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.
It seems to think the problem of the priors does in Bayesianism :-(
Popper seems outdated. Rejecting induction completely is not very realistic.
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.
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 theo...
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:
Any thoughts?