Bayesianism versus Critical Rationalism

Jayson_Virissimo

I have just rediscovered an article by Max Albert on my hard drive which I never got around to reading that might interest others on Less Wrong. You can find the article here. It is an argument against Bayesianism and for Critical Rationalism (of Karl Popper fame).

Abstract:

Economists claim that principles of rationality are normative principles. Nevertheless,
they go on to explain why it is in a person’s own interest to be rational. If this were true,
being rational itself would be a means to an end, and rationality could be interpreted in
a non-normative or naturalistic way. The alternative is not attractive: if the only argument
in favor of principles of rationality were their intrinsic appeal, a commitment to
rationality would be irrational, making the notion of rationality self-defeating. A comprehensive
conception of rationality should recommend itself: it should be rational to be
rational. Moreover, since rational action requires rational beliefs concerning means-ends
relations, a naturalistic conception of rationality has to cover rational belief formation including
the belief that it is rational to be rational. The paper considers four conceptions
of rationality and asks whether they can deliver the goods: Bayesianism, perfect rationality
(just in case that it differs from Bayesianism), ecological rationality (as a version of
bounded rationality), and critical rationality, the conception of rationality characterizing
critical rationalism.

Any thoughts?

A good nutshell description of the type of Bayesianism that many LWers think correct is objective Bayesianism with critical rationalism-like underpinnings. Where recursive justification hits bottom is particularly relevant. On my cursory skim, Albert only seems to be addressing "subjective" Bayesianism which allows for any choice of prior.

4XiXiDu15y

For people like me who have no clue, if you scroll down a bit here there is a comparison (so you get a vague idea): * Subjective Bayesians emphasize the relative lack of rational constraints on prior probabilities. * Objective Bayesians (e.g., Jaynes and Rosenkrantz) emphasize the extent to which prior probabilities are rationally constrained. More here: [...] And of course Critical rationalism: * Critical rationalism explicitly proposes a third decision rule for rational belief formation: it is rational to believe a hypothesis if it has so far withstood serious criticism better than its competitors.

5Matt_Simpson15y

I'll add that a decent summary of the position espoused in Where recursive justification hits bottom (linked in the grandparent) is that critical rationalism (or something like it) entails objective Bayesianism. It both entails the use of Baye's rule to update on information and it entails a set of correct priors.

1Jayson_Virissimo15y

Thanks for helping me realize that Critical Rationalism and Bayesianism can be compliments rather than substitutes.

2Elliot Temple15y

FYI that is a misleading statement of Critical Rationalism. For one thing, Popper was not a "belief philosopher" so he wouldn't have stated it quite like that. There are a lot of misleading statements about CR floating around. Most come from its opponents trying to make sense of it on their own terms. In trying to formulate it in a way that makes sense given their anti-CR premises, they change it. It's best to read primary sources for this.

It seems to think the problem of the priors does in Bayesianism :-(

Popper seems outdated. Rejecting induction completely is not very realistic.

2Jayson_Virissimo15y

Critical Rationalism has advanced somewhat since Popper. [...] I think Hume would agree.

2timtyler15y

Not very significantly. The revolution happened mostly without them.

5Jayson_Virissimo15y

After reconsidering your statement, I have come to agree.

1Elliot Temple15y

Who do you think advanced CR? I think only David Deutsch has improved on Popper.

2Jayson_Virissimo15y

I had in mind Miller and Deutsch.

2Elliot Temple15y

Which Miller publication or argument?

5Jayson_Virissimo15y

Critical Rationalism: A Restatement and Defense and Out of Error: Further Essays On Critical Rationalism.

1Elliot Temple15y

Thanks I ordered them. I'd only read individual articles of his.

-2[anonymous]15y

Hume would agree because he never accepted the full force of his own argument. He couldn't imagine how people can create knowledge without induction even though he could see that induction is impossible. It took Popper to explain how knowledge can be created without induction.

Despite the context, I didn't have Deutsch specifically in mind. Just a general observation over the years.

The issue under discussion here is wider than Popper and appears elsewhere, in the disagreement between small-world and large-world Bayesians, the former being the side that I guess Popper would have been on. (It's a very long time since I read Popper, and I do not recall if he ever says anything about Bayesian inference.) Must Bayesian inference of the sort that takes a parameterised model and a prior distribution on the parameters, and fits it to a data set (a process whose validity everyone except a few hard-core frequentists agree on) be subordinate to some other process when the data do not fit your model at all, for any parameters, and you need to find a different model? The small-worlders say yes, and the large-worlders say no. The small-worlders scoff at the large-worlders, the large-worlders exhibit the Solomonoff universal prior, and if the small-worlders are still paying attention, they usually just scoff some more. Sometimes they will point out that Solomonoff induction is uncomputable, and that computable approximations are exponentially unfeasible, relying as they do on merely enumerating all possible hypotheses in order of size. I haven't seen a large-worlder response to that anywhere, not even here on LessWrong, where large-worldism is the default view.

But then the small worlders, asked just what it is that they put above Bayes, reply only with magic names, such as "human judgement", "criticism", or "argument". All they are doing is describing what the process feels like, not what it is. In chapter 7 of The Fabric of Reality, Deutsch circles around and around the point, but the point never appears.

ETA: And they generally deny that the process can be elucidated any further. Popper himself says (as quoted elsewhere in these threads) that there is no method.

So for me, that is where things stand, and I am not convinced by either side.

Some further context for the above. I've been drafting a posting on this for a while, which this comment and that one are based on.

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