Bayesian Epistemology vs Popper

It's no less founded on unproven axioms, and it's no less arbitrary than induction, it just contains the tenet "we don't reject propositions for being arbitrary" and pats itself on the back for being self consistent. This doesn't do a better job helping people generate true information, it does a worse one.

Why is that a criticism?

Actually I don't know what constitutes a criticism in your book (since you never specified), but you have also said that there are no rules for criticism, so I suppose that it is a criticism. If not, then please say why it is not a criticism.

I am not going to engage in a discussion about my and your biases, since such debates rarely lead to an agreement.

It's not at all canonical, but a paper that neatly summarizes Bayesian epistemology is "Bayesian Epistemology" by Stephan Hartmann and Jan Sprenger.

Yes, by all means feel free.

Err, Bayesian probability doesn't have anything special for morality either. People on LW tend to be moral non-realists, ie people who deny that there is objective moral knowledge, if that's what you're talking about (not sure- sorry!), but that's completely orthogonal to this discussion: there's nothing in Bayesianism that leads inevitably to non-realism. (Also, I'm not convinced that moral realism is right, so saying "Bayesianism leads to moral non-realism" isn't a very effective argument.)

Knowledge is created by an evolutionary process involving conjecture and refutation. By criticizing flaws in ideas, we seek to improve them (by making better conjectures we hope will eliminate the flaws).

I'm inclined to take this formula seriously, but I'd like to start by applying it to innate knowledge, knowledge we are born with, because here we are definitely talking about an evolutionary process involving mutation and natural selection. Some mutations add what amounts to a new innate conjecture (hypothesis, belief) into the cognitive architecture of the creature.

However, what occurs at this point is not that a creature with a false innate conjecture is eliminated. The creature isn't being tested purely against reality in isolation. It's being tested against other members of its species. The creature with the least-false, or least-perilously-false conjecture will tend to do better than the competitors. The competition for survival amounts to a competition between rival conjectures. The truest, or most-usefully-true, or least-wrong, or least-dangerously-wrong innate belief will tend to outdo its competitors and ultimately spread through the species. (With the odd usefully-wrong belief surviving.)

The occasional appearance of new innate conjectures resembles the conjecture part of Popperian conjecture and refutation. However, the contest between rival innate conjectures that occurs as the members of the species struggle against each other for survival seems less Popperian than Bayesian.

The relative success of the members of the species who carry the more successful hypothesis vaguely resembles Bayesian updating, because the winners increase their relative numbers and the losers decrease their relative numbers, which resembles the shift in the probabilities assigned to rival hypotheses that occurs in Bayesian updating. Consider the following substitutions applied to Bayes' formula:

P(H|E) = P(E|H)P(H) / P(E)

• P(H|E) is the new proportion (i.e. in the next generation) of the species carrying the hypothesis H, given that event E occurred (E is "everything that happened to the generation")
• P(E|H) is the degree to which H predicts and thus prepares the individual to handle E (measured in expected number of offspring given E)
• P(H) is the old proportion (i.e. in the previous generation) of the species carrying H
• P(E) is the degree to which the average member of the species predicts and thus is prepared to handle E (measured in expected number of offspring given E)

With these assignments, what the equation means is:

The new proportion of the species with H is equal to the old proportion of the species with H, times the expected number of offspring of members with H, divided by the expected number of offspring of the average member of the species.

One difference between this process and Bayesian updating is that this process allows the occasional introduction of new hypotheses over time, with what amounts to a modest but not vanishing initial prior.

The number of major ideas in epistemology is not very large. After Aristotle, there wasn't very much innovation for a long time. It's a small enough field you can actually trace ideas all the way back to the start of written history. Any professional can look at everything important. Some Bayesian should have. Maybe some did, but I haven't seen anything of decent quality.

As to a professional, I already referred you to Earman. Incidentally, you seem to be narrowing the claim somewhat. Note that I didn't say that the set of major ideas in epistemology isn't small, I referred to the much larger class of philosophical ideas (although I can see how that might not be clear from my wording). And the set is indeed very large. However, I think that your claim about "after Aristotle" is both wrong and misleading. There's a lot of what thought about epistemological issues in both the Islamic and Christian worlds during the Middle Ages. Now, you might argue that that's not helpful or relevant since it gets tangled up in theology and involves bad assumptions. But that's not to say that material doesn't exist. And that's before we get to non-Western stuff (which admittedly I don't know much about at all).

(I agree when you restrict to professionals, and have already recommended Earman to you.)

It works exactly identically to how Popperian epistemology creates any other kind of knowledge. There's nothing special for morality.

Knowledge is created by an evolutionary process involving conjecture and refutation. By criticizing flaws in ideas, we seek to improve them (by making better conjectures we hope will eliminate the flaws).

This is a deeply puzzling set of claims. First of all, a major point of his epistemological system is falsfiability based on data (at least as I understand it from LScD). How that would at all interact with moral issues is unclear to me. Indeed, the semi-canonical example of a non-falsifiable claim in the Popperian sense is Marxism, a set of ideas that has a large set of attached moral claims.

I also don't see how this works given that moral claims can always be criticized by the essential sociopathic argument "I don't care. Why should you?" Obviously, that line of thinking can be/should be expanded. To use your earlier example, how would you discuss "murder is wrong" in a Popperian framework? I would suggest that this isn't going to be any different than simply discussing moral ideas based on shared intuitions with particular attention to the edge cases. You're welcome to expand on these claims, but right now, nothing you've said in this regard is remotely convincing or even helpful since it amounts to just saying "well, do the same thing."

I have a lot of familiarity with the other Popperians. But Popper and Deutsch are by far the best. There isn't really anything non-Popperian that draws on Popper much. Everyone who has understood Popper is a Popperian, IMO. If you disagree, do tell.

I'm going to be obnoxious and quote a friend of mine "Everyone who understands Christianity is a Christian." I don't have any deep examples of other individuals although I would tentatively say that I understood Popper's views in Logic of Scientific Discovery just fine.

Do you have a criticism of his arguments in LScD or not?

Sure. The most obvious one is when he is discussing the law of large numbers and frequentist v. Bayesian interpretations (incidentally to understand those passages it is helpful to note that he uses the term "subjective" to describe Bayesians rather than Bayesian which is consistent with the language of the time, but in modern terminology has a very different meaning (used to distinguish between subject and objective Bayesians)). In that section he argues that (I don't have the page number unfortunately since I'm using my Kindle edition. I have a hard copy somewhere but I don't know where) that "it must be inadmissable to give after the deduction of Bernoulli's theorem a meaning to p different from the one which was given to it before the deduction." This is, simply put, wrong. Mathematicians all the time prove something in one framework and then interpret it in another framework. You just need to show that all the properties of the relevant frameworks overlap in sufficiently non-pathological cases. If someone wrote this as a complaint about say using the complex exponential to understand the symmetries of the Euclidean plane, we'd immediately see this as a bad claim. There's an associated issue in this section which also turns up but it is more subtle; Popper doesn't appreciate what you can do with measure theory and L_p spaces and related ideas to move back and forth between different notions of probability and different metrics on spaces. That's ok, it was a very new idea when he wrote LScD (although the connections were to some extent definitely there). But it does render a lot of what he says simply irrelevant or outright wrong.

The usual way on Less Wrong is to bring in Omega, the all powerful all knowing entity who spends his free time playing games with us mortals, and for some reason most of his games illustrate some point of probability or decision theory. With Omega acting as the bookie you can be forced to assign a probability to any meaningful statement. Some people just respond to such scenarios by asserting that Omega is impossible, I don't know if you're one of those people but I'll try a different approach anyway.

Imagine that in 2050 the physicists have narrowed down all their candidates for a Theory of Everything to just two possibilities, creatively named X-theory and Y-theory.

An engineer who is a passionate supporter of X-theory has designed and built a new power plant. If X-theory is correct, his power plant will produce a limitless supply of free energy and bring humanity into a post-scarcity era.

However, a number of physicists have had a look at his designs, and have shown that if Y-theory is correct his power plant will create a black hole and wipe out humanity as soon as it is turned on. Somehow, it has ended up being your decision whether or not it goes on.

This is one such 'bet', it may not a very likely scenario but you should still be able to handle it. If we combine it with many slightly altered dilemma we can figure out your probability estimate of theory X being correct, whether you admit to having one or not.

So: just bet on things the theory predicts instead.

Yes, I left making up more specific examples as an exercise for the reader.

You can't create moral ideas in the first place, or judge which are good (without, again, assuming a moral standard that you can't evaluate).

You've repeatedly claimed that the Popperian approach can somehow address moral issues. Despite requests you've shown no details of that claim other than to say that you do the same thing you would do but with moral claims. So let's work through a specific moral issue. Can you take an example of a real moral issue that has been controversial historically (like say slavery or free speech) and show how the Popperian would approach? An concrete worked out example would be very helpful.

Yes, given moral assertions you can then analyze them. Well, sort of. You guys rely on empirical evidence. Most moral arguments don't.

First of all, you shouldn't lump me in with the Yudkowskyist Bayesians. Compared to them and to you I am in a distinct third party on epistemology.

Bayes' theorem is an abstraction. If you don't have a reasonable way to transform your problem to a form valid within that abstraction then of course you shouldn't use it. Also, if you have a problem that is solved more efficiently using another abstraction, then use that other abstraction.

This doesn't mean that Bayes' theorem is useless, it just means there are domains of reasonable usage. The same will be true for your Popperian decision making.

You can't create moral ideas in the first place, or judge which are good (without, again, assuming a moral standard that you can't evaluate).

These are just computable processes; if Bayesianism is in some sense Turing complete then it can be used to do all of this; it just might be very inefficient when compared to other approaches.

Aspects of coming up with moral ideas and judging which ones are good would probably be accomplished well with Bayesian methods. Other aspects should probably be accomplished using other methods.

Yes, given moral assertions you can then analyze them. Well, sort of. You guys rely on empirical evidence. Most moral arguments don't.

First of all, you shouldn't lump me in with the Yudkowskyist Bayesians. Compared to them and to you I am in a distinct third party on epistemology.

Bayes' theorem is an abstraction. If you don't have a reasonable way to transform your problem to a form valid within that abstraction then of course you shouldn't use it. Also, if you have a problem that is solved more efficiently using another abstraction, then use that other abstraction.

This doesn't mean that Bayes' theorem is useless, it just means there are domains of reasonable usage. The same will be true for your Popperian decision making.

You can't create moral ideas in the first place, or judge which are good (without, again, assuming a moral standard that you can't evaluate).

These are just computable processes; if Bayesianism is in some sense Turing complete then it can be used to do all of this; it just might be very inefficient when compared to other approaches.

Aspects of coming up with moral ideas and judging which ones are good would probably be accomplished well with Bayesian methods. Other aspects should probably be accomplished using other methods.

Adding a reference for this comment: Münchhausen Trilemma.

Using my epistemology I have learned not to do that kind of thing. Would that serve as an example of a practical benefit of it, and a substantive difference? You learned Bayesian stuff but it apparently didn't solve your problem, whereas my epistemology did solve mine.

It doesn't take Popperian epistemology to learn social fluency. I've learned to limit conflict and improve the productivity of my discussions, and I am (to the best of my ability) Bayesian in my epistemology.

If you want to credit a particular skill to your epistemology, you should first see whether it's more likely to arise among those who share your epistemology than those who don't.

Using my epistemology I have learned not to do that kind of thing. Would that serve as an example of a practical benefit of it, and a substantive difference?

No. It provides an example of a way in which you are better than me. I am overwhelmingly confident that I can find ways in which I am better than you.

Do you assert that? It is wrong and has real world consequence. In The Beginning of Infinity Deutsch takes on a claim of a similar type (50% probability of humanity surviving the next century) using Popperian epistemology. You can find Deutsch explaining some of that material here: http://groupspaces.com/oxfordtranshumanists/pages/past-talks

Could you explain how a Popperian disputes such an assertion? Through only my own fault, I can't listen to an mp3 right now.

My understanding is that anyone would make that argument in the same way: by providing evidence in the Bayesian sense, which would convince a Bayesian. What I am really asking for is a description of why your beliefs aren't the same as mine but better. Why is it that a Popperian disagrees with a Bayesian in this case? What argument do they accept that a Bayesian wouldn't? What is the corresponding calculation a Popperian does when he has to decide how to gamble with the lives of six billion people on an uncertain assertion?

I wonder if you think that all mathematically equivalent ways of thinking are equal. I believe they aren't because some are more convenient, some get to answers more directly, some make it harder to make mistakes, and so on. So even if my approach was compatible with the Bayesian approach, that wouldn't mean we agree or have nothing to discuss.

I agree that different ways of thinking can be better or worse even when they come to the same conclusions. You seem to be arguing that Bayesianism is wrong, which is a very different thing. At best, you seem to be claiming that trying to come up with probabilities is a bad idea. I don't yet understand exactly what you mean. Would you never take a bet? Would never take an action that could possibly be bad and could possibly be good, which requires weighing two uncertain outcomes?

This brings me back to my initial query: give a specific case where Popperian reasoning diverges from Bayesian reasoning, explain why they diverge, and explain why Bayesianism is wrong. Explain why Bayesian's willingness to bet does harm. Explain why Bayesians are slower than Popperians at coming to the same conclusion. Whatever you want.

I do not plan to continue this discussion except in the pursuit of an example about which we could actually argue productively.

Sorry, I over-quoted there; Pearl only discusses causality, and a little bit of epistemology, but he doesn't talk about moral philosophy at all.

His book is all about causal models, which are directed graphs in which each vertex represents a variable and each edge represents a conditional dependence between variables. He shows that the properties of these graphs reproduce what we intuitively think of as "cause and effect", defines algorithms for building them from data and operating on them, and analyzes the circumstances under which causality can and can't be inferred from the data.

Imagine that I have some set of propositions, A through Z, and I don't know the probabilities of any of these. Now let's say I'm using these propositions to explain some experimental result--since I would have uniform priors for A through Z, it follows that an explanation like "M did it" is more probable than "A and B did it," which in turn is more probable than "G and P and H did it."

I use the word prove because I'm doing it deductively in math. I already linked you to the 2+2=3 thing, I believe. Also, the question of how I would, for example, change AI design if a well-known theorem is wrong (pretend it is the future and the best theorems proving Bayesianism are better-known and I am working on AI design) is both extremely hard to answer and unlikely to be necessary. Well unlikely is the wrong word; what is P(X | "There are no probabilities")? :)