The problem is that different equivalent formulations will make different things ontologically primitive.
Perhaps in this case we could say “the ontology of the universe is one or the other but I can’t tell which, so I’ll just have to be uncertain”. Do you see any problems with this, or have any better ideas?
How do you know there is a fundamental level, as opposed something like a void cathedral?
Can you give an example of a mathematical formulation of a void cathedral, just to show that such a thing is possible?
Can you give an example of a mathematical formulation of a void cathedral, just to show that such a thing is possible?
One description is something like the following: take the space of computable universes that agree with our observations so far. Rather than putting an Occam prior over it, put an ultrafilter on it. One can pick the ultrafilter so that the set of universes where any particular level is fundamental has measure zero.
I’m afraid I lack the background knowledge and/or math skills to figure out your idea from this short description. I can’t find any papers after doing a search either, so I guess this is your original idea? If so, why not write it up somewhere?
Perhaps in this case we could say “the ontology of the universe is one or the other but I can’t tell which, so I’ll just have to be uncertain”. Do you see any problems with this, or have any better ideas?
Can you give an example of a mathematical formulation of a void cathedral, just to show that such a thing is possible?
One description is something like the following: take the space of computable universes that agree with our observations so far. Rather than putting an Occam prior over it, put an ultrafilter on it. One can pick the ultrafilter so that the set of universes where any particular level is fundamental has measure zero.
I’m afraid I lack the background knowledge and/or math skills to figure out your idea from this short description. I can’t find any papers after doing a search either, so I guess this is your original idea? If so, why not write it up somewhere?