gjm comments on Harry Potter and the Methods of Rationality discussion thread, July 2014, chapter 102 - Less Wrong Discussion
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In principle I agree with you.
In practice I think "X has the burden of proof" generally means something similar to "The position X is advancing has a rather low prior probability, so substantial evidence would be needed to make it credible, and in particular if X wants us to believe it then s/he would be well advised to offer substantial evidence." Which, yes, involves confusion between an idea and the people who hold it, and might encourage an argument-as-conflict view of things that can work out really badly -- but it's still a convenient short phrase, reasonably well understood by many people, that (fuzzily) denotes something it's often useful to say.
So, yeah, issuing such challenges in such terms is a sign of imperfect enlightenment and certainly doesn't make the one who does it a rationalist in any useful sense. But I don't see it as such a bad sign as I think you do.
Yea, the concept of burden of proof can be a useful social convention, but that's all it is. The thing is that taking a sceptical position and waiting for someone to proof you wrong is the opposite of what a sceptic should do. If you ever see two 'sceptics' both taking turns postinf 'you have the burden of proof', 'no you have the burden of proof!'... You'll see what i mean. Actual rationality isn't supposed to be easy.