I have skimmed through the comments here and smelled a weak odour of a flame war. Well, the discussion is still rather civil and far from a flame war as understood on most internet forums, but it somehow doesn't fit well within what I am used to see here on LW.

The main problem I have is that you (i.e. curi) have repeatedly asserted that the Bayesians, including most of LW users, don't understand Popperianism and that Bayesianism is in fact worse, without properly explaining your position. It is entirely possible, even probable, that most people here don't actually get all subtleties of Popper's worldview. But then, a better strategy may be to first write a post which explains these subtleties and tells why they are important. On the other hand, you don't need to tell us explicitly "you are unscholarly and misinterpret Popper". If you actually explain what you ought to (and if you are right about the issue), people here will likely understand that they were previously wrong, and they will do it without feeling that you seek confrontation rather than truth - which I mildly have.

The assumptions behind Cox's theorem are:

1. Representation of degrees of plausibility by real numbers
2. Qualitative correspondence with common sense
3. Consistency

Would you please clearly state which of these you disagree with, and why? And if you disagree with (1), is it because you don't think degrees of plausibility should be represented, or because you think they should be represented by something other than real numbers, and if so, then what? (Please do not give an answer that cannot be defined precisely by mapping it to a mathematical set. And please do not suggest a representation that is obviously inadequate, such as booleans.)

I don't understand Popper's work beyond the Wikipedia summary of critical rationalism. That summary, as well as the debate here at LW, appear to be confused and essentially without value. If this is not the case, you should update this post to include not just a description of how supporters of Bayesianism don't understand Popper, but why they should care about this discussion--why Bayesianism is not, as it seems, obviously the correct answer to the question Popper is trying to answer.

If you want to make bets about the future, Bayesianism will beat whateve... (read more)

There's an associated problem here that may be getting ignored: Popper isn't a terribly good writer." The Logic of Scientific Discovery" was one of the first phil-sci books I ever read and it almost turned me off of phil-sci. This is in contrast for example with Lakatos or Kuhn who are very readable. Some of the difficulty with reading Popper and understanding his viewpoints is that he's just tough to read.

That said, I think that chapter 3 of that books makes clear that Popper's notion of falsification is more subtle than what I would call &quo... (read more)

I gave a description of how a Bayesian sees the difference between "X supports Y" and "X is consistent with Y" in our previous discussion. I don't know if you saw it, you havn't responded to it and you aren't acting like you accepted it so I'll give it again here:

"X is consistent with Y" is not really a Bayesian way of putting things, I can see two ways of interpreting it. One is as P(X&Y) > 0, meaning it is at least theoretically possible that both X and Y are true. The other is that P(X|Y) is reasonably large, i.e.

A huge strength of Bayesian epistemology is that it tells me how to program computers to form accurate beliefs. Has Popperian epistemology guided the development of any computer program as awesome as Gmail's spam filter?

It has occurred to me before that the lack of a proper explanation on LessWrong of Bayesian epistemology (and not just saying` "Here's Bayes' theorem and how it works, with a neat Java applet") is a serious lack. I've been reduced to linking the Stanford Encyclopedia of Philosophy article, which is really not well written at all.

It is also clear from the comments on this post that people are talking about it without citable sources, and are downvoting as a mark of disagreement rather than anything else. This is bad as it directly discourages thou... (read more)

The naturalist philosopher Peter Godfrey Smith said this of Popper's position:

[F]or Popper, it is never possible to confirm or establish a theory by showing its agreement with observations. Confirmation is a myth. The only thing an observational test can do is to show that a theory is false...Popper, like Hume, was an inductive skeptic, and Popper was skeptical about all forms of confirmation and support other than deductive logic itself...This position, that we can never be completely certain about factual issues, is often known as fallibilism...Accordi

The thing intended as the proof is most of chapter 2. I dislike Jaynes' assumptions there, since I find many of them superfluous compared to other proofs. You probably like them even less, since one is "Representation of degrees of plausibility by real numbers".

Curi,

"Some first chapter assumptions are incorrect or unargued. It begins with an example with a policeman, and says his conclusion is not a logical deduction because the evidence is logically consistent with his conclusion being false."

Popper's epistemology doesn't explain that the conclusion of the argument has no validty, in the sense of being certainly false. In fact, it requires that the conclusion is not certainly false. No conjecture is certainly false.

Perhaps you meant he shows that the argument is invalid in the sense of being a non sequ... (read more)

From the research I have done in the last 5 minutes, it seems as though Popper believed that all good scientific theories should be subject to experiments that could prove them wrong.
Ex:

"the falsificationists or fallibilists say, roughly speaking, that what cannot (at present) in principle be overthrown by criticism is (at present) unworthy of being seriously considered; while what can in principle be so overthrown and yet resists all our critical efforts to do so may quite possibly be false, but is at any rate not unworthy of being seriously considered and perhaps even of being believed" -Popper

This seems to imply that theories can be proved false.