Dear Stefan,
Thank you for your annotations, they bring some useful alternatives.
> "Even if mathematics would be the bottom layer of ultimate reality, i doubt that mathematics would be able to explain why this set of mathematical laws should be reserved to correlate with some physical stuff, or stated more precisely, be that physical stuff."
It is true that there is no known reason why a particular mathematical structure corresponds to our universe. Tegmark tries a sort of anthropic reasoning, which I explain why I didn't find convincing here.
About MUH, I avocate a similar position as Tegmark, but with less restrictions. I would include any mathematical structure.
> "Why not include all inconsistent mathematical descriptions and let there be an inconsistent (chaotic) universe (or infinitely many of them)?".
In my previous essays The Tao of It and Bit and And the math will set you free I advocate to include only a simple contradiction, and use it to derive all possibilities out of it. I add a condition of logical consistency to select the consistent universes. For some reason, I think that one should try first to find a mathematical structure, hence consistent description, for our universe. If it will turn out that only an inconsistent description can work, then that would be strange, and would include all other possibilities, including the consistent ones, into an all-inconsistent mix.
> "there are enough people out there who would say no, reality is absurd and irrational"
It clearly appears irrational to us, at least for the moment. In fact, I think we are irrational as a species. We are easily fooled by visual illusions and cognitive biases. But even if we would be perfect, it may take us long time to fully make sense of the universe. But I wouldn't blame the universe for irrationality yet, given that our brains are not so optimized to rationality as we would like to think.
I think the only chance we have to make sense of the universe is if it is consistent. It is a bit like Dr. Gregory House choosing the only diagnostics that is curable, and apply that treatment, and ignore the other possibilities with the same symptoms, because they can't be cured. We choose consistency because it is the only hope to understand the laws and the metalaws.
Best regards,
Cristi