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. :)
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.