If P is the probability that an ideal Bayesian would assign to a proposition A on hearing A but having observed no relevant evidence, then you have described the meta expected value of P in logical ignorance before doing any calculations (and assuming an ignorance prior on the distribution of propositions one might hear about). It seems to me that you have made excessively harsh criticism against those who have made correct statements about P itself.
[Y]ou have described the meta expected value of P...It seems to me that you have made excessively harsh criticism against those who have made correct statements about P itself.
See my other comments. In my opinion, the correct point of view is that P is a variable (or, if you prefer, a two-argument function); the “correct” statements are about a different value of P from the relevant one (resp. depend on inappropriately fixing one of the two arguments).
EDIT: Also, I think this is the level on which Bayesian Bob was thinking, and the critical comments weren’t taking this into account and were assuming a basic error was being made (just like Rational Rian).
If P is the probability that an ideal Bayesian would assign to a proposition A on hearing A but having observed no relevant evidence, then you have described the meta expected value of P in logical ignorance before doing any calculations (and assuming an ignorance prior on the distribution of propositions one might hear about). It seems to me that you have made excessively harsh criticism against those who have made correct statements about P itself.
See my other comments. In my opinion, the correct point of view is that P is a variable (or, if you prefer, a two-argument function); the “correct” statements are about a different value of P from the relevant one (resp. depend on inappropriately fixing one of the two arguments).
EDIT: Also, I think this is the level on which Bayesian Bob was thinking, and the critical comments weren’t taking this into account and were assuming a basic error was being made (just like Rational Rian).