The 4 given probabilities are actually perfectly consistent within the equations you are using. It is provable that whatever 4 probabilities you use the equations will be consistent.
Therefore the question becomes “where did my maths go wrong?”
P(G|OM) = 0.055, not 0.55
I’m pretty confident that the only way probabilities can actually be inconsistent is if it is over constrained (e.g. in this case you define 5 relevant probabilities instead of 4). The whole point of having axioms is to prevent inconsistencies provided you stay inside them.
P.S. Good job on noticing your confusion!
0.9 = P(Objective Morality) ≠ P(God) * P(Objective Morality | God) + P(No God) * P(Objective Morality | No God) = 0.05 * 0.99 + 0.95 * 0.02 = 0.0685. That’s inconsistent, right?
Argh,you’re right,I didn’t check that one. P(OM) cancels on the P(G) equation so that one isn’t over constrained.
However for the equation for P(OM) 4 variables is over constrained, 3 is enough.