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BrianScurfield comments on Taking Ideas Seriously - Less Wrong
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You do realize that Hume held that induction cannot be logically justified? He noticed there is a "problem of induction". That problem was exploded by Karl Popper. Have you read what he has to say and taken seriously his ideas? Have you read and taken seriously the ideas of philosophers like David Deutsch, David Miller, and Bill Bartley? They all agree with Popper that:
Induction, i.e. inference based on many observations, is a myth. It is neither a psychological fact, nor a fact of ordinary life, nor one of scientific procedure - Karl Popper (Conjectures & Refutations, p 70).
Of course. That is why I mentioned him.
"Exploded". My! What violent imagery. I usually prefer to see problems "dissolved". Less metaphorical debris. And yes, I've read quite a bit of Popper, and admire much of it.
Nope, I haven't.
You know, when giving page citations in printed texts, you should specify the edition. My 1965 Harper Torchbook paperback edition does not show Popper saying that on p 70. But, no matter.
One of the few things I dislike about Popper is that he doesn't seem to understand statistical inference. I mean, he is totally clueless on the subject. It is not just that he isn't a Bayesian - it seems he doesn't "get" Pearson and Fisher either. Well, no philosopher gets everything right. But if he really thinks that "inference based on many observations" cannot happen - not just that it is frequently done wrong, but rather that it is impossible - then all I can say is that this is not one of Sir Karl's better moments.
And if what he means is simply that we cannot infer absolute general truths from repeated observations, then I have to call him a liar for suggesting that anyone else ever suggested that we could make such inferences.
But, since you have been recommending philosophers to me, let me recommend some to you. I. J. Good is fun. Richard Jeffrey is not bad either. E.T. Jaynes explains quite clearly how one makes inferences based on observations - one observation or many observations. You really ought to look at Jaynes before coming to this forum to lecture on epistemology.
Perhaps you should know I have published papers where I have used Bayes extensively. I am well familiar with the topic (edit: though this doesn't make me any kind of infallible authority). I was once enthusiastic about Bayesian epistemology myself. I now see it as sterile. Popperian epistemology - especially as extended by David Deutsch - is where I see fertile ground.
Cool. But more to the point, have you published, or simply written, any papers in which you explain why you now see it as sterile? Or would you care to recommend something by Deutsch which reveals the problems with Bayesianism. Something that actually takes notice of our ideology and tries to refute it will be received here much more favorably than mere diffuse enthusiasm for Popper.
The quote is from 3rd ed. 1968. You say you have read Popper, then you should not be surprised by the quote. Your response above is just the argument from incredulity. Do you have a better criticism?
I'm not surprised by the quote. I just couldn't find it. It apparently wasn't in 2nd edition. But my 2nd edition index had many entries for "induction, myth of _" so I don't doubt you at all that Popper actually said it.
I am incredulous because I know how to do inference based on a single observation, as well as inference based on many. And so does just about everyone who posts regularly at this site. It is called Bayesian inference, and is not really all that difficult. Even you could do it, if you were to simply set aside your prejudice that
I have already provided references. You can find thousands more by Googling.
OK, tell me how you know in advance of having any theory what to observe?
BTW, please don't assume things about me like asserting I hold prejudices. The philosophical position I come from is a full blown one. - it is no mere prejudice. Also, I'm quite willing to change my ideas if they are shown to be wrong.
Ok, I won't assume that you believe, with Popper whom you quote, that inference based on many observations is impossible. I will instead assume that Popper is using the word "inference" very differently than it is used around here. And since you claim to be an ex-Bayesian, I will assume you know how the word is used here. Which makes your behavior up until now pretty inexplicable, but I will make no assumptions about the reasons for that.
Likewise, please do not assume that I believe that observation is neither theory-laden nor theory-directed. As it happens, I do not know in advance of a theory what to observe.
Of course, the natural thing for me to do now would be to challenge you to explain where theories come from in advance of observation. But why don't we both just grow up?
If you have a cite for a careful piece of reasoning which will cause us to drop our Bayesian complaisancy and re-embrace Popper, please provide it and let us read the text in peace.
From the problem-situation. Theories arise out of problems.
And where do problems come from in advance of theories and obs...
Never mind. Someone else can carry on. I have other things to attend to.
It sounds like Scurfield's "cite for a careful piece of reasoning" are the works of Karl Popper, which you are also familiar with. I don't have time to read the works of Karl Popper, but I have plenty of time to read blog comments about them. I've found every single comment in this thread interesting. Why discourage it?
I think the problem is a communication gap--"Bayesian" can mean different things to different people; and my best guess is that Scurfield converted from Laplace's degree-of-belief approach to probability. Around here, though, the dominant Bayesian paradigm is Jaynes', which takes the critiques of Bayes from the 1920 through the 1970s into account and digs through them to the epistemological bedrock below pretty well. Unless Scurfield has something new to say about Jaynes' interpretation, his critiques aren't that interesting to people who already know both Popper and Jaynes.
That can't actually be everyone here. And I hope no one is offended if I say that Scurfield seems to "know Popper" to a greater degree than any of the other participants in this thread. Why the scorn for the guy and the conversation?
He certainly knows Popper better than me. I scorn the conversation because it is not stimulating me - not causing me to consider ideas I have never considered before. I scorn the guy (scorn may be a bit too strong here, but just go with it) because so far he has mostly presented slogans, rather than arguments. (Admitedly, I haven't presented arguments either, but that is because his slogans strike me as either truisms or word games.)
The only thing I gained from this encounter was the link to the Critical Rationalism web site, where can be found links to writings by Popper and others. The CR site itself is, ..., well, not great. For example, check out the "What is CR?" page where CR is contrasted with two other possible approaches to philosophy. Please actually check it out before continuing.
Now weren't those subtle strawmen? :)
I don't see any people here that know both. Eliezer doesn't appear to either. See here and here.
A better phrasing for that might have been "certain knowledge is a myth." What cannot be logically justified is reasoning from particular observations to certainty in universal truths. You're commenting as if you are unaware of the positions and arguments linked from my previous reply, and perhaps Where Recursive Justification Hits Bottom . You have intelligent things to say, but you're not going to be taken seriously here if you're not aware of the pre-existing intelligent responses to them popular enough to amount to public knowledge.
No, that is not equivalent. Popper wrote that "inference based on many observations is a myth". He is saying that we never reason from observations, never mind reasoning to certainty. In order to observe, you need theories. Without those, you cannot know what things you should observe or even make sense of any observation. Observation enables us to test theories, it never enables us to construct theories. Furthermore, Popper throws out the whole idea of justifying theories. We don't need justification at all to progress. Judging from Where Recursive Justification Hits Bottom, this is something Eliezer has not fully taken on board (though I may be wrong). He sees the problem of the tu-quoque, but he still says [e]verything, without exception, needs justification. No, nothing can be justified. Knowledge advances not positively by justifying things but negatively by refuting things. Eliezer does see the importance of criticism, but my impression is that he doesn't know Popper well enough.
For Yudkowsky on Popper, start here:
"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."
...and keep reading - at least as far as:
"On the other hand, Popper's idea that there is only falsification and no such thing as confirmation turns out to be incorrect. Bayes' Theorem shows that falsification is very strong evidence compared to confirmation, but falsification is still probabilistic in nature; it is not governed by fundamentally different rules from confirmation, as Popper argued."
Yudhowsky gets a lot wrong even in a few sentences:
First, Popper's philosophy cannot be accurately described as falsificationism - that is just a component of it, and not the most important component. Popperian philosophy consists of many inter-related ideas and arguments. Yudhowsky makes an error that Popperian newbies make. One suspects from this that Yudhowsky is making himself out to be more familiar with Popper than he actually is. His claim to be dethroning Popper would then be dishonest as he does not have detailed knowledge of the rival position. Also he is wrong that Popper is popular: he isn't. Furthermore, Popper is familiar with Bayesian epistemology and actually discusses it in his books. So calling Popper's philosophy old and making out that Bayesian epistemology is new is wrong also.
Popper never said theories can be definitely falsified. He was a thoroughgoing fallibilist and viewed falsifications as fallible conjectures. Also he said that theories can never be confirmed at all, not that they can be partially or probabilistically confirmed, which the above sentence suggests he said. Saying falsification is a special case of the Bayesian rules also doesn't make sense: falsification is anti-induction whereas Bayesian epistemology is pro-induction.
Further comments on Yudhowski's explanation of Bayes:
Science revolves around explanation and criticism. Most scientific ideas never get to the point of testing (which is a form of criticism), they are rejected via criticism alone. And they are rejected because they are bad explanations. Why is the emphasis in the quote solely on evidence? If science is a special case of Bayes, shouldn't Bayes have something to say about explanation and criticism? Do you assign probabilities to criticism? That seems silly. Explanations and criticism enable us to understand things and to see why they might be true or false. Trying to reduce things to probabilities is to completely ignore the substance of explanations and criticisms. Instead of trying to get a probability that something is true, you should look for criticisms. You accept as tentatively true anything that is currently unproblematic and reject as tentatively false anything that is currently problematic. It's a boolean decision: problematic or unproblematic.
Both bayesian induction (as we currently know it) and Popper fail my test for a complete epistemology.
The test is simple. Can I use the description of the formalism to program a real computer to do science? And it should, in theory, be able to bootstrap itself from no knowledge of science to our level.
I think that the contribution that Bayesian methodology makes toward good criticism of a scientific hypothesis is that to "do the math", you need to be able to compute P(E|H). If H is a bad explanation, you will notice this when you try to determine (before you see E) how you would go about computing P(E|H). Alternately, you discover it when you try to imagine some E such that P(E|H) is different from P(E|not H).
No, you don't assign probabilities to criticisms, as such. But I do think that every atomic criticism of a hypothesis H contains at its heart a conditional proposition of the form (E|H) or else a likelihood odds ratio P(E|H)/P(E|not H) together with a challenge, "So how would you go about calculating that?"
Incidentally, you also ought to look at some of the earlier postings where EY was, in effect, using naive Bayes classifiers to classify (i.e. create ontologies), rather than using Bayes's theorem to evaluate hypotheses that predict. Also take a look at Pearl's book to get a modern Bayesian view of what explanation is all about.
If you were asked to bet on whether it was true or not, then you should assign a probability.
Scientists often do something like that when deciding how to allocate their research funds.
But then we have to develop a quantitative formalism for both beliefs and utilities. Is it really necessary to attack both problems at once?
Human beings don't actually seem to have utility functions, all they really have are "preferences" i.e. a method for choosing between alternatives. But von Neumann and Morgenstern showed that under some conditions this is the same as having a utility function.
Now Scurfield is saying that human beings, even smart ones like scientists, don't have prior probability distributions, all they really have is a database of claims and criticisms of those claims. Is there any result analogous to von Neumann-Morgenstern that says this is the same thing as having a prior, under conditions?
Yes. The question has been addressed repeatedly by a variety of people. John Maynard Keynes may have been the first. Notable formulations since his include de Finetti, Savage, and Jeffrey's online book.
Discovering subjective probabilities is usually done in conjunction with discovering utilities by revealed preferences because much of the machinery (choices between alternatives, lotteries) is shared between the two problems. People like Jaynes who want a pure epistemology uncontaminated by crass utility considerations have to demand that their "test subjects" adhere to some fairly hard-to-justify consistency rules. But people like de Finetti don't impose arbitrary consistency, instead they prove that inconsistent probability assignments lose money to clever gamblers who construct "Dutch books".
I'd be interested in reading more about your views on this (unless you're referring to Halpern's papers on Cox's theorem).
Wild. Is there an exposition of subjective expected utility better than wikipedia's?
Agents can reasonably be expected to quantify both beliefs and utilities. How the ability to do that is developed - is up to the developer.
People are agents, and they are very bad at quantifying their beliefs and utilities.
I like this point a lot. But it seems very convenient and sensible to say that some things are more problematic than others. And at least for certain kinds of claims it's possible to quantify how problematic they are with numbers. This leads one (me at least) to want a formalism -- for handling beliefs -- that involves numbers, and Bayesianism is a good one.
What's the conjectures-and-refutations way of handling claims like "it's going to snow in February"? Do you think it's meaningless or useless to attach a probability to that claim?
There is no problem with theories that make probabilistic predictions. But getting a probabilistic prediction is not tantamount to assigning a probability to the theory that made the prediction.
True. But you seem to be assuming that a "theory" has to be a universal law of nature. You are too attached to physics. But in other sciences, you can have a theory which is quite explanatory, but is not in any sense a "law", but rather it is an event. Examples:
Probabilities can be assigned to these theories.
And even for universal theories, you can talk about the relative odds of competing theories being correct - say between a supersymetric GUT based on E6 and one based on E8. (Notice, I said "talk about the odds", not "calculate them") And you can definitely calculate how much one particular experimental result shifts those odds.
As you pointed out earlier, we have two ostensibly different ways of investigating the theory that the Chinese discovered America in 1421: the Popperian way, in which this theory and alternatives to it are criticized. And the Bayesian way, in which those criticisms are broken down into atomic criticisms, and likelihood ratios are attached and multiplied.
I've seen plenty of rigorous Popperian discussions but not very many very rigorous -- or even modestly rigorous -- Bayesian discussions, even on this website. One piece of evidence for the China-discovered-America theory is some business about old Chinese maps. How does a Bayesian go about estimating the likelihood ratio P(China discovered America | old maps) / P(China discovered America | no old maps)?
I think you want to ask about P(maps|discover) / P(no maps|discover). Unless both wikipedia and my intuition are wrong.
Does catching you in this error relieve me of the responsibility of answering the question? I hope so. Because I would want to instead argue using something like P(maps|discover) vs P(maps|not discover). That doesn't take you all the way to P(discover), but it does at least give you a way to assess the evidential weight of the map evidence.
More from Yudkowsky on the philosophy of science:
http://lesswrong.com/lw/ig/i_defy_the_data/
The chance of a criticism being correct can unproblematically be assigned a probability.
A criticism can have many components, some of which are correct and some of which are incorrect. Breaking a criticism down into its components can be difficult/problematic.
Edit: The way I put that sounds stupid. Let me try again: occasionally, a pair of math papers are released, one purports to prove a conjecture, and one purports to disprove it. The authors then criticize each others papers (let's say). Would you really characterize the task of assigning probabilities in this situation as "unproblematic"?
The point is that - if you were asked to bet on the criticism being correct - you would come up with some odds ratio.
Maybe you would do that. I would instead bog down in a discussion of whether the criticism was a nitpick or a "real" criticism. But I would be interested to see what odds ratio you come up with for this criticism being correct.
Heh - is that your criticism? - or did you get it from Douglas Hofstadter? ;-)
And in the math papers example, how exactly are you going to do that? Presumably you are going to go through the papers and the criticisms in detail and evaluate the content. And when you do that you are going to think of reasons why one is right and the other wrong. And then probabilities become irrelevent. It's your understanding of the content that will enable you to choose.
Right - but you don't "choose" - you assign probabilities. Rejecting something completely would be bad - because of:
http://lesswrong.com/lw/mp/0_and_1_are_not_probabilities/
Popper obviously hadn't read Wikipedia:
http://en.wikipedia.org/wiki/Inductive_reasoning