You don’t just get to use Bayes’ Theorem here without explaining the epistemological framework you used to judge the correctness of Bayes
I certainly do. I said that induction is not impossible, and that inductive reasoning is Bayesian. If you think that Bayesian reasoning is also impossible, you are free to establish that. You have not done so.
Critical Rationalism can be used to improve Critical Rationalism and, consistently, to refute it (though no one has done so).
If this is possible, it would be equally possible to refute induction (if it were impossible) by using induction. For example, if every time something had always happened, it never happened after that, then induction would be refuted by induction.
If you think that is inconsistent (which it is), it would be equally inconsistent to refute CR with CR, since if it was refuted, it could not validly be used to refute anything, including itself.
I certainly do. I said that induction is not impossible, and that inductive reasoning is Bayesian. If you think that Bayesian reasoning is also impossible, you are free to establish that. You have not done so.
If this is possible, it would be equally possible to refute induction (if it were impossible) by using induction. For example, if every time something had always happened, it never happened after that, then induction would be refuted by induction.
If you think that is inconsistent (which it is), it would be equally inconsistent to refute CR with CR, since if it was refuted, it could not validly be used to refute anything, including itself.