Extreme, in this context, was implying far from the consensus expectation. That implies both “seen as radical” and “involving very high [consensus] confidence [against the belief].”
Contra your first paragraph, I think, I claim that this “extremeness” is valid Bayesian evidence for it being false, in the sense that you identify in your third paragraph—it has low prior odds. Given that, I agree that it would be incorrect to double-count the evidence of being extreme. But my claim was that, holding “extremeness” constant, the newness of a claim was independent reason to consider it as otherwise more worthy of examination, (rather than as more likely,) since VoI was higher / the consensus against it is less informative. And that’s why it doesn’t create a loop in the way you suggested.
So I wasn’t clear in my explanation, and thanks for trying to clarify what I meant. I hope this explains better / refined my thinking to a point where it doesn’t have the problem you identified—but if I’m still not understanding your criticism, feel free to try again.
Extreme, in this context, was implying far from the consensus expectation. That implies both “seen as radical” and “involving very high [consensus] confidence [against the belief].”
Contra your first paragraph, I think, I claim that this “extremeness” is valid Bayesian evidence for it being false, in the sense that you identify in your third paragraph—it has low prior odds. Given that, I agree that it would be incorrect to double-count the evidence of being extreme. But my claim was that, holding “extremeness” constant, the newness of a claim was independent reason to consider it as otherwise more worthy of examination, (rather than as more likely,) since VoI was higher / the consensus against it is less informative. And that’s why it doesn’t create a loop in the way you suggested.
So I wasn’t clear in my explanation, and thanks for trying to clarify what I meant. I hope this explains better / refined my thinking to a point where it doesn’t have the problem you identified—but if I’m still not understanding your criticism, feel free to try again.
FWIW, my interpretation of Eliezer’s comment was just that he meant high confidence.