I’d just like to point out that even #1 of the OP’s “lessons” is far more problematic than they make it seem. Consider the statement:
“The fact that there are myths about Zeus is evidence that Zeus exists. Zeus’s existing would make it more likely for myths about him to arise, so the arising of myths about him must make it more likely that he exists.” (supposedly an argument of the form P(E | H) > P(E)).
So first, “Zeus’s existing would make it more likely for myths about him to arise”—more likely than what? Than “a priori”? This is essentially impossible to know, since to compute P(E) you must do P(E) = sum(i) { P(E|H[i])*P(H[i]) }, i.e. marginalise over a mutually exclusive set of hypotheses (and no “Zeus” and “not Zeus” does not help, because “not Zeus” is a compound hypothesis which you also need to marginalise over).
I will grant you that it may seem plausible to guess that the average P(E|H[i]) over all possible explanations for E is lower than P(E|Zeus) (since most of them are bad explanations), but since the average is weighted by the various priors P(H[i]), then if our background knowledge causes some high likelihood explanation for E (high P(E|H[i])) to dominates the average then P(E) may not be less than P(E|Zeus) even if P(E|Zeus) is relatively high! In which case E actually counts against the Zeus hypothesis, since P(H|E)<P(H) if P(E|H)<P(E).
Whether this is the case or not in the example is tough to say, (and of course is relative to the agents background knowledge), but I think it worth emphasising that it is not so easy as it seems.
I’d just like to point out that even #1 of the OP’s “lessons” is far more problematic than they make it seem. Consider the statement:
“The fact that there are myths about Zeus is evidence that Zeus exists. Zeus’s existing would make it more likely for myths about him to arise, so the arising of myths about him must make it more likely that he exists.” (supposedly an argument of the form P(E | H) > P(E)).
So first, “Zeus’s existing would make it more likely for myths about him to arise”—more likely than what? Than “a priori”? This is essentially impossible to know, since to compute P(E) you must do P(E) = sum(i) { P(E|H[i])*P(H[i]) }, i.e. marginalise over a mutually exclusive set of hypotheses (and no “Zeus” and “not Zeus” does not help, because “not Zeus” is a compound hypothesis which you also need to marginalise over).
I will grant you that it may seem plausible to guess that the average P(E|H[i]) over all possible explanations for E is lower than P(E|Zeus) (since most of them are bad explanations), but since the average is weighted by the various priors P(H[i]), then if our background knowledge causes some high likelihood explanation for E (high P(E|H[i])) to dominates the average then P(E) may not be less than P(E|Zeus) even if P(E|Zeus) is relatively high! In which case E actually counts against the Zeus hypothesis, since P(H|E)<P(H) if P(E|H)<P(E).
Whether this is the case or not in the example is tough to say, (and of course is relative to the agents background knowledge), but I think it worth emphasising that it is not so easy as it seems.