I don’t understand how Axiom 2 implies uncomputability; please explain.
The other universes have their own laws, which work together with $L_{\alpha}$ to create them. Axiom 2 just implies there are an infinite number of universes, and every universe exists. Axiom 2 does not imply that $L_{\alpha}$ contains all possible laws.
Which is not a consistent set of axioms, but let’s just pretend you said “classical propositional logic”. Then why this and not something else, say intuitionistic, relevant, modal, etc.?
I don’t understand how Axiom 2 implies uncomputability; please explain.
Well, as per the First Incompleteness Theorem, there’s no recursive set of axioms complete for arithmetics. So if the universe realizes all arithmetic truth at least its set of laws is non-recursive, that is has no finite Kolmogorov complexity. ... unless you meant that the Multiverse realizes all possibilities.
On the other hand, the maximum complexity realizable by a simulation is a function not only of its laws but also of its available space. As entirelyuseless already pointed out, Uc can simulate any computable universe, given enough space.
Re: axiom 1
Logically consistent against what set of logical axioms? There are a bunch of logics out there, and one man inconsistency is another man’s axiom.
Axiom 2 implies that the set of laws in uncomputable, ergo has no Kolmogorov complexity, which contradicts Axiom 3.
The weak hypothesis is false.
And so on.
The principles of Aristotelian logic.
I don’t understand how Axiom 2 implies uncomputability; please explain.
The other universes have their own laws, which work together with $L_{\alpha}$ to create them. Axiom 2 just implies there are an infinite number of universes, and every universe exists. Axiom 2 does not imply that $L_{\alpha}$ contains all possible laws.
Which is not a consistent set of axioms, but let’s just pretend you said “classical propositional logic”. Then why this and not something else, say intuitionistic, relevant, modal, etc.?
Well, as per the First Incompleteness Theorem, there’s no recursive set of axioms complete for arithmetics. So if the universe realizes all arithmetic truth at least its set of laws is non-recursive, that is has no finite Kolmogorov complexity.
...
unless you meant that the Multiverse realizes all possibilities.
On the other hand, the maximum complexity realizable by a simulation is a function not only of its laws but also of its available space. As entirelyuseless already pointed out, Uc can simulate any computable universe, given enough space.