Thanks for the links and references. I will look into them. I urge you once more to work your way through the sequences. It appears you have something to teach us, but I doubt that you will be very successful until you have learned the local jargon, and become sufficiently familiar with our favorite examples to use them against us.
However, I have to say that I was a bit disconcerted by this:
consider the people who have not yet understood that induction is a myth.
Now if you told me that the standard definition of induction misrepresents the evidence-collection process, or that you know how to dissolve the problem of induction, well then I would be all ears. But when you say that “induction is a myth” I hear that as saying that everyone who has thought seriously on the topic, from Hume to the present, …,
well, you seem to be saying that all those smart people were as deluded as the medieval philosophers who worried about angels dancing on the heads of pins.
See the thing is, I would have to keep having to upvote such arrogance and stupidity, just so the comment to which I am responding doesn’t disappear. And I don’t want to do that.
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).
You do realize that Hume held that induction cannot be logically justified? He noticed there is a “problem of induction”.
Of course. That is why I mentioned him.
That problem was exploded by Karl Popper. Have you read what he has to say and taken seriously his ideas?
“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.
Have you read and taken seriously the ideas of philosophers like David Deutsch, David Miller, and Bill Bartley?
Nope, I haven’t.
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).
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.
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.
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
Theories are either true or false: there is no such thing as the probability that a theory is true.
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.
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.
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.
so far he has mostly presented slogans, rather than arguments.
It occurs to me that one thing he could do which would be both interesting and useful would be to go through the sequences, adding comments critiquing Eliezer’s epistemology lessons from the viewpoint of Popper and/or CR. Who knows? I might frequently find myself agreeing with him.
Indeed, that’s why I am in favor of voting on old comments. Ideally, people can continue to leave criticisms on the sequences, and good ones will rise to the top over time.
because so far he has mostly presented slogans, rather than arguments.
Yes, I asked for clarification of the slogans and got more slogans, and asked for arguments supporting the claims and was given the claims again. I decided at that point to disengage.
Now weren’t those subtle strawmen? :)
Indeed—I hadn’t bothered to check out the site, but it seems to me that most of the discipline of Philosophy falls outside “CR”’s “three major schools”, and they’re pretending Popper invented philosophy. It’s really quite terrible.
If I may use another “slogan”: communication is difficult. And another: misunderstandings are common. When you asked for clarification I wasn’t sure what you wanted. I guessed and looks like I got it wrong. So you just withdraw? That’s very Un-Popperian.
It is a reasonable interpretation of the “three major schools” analysis down near the bottom of the “What is CR” page at the “Critical Rationalism” website. See if you can talk someone into cleaning up that bit of enthusiasm. As they say “It’s not helping”.
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.
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.
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.
“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.”
“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:
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.
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.
Karl Popper’s idea that theories can be definitely falsified, but never definitely
confirmed, is yet another special case of the Bayesian rules;
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.
science itself is a special case of Bayes’ Theorem; experimental evidence is Bayesian evidence.
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.
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’m not even familiar with Halpern’s work. The only serious criticism I have seen regarding the usual consistency rules for subjective probabilities dealt with the “sure thing rule”. I didn’t find it particularly convincing.
No, I have no trouble justifying a mathematical argument in favor of this kind of consistency. But not everyone else is all that convinced by mathematics. Their attention can be grabbed, however, by the danger of being taken to the cleaners by Dutch book professional bookies.
One of these days, I will get around to producing a posting on probability, developing it from what I call the “surprisal” of a proposition—the amount, on a scale from zero to positive infinity, by which you would be surprised upon learning that a proposition is true.
Prob(X) = 2^(-Surp(X)).
Surp(coin flip yields heads)= 1 bit.
Surp(A) + Surp(B|A) = Surp(A&B)
That last formula strikes me as particularly easy to justify (surprisals are additive). Given that and the first formula, you can easily derive Bayes law. The middle formula simply fixes the scale for surprisals. I suppose we also need a rule that Surp(True)=0
Cool! Saves me the trouble of writing that posting. :)
Absurdity is probably a better name for the concept. Except that it sounds objective, whereas amount of surprise more obviously depends on who is being surprised.
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.
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:
the theory that the moon was formed by a collision between the earth and a Mars-sized planetesimal.
the theory that modern man originated in Africa within the past 200,000 years and that the Homo erectus population outside of Africa did not contribute to our ancestry.
the theory that Napolean was poisoned with arsenic in St. Helena.
the “aquatic ape theory”
the endosymbiotic theory of the origin of mitochondria
the theory that the Chinese discovered America in 1421.
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.
Here’s another personal example of Bayesianism in action. Do you have a sense of how much you updated by? P(Richard Dawkins praises Steven Pinker | EP is bunk)/ P(Richard Dawkins praises Steven Pinker | EP is not bunk) is .5? .999? Any idea?
P(“Sewing Machine” is a nym) = 1.0 P(Sewing Machine has been disingenuous) = 0.5 and rising P(Dawkins praises Pinker|EP is not bunk) is ill defined because P(EP is not bunk) = ~0 but I have updated P(Dawkins believes EP is not bunk) to at least 0.5
the theory that the moon was formed by a collision between the earth and a Mars-sized planetesimal.
The reason we would accept this theory as true is because it has survived criticism as an explanation while its rivals have not. If another rival theory is still in contention by also having survived criticism then there is a problem and this problem is not going to be resolved by computing, somehow, probabilities that the theories are true. To solve the problem you are going to have to come up with better criticisms or, possibly, alternative theories.
One difference between theories and events is that the counterfactuals of an event exist (in the multiverse). So it makes sense to talk about the probability of an event: the counterfactual events are real and occur to a greater or lesser measure in the multiverse. A false theory, by contrast, is simply false, it has no connection to reality. How do you assign anything other than an arbitrary probability to something that simply cannot be? Fortunately we don’t have to: we have Popperian epistemology.
A false theory, by contrast, is simply false, it has no connection to reality.
How do you assign anything other than an arbitrary probability to something
that simply cannot be?
Intrade knows that one! At the Higgs boson bet over 200 people think they know how to assign a probability to the issue.
1: By using the counterfactuals in the Tegmark Level IV multiverse.
2: By giving it a probability of 0. If T is falsified, that means P(D|T)=0 - we obtained data that T claims is impossible. In this case, Bayes’ theorem sets P(T|D)=0. Bayesianism includes all correct thinking tools, including Popperian epistemology.
But is P(D|T) really 0? We could have made a mistake and not recorded the correct data. Certainly scientists in the past have done so, and thought that they falsified theories that they didn’t falsify. In this case, P(D|T) is very small but nonzero, and so is P(T|D) (unless p(D|~T) is also very small.)
3: You cannot avoid giving a probability. Because of Cox’s theorem, which says we must use probability theory to reason about uncertainty (although I must confess that the assumption that we must use a single real number to reason is rather strong.)
Counterfactuals of the sort of theory that Perplexed describe do exist in a Quantum Multiverse; why not assign them probabilities?
Anyway, why would you want to make your entire epistemology contingent on a particular theory of physics? It sounds like the CR would collapse if Copenhagen turned out to be correct.
Yes, counterfactuals do exist in some of Perplexed examples. There are alternative universes where Earth does not have a moon, or it does have a moon but it was not formed by a collision with a planetesimal. However, in this universe, the one we are observing now, the moon either was or it was not formed in such a way. There is no middle ground. Finding evidence consistent with the theory does not make the theory truer or more likely—what the evidence does is supply us with criticisms of rival theories.
CR is not independent from physics, nor can it be. The laws of physics entail the existence of universal computers and of universal knowledge creators. As David Deutsch has shown, there are deep connections between multiversal quantum physics and the theory of information. If Cophenhagen should turn out to be true it would impact on many things and not the least of which would be CR.
Events have probabilities. Theories don’t. Given some theory of meteorology, you can predict the probability it will snow in Feb. But you can’t say the probability that that theory of meteorology is true.
Did you read the context? Someone asked the Popperian view on giving a probability of future weather. So I answered that. What exactly do you think the context is?
The scientific method as a special case of Bayes theorem and whether the not directly experimental aspects can be mapped on some part of Bayesian reasoning. Now that you pointed it out I can see that you were only referring to the narrow sub-point in the great-gandparent and not the wider context, but it looked to me like you were also arguing that since theories don’t have (frequentlialist) probabilities Popperian reasoning about them couldn’t map to probabilistically framed Bayesian reasoning. Looking at the votes it seems I wasn’t alone in that (mis-)reading.
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”?
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.
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.
I don’t think anyone is falling into this trap. It sounds like the Popperian version is replacing “true” and “false” by “tentatively true” and “tentatively false.”
Theories are either true or false. The word “tentative” is there as an expression of fallibility. We cannot know if a theory is in fact true: it may contain problems that we do not yet know about. All knowledge is tentative. The word is not intended as a synonym for probability or to convey anything about probabilities.
Observers can put probabilities on the truth of theories. They can do it—and will do it—if you ask them to set odds and prepare to receive bets. Quantifying uncertainty allows it to be measured and processed.
It is true that knowledge is fallible—but some knowledge is more fallible than others—and if you can’t measure degrees of uncertainty, you will never develop a quantitative treatment of the subject. Philosophers of science realised this long ago—and developed a useful framework for quantifying uncertainty.
Observers can put probabilities on the truth of theories. They can do it—and will do it—if you ask them to set odds and prepare to receive bets. Quantifying uncertainty allows it to be measured and processed.
Scurfield missed his chance here. He should have asked when it becomes the case that those bets must be paid off, and offered the services of a Popper adept to make that kind of decision. Of course, the Popperite doesn’t rule that one theory is true, he rules that the other theory is refuted.
Short time limits don’t mean that agents can’t meaningfully assign probabilities to the truth of scientific theories—they just decrease the chances of the theories being proven wrong within the time limit a bit.
What is a time limit? Do actual bets on this sort of thing in Britain stipulate a time limit? As a Yank, I have no idea how betting ‘markets’ like this like this actually work.
Prediction markets/betting markets like Intrade or Betfair pretty universally set time limits on their bets. (Browse through Intrade sometime.) This does sometimes require changing the bet/prediction though—from ‘the Higgs boson will be found’ to ‘the Higgs boson will be found by 2020’. Not that this is a bad thing, mind you.
Not really. To the extent that we limit attention to theories of the form:
Always(Everywhere(Forall x (P(x)) ) )
we Bayesians can never “cash in” on a bet that the theory is true—at least not using empirical evidence. All we can do is to continue trying to falsify the theory by experiments at more times, at more places, and for more values of x. As Popper prescribes. Our probabilities that the theory is true grow higher and higher, but they grow more and more slowly, and they can never reach unity.
However, both Bayesians and Popper fans can become pretty certain that such a theory is false—even without checking everywhere, everywhen, and forall x. Popper does not have a monopoly on refutations. Or conjectures either, for that matter.
There are no degrees of fallibility. We are simply fallible: that’s it. You have no way of knowing if a currently unproblematic theory is wrong, no matter how obvious the theory may seem, it may end up being spectacularly wrong.
I agree that we can quantity the uncertainty of events and that this is useful.
But theories are a different kettle of fish. Popperian epistemology tells us that we don’t need to know anything about the uncertainty of theories for knowledge to grow. Hence, one does not need to quantify the uncertainty of theories in order to write a knowledge creating computer program.
The thing is, we have a beautiful theory of uncertainty that deals with uncertainty over events, uncertainty about hypotheses—uncertainty about all beliefs, in fact—and it works just great.
Sure, we could go back to the dark days before Bayes, and struggle on with a boolean conception of certainty, and it probably wouldn’t be so bad that it would actually prevent knowledge from accumulating...
...but what possible reason would motivate us to take such a retrograde step?
I mean: how do you model equiprobable competing theories in such a framework.
How do you model induction? How do you model confirmation?
The answer seems to be that you don’t—you just deny the very existence of these phenomena!
I hope you can see how that is not a step forwards, from our point of view.
The thing is, we have a beautiful theory of uncertainty that deals with uncertainty over events, uncertainty about hypotheses—uncertainty about all beliefs, in fact—and it works just great.
Really? No exaggeration?
Sure, we could go back to the dark days before Bayes, and struggle on with a
boolean conception of certainty, and it probably wouldn’t be so bad that it would
acutually prevent knowledge from growing...
Popperian epistemology was created in the 20th century, after Bayes, so what do you mean by dark days. Certainty is not the lynchpin of knowledge creation and in fact has nothing to do with it. You completely devalue the role of explanations and criticisms. Who cares about probability when you have a good explanation that has withstood criticism?
...but what possible reason would motivate us to take such a retrograde step?
Popperian philosophy is about problem-solving, explanation and criticism and these things are not in any way retrograde. Bayesian epistemology is rooted in the
old philosophy of justificationism, a philosophy that Popperian epistemology overturned.
I mean: how do you model equiprobable competing theories in such a framework.
What you do is attempt further criticism of these theories and if that doesn’t progress come up with a meta-theory of what to do giving that you have two good candidate theories. It is always possible to come up with such a meta-theory.
How do you model induction? How do you model confirmation?
The answer seems to be that you don’t—you just deny the very existence of these
phenomena!
Popper and others have given explanations—they don’t just deny without reason. Are you familiar with their arguments? There are real problems with the very concepts of induction and confirmation, problems that you seem not to have appreciated.
I hope you can see how that is not a step forwards, from our point of view.
Popper showed that knowledge grows perfectly fine without concepts of uncertainty, induction, and confirmation. Yes, it is counter-intuitive—that is why most people do not get Popper.
Popper and others have given explanations—they don’t just deny without reason. Are you familiar with their arguments? There are real problems with the very concepts of induction and confirmation, problems that you seem not to have appreciated.
Maybe you should present them, rather than playing ‘I can assert my philosopher is great more than you can’.
The author of that link thinks Popper is falsification. I have already explained why that view of Popper is wrong. Have you been paying attention? And does the author of the link realize that the leading exponent of the multiverse is David Deutsch, who also happens to be the best living Popperian?
“Popper’s great and tireless efforts to expunge the word induction from scientific and philosophical discourse has utterly failed. Except for a small but noisy group of British Popperians, induction is just too firmly embedded in the way philosophers of science and even ordinary people talk and think.
Confirming instances underlie our beliefs that the Sun will rise tomorrow, that dropped objects will fall, that water will freeze and boil, and a million other events. It is hard to think of another philosophical battle so decisively lost.”—M.Gardner.
Gardner can be taken as seriously on Popper as he can on the MWI, i.e, not at all.
BTW, the sun does not rise in Murmansk in the middle of winter, live flies that are dropped do not fall, and water can be prevented from freezing in my car radiator by adding anti-freeze.
Carnap had a major influence on me. He persuaded me that all metaphysical questions are “meaningless” in the sense that they cannot be answered empirically or by reason. They can be defended only on emotive grounds. Carnap was an atheist, but I managed to retain my youthful theism in the form of what is called “fideism.” I like to call it “theological positivism,” a play on Carnap’s “logical positivism.
As far as we can tell, universes are not as plentiful as even two blackberries. Surely the conjecture that there is just one universe and its Creator is infinitely simpler and easier to believe than that there are countless billions upon billions of worlds, constantly increasing in number and created by nobody. I can only marvel at the low state to which today’s philosophy of science has fallen
So why the downvote? Gardner doesn’t understand quantum physics and he doesn’t understand epistemology.
I still recommend
Subjectively Objective, but I’m no longer confident that your inferential distance from the coverage there is small enough. Perplexed’s recommendation to read all the way through the sequences, or—even better—ET Jaynes’ Probability Theory: The Logic of Science—may be necessary. As he’s said, Critical Rationalism was an important step in the philosophy of science—but the field has moved beyond that to a rigorous, mathematically precise model of the amount of belief any rational agent must hold given identical priors and the same evidence—Popper’s Vs(a)=CT(a)-CTf(a) is not quantitative in this way.
That wasn’t intended to convince you; if you truly wish to subject your conjecture to criticism a contemplative reading of Jaynes is necessary. If you do happen to find Jaynes convincing, all is not lost—we still like Tarski here.
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).
Thanks for the links and references. I will look into them. I urge you once more to work your way through the sequences. It appears you have something to teach us, but I doubt that you will be very successful until you have learned the local jargon, and become sufficiently familiar with our favorite examples to use them against us.
However, I have to say that I was a bit disconcerted by this:
Now if you told me that the standard definition of induction misrepresents the evidence-collection process, or that you know how to dissolve the problem of induction, well then I would be all ears. But when you say that “induction is a myth” I hear that as saying that everyone who has thought seriously on the topic, from Hume to the present, …, well, you seem to be saying that all those smart people were as deluded as the medieval philosophers who worried about angels dancing on the heads of pins.
See the thing is, I would have to keep having to upvote such arrogance and stupidity, just so the comment to which I am responding doesn’t disappear. And I don’t want to do that.
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.
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? :)
It occurs to me that one thing he could do which would be both interesting and useful would be to go through the sequences, adding comments critiquing Eliezer’s epistemology lessons from the viewpoint of Popper and/or CR. Who knows? I might frequently find myself agreeing with him.
Indeed, that’s why I am in favor of voting on old comments. Ideally, people can continue to leave criticisms on the sequences, and good ones will rise to the top over time.
Yes, I asked for clarification of the slogans and got more slogans, and asked for arguments supporting the claims and was given the claims again. I decided at that point to disengage.
Indeed—I hadn’t bothered to check out the site, but it seems to me that most of the discipline of Philosophy falls outside “CR”’s “three major schools”, and they’re pretending Popper invented philosophy. It’s really quite terrible.
If I may use another “slogan”: communication is difficult. And another: misunderstandings are common. When you asked for clarification I wasn’t sure what you wanted. I guessed and looks like I got it wrong. So you just withdraw? That’s very Un-Popperian.
Really? Care to give a quote?
It is a reasonable interpretation of the “three major schools” analysis down near the bottom of the “What is CR” page at the “Critical Rationalism” website. See if you can talk someone into cleaning up that bit of enthusiasm. As they say “It’s not helping”.
That’s a really high standard.
Hmmm. I never thought of that.
If you go as far as:
http://groups.yahoo.com/group/CriticalRationalism/
...you may see some names you recognise.
LOL. That made my day. Be sure to let me know if you run across TH anywhere.
Incidentally, have you looked in at sbe recently? Pretty sad.
I don’t see any people here that know both. Eliezer doesn’t appear to either. See here and here.
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.
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.”
http://yudkowsky.net/rational/bayes
...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.
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).
I’m not even familiar with Halpern’s work. The only serious criticism I have seen regarding the usual consistency rules for subjective probabilities dealt with the “sure thing rule”. I didn’t find it particularly convincing.
No, I have no trouble justifying a mathematical argument in favor of this kind of consistency. But not everyone else is all that convinced by mathematics. Their attention can be grabbed, however, by the danger of being taken to the cleaners by Dutch book professional bookies.
One of these days, I will get around to producing a posting on probability, developing it from what I call the “surprisal” of a proposition—the amount, on a scale from zero to positive infinity, by which you would be surprised upon learning that a proposition is true.
Prob(X) = 2^(-Surp(X)).
Surp(coin flip yields heads)= 1 bit.
Surp(A) + Surp(B|A) = Surp(A&B)
That last formula strikes me as particularly easy to justify (surprisals are additive). Given that and the first formula, you can easily derive Bayes law. The middle formula simply fixes the scale for surprisals. I suppose we also need a rule that Surp(True)=0
Actually “Surprisal” is a pretty standard term, I think.
Yudkowsky suggests calling it “absurdity” here
Cool! Saves me the trouble of writing that posting. :)
Absurdity is probably a better name for the concept. Except that it sounds objective, whereas amount of surprise more obviously depends on who is being surprised.
Wild. Is there an exposition of subjective expected utility better than wikipedia’s?
Jeffrey’s book, which I already linked, or any good text on Game theory. Myerson, for example, or Luce and Raiffa.
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 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.
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:
the theory that the moon was formed by a collision between the earth and a Mars-sized planetesimal.
the theory that modern man originated in Africa within the past 200,000 years and that the Homo erectus population outside of Africa did not contribute to our ancestry.
the theory that Napolean was poisoned with arsenic in St. Helena.
the “aquatic ape theory”
the endosymbiotic theory of the origin of mitochondria
the theory that the Chinese discovered America in 1421.
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.
Now P(Sewing-Machine is a phony) = ?
Here’s another personal example of Bayesianism in action. Do you have a sense of how much you updated by? P(Richard Dawkins praises Steven Pinker | EP is bunk)/ P(Richard Dawkins praises Steven Pinker | EP is not bunk) is .5? .999? Any idea?
P(“Sewing Machine” is a nym) = 1.0
P(Sewing Machine has been disingenuous) = 0.5 and rising
P(Dawkins praises Pinker|EP is not bunk) is ill defined because
P(EP is not bunk) = ~0
but I have updated P(Dawkins believes EP is not bunk) to at least 0.5
I don’t know what “disingenuous” means.
The reason we would accept this theory as true is because it has survived criticism as an explanation while its rivals have not. If another rival theory is still in contention by also having survived criticism then there is a problem and this problem is not going to be resolved by computing, somehow, probabilities that the theories are true. To solve the problem you are going to have to come up with better criticisms or, possibly, alternative theories.
One difference between theories and events is that the counterfactuals of an event exist (in the multiverse). So it makes sense to talk about the probability of an event: the counterfactual events are real and occur to a greater or lesser measure in the multiverse. A false theory, by contrast, is simply false, it has no connection to reality. How do you assign anything other than an arbitrary probability to something that simply cannot be? Fortunately we don’t have to: we have Popperian epistemology.
Intrade knows that one! At the Higgs boson bet over 200 people think they know how to assign a probability to the issue.
http://www.intrade.com/jsp/intrade/common/c_cd.jsp?conDetailID=622297&z=1224442713385
The bet is for an event:
Shrug.
1: By using the counterfactuals in the Tegmark Level IV multiverse.
2: By giving it a probability of 0. If T is falsified, that means P(D|T)=0 - we obtained data that T claims is impossible. In this case, Bayes’ theorem sets P(T|D)=0. Bayesianism includes all correct thinking tools, including Popperian epistemology.
But is P(D|T) really 0? We could have made a mistake and not recorded the correct data. Certainly scientists in the past have done so, and thought that they falsified theories that they didn’t falsify. In this case, P(D|T) is very small but nonzero, and so is P(T|D) (unless p(D|~T) is also very small.)
3: You cannot avoid giving a probability. Because of Cox’s theorem, which says we must use probability theory to reason about uncertainty (although I must confess that the assumption that we must use a single real number to reason is rather strong.)
Counterfactuals of the sort of theory that Perplexed describe do exist in a Quantum Multiverse; why not assign them probabilities?
Anyway, why would you want to make your entire epistemology contingent on a particular theory of physics? It sounds like the CR would collapse if Copenhagen turned out to be correct.
Yes, counterfactuals do exist in some of Perplexed examples. There are alternative universes where Earth does not have a moon, or it does have a moon but it was not formed by a collision with a planetesimal. However, in this universe, the one we are observing now, the moon either was or it was not formed in such a way. There is no middle ground. Finding evidence consistent with the theory does not make the theory truer or more likely—what the evidence does is supply us with criticisms of rival theories.
CR is not independent from physics, nor can it be. The laws of physics entail the existence of universal computers and of universal knowledge creators. As David Deutsch has shown, there are deep connections between multiversal quantum physics and the theory of information. If Cophenhagen should turn out to be true it would impact on many things and not the least of which would be CR.
Events have probabilities. Theories don’t. Given some theory of meteorology, you can predict the probability it will snow in Feb. But you can’t say the probability that that theory of meteorology is true.
That’s true for frequentialist probabilities, but irrelevant in this context.
Did you read the context? Someone asked the Popperian view on giving a probability of future weather. So I answered that. What exactly do you think the context is?
The scientific method as a special case of Bayes theorem and whether the not directly experimental aspects can be mapped on some part of Bayesian reasoning. Now that you pointed it out I can see that you were only referring to the narrow sub-point in the great-gandparent and not the wider context, but it looked to me like you were also arguing that since theories don’t have (frequentlialist) probabilities Popperian reasoning about them couldn’t map to probabilistically framed Bayesian reasoning. Looking at the votes it seems I wasn’t alone in that (mis-)reading.
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/
I don’t think anyone is falling into this trap. It sounds like the Popperian version is replacing “true” and “false” by “tentatively true” and “tentatively false.”
“Tentatively true” and “tentatively false” sound a lot like probabilities which are not expressed in a format which is compatible with Bayes rule.
It is hard to see how that adds anything—but rather easy to see how it subtracts the ability to quantitatively analyse problems.
That’s what I said.
Edit: That refers to the first sentence only.
Theories are either true or false. The word “tentative” is there as an expression of fallibility. We cannot know if a theory is in fact true: it may contain problems that we do not yet know about. All knowledge is tentative. The word is not intended as a synonym for probability or to convey anything about probabilities.
Observers can put probabilities on the truth of theories. They can do it—and will do it—if you ask them to set odds and prepare to receive bets. Quantifying uncertainty allows it to be measured and processed.
It is true that knowledge is fallible—but some knowledge is more fallible than others—and if you can’t measure degrees of uncertainty, you will never develop a quantitative treatment of the subject. Philosophers of science realised this long ago—and developed a useful framework for quantifying uncertainty.
Scurfield missed his chance here. He should have asked when it becomes the case that those bets must be paid off, and offered the services of a Popper adept to make that kind of decision. Of course, the Popperite doesn’t rule that one theory is true, he rules that the other theory is refuted.
Short time limits don’t mean that agents can’t meaningfully assign probabilities to the truth of scientific theories—they just decrease the chances of the theories being proven wrong within the time limit a bit.
What is a time limit? Do actual bets on this sort of thing in Britain stipulate a time limit? As a Yank, I have no idea how betting ‘markets’ like this like this actually work.
Prediction markets/betting markets like Intrade or Betfair pretty universally set time limits on their bets. (Browse through Intrade sometime.) This does sometimes require changing the bet/prediction though—from ‘the Higgs boson will be found’ to ‘the Higgs boson will be found by 2020’. Not that this is a bad thing, mind you.
Do you have an answer to that point-that-should-have-been?
Not really. To the extent that we limit attention to theories of the form:
we Bayesians can never “cash in” on a bet that the theory is true—at least not using empirical evidence. All we can do is to continue trying to falsify the theory by experiments at more times, at more places, and for more values of x. As Popper prescribes. Our probabilities that the theory is true grow higher and higher, but they grow more and more slowly, and they can never reach unity.
However, both Bayesians and Popper fans can become pretty certain that such a theory is false—even without checking everywhere, everywhen, and forall x. Popper does not have a monopoly on refutations. Or conjectures either, for that matter.
There are no degrees of fallibility. We are simply fallible: that’s it. You have no way of knowing if a currently unproblematic theory is wrong, no matter how obvious the theory may seem, it may end up being spectacularly wrong.
I agree that we can quantity the uncertainty of events and that this is useful.
But theories are a different kettle of fish. Popperian epistemology tells us that we don’t need to know anything about the uncertainty of theories for knowledge to grow. Hence, one does not need to quantify the uncertainty of theories in order to write a knowledge creating computer program.
The thing is, we have a beautiful theory of uncertainty that deals with uncertainty over events, uncertainty about hypotheses—uncertainty about all beliefs, in fact—and it works just great.
Sure, we could go back to the dark days before Bayes, and struggle on with a boolean conception of certainty, and it probably wouldn’t be so bad that it would actually prevent knowledge from accumulating...
...but what possible reason would motivate us to take such a retrograde step?
I mean: how do you model equiprobable competing theories in such a framework.
How do you model induction? How do you model confirmation?
The answer seems to be that you don’t—you just deny the very existence of these phenomena!
I hope you can see how that is not a step forwards, from our point of view.
The thing is, we have a beautiful theory of uncertainty that deals with uncertainty over events, uncertainty about hypotheses—uncertainty about all beliefs, in fact—and it works just great.
Really? No exaggeration?
Popperian epistemology was created in the 20th century, after Bayes, so what do you mean by dark days. Certainty is not the lynchpin of knowledge creation and in fact has nothing to do with it. You completely devalue the role of explanations and criticisms. Who cares about probability when you have a good explanation that has withstood criticism?
Popperian philosophy is about problem-solving, explanation and criticism and these things are not in any way retrograde. Bayesian epistemology is rooted in the old philosophy of justificationism, a philosophy that Popperian epistemology overturned.
What you do is attempt further criticism of these theories and if that doesn’t progress come up with a meta-theory of what to do giving that you have two good candidate theories. It is always possible to come up with such a meta-theory.
Popper and others have given explanations—they don’t just deny without reason. Are you familiar with their arguments? There are real problems with the very concepts of induction and confirmation, problems that you seem not to have appreciated.
Popper showed that knowledge grows perfectly fine without concepts of uncertainty, induction, and confirmation. Yes, it is counter-intuitive—that is why most people do not get Popper.
Maybe you should present them, rather than playing ‘I can assert my philosopher is great more than you can’.
Bayesian scientific methods becoming more mainstream is a relatively modern phenomenon. See:
“Do we need to change the definition of science?”
http://postbiota.org/pipermail/tt/2008-May/002997.html
...for a recent overview.
The author of that link thinks Popper is falsification. I have already explained why that view of Popper is wrong. Have you been paying attention? And does the author of the link realize that the leading exponent of the multiverse is David Deutsch, who also happens to be the best living Popperian?
“Popper’s great and tireless efforts to expunge the word induction from scientific and philosophical discourse has utterly failed. Except for a small but noisy group of British Popperians, induction is just too firmly embedded in the way philosophers of science and even ordinary people talk and think.
Confirming instances underlie our beliefs that the Sun will rise tomorrow, that dropped objects will fall, that water will freeze and boil, and a million other events. It is hard to think of another philosophical battle so decisively lost.”—M.Gardner.
http://www.stephenjaygould.org/ctrl/gardner_popper.html
Gardner can be taken as seriously on Popper as he can on the MWI, i.e, not at all.
BTW, the sun does not rise in Murmansk in the middle of winter, live flies that are dropped do not fall, and water can be prevented from freezing in my car radiator by adding anti-freeze.
Edit: Here are some quotes from Gardner:
http://www.csicop.org/si/show/mind_at_play_an_interview_with_martin_gardner/
Carnap had a major influence on me. He persuaded me that all metaphysical questions are “meaningless” in the sense that they cannot be answered empirically or by reason. They can be defended only on emotive grounds. Carnap was an atheist, but I managed to retain my youthful theism in the form of what is called “fideism.” I like to call it “theological positivism,” a play on Carnap’s “logical positivism.
http://www.csicop.org/si/show/multiverses_and_blackberries/
As far as we can tell, universes are not as plentiful as even two blackberries. Surely the conjecture that there is just one universe and its Creator is infinitely simpler and easier to believe than that there are countless billions upon billions of worlds, constantly increasing in number and created by nobody. I can only marvel at the low state to which today’s philosophy of science has fallen
So why the downvote? Gardner doesn’t understand quantum physics and he doesn’t understand epistemology.
I still recommend Subjectively Objective, but I’m no longer confident that your inferential distance from the coverage there is small enough. Perplexed’s recommendation to read all the way through the sequences, or—even better—ET Jaynes’ Probability Theory: The Logic of Science—may be necessary. As he’s said, Critical Rationalism was an important step in the philosophy of science—but the field has moved beyond that to a rigorous, mathematically precise model of the amount of belief any rational agent must hold given identical priors and the same evidence—Popper’s Vs(a)=CT(a)-CTf(a) is not quantitative in this way.
That wasn’t intended to convince you; if you truly wish to subject your conjecture to criticism a contemplative reading of Jaynes is necessary. If you do happen to find Jaynes convincing, all is not lost—we still like Tarski here.
Popper obviously hadn’t read Wikipedia:
http://en.wikipedia.org/wiki/Inductive_reasoning