What you're describing is "the best way to do science, so we can make some progress". That's all well and good but what other people are talking about is the nature of reality which, in pursuit of, those crazy people, they are perfectly willing to doubt axioms.
As well they should and as is their right since a set of axioms are effectively ground facts which are selected to make logical reasoning across a domain possible, nothing more.
That doesn't make them true in the big sense of True, it makes them expedient, productive of theory, generative, a lot of wonderful things, maybe even strongly implied by all evidence, but not apriori true. They're dubitable.
> That's all well and good but what other people are talking about is the nature of reality which, in pursuit of, those crazy people, they are perfectly willing to doubt axioms.
Solomonoff induction does doubt and change axioms. It's a fundamental part of the whole process in fact.
> That doesn't make them true in the big sense of True, it makes them expedient, productive of theory, generative, a lot of wonderful things, maybe even strongly implied by all evidence, but not apriori true. They're dubitable.
Logic is used to make distinctions. Two theories with differing axiomatic bases will make different distinctions, but if they make the same predictions in all cases, then they are logically the same, ie. there is a fundamental isomorphism between them. In this case, it literally doesn't matter if one is "actually really true", and the other is a mathematical dual of some sort.
For instance, polar and Cartesian coordinates are completely equivalent. A theory cast in one might be easier for us to work with, but even if reality really used the other coordinate system, it quite literally doesn't matter.
In the case when the two theories do differ in their predictions, we should epistemically prefer one over the other, and Solomonoff Induction shows us how to do this rigourously.
Someone, a woman, I forget her name, a physicist has lately questioned the parsimonius assumption or more accurately the whole beauty assumption, meaning, roughly, the most beautiful or parsimonious theory is correct. Just a data point to this conversation, not an argument.
Re: Solomonoff, if you're chucking away unnecessaries, which is what I understand Solomonoff to be doing (I had to be reminded what his theory was truthfully) then that's all well and good, let's chuck. But you still are left with the problem of whether the axioms are true. That's a different thing entirely except to the extent we define true operationally, as having predictive power over the things we understand and know about in the way we understand them.
We moderns are all deeply enmeshed with Scientism which is an ism that says logic and reasoning and the scientific method etc. are the only valid tools for aquiring certain (indubitable) knowledge. What if it's just not true ? Then what ?
