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DanielLC comments on Evidence and counterexample to positive relevance - Less Wrong
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Comments (37)
In the counterexample, e1 and e2 are each evidence of h on there own, but when the other is known, they are not.
By this definition, if e and h are independent, but h has a prior probability higher than k, then e is evidence for h. For that matter, you could get something like P(h|e) = k+ε, P(h) = 1-ε. By this definition, e is evidence of h, even though e makes h dramatically less likely.
Also, this means that a confession is not evidence for a crime, because you need to know the language for it to mean anything.
No, because in that case Achinstein's first condition won't be satisfied. If I'm reading the post right, both conditions need to be satisfied in order for e to count as evidence for h according to this definition.
Actually, Achinstein's claim is that the first one does not need to be satisfied - the probability of h does not need to be increased by e in order for e to be evidence that h. He gives up the first condition because of the counterexamples.
Well, duh. You're right, the post was pretty clear about this. I need to read more carefully. So does he believe that the second condition is both necessary and sufficient? That seems prone to a bunch of counterexamples also.
So, he claims that it is just a necessary condition - not a sufficient one. I didn't reach the point where he offers the further conditions that, together with high probability, are supposed to be sufficient for evidential support.
p.s: still, you earned a point for the comment =|