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Matt_Simpson comments on The Useful Idea of Truth - Less Wrong
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Yeah, I'm not really sure how to interpret "exist" in that statement. Someone that knows more about Tegmark level IV than I do should weigh in, but my intuition is that if parallel mathematical structures exist that we can't, in principle, even interact with, it's impossible to obtain Bayesian evidence about whether they exist.
If we couldn't, even in principle, find any evidence that would make the theory more likely or less, then yeah I think that theory would be correctly labeled meaningless.
But, I can immediately think of some evidence that would move my posterior probability. If all definable universes exist, we should expect (by Occam) to be in a simple one, and (by anthropic reasoning) in a survivable one, but we should not expect it to be elegant. The laws should be quirky, because the number of possible universes (that are simple and survivable) is larger than the subset thereof that are elegant.
Why? That assumes the universes are weighted by complexity, which isn't true in all Tegmark level IV theories.