Hi! My main issue with this is not that P(“2+2=4”) = 0.99 is extravagant, but rather that it allows us to use the Bayesian framework to make judgments about the Bayesian framework itself. Such self-referential instruments/mixing metalanguage with the object language usually require additional care in mathematical logic and can be dangerous (e.g., the liar paradox).
Don’t you find the application of law of the total probability to the statement/event “law of the total probability is true”, with a prior of P(“law of the total probability is true”) = 0.99, at least slightly problematic? The one issue: law of the total probability (on the meta-level) requires us to consider both cases (with appropriate weights): law of the total probability is true and law of the total probability is false, but if we assume it is false, then the very application of the law of the total probability is unjustified. This is very similar to liar paradox.
Hi! My main issue with this is not that P(“2+2=4”) = 0.99 is extravagant, but rather that it allows us to use the Bayesian framework to make judgments about the Bayesian framework itself. Such self-referential instruments/mixing metalanguage with the object language usually require additional care in mathematical logic and can be dangerous (e.g., the liar paradox).
Don’t you find the application of law of the total probability to the statement/event “law of the total probability is true”, with a prior of P(“law of the total probability is true”) = 0.99, at least slightly problematic? The one issue: law of the total probability (on the meta-level) requires us to consider both cases (with appropriate weights): law of the total probability is true and law of the total probability is false, but if we assume it is false, then the very application of the law of the total probability is unjustified. This is very similar to liar paradox.
P(“2+2=4”) = 0.99 induces similar complications.