All of this seems correct to me;

Hooray! I was hoping we'd be able to find some common ground.

My concerns with AIXI and AIXItl are largely of the form "this model doesn't quite capture what I'm looking for" and "AGI is not reduced to building better and better approximations of AIXI". These seem like fairly week and obvious claims to me, so I'm glad they are not contested.

(From some of the previous discussion, I was not sure that we agreed here.)

My objection was to the claim that the Solomonoff updating rule is incapable of learning these facts.

Cool. I make no such claim here.

Since you seem really interested in talking about Solomonoff induction and it's ability to deal with these situations, I'll say a few things that I think we can both agree upon. Correct me if I'm wrong:

1. A Solomonoff inductor outside of a computable universe, with a search space including Turing machines large enough to compute this universe, and with access to sufficient information, will in the limit construct a perfect model of the universe.
2. An AI sitting outside of a computable universe interacting only via I/O channels and using Solomonoff induction as above will in the limit have a perfect model of the universe, and will thus be able to act optimally.
3. A Solomonoff inductor inside its universe cannot consider hypotheses that actually perfectly describe the universe.
4. Agents inside the universe using Solomonoff induction thus lack the strict optimality-in-the-limit that an extra-universal AIXI would possess.

Does that mean they are dumb? No, of course not. Nothing that you can do inside the universe is going to give you the optimality principle of an AIXI that is actually sitting outside the universe using a hypercomputer. You can't get a perfect model of the universe from inside the universe, and it's unreasonable to expect that you should.

While doing Solomonoff induction inside the universe can never give you a perfect model, it can indeed get you a good computable approximation (one of the best computable approximations around, in fact).

(I assume we agree so far?)

The thing is, when we're inside a universe and we can't have that optimality principle, I already know how to build the best universe model that I can: I just do Bayesian updates using all my evidence. I don't need new intractable methods for building good environment models, because I already have one. The problem, of course, is that to be a perfect Bayesian, I need a good prior.

And in fact, Solomonoff induction is just Bayesian updating with a Komolgorov prior. So of course it will give you good results. As I stated here, I don't view my concerns with Solomonoff induction as an "induction problem" but rather as a "priors problem": Solomonoff induction works very well (and, indeed, is basically just Bayesian updating), but the question is, did it pick the right prior?

Maybe Komolgorov complexity priors will turn out to be the correct answer, but I'm far from convinced (for a number of reasons that go beyond the scope of this discussion). Regardless, though, Solomonoff induction surely gives you the best model you can get given the prior.

(In fact, the argument with AlexMennen is an argument about whether AIXItl's prior stating that it is absolutely impossible that the universe is a Turing machine with length > l is bad enough to hurt AIXItl. I won't hop into that argument today, but instead I will note that this line of argument does not seem like a good way to approach the question of which prior we should use.)

I'm not trying to condemn Solomonoff induction in this post. I'm trying to illustrate the fact that even if you could build an AIXItl, it wouldn't be an ideal agent.

There's one obvious way to embed AIXItl into its environment (hook its output register to its motor output channel) that prevents it from self-modifying, which results in failures. There's another way to embed AIXItl into its environment (hook its program registers to its output channel) that requires you to do a lot more work before the variant becomes useful.

Is it possible to make an AIXItl variant useful in the latter case? Sure, probably, but this seems like a pretty backwards way to go about studying self-modification when we could just use a toy model that was designed to study this problem in the first place.

As an aside, I'm betting that we disagree less than you think. I spent some time carefully laying out my concerns in this post, and alluding to other concerns that I didn't have time to cover (e.g., that the Legg-Hutter intelligence metric fails to capture some aspects of intelligence that I find important), in an attempt to make my position very clear. From your own response, it sounds like you largely agree with my concerns.

And yet, you still put very different words about very different concerns into my mouth when arguing with other people against positions that you believed I held.

I find this somewhat frustrating, and while I'm sure it was an honest mistake, I hope that you will be a bit more careful in the future.