I've recently been reading about a rationalist blogger who converted to Catholicism. She may have assigned subjective probabilities like:
Then she may have introspected and come up with:
We can calculate:
Abbreviating Objective Morality by "OM", and "God" by "G", this state of affairs is inconsistent, because we intuitively see that:
To resolve it, she could either increase her subjective probability of there being a God
or she could reduce her probability of there being some kind of objective morality
She could also reconsider P(God|Objective Morality) or P(Objective Morality|God).
Anyways, I find myself very confused by this state of affairs. Is this a solved question? Is there a purely principled way of resolving this which only takes into account the 4 numbers P(OM), P(G), P(OM|G) and P(G|OM)? Is there a standard way of using some kind of metaprobabilities?