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jimrandomh comments on Your Strength as a Rationalist - Less Wrong
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The easy solution is to stop arguing about the definition of evidence. This community uses it to mean one thing, you're using it to mean something else, and any sort of conflict goes away as soon as people make clear which definition they're using. Since this community already has an accepted definition, you would be safe in assuming that that definition is what other posters here have in mind when they use the word "evidence". By the same token, you should probably find a more precise way to refer to the definition of evidence that you are using in order to avoid being misinterpreted.
Sticking an adjective in front of the word evidence seems to work. "Evidence" includes things that give you 10^-15 bits of information; on the other hand "good evidence", "usable evidence" and "credible evidence" all imply that the strength of the evidence is at least not exponentially tiny.
I thought that "evidence", unmodified, would mean non-trivial evidence; otherwise, everything has to count as evidence because it will have some connection to the hypothesis, however weak. To specify a kind of evidence that includes the 1e-15 bit case, I think you would need to say "weak evidence" or "very weak evidence".
But I'm not the authority on this: How do others here interpret the term "evidence" (in the Bayesian sense) when it's unmodified?
I'm sympathetic to both views.
I have encountered a number of disputes that revolve around using these two different senses of the word, and am nonetheless blindsided by them consistently.
I try to always specify the strength of evidence in some sense when using the word. I think when I do use it unmodified I tend to use it in the technical sense (including even weak evidence).
It would be odd if 'evidence' excluded weak evidence, since then 'weak evidence' would be a contradiction in terms, or you could see people arguing things like "When I said 'weak evidence' I didn't mean the 1e-15 bit case, since that's not evidence at all!"
Hmm. Maybe the strength of the evidence isn't the right thing to use, but rather the confidence with which we know the sign of the correlation.
I would if I were talking to a Bayesian, interpret it as meaning something where a "B is evidence for A" if rough calculation shows that P(A|B) > P(A). I don't generally expect rationalists to even mention individual data points unless P(A|B)/P(A) is large, but if someone else gave the data as an example, then I wouldn't expect it to be necessarily large if a Bayesian referred to as evidence. So for example, I could see a Bayesian asserting that the writing of the Bible is evidence for a global flood some 5000 years ago, but I'd be deeply surprised if a Bayesian brought this up in almost any context because the evidence is so weak (in this case P(A|B)>P(A) but P(A|B)/P(A) is very close to 1).
I agree, this sounds exactly right to me. Unfortunately, I remember that in a lot of Robin Hanson's earlier OvercomingBias posts, my reaction to them would be, "Yes, B is technically evidence in favor of A, but it's extremely weak -- why even mention it?" For example, Suicide Rock.
(I think I have a picture of one of those somewhere...)