Is there some level of evidence more convincing than study published in reputable, peer-reviewed journal with lots of replication?
I would say so. For instance, the claim that letting go of my pen in mid-air will cause it to fall onto the floor and not the ceiling. The above is backed up by so much evidence and in so many different ways* that it is even if a replicated study were to contradict it, I would continue to believe it (it's one of the few claims that really does deserve a subjective probability in the region of 99.9%).
I don't know about Yudkowsky, but the threshold for 'what would be enough evidence to convince me of the existence of ESP" lies somewhere between those two.
I initially took 'some claims are just too extraordinary' to be talking about the first level, while 'how to convince me that 2+2=3' talks about the second level, but maybe I'm being too charitable.
For evidence: * thousands of trials from my own experience, millions from other people, universal agreement from everyone I know or have heard, coherent scientific theory explaining how and why it happens etc...
(it's [that letting go of a pen will cause it to fall to the floor and not the ceiling] one of the few claims that really does deserve a subjective probability in the region of 99.9%).
Only three nines? This seems very underconfident. I would assign it more like twelve-nines confidence.
Today's post, Some Claims Are Just Too Extraordinary was originally published on 20 January 2007. A summary (taken from the LW wiki):
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