Take Bayes’ theorem: P(H|O) = P(O|H) × P(H) / P(O). If H is a hypothesis and O is an observation, P(O|H) means “what is the probability of making that observation if the hypothesis is true?”
If a hypothesis has as consequence “nobody can observe O” (say, because no humans can exist), then that P(O|H) is 0 (actually, it’s about the probability that you didn’t get the consequence right). Which means that, once you made the observation, you will probably decide that the hypothesis is unlikely. However, if you don’t notice that consequence, you might decide that P(O|H) is large, and incorrectly assign high likelihood to the hypothesis.
For a completely ridiculous example, imagine that there’s a deadly cat-flu epidemic; it gives 90% of cats that catch it a runny nose. Your cat’s nose becomes runny. You might be justified to think that it’s likely your cat got cat-flu. However, if you know that all cases, the cat’s owner dies of the flu before the cat has any symptoms, the conclusion would be the opposite. (Since, if it were the flu, you wouldn’t see the cat’s runny nose, because you’d be dead.) The same evidence, opposite effect.
Anthropics is kind of the same thing, except you’re mostly guessing about the flu.
Take Bayes’ theorem: P(H|O) = P(O|H) × P(H) / P(O). If H is a hypothesis and O is an observation, P(O|H) means “what is the probability of making that observation if the hypothesis is true?”
If a hypothesis has as consequence “nobody can observe O” (say, because no humans can exist), then that P(O|H) is 0 (actually, it’s about the probability that you didn’t get the consequence right). Which means that, once you made the observation, you will probably decide that the hypothesis is unlikely. However, if you don’t notice that consequence, you might decide that P(O|H) is large, and incorrectly assign high likelihood to the hypothesis.
For a completely ridiculous example, imagine that there’s a deadly cat-flu epidemic; it gives 90% of cats that catch it a runny nose. Your cat’s nose becomes runny. You might be justified to think that it’s likely your cat got cat-flu. However, if you know that all cases, the cat’s owner dies of the flu before the cat has any symptoms, the conclusion would be the opposite. (Since, if it were the flu, you wouldn’t see the cat’s runny nose, because you’d be dead.) The same evidence, opposite effect.
Anthropics is kind of the same thing, except you’re mostly guessing about the flu.