http://vimeo.com/22099396

What do people think of this, from a Bayesian perspective?

It is a talk given to the Oxford Transhumanists. Their previous speaker was Eliezer Yudkowsky. Audio version and past talks here: http://groupspaces.com/oxfordtranshumanists/pages/past-talks

The conjunction fallacy says that people attribute higher probability to X&Y than to Y.

This is false and misleading. It is based on bad pseudo-scientific research designed to prove that people are biased idiots. One of the intended implications, which the research does nothing to address, is that this is caused by genetics and isn't something people can change except by being aware of the bias and compensating for it when it will happen.

In order to achieve these results, the researchers choose X, Y, and the question they ask in a special way. Here's what they don't ask:

What's more likely this week, both a cure for cancer and a flood, or a flood?

Instead they do it like this:

http://en.wikipedia.org/wiki/Conjunction_fallacy

Linda is 31 years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations.

Which is more probable?

Linda is a bank teller.

Linda is a bank teller and is active in the feminist movement.

Or like this:

http://lesswrong.com/lw/ji/conjunction_fallacy/

"A complete suspension of diplomatic relations between the USA and the Soviet Union, sometime in 1983."

"A Russian invasion of Poland, and a complete suspension of diplomatic relations between the USA and the Soviet Union, sometime in 1983."

These use different tricks. But both are biased in a way that biases the results.

By the way, this is a case of the general phenomenon that bad research often gets more impressive results, which is explained in _The Beginning of Infinity_ by David Deutsch. If they weren't bad researchers and didn't bias their research, they would have gotten a negative result and not had anything impressive to publish.

The trick with the first one is that the second answer is more evidence based than the first one. The first answer choice has nothing to do with the provided context. The second answer choice has something to do with the provided context: it is partially evidence based. Instead of taking the question really literally as to be about the mathematics of probability, they are deciding which answer makes more sense and saying that. The first one makes no sense (having nothing to do with the provided information). The second one partially makes sense, so they say it's better.

A more literally minded person would catch on to the trick. But so what? Why should people learn to split hairs so that they can give literally correct answers to bad and pointless questions? That's not a useful skill so most people don't learn it.

The trick with the second one is that the second answer is a better explanation. The first part provides a reason for the second part to happen. Claims that have explanatory reasons are better than claims that don't. People are helpfully reading "and" as expressing a relationship -- just as they would do if their friend asked them about the possibility of Russia invading Poland and the US suspending diplomacy. They think the two parts are relevant, and make sense together. With the first one, they don't see any good explanation offered so they reject the idea. Did it happen for no reason? Bad claim. Did it happen without an invasion of Poland or any other notable event worth mentioning? Bad claim.

People are using valuable real life skills, such as looking for good explanations and trying to figure out what reasonable question people intend to ask, rather than splitting hairs. This is not a horrible bias about X&Y being more likely than Y. It's just common sense. All the conjunction fallacy research shows is that you can miscommunicate with people and then and then blame them for the misunderstanding you caused. If you speak in a way such that you can reasonably expect to be misunderstood, you can then say people are wrong for not giving correct answers to what you meant and failed to communicate to them.

The conjunction fallacy does not exist, as it claims to, for all X and all Y. That it does exist for specially chosen X, Y and context is incapable of reaching the stated conclusion that it exists for all X and Y. The research is wrong and biased. It should become less wrong by recanting.

This insight was created by philosophical thinking of the type explained in _The Beginning of Infinity_ by David Deutsch. It was not created by empirical research, prediction, or Bayesian epistemology. It's one of many examples of how good philosophy leads to better results and helps us spot mistakes instead of making them. It also wasn't discovered by empirical research. As Deutsch explained, bad explanations can be rejected without testing, and testing them is pointless anyway (because they can just make ad hoc retreats to other bad explanations to avoid refutation by the data. Only good explanations can't do that.).

Please correct me if I'm wrong. Show me an unbiased study on this topic and I'll concede.

This is a discussion page because I got the message "Comment too long". Apparently the same formatting magic doesn't work here for quotes :(  It is a reply to:

http://lesswrong.com/lw/3ox/bayesianism_versus_critical_rationalism/3ulv

> > You can conjecture Bayes' theorem. You can also conjecture all the rest, however some things (such as induction, justificationism, foundationalism) contradict Popper's epistemology. So at least one of them has a mistake to fix. Fixing that may or may not lead to drastic changes, abandonment of the main ideas, etc

> Fully agreed. In principle, if Popper's epistemology is of the second, self-modifying type, there would be nothing wrong with drastic changes. One could argue that something like that is exactly how I arrived at my current beliefs, I wasn't born a Bayesian.

OK great.

If the changes were large enough, to important parts (for example if it lost the ability to self-modify) I wouldn't want to call it Popper's epistemology anymore (unless maybe the changes were made very gradually, with Popper's ideas being valued the whole time, and still valued at the end). It would be departing from his tradition too much, so it would be something else. A minor issue in some ways, but tradition matters.

> I can also see some ways to make induction and foundationalism easer to swallow.

> A discussion post sounds about right for this, if enough people like it you might consider moving it to the main site.

104 comments later it's at 0 karma. There is interest, but not so much liking. I don't think the main site is the right place for me ;-)

> > I think you are claiming that seeing a white swan is positive support for the assertion that all swans are white. (If not, please clarify).

> This is precisely what I am saying.

Based on what you say later, I'm not sure if you mean this in the same way I meant it. I meant: it is positive support for "all swans are white" *over* all theories which assert "all swans are black" (I disagree with that claim). If it doesn't support them *more than those other theories* then I regard it as vaccuous. I don't believe the math you offered meets this challenge over supporting "all swans are white" more than various opposites of it. I'm not sure if you intended it to.

> > If so, this gets into important issues. Popper disputed the idea of positive support. The criticism of the concept begins by considering: what is support? And in particular, what is the difference between "X supports Y" and "X is consistent with Y"?

> The beauty of Bayes is how it answers these questions. To distinguish between the two statements we express them each in terms of probabilities.

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

Consistent means "doesn't contradict". It's the first one. Plausible is definitely not what I wanted.

> "X supports Y" means P(Y|X) > P(Y), X supports Y if and only if Y becomes more plausible when we learn of X. Bayes tells us that this is equivalent to P(X|Y) > P(X), i.e. if Y would suggest that X is more likely that we might think otherwise then X is support of Y.

This is true but fairly vaccous, in my view. I don't want to argue over what counts as significant. If you like it, shrug. It is important that, e.g., we reject ideas refuted by evidence. But I don't think this addresses the major problems in epistemology which come after we decide to reject things which are refuted by evidence.

The reason it doesn't is there's always infinitely many things supported by any evidence, in this sense. Infinitely many things which make wildly different predictions about the future, but identical predictions about whatever our evidence covers. If Y is 10 white swans, and X is "all swans are white" then X is supported, by your statement. But also supported are infinitely many different theories claiming that all swans are black, and that you hallucinated. You saw exactly what you would see if any of those theories were true, so they get as much support as anything else. There is nothing (in the concept of support) to differentiate between "all swans are white" and those other theories.

If you do add something else to differentiate, I will say the support concept is useless. The new thing does all the work. And further, the support concept is frequently abused. I have had people tell me that "all swans are black, but tomorrow you will hallucinated 10 white swans" is supported less by seeing 10 white swans tomorrow than "all swans are white" is, even though they made identical predictions (and asserted them with 100% probability, and would both have been definitely refuted by anything else). That kind of stuff is just wrong. I don't know if you think that kind of thing or not. What you said here does clearly disown it, nor advocate it. But that's the kind of thing that concerns me.

> Suppose we make X the statement "the first swan I see today is white" and Y the statement "all swans are white". P(X|Y) is very close to 1, P(X|~Y) is less than 1 so P(X|Y) > P(X), so seeing a white swan offers support for the view that all swans are white. Very, very weak support, but support nonetheless.

The problem I have is that it's not supported over infinitely many rivals. So how is that really support? It's useless. The only stuff not being supported is that which contradicts the evidence (like, literally contradicts, with no hallucination claims. e.g. a theory that predicts you will think you saw a green swan tomororw. but then you don't, just the white ones. that one is refuted). The inconsistent theories are refuted. The theories which make probabalistic predictions are partially supported. And the theories that say "screw probability, 100% every time" for all predictions get maximally supported, and between them support does not differentiate. (BTW I think it's ironic that I score better on support when I just stick 100% in front of every prediction in all theories I mention, while you score lower by putting in other numbers, and so your support concept discourages ever making predictions with under 100% confidence).

> (The above is not meant to be condescending, I apologise if you know all of it already).

It is not condescending. I think (following Popper) that explaining things is important and that nothing is obvious, and that communication is difficult enough without people refusing go over the "basics" in order to better understand each other. Of course this is a case where Popper's idea is not unique. Other people have said similar. But this idea, and others, are integrated into his epistemology closely. There's also *far more detail and precision* available, to explain *why* this stuff is true (e.g. lengthy theories about the nature of communication, also integrated into his epistemology). I don't think ideas about interpretting people's writing in kind ways, and miscommunication being a major hurdle, are so closely integrated with Bayesian approaches with are more math focussed and don't integrate so nicely with explanations.

My reply about support is basic stuff too, to my eye. But maybe not yours. I don't know. I expect not, since if it was you could have addressed it in advance. Oh well. It doesn't matter. Reply as you will. No doubt I'm also failing to address in advance something you regard as important.

> > To show they are correct. Popper's epistemology is different: ideas never have any positive support, confirmation, verification, justification, high probability, etc...

> This is a very tough bullet to bite.

Yes it is tough. Because this stuff has been integral to the Western philosophy tradition since Aristotle until Popper. That's a long time. It became common sense, intuitive, etc...

> > How do we decide which idea is better than the others? We can differentiate ideas by criticism. When we see a mistake in an idea, we criticize it (criticism = explaining a mistake/flaw). That refutes the idea. We should act on or use non-refuted ideas in preference over refuted ideas.

> One thing I don't like about this is the whole 'one strike and you're out' feel of it. It's very boolean,

Hmm. FYI that is my emphasis more than Popper's. I think it simplifies the theory a bit to regard all changes to theories as new theories. Keep in mind you can always invent a new theory with one thing changed. So the ways it matters have some limits, it's party just a terminology thing (terminolgoy has meaning, and some is better than others. Mine is chosen with Popperian considerations in mind. A lot of Popper's is chosen with considerations in mind of talking with his critics). Popper sometimes emphasized that it's important not to give up on theories too easily, but to look for ways to improve them when they are criticized. I agree with that. So, the "one strike you're out" way of expressing this is misleading, and isn't *substantially* implied in my statements (b/c of the possibility of creating new and similar theories). Other terminologies have different problems.

> the real world isn't usually so crisp. Even a correct theory will sometimes have some evidence pointing against it, and in policy debates almost every suggestion will have some kind of downside.

This is a substantive, not terminological, disagreement, I believe. I think it's one of the *advantages* of my terminology that it helped highlight this disagreement.

Note the idea that evidence "points" is the support idea.

In the Popperian scheme of things, evidence does not point. It contradicts, or it doesn't (given some interpretation and explanation, which are often more important than the evidence itself). That's it. Evidence can thus be used in criticisms, but is not itself inherently a criticism or argument.

So let me rephrase what you were saying. "Even a correct theory will sometimes have critical arguments against it".

Part of the Popperian view is that if an idea has one false aspect, it is false. There is a sense in which any flaw must be decisive. We can't just go around admitting mistakes into our ideas on purpose.

One way to explain the issue is: for each criticism, consider it. Judge if it's right or wrong. Do your best and act on the consequence. If you think the criticism is correct, you absolutely must reject the idea it criticizes. If you don't, then you can regard the theory as not having any *true* critical arguments against it, so that's fine.

When you reject an idea for having one false part, you can try to form a new theory to rescue the parts you still value. This runs into dangers of arbitrarily rescuing everything in an ad hoc way. There's two answers to that. The first is: who cares? Popperian epistemology is not about laying out rules to prevent you from thinking badly. It's about offering advice to help you think better. We don't really care very much if you find a way to game the system and do something dumb, such as making a series of 200 ad hoc and silly arguments to try to defend a theory you are attached to. All we'll do is criticize you for it. And we think that is good enough: there are criticisms of bad methodologies, but no formal rules that definitively ban them. Now the second answer, which Deutsch presents in The Fabric of Reality, is that when you modify theories you often ruin their explanation. If you don't, then the modification is OK, it's good to consider this new theory, it's worth considering. But if the explanation is ruined, that puts an end to trying to rescue it (unless you can come up with a good idea for a new way to modify it that wont' ruin the explanation).

This concept of ruining explanations is important and not simple. Reading the book would be great (it is polished! edited!) but I'll try to explain it briefly. This example is actually from his other book, _The Beginning of Infinity_ chapter 1. We'll start with a bad theory: the seasons are caused by Persephone's imprisonment, for 6 months of the year, in the underworld (via her mother Demeter's magic powers which she uses to express her emotions). This theory has a bad explanation in the first place, so it can be easily rescued when it's emprically contradicted. For example this theory predicts the seasons will be the same all over the globe, at the same time. That's false. But you can modify the theory very easily to account for the empirical data. You can say that Demeter only cares about the area where she lives. She makes it cold when Persephone is gone, and hot when she's present. The cold or hot has to go somewhere, so she puts it far away. So, the theory is saved by an ad hoc modification. It's no worse than before. Its substantive content was "Demeter's emotions and magic account for the seasons". And when the facts change, that explanation remains in tact. This is a warning against bad explanations (which can be criticized directly for being bad explanations, so there's no big problem here).

But when you have a good explanation, such as the real explanation for the seasons, based on the Earth orbitting the sun, and the axis being tilted, and so on, ad hoc modifications cause bigger problems. Suppose we found out the seasons are the same all around the world at the same time. That would refute the axis tilt theory of seasons. You could try to save it, but it's hard. If you added magic you would be ruining the axis tilt *explantion* and resorting to a very different explanation. I can't think of any way to save the axis tilt theory from the observation that the whole world has the same seasons as the same time, without contradicting or replacing its explanation. So that's why ad hoc modifications sometimes fail (for good explanatory theories only). In the cases where there is not a failure of this type -- if there is a way to keep a good explanation and still account for new data -- then that new theory is genuinely worth consideration (and if there is some thing wrong with it, you can criticize it).

> There is also the worry that there could be more than one non-refuted idea, which makes it a bit difficult to make decisions.

Yes I know. This is an important problem. I regard it as solved. For discussion of this problem, go to:

http://lesswrong.com/r/discussion/lw/551/popperian_decision_making/

> Bayesianism, on the other hand, when combined with expected utility theory, is perfect for making decisions.

Bayesianism works when you assume a bunch of stuff (e.g. some evidence), and you set up a clean example, and you choose an issue it's good at handling. I don't think it is very helpful in a lot of real world cases. Certaintly it helps in some. I regard Bayes' theorem itself as "how not to get probability wrong". That matters to a good amount of stuff. But hard real world scenarios usually have rival explanations of the proper interpretation of the available evidence, they have fallible evidence that is in doubt, they have often many different arguments that are hard to assign any numbers to, and so on. Using solomonoff induction is assign numbers, for example, doesn't work in practice as far as i know (e.g. people don't actually compute the numbers for dozens of political arugments using it). Another assumption being made is *what is a desirable (high utility) outcome* -- Bayesianism doesn't help you figure that out, it just lets you assume it (I see that as entrenching bias and subjectivism in reagards to morality -- we *can* make objective criticisms of moral values).

Branching from: http://lesswrong.com/lw/54u/bayesian_epistemology_vs_popper/3uta?context=4

The question is: how do you make decisions without justifying decisions, and without foundations?

If you can do that, I claim the regress problem is solved. Whereas induction, for example, is refuted by the regress problem (no, arbitrary foundations or circular arguments are not solutions).

OK stepping back a bit, and explaining less briefly:

Infinite regresses are nasty problems for epistemologies.

All justificationist epistemologies have an infinite regress.

That means they are false. They don't work. End of story.

There's options of course. Don't want a regress? No problem. Have an arbitrary foundation. Have an unjustified proposition. Have a circular argument. Or have something else even sillier.

The regress goes like this, and the details of the justification don't matter.

If you want to justify a theory, T0, you have to justify it with another theory, T1. Then T1 needs justify by T2. Which needs justifying by T3. Forever. And if T25 turns out wrong, then T24 loses it's justification. And with T24 unjustified, T23 loses its justification. And it cascades all the way back to the start.

I'll give one more example. Consider probabilistic justification. You assign T0 a probability, say 99.999%. Never mind how or why, the probability people aren't big on explanations like that. Just do your best. It doesn't matter. Moving on, what we have to wonder if that 99.999% figure is correct. If it's not correct then it could be anything such at 90% or 1% or whatever. So it better be correct. So we better justify that it's a good theory. How? Simple. We'll use our whim to assign it a probability of 99.99999%. OK! Now we're getting somewhere. I put a lot of 9s so we're almost certain to be correct! Except, what if I had that figure wrong? If it's wrong it could be anything such as 2% or 0.0001%. Uh oh. I better justify my second probability estimate. How? Well we're trying to defend this probabilistic justification method. Let's not give up yet and do something totally differently, instead we'll give it another probability. How about 80%? OK! Next I ask: is that 80% figure correct? If it's not correct, the probability could be anything, such as 5%. So we better justify it. So it goes on and on forever. Now there's two problems. First it goes forever, and you can't ever stop, you've got an infinite regress. Second, suppose you stopped have some very large but finite number of steps. Then the probability the first theory is correct is arbitrarily small. Because remember that at each step we didn't even have a guarantee, only a high probability. And if you roll the dice a lot of times, even with very good odds, eventually you lose. And you only have to lose once for the whole thing to fail.

OK so regresses are a nasty problem. They totally ruin all justificationist epistemologies. That's basically every epistemology anyone cares about except skepticism and Popperian epistemology. And forget about skepticism, that's more of an anti-epistemology than an epistemology: skepticism consists of giving up on knowledge.

Now we'll take a look at Popper and Deutsch's solution. In my words, with minor improvements.

Regresses all go away if we drop justification. Don't justify anything, ever. Simple.

But justification had a purpose.

The purpose of justification is to sort out good ideas from bad ideas. How do we know which ideas are any good? Which should we believe are true? Which should we act on?

BTW that's the same general problem that induction was trying to address. And induction is false. So that's another reason we need a solution to this issue.

The method of addressing this issue has several steps, so try to follow along.

Step 1) You can suggest any ideas you want. There's no rules, just anything you have the slightest suspicion might be useful. The source of the ideas, and the method of coming up with them, doesn't matter to anything. This part is easy.

Step 2) You can criticize any idea you want. There's no rules again. If you don't understand it, that's a criticism -- it should have been easier to understand. If you find it confusing, that's a criticism -- it should have been clearer. If you think you see something wrong with it, that's a criticism -- it shouldn't have been wrong it that way, *or* it should have included an explanation so you wouldn't make a mistaken criticism. This step is easy too.

Step 3) All criticized ideas are rejected. They're flawed. They're not good enough. Let's do better. This is easy too. Only the *exact* ideas criticized are rejected. Any idea with at least one difference is deemed a new idea. It's OK to suggest new ideas which are similar to old ideas (in fact it's a good idea: when you find something wrong with an idea you should try to work out a way to change it so it won't have that flaw anymore).

Step 4) If we have exactly one idea remaining to address some problem or question, and no one wants to revisit the previous steps at this time, then we're done for now (you can always change your mind and go back to the previous steps later if you want to). Use that idea. Why? Because it's the only one. It has no rivals, no known alternatives. It stands alone as the only non-refuted idea. We have sorted out the good ideas from the bad -- as best we know how -- and come to a definite answer, so use that answer. This step is easy too!

Step 5) What if we have a different number of ideas left over which is not exactly one? We'll divide that into two cases:

Case 1) What if we have two or more ideas? This one is easy. There is a particular criticism you can use to refute all the remaining theories. It's the same every time so there's not much to remember. It goes like this: idea A ought to tell me why B and C and D are wrong. If it doesn't, it could be better! So that's a flaw. Bye bye A. On to idea B: if B is so great, why hasn't it explained to me what's wrong with A, C and D? Sorry B, you didn't answer all my questions, you're not good enough. Then we come to idea C and we complain that it should have been more help and it wasn't. And D is gone too since it didn't settle the matter either. And that's it. Each idea should have settled the matter by giving us criticisms of all its rivals. They didn't. So they lose. So whenever there is a stalemate or a tie with two or more ideas then they all fail.

Case 2) What if we have zero ideas? This is crucial because case one always turns into this! The answer comes in two main parts. The first part is: think of more ideas. I know, I know, that sounds hard. What if you get stuck? But the second part makes it easier. And you can use the second part over and over and it keeps making it easier every time. So you just use the second part until it's easy enough, then you think of more ideas when you can. And that's all there is to it.

OK so the second part is this: be less ambitious. You might worry: but what about advanced science with its cutting edge breakthroughs? Well, this part is optional. If you can wait for an answer, don't do it. If there's no hurry, then work on the other steps more. Make more guesses and think of more criticisms and thus learn more and improve your knowledge. It might not be easy, but hey, the problem we were looking at is how to sort out good ideas from bad ideas. If you want to solve hard problems then it's not easy. Sorry. But you've got a method, just keep at it.

But if you have a decision to make then you need an answer now so you can make your decision. So in that case, if you actually want to reach a state of having exactly one theory which you can use now, then the trick is when you get stuck be less ambitious. I think how you can see how that would work in general terms. Basically if human knowledge isn't good enough to give you an answer of a certain quality right now, then your choices are either to work on it more and not have an answer now, or accept a lower quality answer. You can see why there isn't really any way around that. There's no magic way to always get a top quality answer now. If you want a cure for cancer, well I can't tell you how to come up with one in the next five minutes, sorry.

This is a bit vague so far. How does lowering your standards address the problem. So what you do is propose a new idea like this, "I need to do something, so I will do..." and then you put whatever you want (idea A, idea B, some combination, whatever).

This new idea is not refuted by any of the existing criticisms. So now you have one idea, it isn't refuted, and you might be done. If you're happy with it, great. But you might not be. Maybe you see something wrong with it, or you have another proposal. That's fine; just go back to the first three steps and do them more. Then you'll get to step 4 or 5 again.

What if we get back here? What do we do the second time? The third time? We simply get less ambitious each time. The harder a time we're having, the less we should expect. And so we can start criticizing any ideas that aim too high.

BTW it's explained on my website here, including an example:

http://fallibleideas.com/avoiding-coercion

Read that essay, keeping in mind what what I've been saying, and hopefully everything will click. Just bear in mind that when it talks about cooperation between people, and disagreements between people, and coming up with solutions for people -- when it discusses ideas in two or more separate minds -- everything applies exactly the same if the two or more conflicting ideas are all in the same mind.

What if you get real stuck? Well why not do the first thing that pops into your head? You don't want to? Why not? Got a criticism of it? It's better than nothing, right? No? If it's not better than nothing, do nothing! You think it's silly or dumb? Well so what? If it's the best idea you have then it doesn't matter if it's dumb. You can't magically instantly become super smart. You have to use your best idea even if you'd like to have better ideas.

Now you may be wondering whether this approach is truth-seeking. It is, but it doesn't always find the truth immediately. If you want a resolution to a question immediately then its quality cannot exceed today's knowledge (plus whatever you can learn in the time allotted). It can't do better than the best that is known how to do. But as far as long term progress, the truth seeking came in those first three steps. You come up with ideas. You criticize those ideas. Thereby you eliminate flaws. Every time you find a mistake and point it out you are making progress towards the truth. That's how we approach the truth: not by justifying but by identify mistakes and learning better. This is evolution, it's the solution to Paley's problem, it's discussed in BoI and on my Fallible Ideas website. And it's not too hard to understand: improve stuff, keep at it, and you get closer to the truth. Mistake correcting -- criticism -- is a truth-seeking method. That's where the truth-seeking comes from.

I was directed to this book (http://www-biba.inrialpes.fr/Jaynes/prob.html) in conversation here:

http://lesswrong.com/lw/3ox/bayesianism_versus_critical_rationalism/3ug7?context=1#3ug7

I was told it had a proof of Bayesian epistemology in the first two chapters. One of the things we were discussing is Popper's epistemology.

Here are those chapters:

http://www-biba.inrialpes.fr/Jaynes/cc01p.pdf

http://www-biba.inrialpes.fr/Jaynes/cc02m.pdf

I have not found any proof here that Bayesian epistemology is correct. There is not even an attempt to prove it. Various things are assumed in the first chapter. In the second chapter, some things are proven given those assumptions.

Some first chapter assumptions are incorrect or unargued. It begins with an example with a policeman, and says his conclusion is not a logical deduction because the evidence is logically consistent with his conclusion being false. I agree so far. Next it says "we will grant that it had a certain degree of validity". But I will not grant that. Popper's epistemology explains that *this is a mistake* (and Jaynes makes no attempt at all to address Popper's arguments). In any case, simply assuming his readers will grant his substantive claims is no way to argue.

The next sentences blithely assert that we all reason in this way. Jaynes' is basically presenting the issues of this kind of reasoning as his topic. This simply ignores Popper and makes no attempt to prove Jaynes' approach is correct.

Jaynes goes on to give syllogisms, which he calls "weaker" than deduction, which he acknowledges are not deductively correct. And then he just says we use that kind of reasoning all the time. That sort of assertion only appeals to the already converted. Jaynes starts with arguments which appeal to the *intuition* of his readers, not on arguments which could persuade someone who disagreed with him (that is, good rational arguments). Later when he gets into more mathematical stuff which doesn't (directly) rest on appeals to intution, it does rest on the ideas he (supposedly) established early on with his appeals to intuition.

The outline of the approach here is to quickly gloss over substantive philosophical assumptions, never provide serious arguments for them, take them as common sense, do not detail them, and then later provide arguments which are rigorous *given the assumptions glossed over earlier*. This is a mistake.

So we get, e.g., a section on Boolean Algebra which says it will state previous ideas more formally. This briefly acknowledges that the rigorous parts depend on the non-rigorous parts. Also the very important problem of carefully detailing how the mathematical objects discussed correspond to the real world things they are supposed to help us understand does not receive adequate attention.

Chapter 2 begins by saying we've now formulated our problem and the rest is just math. What I take from that is that the early assumptions won't be revisted but simply used as premises. So the rest is pointless if those early assumptions are mistaken, and Bayesian Epistemology cannot be proven in this way to anyone who doesn't grant the assumptions (such as a Popperian).

Moving on to Popper, Jaynes is ignorant of the topic and unscholarly. He writes:

http://www-biba.inrialpes.fr/Jaynes/crefsv.pdf

> Karl Popper is famous mostly through making a career out of the doctrine that theories may not be proved true, only false

This is pure fiction. Popper is a fallibilist and said (repeatedly) that theories cannot be proved false (or anything else).

It's important to criticize unscholarly books promoting myths about rival philosophers rather than addressing their actual arguments. That's a major flaw not just in a particular paragraph but in the author's way of thinking. It's especially relevant in this case since the author of the books tries to tell us about how to think.

Note that Yudkowsky made a similar unscholarly mistake, about the same rival philosopher, here:

http://yudkowsky.net/rational/bayes

> Previously, the most popular philosophy of science was probably Karl Popper's falsificationism - this is the old philosophy that the Bayesian revolution is currently dethroning.  Karl Popper's idea that theories can be definitely falsified, but never definitely confirmed

Popper's philosophy is not falsificationism, it was never the most popular, and it is fallibilist: it says ideas cannot be definitely falsified. It's bad to make this kind of mistake about what a rival's basic claims are when claiming to be dethroning him. The correct method of dethroning a rival philosophy involves understanding what it does say and criticizing that.

If Bayesians wish to challenge Popper they should learn his ideas and address his arguments. For example he questioned the concept of positive support for ideas. Part of this argument involves asking the questions: 'What is support?' (This is not asking for its essential nature or a perfect definition, just to explain clearly and precisely what the support idea actually says) and 'What is the difference between "X supports Y" and "X is consistent with Y"?' If anyone has the answer, please tell me.