godelian wrote: ↑Fri May 03, 2024 6:18 am
Age wrote: ↑Fri May 03, 2024 4:53 am
But, how does this relate to trying to prove that 'God exists', through mathematics, and/or how heaven and hell are not just illusory?
This post is not about proving that God exists. It is not about Gödel's ontological proof.
It is about the possible structural similarity between the arithmetical multiverse and its physical counterpart.
Okay, so why did you end up telling me about what you think so-called "leaders" of different should be doing?
And, how is the impossible structural similarity between a made up 'arithmetical universe' and the actual Universe, Itself, got to do with heaven and hell supposedly not being just illusory?
godelian wrote: ↑Fri May 03, 2024 6:18 am
In the end, it is the old Pythagorean idea of structural similarity between the world of numbers and the physical world.
you are not wrong when you said, 'old', here.
godelian wrote: ↑Fri May 03, 2024 6:18 am
So, on the one side we have the arithmetical multiverse. Victoria Gitman has produced an excellent lecture on nonstandard models of arithmetic:
https://victoriagitman.github.io/talks/ ... metic.html
If you expand the standard model with the smallest infinite cardinality, aleph0, then you get the countable nonstandard models of arithmetic:
Gitman's lecture does not handle the advanced subject of expansion with uncountable transfinite cardinals. The beth (or aleph) sequence for uncountable cardinals is obtained by successively using the powerset operation for every previous infinite cardinal into a new set cardinal.
https://en.wikipedia.org/wiki/Zero_sharp
In the mathematical discipline of set theory, 0# (zero sharp, also 0#) is the set of true formulae about indiscernibles and order-indiscernibles in the Gödel constructible universe. It is often encoded as a subset of the natural numbers (using Gödel numbering), or as a subset of the hereditarily finite sets, or as a real number.
https://en.wikipedia.org/wiki/Large_cardinal
Large cardinals are understood in the context of the von Neumann universe V, which is built up by transfinitely iterating the powerset operation, which collects together all subsets of a given set.
If there is a measurable cardinal, then iterating the definable powerset operation rather than the full one yields Gödel's constructible universe, L, which does not satisfy the statement "there is a measurable cardinal" (even though it contains the measurable cardinal as an ordinal).
The arithmetical multiverse is very large and contains innumerable universes that influence each other by making true facts in other universes unpredictable. This arithmetical cross-universe influence is provable. If our standard physical universe is structurally similar, then it is subject to similar influences from nonstandard physical ones.
But, the actual One and only Universe is absolutely nothing like what you go on about here.
Because of what the One Universe is actually made up of, and how the One Universe, actually works any idea of 'universes' existing within a 'multiverse' is just insanity, in the extreme.
It could be said and argued that there are multi-verses within the Universe, Itself, but any talk of 'universes' within 'a multiverse' is just a self-contradiction and an oxymoron, to say the least.
As has already been proved irrefutably True, Right, Accurate, and Correct.