For a belief to be meaningful you have to be able to describe evidence that would move your posterior probability of it being true after a Bayesian update.
This is a generalization of falsifiability that allows, for example, indirect evidence pertaining to universal laws.
How about basic logical statements? For example: If P, then P. I think that belief is meaningful, but I don’t think I could coherently describe evidence that would make me change it’s probability of being true.
You’d have to define “exist”, because mathematical structures in themselves are just generalized relations that hold under specified constraints. And once you defined “exist”, it might be easier to look for Bayesian evidence—either for them existing, or for a law that would require them to exist.
As a general thing, my definition does consider under-defined assertions meaningless, but that seems correct.
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.
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,
Why? That assumes the universes are weighted by complexity, which isn’t true in all Tegmark level IV theories.
For a belief to be meaningful you have to be able to describe evidence that would move your posterior probability of it being true after a Bayesian update.
This is a generalization of falsifiability that allows, for example, indirect evidence pertaining to universal laws.
How about basic logical statements? For example: If P, then P. I think that belief is meaningful, but I don’t think I could coherently describe evidence that would make me change it’s probability of being true.
Possible counterexample: “All possible mathematical structures exist.”
You’d have to define “exist”, because mathematical structures in themselves are just generalized relations that hold under specified constraints. And once you defined “exist”, it might be easier to look for Bayesian evidence—either for them existing, or for a law that would require them to exist.
As a general thing, my definition does consider under-defined assertions meaningless, but that seems correct.
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.