Chalnoth &
Dmitry67, your latest talk about 'islands' and Hamiltonian is way above my 'horizon', but I have been thinking some more about the Mathematical Universe Hypothesis.
Dmitry67, when you mentioned
"7. Can we somehow transfer our consciousness into such universes?", I started thinking about 'brains' and mathematics. If MUH is correct, our brain is 'just' a mathematical formula, right? Then we must have the 'mother lode' of formulas inside our heads, if we are going to explain 'ourselves', AND the universe, AND 'everything else', right?
Then I started thinking about something else, which is so 'simple', that Tegmark just couldn’t have missed it:
Gödel's incompleteness theorems
I know this must be wrong, but I can’t find the error myself...

(
I also have to live up to my username hehe 
)
Second incompleteness theorem
For any formal effectively generated theory T including basic arithmetical truths and also certain truths about formal provability, T includes a statement of its own consistency if and only if T is inconsistent.
To me, this must mean
we already know that your (Chalnoth) 1-2-3 boiling down of Tegmark’s arguments is inconsistent in the very first sentence:
Chalnoth said:
1. A mathematical structure is just a fully-consistent set of rules.
2. If our universe is fully consistent, then it is isomorphic to some mathematical structure (which we don't yet know). This would indicate that at least some mathematical structures have real existence.
3. It is generally easier for all things of a class to exist than for only some of them to, so it is simpler to propose that all mathematical structures exist.
If our universe is fully consistent and thus isomorphic to a mathematical structure, then TOE
must be inconsistent to be able to prove the consistency of the universe!? Therefore the universe (=TOE) also
must be inconsistent!? And if the universe is inconsistent, it
cannot be a mathematical structure, therefore TOE can never be found (
from 'inside')!?
Que? What am I missing...
