I certainly agree that the situation you describe can occur. (I could quibble about whether the probability-shift for Mary actually depends on the quality of her alibi here, as that seems like double-counting evidence, but either way it’s entirely possible for the posterior probabilities to come out the way you describe.)
And, OK, sure, if “more likely to be correct” is understood as “more likely [than some other hypothesis] to be correct”, rather than “more likely [than it was before that evidence arrived] to be correct”, I agree that the phrase describes the situation. That is, as you say, a bit confusing, but not false.
So, OK. Provisionally adopting that interpretation and returning to the original comment… their initial comment was “situations can arise where evidence comes out which contradicts a hypothesis but still makes that hypothesis more likely to be correct”. Which, sure, if I understand that to mean “more likely [than some other hypothesis] to be correct” is absolutely true.
All of which was meant, I think, to refute bigjeff5′s comment about what sort of evidence should increase confidence in the belief that there is no bias. Which I understood to refer to increasing confidence relative to earlier confidence.
I certainly agree that the situation you describe can occur. (I could quibble about whether the probability-shift for Mary actually depends on the quality of her alibi here, as that seems like double-counting evidence, but either way it’s entirely possible for the posterior probabilities to come out the way you describe.)
And, OK, sure, if “more likely to be correct” is understood as “more likely [than some other hypothesis] to be correct”, rather than “more likely [than it was before that evidence arrived] to be correct”, I agree that the phrase describes the situation. That is, as you say, a bit confusing, but not false.
So, OK. Provisionally adopting that interpretation and returning to the original comment… their initial comment was “situations can arise where evidence comes out which contradicts a hypothesis but still makes that hypothesis more likely to be correct”. Which, sure, if I understand that to mean “more likely [than some other hypothesis] to be correct” is absolutely true.
All of which was meant, I think, to refute bigjeff5′s comment about what sort of evidence should increase confidence in the belief that there is no bias. Which I understood to refer to increasing confidence relative to earlier confidence.