I feel like this is mostly a question of what you mean with “atlantis”.
If you want to calculate P(evidence | the_specific_atlantis_that_newagers_specified_after_hearing_the_evidence) * P(the_specific_atlantis_that_newagers_specified_after_hearing_the_evidence), then the first term is going to be pretty high, and the second term would be very low (because it specifies a lot of things about what the atleantans did).
But if you want to calculate P(evidence | the_type_of_atlantis_that_people_mostly_associate_to_before_thinking_about_the_sphinx) * P(the_type_of_atlantis_that_people_mostly_associate_to_before_thinking_about_the_sphinx), the first term would be very low, while the second term would be somewhat higher.
The difference between the two cases is whether you think about the new agers as holding exactly one hypothesis and lying about what it predicts (as it cannot assign high probability to all of the things, since you’re correct that the different probabilities must sum to 1), or whether you think about the new agers as switching to a new hypothesis every time they discover a new fact about the sphinx / every time they’re asked a new question.
In this particular article, Scott mostly wants to make a point about cases where theories have similar P(E|T) but differ in the prior probabilities, so he focused on the first case.
I feel like this is mostly a question of what you mean with “atlantis”.
If you want to calculate P(evidence | the_specific_atlantis_that_newagers_specified_after_hearing_the_evidence) * P(the_specific_atlantis_that_newagers_specified_after_hearing_the_evidence), then the first term is going to be pretty high, and the second term would be very low (because it specifies a lot of things about what the atleantans did).
But if you want to calculate P(evidence | the_type_of_atlantis_that_people_mostly_associate_to_before_thinking_about_the_sphinx) * P(the_type_of_atlantis_that_people_mostly_associate_to_before_thinking_about_the_sphinx), the first term would be very low, while the second term would be somewhat higher.
The difference between the two cases is whether you think about the new agers as holding exactly one hypothesis and lying about what it predicts (as it cannot assign high probability to all of the things, since you’re correct that the different probabilities must sum to 1), or whether you think about the new agers as switching to a new hypothesis every time they discover a new fact about the sphinx / every time they’re asked a new question.
In this particular article, Scott mostly wants to make a point about cases where theories have similar P(E|T) but differ in the prior probabilities, so he focused on the first case.
Ah, I see. Thanks.