follow that they are wrong. There might be another non-fallacious argument that proves their point.
An analogy: say you find an error in someone's proof of a math theorem. It's possible that an alternate argument can be constructed that avoids that error.