@QiaochuYuan - okay. so, i think about this in terms of tegmark IV but

okay. so, i think about this in terms of tegmark IV but however you phrase it you could imagine, like, the collection of all possible universes. the largest possible multiverse. tegmark roughly identifies this with the collection of all mathematical structures or something. so, one way you might think it works is that of all the possible universes, only one of them “really exists,” like that one has a special “existence” tag on it, and the others are only theoretical. or if you believe in some version of many-worlds you might believe there’s only one “actual universal wave function” which contains this universe and a bunch of others in quantum superposition, which is a lot more but still a tiny fragment of tegmark IV. now consider the following thought experiment (this is roughly the premise of permutation city iirc): suppose we ran a perfect simulation of another universe, say one with radically different laws of physics. a whole other universe with its own forms of life, its own beings living and dying, etc. even if we never interacted with the simulation this universe sort of exists in some sense now, we can make meaningful claims about what happens in it in the same way we can make meaningful claims about what happens in parts of the universe very far away from us. now suppose we stop running this simulation. has this universe now blinked out of existence? but we can still make claims about it. maybe we understand its physics in enough detail to make predictions about how it plays out. all the facts of the matter about what happens in this universe remain true. and we weren’t interacting with it either way. so maybe it exists now exactly as much as it did when we ran it? (permutation city continues from here: what happens if we repeatedly stop and restart the simulation? in the simulated universe, nothing. what if we run the different time slices out of order? still nothing. etc) this isn’t an airtight argument but to me when you ponder this stuff for awhile it starts to feel deeply inelegant to have a special “really exists” universe sitting in the much larger collection of all possible universes. actually one can dispense with the concept of existence entirely. it is just a fact that the universe we inhabit is a possible universe, as in it is logically coherent, it’s a consistent mathematical structure, and there are facts about what’s in it such as facts about ourselves which are in some sense ultimately mathematical facts (“in the universe with laws of physics X and initial conditions Y, after 14 billion years, the following observers exist and experience…”) those facts are true platonically, not only throughout time and space but throughout tegmark IV. they are just true, period. so my tentative conclusion is that we can dissolve the concept of existence as it applies to the universe. the universe simply is what it is, a particular mathematical structure, whose nature logically entails that we exist to observe it. it’s not even coherent to talk about what it would be like for the universe not to exist!