MS in mathematics, and philosophy amateur, I generally align myself with critical rationalist views (apologies to my Bayesian friends), and socially liberal values.
This is a bit of an old post, but I felt I might be able to add to the discussion. Keep in mind this is my own informal take on a rigorous philosophical topic, and I am by no means a professional. My bias leans towards critical rationalism (Popperianism), but I'll try to be fair.
I think you are correct in identifying induction as the fundamental tension between the two epistemologies. Bayesian epistemology (as distinct from Bayes' Theorem) utilizes Solomonoff induction, whereas Popper is highly critical of inductive and probabilistic reasoning. For Popper, induction isn't reasoning at all, if we view reasoning as a method by which we generate knowledge. I'm sometimes tempted to call it "pseudo-inductive reasoning," which is just the fancy way of saying "guessing."
To understand Popper's views, it's important to understand that knowledge for Popper has nothing to do with belief, credence, or confidence; those are all subjective states of one's mind. Perhaps we can psychologically manipulate these mental states (perhaps upon realizing the Bayesian calculus), but those mental states don't constitute knowledge.
If we view the scientific endeavor in three pieces, it might become more clear: 1) We propose ideas, hypotheses, and conjectures 2) We scrutinize these hypotheses and eliminate the falsified ones, and 3) We adopt those hypotheses which have been highly scrutinized as our new scientific theories, acting as if they are true until they are usurped. For Popper, only (2) is the knowledge-generation process, while Bayesians greatly concern themselves with (1) and (3) (they don't neglect (2), but they don't see it as identically the essence of knowledge-generation).
Popper gave a simple example of how knowledge can be contained inside books, and so is not intrinsically tied to our beliefs or actions. Rather, (in my understanding) knowledge is the record of the progress of falsification, and the hypotheses at the top of the current leaderboard. How we generated it and what we do with it once we have it are problems for psychology and rationality, not epistemology.
This is a bit of an old post, but I felt I might be able to add to the discussion. Keep in mind this is my own informal take on a rigorous philosophical topic, and I am by no means a professional. My bias leans towards critical rationalism (Popperianism), but I'll try to be fair.
I think you are correct in identifying induction as the fundamental tension between the two epistemologies. Bayesian epistemology (as distinct from Bayes' Theorem) utilizes Solomonoff induction, whereas Popper is highly critical of inductive and probabilistic reasoning. For Popper, induction isn't reasoning at all, if we view reasoning as a method by which we generate knowledge. I'm sometimes tempted to call it "pseudo-inductive reasoning," which is just the fancy way of saying "guessing."
To understand Popper's views, it's important to understand that knowledge for Popper has nothing to do with belief, credence, or confidence; those are all subjective states of one's mind. Perhaps we can psychologically manipulate these mental states (perhaps upon realizing the Bayesian calculus), but those mental states don't constitute knowledge.
If we view the scientific endeavor in three pieces, it might become more clear: 1) We propose ideas, hypotheses, and conjectures 2) We scrutinize these hypotheses and eliminate the falsified ones, and 3) We adopt those hypotheses which have been highly scrutinized as our new scientific theories, acting as if they are true until they are usurped. For Popper, only (2) is the knowledge-generation process, while Bayesians greatly concern themselves with (1) and (3) (they don't neglect (2), but they don't see it as identically the essence of knowledge-generation).
Popper gave a simple example of how knowledge can be contained inside books, and so is not intrinsically tied to our beliefs or actions. Rather, (in my understanding) knowledge is the record of the progress of falsification, and the hypotheses at the top of the current leaderboard. How we generated it and what we do with it once we have it are problems for psychology and rationality, not epistemology.