I wrote this in Feb 2009. There was no reply.
Dear Eliezer Yudkowsky,
I am writing to criticize some of your statements regarding Karl Popper. I hope this will be of interest.
Previously, the most popular philosophy of science was probably Karl Popper's falsificationism - this is the old philosophy that the Bayesian revolution is currently dethroning. Karl Popper's idea that theories can be definitely falsified, but never definitely confirmed, is yet another special case of the Bayesian rules
That isn't Popper's idea because he doesn't believe in definite falsifications. Falsifications are themselves tentative conjectures which must be held open to criticism and reconsidering.
Popper also doesn't assert that confirmations are never definite, rather he denies there is confirmation at all. The reason is that any given confirming evidence for theory T is logically consistent with T being false.
More generally, Popper's philosophy is not about what we can do definitely. He does not address himself to the traditional philosophical problem of what we can and can't be certain of, or what is and isn't a justified, true belief. While he did comment on those issues, his epistemic philosophy is not an alternative answer to those questions. Rather, his positive contributions focus on a more fruitful issue: conjectural knowledge. How do people acquire conjectural knowledge? What is its nature? And so on.
BTW, conjectural knowledge does not mean the probabilistic knowledge that Bayesians are fond of. Probabilistic knowledge is just as much of an anathema to Popper as certain knowledge, because the same criticisms (for example that attempting justification leads to regress or circularity) apply equally well to each.
Your claim at the end of the quote that Popperian epistemology is a special case of Bayesian epistemology is especially striking. Popper considered the Bayesian approach and told us where he stands on it. On page 141 of Objective Knowledge he states, "I have combated [Bayesian epistemology] for thirty-three years."
To say that something which Popper combatted for over three decades is a more general version of his own work is an extraordinary claim. It should be accompanied with extraordinary substantiation, and some account of where Popper's arguments on the subject go wrong, but it is not.
Popper was a hardworking, academic person who read and thought about philosophy extensively, including ideas he disagreed with. He would often try to present the best possible version of an idea, as well as a history of the problem in question, before offering his criticism of it. I would ask that a similar approach be taken in criticizing Popper. Both as a matter of respect, and because it improves discussion.