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:
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.)
You may have valid points to make but it might help in getting people to listen to you if you don't exhibit apparent double standards. In particular, your main criticism seems to be that people aren't reading Popper's texts and related texts enough. Yet, at the same time, you are apparently unaware of the basic philosophical arguments for Bayesianism. This doesn't reduce the validity of anything you have to say but as an issue of trying to get people to listen, it isn't going to work well with fallible humans.
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...
Here let me ask you a question: has any Bayesian ever published any substantive criticism of an important idea in Popper's epistemology? Someone should have done it, right?
Most things in the space of possible documents can't be refuted, because they don't correspond to anything refutable. They are simply confused, and irredeemably. In the case of epistemology, virtually everything that has ever been said falls into this category. I am glad that I don't have to spend time thinking about it, because it is solved. I would not generally criticize a rival's ideas, because I no longer care. The problem is solved, and I can go work on things that still matter.
Are you so sure of yourself -- that you are right about many things -- that you will dismiss all rival ideas without even having to know what they say?
Once I know the definitive answer to a question, I will dismiss all other answers (rather than trying to poke holes in them). The only sort of argument which warrants response is an objection to my current definitive answer. So ignorance of Popper is essentially irrelevant (and I suspect I couldn't object to anything in his philosophy, because it has essentially no content conc...
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...
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...
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?
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...
"'What is support?' (This is not asking for its essential nature or a perfect definition, just to explain clearly and precisely what the support idea actually says) and 'What is the difference between "X supports Y" and "X is consistent with Y"?' If anyone has the answer, please tell me."
Bayesians appear to have answers to these questions. Moreovoer, far from wishing to refute Popper, they can actually incorporate a fomr of Popperianism.
"On the other hand, Popper's idea that there is only falsification and no such thing a...
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.
Which you stated you had not read. I have rather low standards for recommendations of things to read, but "I never read it myself" isn't good enough.
Earman is a philosopher and the book has gotten positive reviews from other philosophers. I don't know what else to say in that regard.
I don't agree with "restrict to professionals". How is it to be determined who is a professional? I don't want to set up arbitrary, authoritative criteria for dismissing ideas based on their source.
Hrrm? You mentioned professionals first. I'm not sure why you are now objecting to the use of professionals as a relevant category.
That is a major point for scientific research where the problem "how do we use evidence?" is important. And the answer is "criticisms can refer to evidence". Note by "science" here I mean any empirical field. What do you do in non-scientific fields? You simply make criticisms that don't refer to evidence. Same method, just missing one type of criticism which is rather useful in science but not fundamental to the methodology
I'm not at all convinced that this is what Popper intended (but again I've only read LScD) but if this is accurate then Popper isn't just wrong in an interesting way but is just wrong. Does one mean for example to claim that pure mathematics works off of criticism? I'm a mathematician. We don't do this. Moreover, it isn't clear what it would even mean for us to try to do this as our primary method of inquiry. Are we supposed to spend all our time going through pre-existing proofs trying to find holes in them?
He has like 20 books. There's way more to it. When one reads a lot of them, a whole worldview comes across that is very hard to understand from just a couple books.
Yes, and I'm quite sure that I get much more of a worldview if I read all of Hegel rather than just some of it. That doesn't mean I need to read all of it. Similar remarks would apply to Aquinas or more starkly the New Testament. Do you need to read all of the New Testament to decide that Christianity is bunk? Do you need to read the entire Talmud to decide that Judaism is incorrect? But you get a whole worldview that you don't obtain from just reading the major texts.
The short answer is: since we don't care to have justified foundations, you can discuss it any way you like. You can say it's bad because it hurts people. You can say it's good because it prevents overpopulation. You can say it's bad because it's mean. These kinds of normal arguments, made by normal people, are not deemed automatically invalid and ignored. Many of them are indeed mistakes. But some make good points
Right, and then we just the criticism "why bother" or "and how does that maximize the number of paperclip in the universe?" Or one can say "mean" "good" bad" are all hideously ill-defined. In any event, does it not bother you that you are essentially claiming that your moral discussion with your great epistemological system looks just like a discussion about morality by a bunch of random individuals? There's nothing in the above that uses your epistemology in any substantial way.
Are you really telling me that you can prove something, then take the conclusion, redefine a term, and work with that, and consider it still proven? You could only do that if you created a second proof that the change doesn't break anything, you can't just do it.
Right! And conveniently in the case Popper cares about you can prove that.
Popper doesn't appreciate what you can do with measure theory and L_p spacesWould you understand if I said this has no relevance at all to 99.99% of Popper's philosophy? Note that his later books generally have considerably less mention of math or logic.
Do you mean understand or do you mean care? I don't understand why you are making this statement given that my remark was addressing the question you asked of whether I had specific problems with Popper's handling of Bayesianism in LScD. This is a specific problem there.
Does one mean for example to claim that pure mathematics works off of criticism? I'm a mathematician. We don't do this.
I don't know what Popper himself would say, but one of his more insightful followers, namely Lakatos, argues for exactly that position.
I read Proofs and Refutations too many years ago to say anything precise about it. I remember finding it interesting but also frustrating. Lakatos seems determined to ignore/deny/downplay the fact of mathematical practice that we only call something a 'theorem' when we've got a proof, and we only call so...
I was directed to this book (http://www-biba.inrialpes.fr/Jaynes/prob.html) in conversation here:
http://lesswrong.com/lw/3ox/bayesianism_versus_critical_rationalism/3ug7?context=1#3ug7
I was told it had a proof of Bayesian epistemology in the first two chapters. One of the things we were discussing is Popper's epistemology.
Here are those chapters:
http://www-biba.inrialpes.fr/Jaynes/cc01p.pdf
http://www-biba.inrialpes.fr/Jaynes/cc02m.pdf
I have not found any proof here that Bayesian epistemology is correct. There is not even an attempt to prove it. Various things are assumed in the first chapter. In the second chapter, some things are proven given those assumptions.
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. I agree so far. Next it says "we will grant that it had a certain degree of validity". But I will not grant that. Popper's epistemology explains that *this is a mistake* (and Jaynes makes no attempt at all to address Popper's arguments). In any case, simply assuming his readers will grant his substantive claims is no way to argue.
The next sentences blithely assert that we all reason in this way. Jaynes' is basically presenting the issues of this kind of reasoning as his topic. This simply ignores Popper and makes no attempt to prove Jaynes' approach is correct.
Jaynes goes on to give syllogisms, which he calls "weaker" than deduction, which he acknowledges are not deductively correct. And then he just says we use that kind of reasoning all the time. That sort of assertion only appeals to the already converted. Jaynes starts with arguments which appeal to the *intuition* of his readers, not on arguments which could persuade someone who disagreed with him (that is, good rational arguments). Later when he gets into more mathematical stuff which doesn't (directly) rest on appeals to intution, it does rest on the ideas he (supposedly) established early on with his appeals to intuition.
The outline of the approach here is to quickly gloss over substantive philosophical assumptions, never provide serious arguments for them, take them as common sense, do not detail them, and then later provide arguments which are rigorous *given the assumptions glossed over earlier*. This is a mistake.
So we get, e.g., a section on Boolean Algebra which says it will state previous ideas more formally. This briefly acknowledges that the rigorous parts depend on the non-rigorous parts. Also the very important problem of carefully detailing how the mathematical objects discussed correspond to the real world things they are supposed to help us understand does not receive adequate attention.
Chapter 2 begins by saying we've now formulated our problem and the rest is just math. What I take from that is that the early assumptions won't be revisted but simply used as premises. So the rest is pointless if those early assumptions are mistaken, and Bayesian Epistemology cannot be proven in this way to anyone who doesn't grant the assumptions (such as a Popperian).
Moving on to Popper, Jaynes is ignorant of the topic and unscholarly. He writes:
http://www-biba.inrialpes.fr/Jaynes/crefsv.pdf
> Karl Popper is famous mostly through making a career out of the doctrine that theories may not be proved true, only false
This is pure fiction. Popper is a fallibilist and said (repeatedly) that theories cannot be proved false (or anything else).
It's important to criticize unscholarly books promoting myths about rival philosophers rather than addressing their actual arguments. That's a major flaw not just in a particular paragraph but in the author's way of thinking. It's especially relevant in this case since the author of the books tries to tell us about how to think.
Note that Yudkowsky made a similar unscholarly mistake, about the same rival philosopher, here:
http://yudkowsky.net/rational/bayes
> 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
Popper's philosophy is not falsificationism, it was never the most popular, and it is fallibilist: it says ideas cannot be definitely falsified. It's bad to make this kind of mistake about what a rival's basic claims are when claiming to be dethroning him. The correct method of dethroning a rival philosophy involves understanding what it does say and criticizing that.
If Bayesians wish to challenge Popper they should learn his ideas and address his arguments. For example he questioned the concept of positive support for ideas. Part of this argument involves asking the questions: 'What is support?' (This is not asking for its essential nature or a perfect definition, just to explain clearly and precisely what the support idea actually says) and 'What is the difference between "X supports Y" and "X is consistent with Y"?' If anyone has the answer, please tell me.