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TimS comments on "Stupid" questions thread - Less Wrong Discussion
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P(religion is true | overwhelming professing of belief) > P(religion is true | absence of overwhelming professing of belief).
In other words, I think my two formulations are isomorphic. If we define evidence such that absence of evidence is evidence of absence, then one implication is that it is possible for some evidence to exist in favor of false propositions.
This is possible with any definition of evidence. Every bit of information you receive makes you discard some theories which have been disproven, so it's evidence in favour of each of the ones you don't discard. But only one of those is fully true; the others are false.