Yes, by all means feel free.

The number of major ideas in epistemology is not very large. After Aristotle, there wasn't very much innovation for a long time. It's a small enough field you can actually trace ideas all the way back to the start of written history. Any professional can look at everything important. Some Bayesian should have. Maybe some did, but I haven't seen anything of decent quality.

As to a professional, I already referred you to Earman. Incidentally, you seem to be narrowing the claim somewhat. Note that I didn't say that the set of major ideas in epistemology isn't small, I referred to the much larger class of philosophical ideas (although I can see how that might not be clear from my wording). And the set is indeed very large. However, I think that your claim about "after Aristotle" is both wrong and misleading. There's a lot of what thought about epistemological issues in both the Islamic and Christian worlds during the Middle Ages. Now, you might argue that that's not helpful or relevant since it gets tangled up in theology and involves bad assumptions. But that's not to say that material doesn't exist. And that's before we get to non-Western stuff (which admittedly I don't know much about at all).

(I agree when you restrict to professionals, and have already recommended Earman to you.)

It works exactly identically to how Popperian epistemology creates any other kind of knowledge. There's nothing special for morality.

Knowledge is created by an evolutionary process involving conjecture and refutation. By criticizing flaws in ideas, we seek to improve them (by making better conjectures we hope will eliminate the flaws).

This is a deeply puzzling set of claims. First of all, a major point of his epistemological system is falsfiability based on data (at least as I understand it from LScD). How that would at all interact with moral issues is unclear to me. Indeed, the semi-canonical example of a non-falsifiable claim in the Popperian sense is Marxism, a set of ideas that has a large set of attached moral claims.

I also don't see how this works given that moral claims can always be criticized by the essential sociopathic argument "I don't care. Why should you?" Obviously, that line of thinking can be/should be expanded. To use your earlier example, how would you discuss "murder is wrong" in a Popperian framework? I would suggest that this isn't going to be any different than simply discussing moral ideas based on shared intuitions with particular attention to the edge cases. You're welcome to expand on these claims, but right now, nothing you've said in this regard is remotely convincing or even helpful since it amounts to just saying "well, do the same thing."

I have a lot of familiarity with the other Popperians. But Popper and Deutsch are by far the best. There isn't really anything non-Popperian that draws on Popper much. Everyone who has understood Popper is a Popperian, IMO. If you disagree, do tell.

I'm going to be obnoxious and quote a friend of mine "Everyone who understands Christianity is a Christian." I don't have any deep examples of other individuals although I would tentatively say that I understood Popper's views in Logic of Scientific Discovery just fine.

Do you have a criticism of his arguments in LScD or not?

Sure. The most obvious one is when he is discussing the law of large numbers and frequentist v. Bayesian interpretations (incidentally to understand those passages it is helpful to note that he uses the term "subjective" to describe Bayesians rather than Bayesian which is consistent with the language of the time, but in modern terminology has a very different meaning (used to distinguish between subject and objective Bayesians)). In that section he argues that (I don't have the page number unfortunately since I'm using my Kindle edition. I have a hard copy somewhere but I don't know where) that "it must be inadmissable to give after the deduction of Bernoulli's theorem a meaning to p different from the one which was given to it before the deduction." This is, simply put, wrong. Mathematicians all the time prove something in one framework and then interpret it in another framework. You just need to show that all the properties of the relevant frameworks overlap in sufficiently non-pathological cases. If someone wrote this as a complaint about say using the complex exponential to understand the symmetries of the Euclidean plane, we'd immediately see this as a bad claim. There's an associated issue in this section which also turns up but it is more subtle; Popper doesn't appreciate what you can do with measure theory and L_p spaces and related ideas to move back and forth between different notions of probability and different metrics on spaces. That's ok, it was a very new idea when he wrote LScD (although the connections were to some extent definitely there). But it does render a lot of what he says simply irrelevant or outright wrong.

Err, Bayesian probability doesn't have anything special for morality either. People on LW tend to be moral non-realists, ie people who deny that there is objective moral knowledge, if that's what you're talking about (not sure- sorry!), but that's completely orthogonal to this discussion: there's nothing in Bayesianism that leads inevitably to non-realism. (Also, I'm not convinced that moral realism is right, so saying "Bayesianism leads to moral non-realism" isn't a very effective argument.)

Knowledge is created by an evolutionary process involving conjecture and refutation. By criticizing flaws in ideas, we seek to improve them (by making better conjectures we hope will eliminate the flaws).

I'm inclined to take this formula seriously, but I'd like to start by applying it to innate knowledge, knowledge we are born with, because here we are definitely talking about an evolutionary process involving mutation and natural selection. Some mutations add what amounts to a new innate conjecture (hypothesis, belief) into the cognitive architecture of the creature.

However, what occurs at this point is not that a creature with a false innate conjecture is eliminated. The creature isn't being tested purely against reality in isolation. It's being tested against other members of its species. The creature with the least-false, or least-perilously-false conjecture will tend to do better than the competitors. The competition for survival amounts to a competition between rival conjectures. The truest, or most-usefully-true, or least-wrong, or least-dangerously-wrong innate belief will tend to outdo its competitors and ultimately spread through the species. (With the odd usefully-wrong belief surviving.)

The occasional appearance of new innate conjectures resembles the conjecture part of Popperian conjecture and refutation. However, the contest between rival innate conjectures that occurs as the members of the species struggle against each other for survival seems less Popperian than Bayesian.

The relative success of the members of the species who carry the more successful hypothesis vaguely resembles Bayesian updating, because the winners increase their relative numbers and the losers decrease their relative numbers, which resembles the shift in the probabilities assigned to rival hypotheses that occurs in Bayesian updating. Consider the following substitutions applied to Bayes' formula:

P(H|E) = P(E|H)P(H) / P(E)

• P(H|E) is the new proportion (i.e. in the next generation) of the species carrying the hypothesis H, given that event E occurred (E is "everything that happened to the generation")
• P(E|H) is the degree to which H predicts and thus prepares the individual to handle E (measured in expected number of offspring given E)
• P(H) is the old proportion (i.e. in the previous generation) of the species carrying H
• P(E) is the degree to which the average member of the species predicts and thus is prepared to handle E (measured in expected number of offspring given E)

With these assignments, what the equation means is:

The new proportion of the species with H is equal to the old proportion of the species with H, times the expected number of offspring of members with H, divided by the expected number of offspring of the average member of the species.

One difference between this process and Bayesian updating is that this process allows the occasional introduction of new hypotheses over time, with what amounts to a modest but not vanishing initial prior.