Desrtopa comments on Bayesian Epistemology vs Popper - Less Wrong Discussion
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It's no less founded on unproven axioms, and it's no less arbitrary than induction, it just contains the tenet "we don't reject propositions for being arbitrary" and pats itself on the back for being self consistent. This doesn't do a better job helping people generate true information, it does a worse one.
Being arbitrary is a criticism, so a critical rationalist can and does reject propositions for being arbitrary. Rejecting the idea of justification does not mean accepting any old arbitrary thing. If your idea doesn't stand up to criticism, including criticism that it is just arbitrary, then it is gone.