Hutter's strong confidence in a computable universe

[fryolysis]

In his "A complete theory of everything" paper, he made the assumption that the universe (or multiverse) is a computable entity and he expressed a strong confidence in it. He says,"The assumption that the world has some structure is as safe as (or I think even weaker than) the assumption that e.g. classical logic is good for reasoning about the world (and the latter one has to assume to make science meaningful)."

I can't convince myself that this is indeed a weak assumption. Am I missing some justifications somewhere else in the literature? Do you have any suggested readings for me?

Thank you

[Gabriel Leuenberger]

So the strong assumption that you are referring to seems to be where Hutter writes:  "Assume we live in the universal multiverse u that consists of all computable universes".
Earlier in the paper, he assumes a deterministic universe, which would be quite a strong assumption, but later he just assumes that the universe follows a computable probability distribution. 

The assumption that the universe follows a computable probability distribution at its most fundamental level of physics may still be a strong assumption while the assumption that at some higher level, physics is describable by some computable probability distribution may be a weaker assumption. Perhaps one should not make any assumption about the universe at all and instead make the weaker assumption that the modeling capability of science is restricted to computable models only, and therefore, alternative modeling attempts are futile, which would prove that the best we can hope to do is to follow Occam's razor, or so. This would then still count as a proof of Occam's razor.

[Ahmet]

In prediction with expert advice literature no assumption is made about the nature, and they can still prove worst-case bounds on the regret (performance gap of the statistician with the best expert available) and show that a quite simple weighted average algorithm is close to optimal. The bound holds even if the statistician is playing the prediction game against an adversary God. God chooses the predictions of the experts, statistician chooses his prediction by looking at the experts' decisions, and then God set the true outcome which maximizes the regret of the statistician. The game continues in rounds, potentially to the infinity. The assumptions of the setting are that there is a fixed finite number of experts whose predictions are available to the statistician at every step, the God is not allowed to mess with the statistician's ratings for each expert, the number of potential outcomes for each step is fixed and finite, and the result of each prediction is revealed before the next round. The outcome was originally binary 0,1 but generalized to continous range [0,1] later. The loss measure is the sum of absolute differences. At this level of generality, no performance guarantees can be given, but regret guarantees can, that is, we can still claim that we are doing our best with respect to a finite set of alternatives.

In my humble opinion, generalizing this scheme to drop some other assumptions (more alternatives whose predictions are not always available, or continous time step, or infinite set of outcomes) could lead to a "razor-free" justification of science and inductive reasoning.