Bayesianism versus Critical Rationalism

4 Post author: Jayson_Virissimo 10 January 2011 04:54AM

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?

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Comment author: Matt_Simpson 10 January 2011 09:35:22AM * 2 points [-]

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.

Comment author: XiXiDu 10 January 2011 11:52:43AM * 3 points [-]

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:

Some attempts have been made at finding a priori probabilities, i.e. probability distributions in some sense logically required by the nature of one's state of uncertainty; these are a subject of philosophical controversy, with Bayesians being roughly divided into two schools: "objective Bayesians", who believe such priors exist in many useful situations, and "subjective Bayesians" who believe that in practice priors usually represent subjective judgements of opinion that cannot be rigorously justified (Williamson 2010). Perhaps the strongest arguments for objective Bayesianism were given by Edwin T. Jaynes.

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.

Comment author: curi 02 April 2011 03:35:37PM 2 points [-]

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.

Comment author: Matt_Simpson 10 January 2011 04:04:37PM 3 points [-]

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.

Comment author: Jayson_Virissimo 12 January 2011 05:07:32AM 1 point [-]

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

Comment author: timtyler 10 January 2011 10:10:49PM 0 points [-]

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

Popper seems outdated.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

Comment author: [deleted] comment score below threshold [+] (258 children)

Comment author: timtyler 01 April 2011 07:52:54AM * -1 points [-]

So you're just going to reject it somewhat, whatever that may mean.

I am not rejecting induction. Science consists primary of induction.

Without induction, we don't even know whether the sun will rise tomorrow.

Popper seems out of date - since now we know what the rules governing induction actually are.

Comment author: [deleted] 03 April 2011 08:59:19AM 3 points [-]

According to Popper, the sun will rise tomorrow was refuted in the form it was originally meant:

'The sun rises every day' was meant to say 'Wherever you go the sun rises every day'. That this was its original meaning is shown by the fact that Pytheas of Marseilles, the first known traveller to cross the polar circle and to describe 'the frozen sea and the midnight sun' was for centuries made the paradigm of a liar, and that the term 'travellers' tales' was derived from him. Objective Knowledge, 1978, p 97

Comment author: curi 03 April 2011 09:15:05AM 1 point [-]

ditto "bread nourishes" and one other famous example i forgot.

Comment author: [deleted] 03 April 2011 10:32:20AM 1 point [-]

That would be "All men are mortal".

Comment author: [deleted] comment score below threshold [+] (253 children)

Comment author: [deleted] 02 April 2011 06:42:57AM -4 points [-]

Solomonoff Induction is just another failed attempt at solving the misbegotten problem of induction.

The goal of Solomonoff Induction is prediction; you want to obtain a compact algorithmic description of past data so that future data can be predicted. Such a description you call a theory although you don't care what the theory is or how it stands up as an explanation. In philosophy this is called instrumentalism and it is a wrong-headed approach to science, as Karl Popper made clear.

Solomonoff Induction will keep going wrong in random and perverse ways because it pays no heed to theories as explanations. You just think that shorter length theories which are consistent with the data are somehow more likely, regardless of content and how silly that content may be. Consequently, things may seem to be going alright for a while, although you won't know if that was just luck, and then suddenly it has joined the Ministry of Silly Walks. You won't get the steady improvement that you do when you treat theories as explanations and focus on correcting errors in those explanations (aka Critical Rationalism).

When a theory starts being inconsistent with the data you just throw it out. But what if you were wrong about the theory being inconsistent? Data needs interpretation and we can be wrong about our interpretation. As Popper explained, all data is theory-laden and there is no way around this.

A related point is that science does not start with a set of observations or data. Science starts with problems. We collect data to try to refute theories that have already been advanced to solve a problem. Without a theory, one has no idea which data is relevant or what to observe. So you don't collect data and then fit theories to that data with the goal of making correct predictions.

The focus on data to the exclusion of anything else is empiricist. Most theories get rejected not because they were falsified by contradictory data but because they were refuted by criticism. Solomonoff induction doesn't care about criticism, let alone that it is pivotal in knowledge creation. Also some theories can't be refuted by empirical means, so what does Solomonoff Induction do about those?

Solomonoff Induction may be nice mathematically but it is bad philosophy and it is old-hat.

Comment author: AlephNeil 02 April 2011 07:38:40AM * 4 points [-]

I hope you stick around - LW needs people who've read Popper. (However, I take that back if it turns out that you've only read Deutsch's simplified, evangelical caricature of him.)

Solomonoff Induction will keep going wrong in random and perverse ways because it pays no heed to theories as explanations.

This is at best unclear. If a person, or the entire scientific community, were given the task of competing with Solomonoff induction to predict an incoming data stream, then either (i) Solomonoff induction would eventually arrive at "the correct theory" (at least in the sense that it no longer 'keeps going wrong') or (ii) the human scientists would 'keep going wrong in random ways' (i.e. ways that seem random to the scientists) or both.

Talking about the need for 'good explanations' over and above mere predictive success is all very well, but it's not that helpful unless you can say something about what makes an explanation good. (It would be even more helpful if you could say something about how an AI could recognize a good explanation.)

I think the point you should be concentrating on is that human scientists do not face the same problem-situation as Solomonoff induction. We can choose what questions to work on, design experiments, and we're also blessed/cursed with the lack of any stable boundary between 'data' and 'theory'.

Comment author: RichardKennaway 06 April 2011 10:22:18AM 4 points [-]

I hope you stick around - LW needs people who've read Popper. (However, I take that back if it turns out that you've only read Deutsch's simplified, evangelical caricature of him.)

Turning into a simplified caricature of Popper appears to be a memetic hazard of reading Popper. Not as bad as reading Rand, though.

Comment author: [deleted] 06 April 2011 10:49:21AM 0 points [-]

Would you care to explain in what way Deutsch is a simplified caricature of Popper or are you just going to be content to make assertions like the other commenter? I doubt very much that you have any idea what Popperians such as David Deutsch are like.

Comment author: RichardKennaway 07 April 2011 09:00:59AM * 3 points [-]

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.

Comment author: curi 02 April 2011 09:50:25PM 1 point [-]

Deutsch does say what makes an explanation good. He has a TED talk about it, and a new book, The Beginning of Infinity (came out 2 days ago in the UK) which has this as a major theme. Good explanations are hard to change while they still solve the same problem. The book has examples and elaboration.

Comment author: [deleted] 02 April 2011 09:10:46PM 1 point [-]

I have read both Popper and Deutsch. Could you explain your comment about Deutsch?

You say human scientists do not face the same problem situation as Solomonoff Induction. But both are trying to create knowledge right? In Solomonoff Induction it is assumed that all knowledge comes to us via sensory organs as data streams and the task of the knowledge creator is to compress that data with the aim of making good predictions. This, it is held, is in some sense what scientists and all people do when they create knowledge and it is what the ideal knowledge creator should do. Critical rationalism rejects the idea that all knowledge comes to us via the senses - that is empiricism - and it rejects the idea that theories are just instruments for making predictions - that is instrumentalism.

You seem to think that predictive success can come without underlying explanations, as though explanations are optional. They are not. We can't just neglect explanations and think we can get on with the process of building an AI. That we cannot formalize our current knowledge about explanations in a nice piece of mathematics should not be a deterrent to trying to learn more.

Comment author: curi 02 April 2011 09:19:04PM 0 points [-]

I wonder what they think of the discussion of the Oracle in The Fabric of Reality, ch1.

Comment author: timtyler 02 April 2011 07:24:21AM * 0 points [-]

When a theory starts being inconsistent with the data you just throw it out. But what if you were wrong about the theory being inconsistent?

That's just not what you do. "Throwing out theories" is more strongly suggested by falsificationism. A Bayesian approach recognises that observations are uncertain and fallible. Observations inconsistent with a theory are strong negative evidence, but they don't really "falsify" a theory.

Here is Yudkowsky on the topic:

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.

Popper "missed" confirmation by rejecting induction. He didn't get it, and now we know better.

A related point is that science does not start with a set of observations or data.

Observations come second. Priors come first.

Solomonoff induction doesn't care about criticism, let alone that it is pivotal in knowledge creation.

Critics might have a role to play for a resource-limited agent - for instance if they pointed out explanations that were short and were not yet receiving the proper consideration - or if they supplied more data.

Also some theories can't be refuted by empirical means, so what does Solomonoff Induction do about those?

It says to prefer the shorter one.

Comment author: curi 02 April 2011 02:54:45PM 5 points [-]

Yudkowsky hasn't read Popper or wasn't paying attention. Popper's didn't advocate that position; it's a myth which Popper repeatedly denied. See e.g. "The Popper Legend" section in Popper's replies to his critics in the Schilpp book.

Comment author: timtyler 02 April 2011 08:23:41PM * 0 points [-]

Here is Popper's denial:

There is neither a psychological nor a logical induction. Only the falsity of the theory can be inferred from empirical evidence and this inference is a purely deductive one.

That's not right. Martin Gardner, explains why:

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.

Comment author: curi 02 April 2011 09:16:08PM 1 point [-]

You haven't understood which part is the myth I was talking about or read the source I gave.

You've now given a short statement of the conclusion of an argument Popper made in LScD (but not the argument itself, and also missing too much detail to even understand his point). It is a purely logical argument and unexceptionable. The Gardner passage doesn't address it at all, nor make any argument, but merely asserts.

Please do your homework instead of just googling out of context snippets. You don't know what the Popper legend is, nor what Popper's argument for the quoted conclusion you pasted is.

Comment author: timtyler 02 April 2011 10:29:53PM * 1 point [-]

Yudkowsky:

On the other hand, Popper's idea that there is only falsification and no such thing as confirmation turns out to be incorrect.

Popper:

There is neither a psychological nor a logical induction. Only the falsity of the theory can be inferred from empirical evidence and this inference is a purely deductive one.

That seems pretty cut and dried - so long as you understand the relationship between confirmation and induction. Popper asserts what Yudkowsky claims he says.

Also, Popper's position is wrong. Few philosophers of science ever bought it in the first place - and now things have moved on, so this is merely of historical interest.

Comment author: curi 02 April 2011 11:09:40PM * 3 points [-]

You have to actually read Popper's books to understand what he means. You are taking short summaries of conclusions without understanding Popper's arguments behind them.

For example, when Popper says "theory" there he does not mean any theory. He means a universal theory. This is the kind of thing one finds out by reading him.

Popper gave an argument in LScD along these lines:

Consider a theory, T, that all swans are white. T is a universal theory.

No confirming evidence can prove T is true. You can see 5 white swans or 500 or 50 million. Still might be false.

But if you see one black swan it is false.

This is an asymmetry between confirmation and falsification when applied to universal theories. It does not hold for all theories.

Consider the negation ~T. At least one swan is not white. This theory cannot be refuted by any amount of observations. But it can be confirmed with only one observation. ~T is a non-universal theory and not the kind science is after.

Is he wrong? This is pure logic. Popper in LScD was interest in scientific laws -- that is, universal theories -- and in that context he was unobjectionably correct about confirmation and falsification.

What you are doing is taking short quotes and imagining the context isn't relevant, and that they only have one possible meaning. That is an unscholarly beginner's mistake.

I've simplified various things here (for example Popper's approach is not falsificationism; saying it is is a myth; linking to a page titled Falsifiability and calling it a refutation of Popper demonstrates your ignorance; and I ignored the duhem-quine problem which Popper did address from the start). And Popper had more and better arguments later. But you get the idea?

continue this thread »

Comment author: [deleted] 04 April 2011 01:48:39AM 0 points [-]

If Solomonoff Induction does not discard theories inconsistent with the data, then this is wrong:

http://wiki.lesswrong.com/wiki/Solomonoff_induction

Whether it does or does not isn't important to the main argument here.

Critics might have a role to play for a resource-limited agent - for instance if they pointed out explanations that were short and were not yet receiving the proper consideration - or if they supplied more data.

If consistent data makes a theory more probable, I might have expected a theory that has survived (non-empirical) criticism to become more probable. Because you are an empiricist, you relegate criticism to a minor role when in fact criticism is a major driving force in science. Most theories don't get tested empirically, they are refuted by criticism alone. Critical rationalism knows this.

Also some theories can't be refuted by empirical means, so what does Solomonoff Induction do about those?

It says to prefer the shorter one.

Is that it? And how is the algorithm supposed to work anyway? If the theory is non-empirical, it can't be a compression of an empirical dataset.

Comment author: timtyler 04 April 2011 06:23:59AM * 2 points [-]

Because you are an empiricist, you relegate criticism to a minor role when in fact criticism is a major driving force in science.

Checking with the definition that apparently boils down to whether I think there is much innate knowledge. Humans have some innate knowledge, so I figure: probably not an empiricist.

I have no particular beef with criticism. Solomonoff induction is not given as a model of how humans actually do science. It is given as a formalisation of the maths of induction.

And how is the algorithm supposed to work anyway? If the theory is non-empirical, it can't be a compression of an empirical dataset.

Theories are constructed from datasets. Solomonoff induction is an abstract model of sequence prediction. Given a serial stream of sense data, it maintains models of it, and uses those models to predict future observations. The models embody theories about what it being observed - and smaller models are preferred.

Comment author: [deleted] 05 April 2011 01:23:20AM * 1 point [-]

Solomonoff Induction is empiricist because it assumes all knowledge comes from the data. Theories arising from Solomonoff Induction are, at most, only as reliable as the data and it can't come up with theories that make more precise predictions than the data or that contain more knowledge than the data. This is complicated by the fact that in real life applications it will have to deal with noise in the data and this is going to get deeply subjective very quickly.

Another problem is: how is the dataset itself constructed? You don't just go out and collect data; you need to know what you are looking for. Among the infinite number of things you can observe, you need to know what is important and to know this you need a theory. Where does this theory come from? It arises as a conjectural explanation to a problem-situation and specific predictions arising from the explanation guide your observations. So Solomonoff Induction has things backward.

Comment author: timtyler 07 April 2011 01:09:29PM 0 points [-]

Solomonoff Induction is just about prediction. It models a forecasting agent that observes a stream, and emits probabilities of the next symbol. It doesn't do anything else. Complaining that it can't create its own experiments seems rather futile. Of course it can't - it is a forecaster. Real agents do more than just forecast, of course, but that isn't a criticism for forecasting, or the idea of a forecaster.

Comment author: Jayson_Virissimo 12 January 2011 05:08:29AM * 1 point [-]

Popper seems outdated.

Critical Rationalism has advanced somewhat since Popper.

Rejecting induction completely is not very realistic.

I think Hume would agree.

Comment author: timtyler 12 January 2011 09:29:42AM * 1 point [-]

Popper seems outdated.

Critical Rationalism has advanced somewhat since Popper.

Not very significantly. The revolution happened mostly without them.

Comment author: Jayson_Virissimo 12 January 2011 01:15:33PM 2 points [-]

After reconsidering your statement, I have come to agree.

Comment author: [deleted] 01 April 2011 02:48:17AM 0 points [-]

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.

Comment author: curi 02 April 2011 03:33:28PM 1 point [-]

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

Comment author: Jayson_Virissimo 02 April 2011 06:13:39PM 1 point [-]

I had in mind Miller and Deutsch.

Comment author: curi 02 April 2011 09:16:48PM 1 point [-]

Which Miller publication or argument?

Comment author: Jayson_Virissimo 03 April 2011 02:50:41AM * 4 points [-]

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

Comment author: curi 03 April 2011 03:05:46AM 1 point [-]

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

Bayesianism versus Critical Rationalism

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