When I asked him about it on his Discord, that’s when he responded with the Löwenheim-Skolem. I didn’t want to bother him more until I’ve read up on set theory.
OK, I see it referenced in the fourth comment. Usually Löwenheim-Skolem is referenced in order to state that any uncountably large object has a countably large model (part of “downward L-S”), but here he’s citing “upward L-S”, about the existence of models with arbitrarily greater cardinalities.
L-S is logically independent of well-foundedness, and in any case the speaker appeals to some vague further principle about the conditions under which you “find yourself” (to be existing? to be existing at an exactly identifiable time?). The role of upward L-S seems to be to argue that if past time is infinite, the cardinality of that infinity is indeterminate and therefore so is your exact location in time.
Bear in mind that this is metaphysical technobabble from a work of fiction about beings who know more about reality than we do. Its primary job is to sound like an example of such knowledge. The author may or may not take it seriously.
“The idea is that all the existing things are finite and descended of finite causal graphs. This could potentially be true of a countably infinite set of finite things. But something with an infinite past is not a finite point to obtain some realityfluid from its finite past.”
This is from the invite-only fanfic Discord, not from fanfic itself. I’m not sure I should be sharing it, because I assume a degree of expected privacy, so I won’t share any more direct quotes. But I hope this much is okay; I model Yudkowsky as wanting people to better understand this stuff.
Google can’t find any reference to Skolem, Lowenheim-Skolem, Löwenheim-Skolem in the projectawful site...
They don’t name it. This is my inference based on Googling
Here is where Yudkowsky talks about well-foundedness:
https://www.glowfic.com/posts/6827
When I asked him about it on his Discord, that’s when he responded with the Löwenheim-Skolem. I didn’t want to bother him more until I’ve read up on set theory.
OK, I see it referenced in the fourth comment. Usually Löwenheim-Skolem is referenced in order to state that any uncountably large object has a countably large model (part of “downward L-S”), but here he’s citing “upward L-S”, about the existence of models with arbitrarily greater cardinalities.
L-S is logically independent of well-foundedness, and in any case the speaker appeals to some vague further principle about the conditions under which you “find yourself” (to be existing? to be existing at an exactly identifiable time?). The role of upward L-S seems to be to argue that if past time is infinite, the cardinality of that infinity is indeterminate and therefore so is your exact location in time.
Bear in mind that this is metaphysical technobabble from a work of fiction about beings who know more about reality than we do. Its primary job is to sound like an example of such knowledge. The author may or may not take it seriously.
Eli wrote:
“The idea is that all the existing things are finite and descended of finite causal graphs. This could potentially be true of a countably infinite set of finite things. But something with an infinite past is not a finite point to obtain some realityfluid from its finite past.”
This is from the invite-only fanfic Discord, not from fanfic itself. I’m not sure I should be sharing it, because I assume a degree of expected privacy, so I won’t share any more direct quotes. But I hope this much is okay; I model Yudkowsky as wanting people to better understand this stuff.