Consider Proposition H: “God is watching out for me, and has a special purpose for me and me alone. Therefore, God will not let me die. No matter how dangerous a threat seems, it cannot possibly kill me, because God is looking out for me – and only me – at all times.” Suppose that you believe that there is a nonzero probability that H is true. And suppose you are a Bayesian – you update your beliefs according to Bayes’ Rule. As you survive longer and longer – as more and more threats fail to kill you – your belief about the probability that H is true must increase and increase. It’s just mechanical application of Bayes’ Rule.
Gene Wolfe, The Citadel of the Autarch
Often their chants sounded so clearly that I could make out the words, though they were in no language I had ever heard. Once one actually stood on his saddle like a performer in a riding exhibition, lifting a hand to the sun and extending the other toward the Ascians. Each rider seemed to have a personal spell; and it was easy to see, as I watched their numbers shrink under the bombardment, how such primitive minds come to believe in their charms, for the survivors could not but feel their thaumaturgy had saved them, and the rest could not complain of the failure of theirs.