Imagine there are many planets with a civilization on each planet. On half of all planets, for various ecological reasons, plagues are more deadly and have a 2⁄3 chance of wiping out the civilization in its first 10000 years. On the other planets, plagues only have a 1⁄3 chance of wiping out the civilization. The people don’t know if they’re on a safe planet or an unsafe planet.
After 10000 years, 2⁄3 of the civilizations on unsafe planets have been wiped out and 1⁄3 of those on safe planets have been wiped out. Of the remaining civilizations, 2⁄3 are on safe planets, so the fact that your civilization survived for 10000 years is evidence that your planet is safe from plagues. You can just apply Bayes’ rule:
EDIT: on the other hand, if logical uncertainty is involved, it’s a lot less clear. Supposed either all planets are safe or none of them are safe, based on the truth-value of a logical proposition (say, the trillionth digit of pi being odd) that is estimated to be 50% likely a priori. Should the fact that your civilization survived be used as evidence of the logical coin flip? SSA suggests no, SIA suggests yes because more civilizations survive when the coin flip makes all planets safe. On the other hand, if we changed the thought experiment so that no civilization survives if the logical proposition is false, then the fact that we survived is proof that the logical proposition is true.
Yes! I thought of this too. So, the anthropic bias does not give us a reason to ignore evidence; it merely changes the structure of specific inferences. We find that we are in an interestingly bad position to estimate those probabilities (the probability will appear to be 0%, if we look just at our history). Yet, it does seem to provide some evidence of higher survival probabilities; we just need to do the math carefully...
For the second question:
Imagine there are many planets with a civilization on each planet. On half of all planets, for various ecological reasons, plagues are more deadly and have a 2⁄3 chance of wiping out the civilization in its first 10000 years. On the other planets, plagues only have a 1⁄3 chance of wiping out the civilization. The people don’t know if they’re on a safe planet or an unsafe planet.
After 10000 years, 2⁄3 of the civilizations on unsafe planets have been wiped out and 1⁄3 of those on safe planets have been wiped out. Of the remaining civilizations, 2⁄3 are on safe planets, so the fact that your civilization survived for 10000 years is evidence that your planet is safe from plagues. You can just apply Bayes’ rule:
P(safe planet | survive) = P(safe planet) P(survive | safe planet) / P(survive) = 0.5 * 2⁄3 / 0.5 = 2⁄3
EDIT: on the other hand, if logical uncertainty is involved, it’s a lot less clear. Supposed either all planets are safe or none of them are safe, based on the truth-value of a logical proposition (say, the trillionth digit of pi being odd) that is estimated to be 50% likely a priori. Should the fact that your civilization survived be used as evidence of the logical coin flip? SSA suggests no, SIA suggests yes because more civilizations survive when the coin flip makes all planets safe. On the other hand, if we changed the thought experiment so that no civilization survives if the logical proposition is false, then the fact that we survived is proof that the logical proposition is true.
Yes! I thought of this too. So, the anthropic bias does not give us a reason to ignore evidence; it merely changes the structure of specific inferences. We find that we are in an interestingly bad position to estimate those probabilities (the probability will appear to be 0%, if we look just at our history). Yet, it does seem to provide some evidence of higher survival probabilities; we just need to do the math carefully...