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Lumifer comments on Welcome to Less Wrong! (7th thread, December 2014) - Less Wrong
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Be careful about distinguishing two very different propositions:
(1) There was a preacher named Jesus of Nazareth who lived in a certain time in a certain place.
(2) Jesus of Nazareth rose from the dead and was the Son of God.
Specifically, evidence in favor of (1) usually has nothing to do (2).
That doesn't sound quite right to me, at least if you mean "nothing" literally", given that not-(1) logically implies not-(2).
I think the much smaller posterior probability of (2) than (1) has more to do with the much smaller prior than with the evidence.
A fair point, though "normal" people have a strong tendency to jump from "not-(1) logically implies not-(2)" to "therefore (1) implies (2)".
No worries, I knew what you meant. I am pretty good at logic though, so no need to worry about illogical jumps here. I may not have very much background knowledge about terminology or history or science or anything (yet), and I may not be a very articulate writer (yet), but the one thing I can usually do very well is think clearly. I am even feeling a bit smug after finding the mammography Bayesian reasoning problem that apparently only 15% of doctors get correct to be easy and obvious. :)
Ah, yes, the ever-popular fallacy of the inverse.